Calculi: An abnormal concretion occurring mostly in the urinary and biliary tracts, usually composed of mineral salts. Also called stones.Urinary Calculi: Low-density crystals or stones in any part of the URINARY TRACT. Their chemical compositions often include CALCIUM OXALATE, magnesium ammonium phosphate (struvite), CYSTINE, or URIC ACID.Ureteral Calculi: Stones in the URETER that are formed in the KIDNEY. They are rarely more than 5 mm in diameter for larger renal stones cannot enter ureters. They are often lodged at the ureteral narrowing and can cause excruciating renal colic.Kidney Calculi: Stones in the KIDNEY, usually formed in the urine-collecting area of the kidney (KIDNEY PELVIS). Their sizes vary and most contains CALCIUM OXALATE.Urinary Bladder Calculi: Stones in the URINARY BLADDER; also known as vesical calculi, bladder stones, or cystoliths.Dental Calculus: Abnormal concretion or calcified deposit that forms around the teeth or dental prostheses.Lithotripsy: The destruction of a calculus of the kidney, ureter, bladder, or gallbladder by physical forces, including crushing with a lithotriptor through a catheter. Focused percutaneous ultrasound and focused hydraulic shock waves may be used without surgery. Lithotripsy does not include the dissolving of stones by acids or litholysis. Lithotripsy by laser is LITHOTRIPSY, LASER.Salivary Duct Calculi: Presence of small calculi in the terminal salivary ducts (salivary sand), or stones (larger calculi) found in the larger ducts.Ureteroscopy: Endoscopic examination, therapy or surgery of the ureter.Nephrostomy, Percutaneous: The insertion of a catheter through the skin and body wall into the kidney pelvis, mainly to provide urine drainage where the ureter is not functional. It is used also to remove or dissolve renal calculi and to diagnose ureteral obstruction.Salivary Gland Calculi: Calculi occurring in a salivary gland. Most salivary gland calculi occur in the submandibular gland, but can also occur in the parotid gland and in the sublingual and minor salivary glands.Lithotripsy, Laser: Fragmentation of CALCULI, notably urinary or biliary, by LASER.Prostatic Diseases: Pathological processes involving the PROSTATE or its component tissues.Urolithiasis: Formation of stones in any part of the URINARY TRACT, usually in the KIDNEY; URINARY BLADDER; or the URETER.Calcium Oxalate: The calcium salt of oxalic acid, occurring in the urine as crystals and in certain calculi.Urography: Radiography of any part of the urinary tract.Salivary Calculi: The presence of calculi in a salivary duct or gland.Gallstones: Solid crystalline precipitates in the BILIARY TRACT, usually formed in the GALLBLADDER, resulting in the condition of CHOLELITHIASIS. Gallstones, derived from the BILE, consist mainly of calcium, cholesterol, or bilirubin.Cholelithiasis: Presence or formation of GALLSTONES in the BILIARY TRACT, usually in the gallbladder (CHOLECYSTOLITHIASIS) or the common bile duct (CHOLEDOCHOLITHIASIS).Reference Books, Medical: Books in the field of medicine intended primarily for consultation.Urologic Surgical Procedures: Surgery performed on the urinary tract or its parts in the male or female. For surgery of the male genitalia, UROLOGIC SURGICAL PROCEDURES, MALE is available.Magnesium Compounds: Inorganic compounds that contain magnesium as an integral part of the molecule.Cystinuria: An inherited disorder due to defective reabsorption of CYSTINE and other BASIC AMINO ACIDS by the PROXIMAL RENAL TUBULES. This form of aminoaciduria is characterized by the abnormally high urinary levels of cystine; LYSINE; ARGININE; and ORNITHINE. Mutations involve the amino acid transport protein gene SLC3A1.Calcium Phosphates: Calcium salts of phosphoric acid. These compounds are frequently used as calcium supplements.Colic: A clinical syndrome with intermittent abdominal pain characterized by sudden onset and cessation that is commonly seen in infants. It is usually associated with obstruction of the INTESTINES; of the CYSTIC DUCT; or of the URINARY TRACT.Kidney Pelvis: The flattened, funnel-shaped expansion connecting the URETER to the KIDNEY CALICES.Ethylene Glycol: A colorless, odorless, viscous dihydroxy alcohol. It has a sweet taste, but is poisonous if ingested. Ethylene glycol is the most important glycol commercially available and is manufactured on a large scale in the United States. It is used as an antifreeze and coolant, in hydraulic fluids, and in the manufacture of low-freezing dynamites and resins.Postcholecystectomy Syndrome: Abdominal symptoms after removal of the GALLBLADDER. The common postoperative symptoms are often the same as those present before the operation, such as COLIC, bloating, NAUSEA, and VOMITING. There is pain on palpation of the right upper quadrant and sometimes JAUNDICE. The term is often used, inaccurately, to describe such postoperative symptoms not due to gallbladder removal.Urology: A surgical specialty concerned with the study, diagnosis, and treatment of diseases of the urinary tract in both sexes, and the genital tract in the male. Common urological problems include urinary obstruction, URINARY INCONTINENCE, infections, and UROGENITAL NEOPLASMS.Urologic Diseases: Pathological processes of the URINARY TRACT in both males and females.Diverticulum: A pouch or sac developed from a tubular or saccular organ, such as the GASTROINTESTINAL TRACT.Hydronephrosis: Abnormal enlargement or swelling of a KIDNEY due to dilation of the KIDNEY CALICES and the KIDNEY PELVIS. It is often associated with obstruction of the URETER or chronic kidney diseases that prevents normal drainage of urine into the URINARY BLADDER.Holmium: Holmium. An element of the rare earth family of metals. It has the atomic symbol Ho, atomic number 67, and atomic weight 164.93.Apatites: A group of phosphate minerals that includes ten mineral species and has the general formula X5(YO4)3Z, where X is usually calcium or lead, Y is phosphorus or arsenic, and Z is chlorine, fluorine, or OH-. (McGraw-Hill Dictionary of Scientific and Technical Terms, 4th ed)Lithiasis: A condition characterized by the formation of CALCULI and concretions in the hollow organs or ducts of the body. They occur most often in the gallbladder, kidney, and lower urinary tract.Cystic Duct: The duct that is connected to the GALLBLADDER and allows the emptying of bile into the COMMON BILE DUCT.Pyelonephritis, Xanthogranulomatous: A chronic inflammatory condition of the KIDNEY resulting in diffuse renal destruction, a grossly enlarged and nonfunctioning kidney associated with NEPHROLITHIASIS and KIDNEY STONES.Testicular Diseases: Pathological processes of the TESTIS.Cholangiography: An imaging test of the BILIARY TRACT in which a contrast dye (RADIOPAQUE MEDIA) is injected into the BILE DUCT and x-ray pictures are taken.Bile Duct Diseases: Diseases in any part of the ductal system of the BILIARY TRACT from the smallest BILE CANALICULI to the largest COMMON BILE DUCT.Submandibular Gland DiseasesOxalates: Derivatives of OXALIC ACID. Included under this heading are a broad variety of acid forms, salts, esters, and amides that are derived from the ethanedioic acid structure.Oxalic Acid: A strong dicarboxylic acid occurring in many plants and vegetables. It is produced in the body by metabolism of glyoxylic acid or ascorbic acid. It is not metabolized but excreted in the urine. It is used as an analytical reagent and general reducing agent.Hypercalciuria: Excretion of abnormally high level of CALCIUM in the URINE, greater than 4 mg/kg/day.Triazines: Heterocyclic rings containing three nitrogen atoms, commonly in 1,2,4 or 1,3,5 or 2,4,6 formats. Some are used as HERBICIDES.Kidney Calices: Recesses of the kidney pelvis which divides into two wide, cup-shaped major renal calices, with each major calix subdivided into 7 to 14 minor calices. Urine empties into a minor calix from collecting tubules, then passes through the major calix, renal pelvis, and ureter to enter the urinary bladder. (From Moore, Clinically Oriented Anatomy, 3d ed, p211)Urine: Liquid by-product of excretion produced in the kidneys, temporarily stored in the bladder until discharge through the URETHRA.Dental Prophylaxis: Treatment for the prevention of periodontal diseases or other dental diseases by the cleaning of the teeth in the dental office using the procedures of DENTAL SCALING and DENTAL POLISHING. The treatment may include plaque detection, removal of supra- and subgingival plaque and calculus, application of caries-preventing agents, checking of restorations and prostheses and correcting overhanging margins and proximal contours of restorations, and checking for signs of food impaction.Urachus: An embryonic structure originating from the ALLANTOIS. It is a canal connecting the fetal URINARY BLADDER and the UMBILICUS. It is normally converted into a fibrous cord postnatally. When the canal fails to be filled and remains open (patent urachus), urine leaks through the umbilicus.Periodontal Index: A numerical rating scale for classifying the periodontal status of a person or population with a single figure which takes into consideration prevalence as well as severity of the condition. It is based upon probe measurement of periodontal pockets and on gingival tissue status.Uric Acid: An oxidation product, via XANTHINE OXIDASE, of oxypurines such as XANTHINE and HYPOXANTHINE. It is the final oxidation product of purine catabolism in humans and primates, whereas in most other mammals URATE OXIDASE further oxidizes it to ALLANTOIN.Gingivitis: Inflammation of gum tissue (GINGIVA) without loss of connective tissue.Ureteroscopes: Endoscopes for examining the interior of the ureter.Persia: An ancient civilization, known as early as 2000 B.C. The Persian Empire was founded by Cyrus the Great (550-529 B.C.) and for 200 years, from 550 to 331 B.C., the Persians ruled the ancient world from India to Egypt. The territory west of India was called Persis by the Greeks who later called the entire empire Persia. In 331 B.C. the Persian wars against the Greeks ended disastrously under the counterattacks by Alexander the Great. The name Persia in modern times for the modern country was changed to Iran in 1935. (From Webster's New Geographical Dictionary, 1988, p546 & Asimov, Words on the Map, 1962, p176)Ureteral Diseases: Pathological processes involving the URETERS.Dental Pellicle: A thin protein film on the surface of DENTAL ENAMEL. It is widely believed to result from the selective adsorption of precursor proteins present in SALIVA onto tooth surfaces, and to reduce microbial adherence to the TEETH.Hyperoxaluria: Excretion of an excessive amount of OXALATES in the urine.Oral Hygiene Index: A combination of the debris index and the dental calculus index to determine the status of oral hygiene.Cystoscopy: Endoscopic examination, therapy or surgery of the urinary bladder.Endoscopes: Instruments for the visual examination of interior structures of the body. There are rigid endoscopes and flexible fiberoptic endoscopes for various types of viewing in ENDOSCOPY.Scrotum: A cutaneous pouch of skin containing the testicles and spermatic cords.Nephrolithiasis: Formation of stones in the KIDNEY.Nephrocalcinosis: A condition characterized by calcification of the renal tissue itself. It is usually seen in distal RENAL TUBULAR ACIDOSIS with calcium deposition in the DISTAL KIDNEY TUBULES and the surrounding interstitium. Nephrocalcinosis causes RENAL INSUFFICIENCY.Cholangiopancreatography, Endoscopic Retrograde: Fiberoptic endoscopy designed for duodenal observation and cannulation of VATER'S AMPULLA, in order to visualize the pancreatic and biliary duct system by retrograde injection of contrast media. Endoscopic (Vater) papillotomy (SPHINCTEROTOMY, ENDOSCOPIC) may be performed during this procedure.Urethral Obstruction: Partial or complete blockage in any part of the URETHRA that can lead to difficulty or inability to empty the URINARY BLADDER. It is characterized by an enlarged, often damaged, bladder with frequent urges to void.Dental Plaque: A film that attaches to teeth, often causing DENTAL CARIES and GINGIVITIS. It is composed of MUCINS, secreted from salivary glands, and microorganisms.Cystoscopes: Endoscopes for visual examination of the urinary bladder.Nigella sativa: A plant genus of the family RANUNCULACEAE that contains alpha-hederin, a triterpene saponin in the seeds, and is the source of black seed oil.Pedaliaceae: The sesame family of the order Lamiales that are mainly herbs and shrubs growing in warm regions.Cholecystectomy: Surgical removal of the GALLBLADDER.Dysuria: Painful URINATION. It is often associated with infections of the lower URINARY TRACT.Potassium Citrate: A powder that dissolves in water, which is administered orally, and is used as a diuretic, expectorant, systemic alkalizer, and electrolyte replenisher.Knowledge of Results (Psychology): A principle that learning is facilitated when the learner receives immediate evaluation of learning performance. The concept also hypothesizes that learning is facilitated when the learner is promptly informed whether a response is correct, and, if incorrect, of the direction of error.Potassium Compounds: Inorganic compounds that contain potassium as an integral part of the molecule.Hematuria: Presence of blood in the urine.Sialography: Radiography of the SALIVARY GLANDS or ducts following injection of contrast medium.Tooth Discoloration: Any change in the hue, color, or translucency of a tooth due to any cause. Restorative filling materials, drugs (both topical and systemic), pulpal necrosis, or hemorrhage may be responsible. (Jablonski, Dictionary of Dentistry, 1992, p253)Anuria: Absence of urine formation. It is usually associated with complete bilateral ureteral (URETER) obstruction, complete lower urinary tract obstruction, or unilateral ureteral obstruction when a solitary kidney is present.Cystostomy: Surgical creation of an opening (stoma) in the URINARY BLADDER for drainage.Pharmaceutic Aids: Substances which are of little or no therapeutic value, but are necessary in the manufacture, compounding, storage, etc., of pharmaceutical preparations or drug dosage forms. They include SOLVENTS, diluting agents, and suspending agents, and emulsifying agents. Also, ANTIOXIDANTS; PRESERVATIVES, PHARMACEUTICAL; COLORING AGENTS; FLAVORING AGENTS; VEHICLES; EXCIPIENTS; OINTMENT BASES.Gingival Pocket: An abnormal extension of a gingival sulcus not accompanied by the apical migration of the epithelial attachment.Ultrasonography: The visualization of deep structures of the body by recording the reflections or echoes of ultrasonic pulses directed into the tissues. Use of ultrasound for imaging or diagnostic purposes employs frequencies ranging from 1.6 to 10 megahertz.Ureteral Obstruction: Blockage in any part of the URETER causing obstruction of urine flow from the kidney to the URINARY BLADDER. The obstruction may be congenital, acquired, unilateral, bilateral, complete, partial, acute, or chronic. Depending on the degree and duration of the obstruction, clinical features vary greatly such as HYDRONEPHROSIS and obstructive nephropathy.Urethral Diseases: Pathological processes involving the URETHRA.Cholecystectomy, Laparoscopic: Excision of the gallbladder through an abdominal incision using a laparoscope.Lasers, Solid-State: Lasers which use a solid, as opposed to a liquid or gas, as the lasing medium. Common materials used are crystals, such as YAG (YTTRIUM aluminum garnet); alexandrite; and CORUNDUM, doped with a rare earth element such as a NEODYMIUM; ERBIUM; or HOLMIUM. The output is sometimes additionally modified by addition of non-linear optical materials such as potassium titanyl phosphate crystal, which for example is used with neodymium YAG lasers to convert the output light to the visible range.Parotid DiseasesHistory, Medieval: The period of history from the year 500 through 1450 of the common era.Urinalysis: Examination of urine by chemical, physical, or microscopic means. Routine urinalysis usually includes performing chemical screening tests, determining specific gravity, observing any unusual color or odor, screening for bacteriuria, and examining the sediment microscopically.CitratesSpectrophotometry, Infrared: Spectrophotometry in the infrared region, usually for the purpose of chemical analysis through measurement of absorption spectra associated with rotational and vibrational energy levels of molecules. (McGraw-Hill Dictionary of Scientific and Technical Terms, 4th ed)Root Planing: A procedure for smoothing of the roughened root surface or cementum of a tooth after subgingival curettage or scaling, as part of periodontal therapy.Pyelonephritis: Inflammation of the KIDNEY involving the renal parenchyma (the NEPHRONS); KIDNEY PELVIS; and KIDNEY CALICES. It is characterized by ABDOMINAL PAIN; FEVER; NAUSEA; VOMITING; and occasionally DIARRHEA.Alcian Blue: A copper-containing dye used as a gelling agent for lubricants, for staining of bacteria and for the dyeing of histiocytes and fibroblasts in vivo.Tomography, Spiral Computed: Computed tomography where there is continuous X-ray exposure to the patient while being transported in a spiral or helical pattern through the beam of irradiation. This provides improved three-dimensional contrast and spatial resolution compared to conventional computed tomography, where data is obtained and computed from individual sequential exposures.Periodontal Diseases: Pathological processes involving the PERIODONTIUM including the gum (GINGIVA), the alveolar bone (ALVEOLAR PROCESS), the DENTAL CEMENTUM, and the PERIODONTAL LIGAMENT.IranMetabolic Diseases: Generic term for diseases caused by an abnormal metabolic process. It can be congenital due to inherited enzyme abnormality (METABOLISM, INBORN ERRORS) or acquired due to disease of an endocrine organ or failure of a metabolically important organ such as the liver. (Stedman, 26th ed)Treatment Outcome: Evaluation undertaken to assess the results or consequences of management and procedures used in combating disease in order to determine the efficacy, effectiveness, safety, and practicability of these interventions in individual cases or series.Calcium Carbonate: Carbonic acid calcium salt (CaCO3). An odorless, tasteless powder or crystal that occurs in nature. It is used therapeutically as a phosphate buffer in hemodialysis patients and as a calcium supplement.Operative Time: The duration of a surgical procedure in hours and minutes.Petroselinum: A plant genus of the family APIACEAE used for flavoring food.Dental Plaque Index: An index which scores the degree of dental plaque accumulation.Pancreatic Diseases: Pathological processes of the PANCREAS.Dental Scaling: Removal of dental plaque and dental calculus from the surface of a tooth, from the surface of a tooth apical to the gingival margin accumulated in periodontal pockets, or from the surface coronal to the gingival margin.Urinary Tract Infections: Inflammatory responses of the epithelium of the URINARY TRACT to microbial invasions. They are often bacterial infections with associated BACTERIURIA and PYURIA.Cholecystitis: Inflammation of the GALLBLADDER; generally caused by impairment of BILE flow, GALLSTONES in the BILIARY TRACT, infections, or other diseases.Propantheline: A muscarinic antagonist used as an antispasmodic, in rhinitis, in urinary incontinence, and in the treatment of ulcers. At high doses it has nicotinic effects resulting in neuromuscular blocking.Endoscopy: Procedures of applying ENDOSCOPES for disease diagnosis and treatment. Endoscopy involves passing an optical instrument through a small incision in the skin i.e., percutaneous; or through a natural orifice and along natural body pathways such as the digestive tract; and/or through an incision in the wall of a tubular structure or organ, i.e. transluminal, to examine or perform surgery on the interior parts of the body.Phosphates: Inorganic salts of phosphoric acid.Crystallization: The formation of crystalline substances from solutions or melts. (McGraw-Hill Dictionary of Scientific and Technical Terms, 4th ed)Gallbladder: A storage reservoir for BILE secretion. Gallbladder allows the delivery of bile acids at a high concentration and in a controlled manner, via the CYSTIC DUCT to the DUODENUM, for degradation of dietary lipid.Pancreatic Ducts: Ducts that collect PANCREATIC JUICE from the PANCREAS and supply it to the DUODENUM.Gingival Hemorrhage: The flowing of blood from the marginal gingival area, particularly the sulcus, seen in such conditions as GINGIVITIS, marginal PERIODONTITIS, injury, and ASCORBIC ACID DEFICIENCY.Sphincter of Oddi: The sphincter of the hepatopancreatic ampulla within the duodenal papilla. The COMMON BILE DUCT and main pancreatic duct pass through this sphincter.Cholecystography: Radiography of the gallbladder after ingestion of a contrast medium.Islam: A monotheistic religion promulgated by the Prophet Mohammed with Allah as the deity.Cholangiopancreatography, Magnetic Resonance: Non-invasive diagnostic technique for visualizing the PANCREATIC DUCTS and BILE DUCTS without the use of injected CONTRAST MEDIA or x-ray. MRI scans provide excellent sensitivity for duct dilatation, biliary stricture, and intraductal abnormalities.Urinary Bladder: A musculomembranous sac along the URINARY TRACT. URINE flows from the KIDNEYS into the bladder via the ureters (URETER), and is held there until URINATION.Common Bile Duct: The largest bile duct. It is formed by the junction of the CYSTIC DUCT and the COMMON HEPATIC DUCT.Sphincterotomy, Endoscopic: Incision of Oddi's sphincter or Vater's ampulla performed by inserting a sphincterotome through an endoscope (DUODENOSCOPE) often following retrograde cholangiography (CHOLANGIOPANCREATOGRAPHY, ENDOSCOPIC RETROGRADE). Endoscopic treatment by sphincterotomy is the preferred method of treatment for patients with retained or recurrent bile duct stones post-cholecystectomy, and for poor-surgical-risk patients that have the gallbladder still present.Proteus Infections: Infections with bacteria of the genus PROTEUS.Citric Acid: A key intermediate in metabolism. It is an acid compound found in citrus fruits. The salts of citric acid (citrates) can be used as anticoagulants due to their calcium chelating ability.Retrospective Studies: Studies used to test etiologic hypotheses in which inferences about an exposure to putative causal factors are derived from data relating to characteristics of persons under study or to events or experiences in their past. The essential feature is that some of the persons under study have the disease or outcome of interest and their characteristics are compared with those of unaffected persons.Magnesium: A metallic element that has the atomic symbol Mg, atomic number 12, and atomic weight 24.31. It is important for the activity of many enzymes, especially those involved in OXIDATIVE PHOSPHORYLATION.Urinary Bladder Neck Obstruction: Blocked urine flow through the bladder neck, the narrow internal urethral opening at the base of the URINARY BLADDER. Narrowing or strictures of the URETHRA can be congenital or acquired. It is often observed in males with enlarged PROSTATE glands.Retroperitoneal Space: An area occupying the most posterior aspect of the ABDOMINAL CAVITY. It is bounded laterally by the borders of the quadratus lumborum muscles and extends from the DIAPHRAGM to the brim of the true PELVIS, where it continues as the pelvic extraperitoneal space.Ureter: One of a pair of thick-walled tubes that transports urine from the KIDNEY PELVIS to the URINARY BLADDER.Radiography, Abdominal: Radiographic visualization of the body between the thorax and the pelvis, i.e., within the peritoneal cavity.Durapatite: The mineral component of bones and teeth; it has been used therapeutically as a prosthetic aid and in the prevention and treatment of osteoporosis.Urinary Retention: Inability to empty the URINARY BLADDER with voiding (URINATION).Optical Fibers: Thin strands of transparent material, usually glass, that are used for transmitting light waves over long distances.Powder Diffraction: Method of using a polycrystalline powder and Rietveld refinement (LEAST SQUARES ANALYSIS) of X-RAY DIFFRACTION or NEUTRON DIFFRACTION. It circumvents the difficulties of producing single large crystals.Sulfadiazine: One of the short-acting SULFONAMIDES used in combination with PYRIMETHAMINE to treat toxoplasmosis in patients with acquired immunodeficiency syndrome and in newborns with congenital infections.Methods: A series of steps taken in order to conduct research.Calcinosis: Pathologic deposition of calcium salts in tissues.Oral Hygiene: The practice of personal hygiene of the mouth. It includes the maintenance of oral cleanliness, tissue tone, and general preservation of oral health.Postoperative Complications: Pathologic processes that affect patients after a surgical procedure. They may or may not be related to the disease for which the surgery was done, and they may or may not be direct results of the surgery.Kidney Diseases: Pathological processes of the KIDNEY or its component tissues.Gallbladder Diseases: Diseases of the GALLBLADDER. They generally involve the impairment of BILE flow, GALLSTONES in the BILIARY TRACT, infections, neoplasms, or other diseases.Choledocholithiasis: Presence or formation of GALLSTONES in the COMMON BILE DUCT.Kidney: Body organ that filters blood for the secretion of URINE and that regulates ion concentrations.Tomography, X-Ray Computed: Tomography using x-ray transmission and a computer algorithm to reconstruct the image.Paraplegia: Severe or complete loss of motor function in the lower extremities and lower portions of the trunk. This condition is most often associated with SPINAL CORD DISEASES, although BRAIN DISEASES; PERIPHERAL NERVOUS SYSTEM DISEASES; NEUROMUSCULAR DISEASES; and MUSCULAR DISEASES may also cause bilateral leg weakness.Urinary Tract: The duct which coveys URINE from the pelvis of the KIDNEY through the URETERS, BLADDER, and URETHRA.Oral Health: The optimal state of the mouth and normal functioning of the organs of the mouth without evidence of disease.Urinary Catheterization: Passage of a CATHETER into the URINARY BLADDER or kidney.Cystine: A covalently linked dimeric nonessential amino acid formed by the oxidation of CYSTEINE. Two molecules of cysteine are joined together by a disulfide bridge to form cystine.Ampulla of Vater: A dilation of the duodenal papilla that is the opening of the juncture of the COMMON BILE DUCT and the MAIN PANCREATIC DUCT, also known as the hepatopancreatic ampulla.Silicon: A trace element that constitutes about 27.6% of the earth's crust in the form of SILICON DIOXIDE. It does not occur free in nature. Silicon has the atomic symbol Si, atomic number 14, and atomic weight [28.084; 28.086].Phosphorus: A non-metal element that has the atomic symbol P, atomic number 15, and atomic weight 31. It is an essential element that takes part in a broad variety of biochemical reactions.Nephrectomy: Excision of kidney.Diphosphates: Inorganic salts of phosphoric acid that contain two phosphate groups.Microscopy, Electron, Scanning: Microscopy in which the object is examined directly by an electron beam scanning the specimen point-by-point. The image is constructed by detecting the products of specimen interactions that are projected above the plane of the sample, such as backscattered electrons. Although SCANNING TRANSMISSION ELECTRON MICROSCOPY also scans the specimen point by point with the electron beam, the image is constructed by detecting the electrons, or their interaction products that are transmitted through the sample plane, so that is a form of TRANSMISSION ELECTRON MICROSCOPY.Periodontal Pocket: An abnormal extension of a gingival sulcus accompanied by the apical migration of the epithelial attachment and bone resorption.Prospective Studies: Observation of a population for a sufficient number of persons over a sufficient number of years to generate incidence or mortality rates subsequent to the selection of the study group.Calcium: A basic element found in nearly all organized tissues. It is a member of the alkaline earth family of metals with the atomic symbol Ca, atomic number 20, and atomic weight 40. Calcium is the most abundant mineral in the body and combines with phosphorus to form calcium phosphate in the bones and teeth. It is essential for the normal functioning of nerves and muscles and plays a role in blood coagulation (as factor IV) and in many enzymatic processes.

Dacryolith formation around an eyelash retained in the lacrimal sac. (1/113)

A dacryolith was discovered in the lacrimal sac during a dacryocystorhinostomy for chronic dacryocystitis in which there was mucocele formation. Morphological examination confirmed the presence of an eyelash at the centre of the stone and electron microscopy demonstrated the presence of fungi (Candida sp.) in a matrix which was of markedly vairable morphology. The mechanism by which a hair enters the punctum and passes along the canaliculus may be attributed to the step-like pattern of ridges on the surface of a hair. The directional nature of these ridges dictates preferential movement towards the root end of the hair and prevents movements in the opposite direction.  (+info)

Long term follow up of patients with chronic pancreatitis and pancreatic stones treated with extracorporeal shock wave lithotripsy. (2/113)

BACKGROUND: There have been conflicting reports as to whether pancreatic ductal drainage achieved by endoscopy and lithotripsy improves the clinical outcome of patients with chronic pancreatitis. AIMS: To determine the clinical outcome in patients with chronic pancreatitis who received extracorporeal shock wave lithotripsy (ESWL), and were followed up for two to eight years. METHODS: Eighty patients with severe chronic pancreatitis and endoscopically unretrievable obstructive stones underwent ESWL with a piezoelectric lithotripter between 1989 and 1996. Clinical status, relief of symptoms, further endoscopic or surgical interventions, and mortality were defined. RESULTS: Forty three (54%) patients were treated successfully with ESWL. The only feature associated with treatment success was the presence of a single stone rather than multiple stones. Successfully treated patients tended to experience less pain, although this did not reach statistical significance. A slight increase in weight was noted in our patients; however, there was no notable improvement in anomalous stools and diabetes mellitus. Five patients died due to extrapancreatic reasons. No pancreatic carcinomas developed. CONCLUSIONS: ESWL associated with endoscopic drainage is a safe technique that is particularly successful in patients with a single stone. However, pancreatic drainage by endoscopy and ESWL has almost no effect on pain in chronic pancreatitis. Furthermore, endoscopic management and ESWL does not prevent or postpone the development of glandular insufficiency.  (+info)

Pulmonary alveolar microlithiasis: a rare familial inheritance with report of six cases in a family. Contribution of six new cases to the number of case reports in Turkey. (3/113)

Pulmonary alveolar microlithiasis (PAM) is a lung disease characterized by deposits of calcium within the alveoli. Our aim was to emphasize the familial character and the clinical features of the disease, and to draw attention to the increasing number of Turkish patients reported in the world. We detected 6 cases of PAM. Three cases had been diagnosed 4 years earlier, and 3 new cases were detected during the screening of the family members. All patients were male and the mean age was 11.5 ranging between 5 and 29 years. Five of the patients were cousins and the other one was their uncle. Radiographic studies showed a sand-like appearance in all patients. One case showed small subpleural bullae and bronchiectatic changes in both lower lobes in recent high-resolution CT scans, while his CT performed 4 years ago showed only sand-like appearance. The cases were diagnosed with the demonstration of microliths by bronchoalveolar lavage in 5 patients and transbronchial biopsy in 1. Recently reported cases from Turkey have constituted a considerable percentage among all cases in the world. In conclusion, (1) our patients constitute one of the largest series of cases reported in one family in the world. The disease seems to have familial and racial characteristics. The Turkish race has to be further investigated for genetic transmission. (2) Contrary to female predominance in previous reports, all 6 cases were male and 5 of them were below 12 years of age. (3) The disorder may show rapid progression in some cases probably due to the severity of the genetic disturbance.  (+info)

Histochemical studies of pancreatic calculi. (4/113)

Fourteen pancreatic calculi from the corresponding number of pancreatic lithiasis patients were examined mineralogically and histochemically. The following results were obtained. The main components of calculi were calcium carbonate in 13 of the 14 cases, and calcium phosphate in the remaining one. Calcium carbonate calculi were all so-called intraductal calculi, with acidic glycoprotein apparently enwrapping the component particles. Acidic glycoproteins acted to bridge calcium carbonate particles, as in the cases of gallstone and urinary stone. The calcium phosphate calculus had a histochemical feature of pathologic calcification with degenerated collagen fibrils as the matrix, suggesting the calcification of the fibrotic pancreatic parenchyma after pancreatitis.  (+info)

Urinary stones following renal transplantation. (5/113)

BACKGROUND: The formation of urinary tract stones following renal transplantation is a rare complication. The clinical features of stones after transplantation differ from those of non-transplant patients. Renal colic or pain is usually absent and rarely resembles acute rejection. METHODS: We retrospectively studied 849 consecutive kidney transplant patients in The Rogosin Institute/The Weill-Cornell Medical Center, New York who were transplanted between 1980 and 1997 and had functioning grafts for more than 3 months, to determine the incidence of stone formation, composition, risk factors and patient outcome. RESULTS: At our center, urinary stones were diagnosed in 15 patients (1.8%) of 849 functioning renal grafts for 3 or more months. Of the 15 patients, 10 were males and 5 were females in their third and fourth decade. Eight patients received their transplant from living donors and 7 from cadaveric donors. The stones were first diagnosed between 3 and 109 months after transplantation (mean 17.8 months) and 5 patients had recurrent episodes. The stones were located in the bladder in 11 cases (73.3%), transplanted kidney in 3 cases and in multiple sites in one case. The size of stones varied from 3.4 mm to 40 mm (mean 12 mm). The composition of stones was a mixed form of calcium oxalate and calcium phosphate in 5 cases and 4 patients had infected stones consisting of struvite or mixed form of struvite and calcium phosphate. Factors predisposing to stone formation included tertiary hyperparathyroidism (n = 8), hypercalciuria (n = 5), recurrent urinary tract infection (n = 5), hypocitraturia (n = 4), and obstructive uropathy (n = 2). Many cases had more than one risk factor. Clinically, painless hematuria was observed in 6 patients and dysuria without bacteriuria in 5 patients. None had renal colic or severe pain at any time. There were no changes in graft function at diagnosis and after removal of stones. Five patients passed stones spontaneously and 8 patients underwent cystoscopy for stone removal. CONCLUSION: Urinary stone formation following kidney transplantation is a rare complication (1.8%). Hyperparathyroidism, hypercalciuria, recurrent urinary tract infection and hypocitraturia are the most common risk factors, but often there are multiple factors which predispose to stone formation. To detect stones and determine their location and size, ultrasonography appears to be the most useful diagnostic tool. Prompt diagnosis, the removal of stones and stone-preventive measures can prevent adverse effects on renal graft outcome.  (+info)

Radiological changes in pica. (6/113)

The significance of pica and geophagia as a public health problem is well known. The objective radiographic diagnosis of geophagia depends on the abnormal opacification of the bowel as an immediate manifestitation of the condition. The chance of detectability of geophagia is highest in the colon and can be improved by using low penetration films, particularly for smaller amounts of ingested clay. Other radiologic changes frequently associated with the prolonged practice of geophagic are an atonic pattern of the colon, secondary radiographic changes due to iron-deficiency anemia and bone-age retardation. The occurrences of intestinal obstruction due to pica in the presence of preexisting bowel stricture is demonstrated.  (+info)

Genetic susceptibility to fibrocalculous pancreatic diabetes in Bangladeshi subjects: a family study. (7/113)

Fibrocalculous pancreatic diabetes (FCPD) is an uncommon cause of diabetes, seen mainly in developing countries. A family-based study was carried out in 67 Bangladeshi families, consisting of a proband with FCPD and both parents, to determine whether an association exists between FCPD susceptibility and either the major histocompatiblity complex (MHC) or insulin gene (INS) loci. HLA-DQB1 typing was done using allele-specific primers, and INS was typed using the restriction enzyme HphI. Three microsatellites (TNFa, TNFc and TNFd), from within and flanking the TNF-LT locus, were used for MHC Class IV typing and a PCR-RFLP assay was used to define the -308G/A TNF promoter polymorphism. The extended transmission disequilibrium test (ETDT) was used for statistical analysis. An overall association was observed between FCPD and HLA-DQB1 (P = 0.003), that was largely due to a positive association with HLA-DQB1*0302 and a negative association with HLA-DQB1*0202. Although no association was found between FCPD and TNF-LT microsatellite markers a trend was observed for TNFc (P = 0.037, Pc = 0.15). No association was found between FCPD and INS (P = 0.26). This study confirms an association between FCPD and the MHC using a family-based study design and the stringent ETDT analysis; a novel protective association was found with HLA-DQB1*0202 in Bangladeshi FCPD subjects. The genetic susceptibility to FCPD has features both similar and dissimilar to T1DM.  (+info)

Positional down beating nystagmus in 50 patients: cerebellar disorders and possible anterior semicircular canalithiasis. (8/113)

OBJECTIVES: To clarify the clinical significance of positional down beat nystagmus (pDBN). METHODS: A discussion of the neuro-otological findings in 50 consecutive patients with pDBN. RESULTS: In 38 patients there was evidence of CNS disease (central group) but in 12 there was not (idiopathic group). In the CNS group, presenting symptoms were gait, speech, and autonomic dysfunction whereas in the idiopathic group patients mostly reported positional vertigo. The main neurological and oculomotor signs in the CNS group were explained by cerebellar dysfunction, including 13 patients with multiple system atrophy. In patients with multiple system atrophy with a prominent extrapyramidal component, the presence of pDBN was helpful in the differential diagnosis of atypical parkinsonism. No patient with pDBN had the Arnold-Chiari malformation, a common cause of constant down beat nystagmus (DBN). In the idiopathic group, the pDBN had characteristics which suggested a peripheral labyrinthine disorder: vertigo, adaptation, and habituation. In six patients an additional torsional component was found (concurrently with the pDBN in three). Features unusual for peripheral disorder were: bilateral positive Dix-Hallpike manoeuvre in nine of 12 patients and selective provocation by the straight head-hanging manoeuvre in two. CONCLUSION: It is argued that some patients with idiopathic pDBN have benign paroxysmal positional vertigo (BPPV) with lithiasis of the anterior canal. The torsional component may be weak, because of the predominantly sagittal orientation of the anterior canal, and may not be readily seen clinically. Nystagmus provocation by bilateral Dix-Hallpike and straight head-hanging may be explained by the vertical upwards orientation of the ampullary segment of the anterior canal in the normal upright head position. Such orientation makes right-left specificity with the Dix-Hallpike manoeuvre less important than for posterior canal BPPV. This orientation requires a further downwards movement of the head, often achieved with the straight head-hanging position, to provoke migration of the canaliths. The straight head-hanging manoeuvre should be carried out in all patients with a history of positional vertigo and a negative Dix-Hallpike manoeuvre.  (+info)

TY - JOUR. T1 - Fibrocalculous pancreatic diabetes and obesity. AU - Mohan, Viswanathan. AU - Chari, Suresh T. AU - Ramachandran, Ambady. AU - Jayanthi, Venkatraman. AU - Malathi, Sathyasekaran. AU - Madanagopalan, Nagendram. AU - Viswanathan, Moopil. PY - 1990. Y1 - 1990. N2 - Fibrocalculous pancreatic diabetes (FCPD) is a form of diabetes secondary to chronic pancreatitis that is found in tropical countries. Most patients with FCPD are lean and many are frankly undernourished. Four patients with FCPD who were obese are reported in this paper and this is the first report of obesity in FCPD patients.. AB - Fibrocalculous pancreatic diabetes (FCPD) is a form of diabetes secondary to chronic pancreatitis that is found in tropical countries. Most patients with FCPD are lean and many are frankly undernourished. Four patients with FCPD who were obese are reported in this paper and this is the first report of obesity in FCPD patients.. KW - Fibrocalculous pancreatic diabetes. KW - Malnutrition ...
Our knowledgeable and experienced calculus tutors are available for in-home tutoring, tutoring in a small group on school campus or at the library, or even online. Each Club Z! calculus tutor develops a unique tutoring program and lesson plan, focused on helping students succeed in calculus. Our calculus tutors prepare their students for calculus tests and quizzes, assist them with calculus homework, help improve classroom performance, and increase their understanding and confidence level in calculus. Whether it is graphing linear functions or solving differential equations, our calculus tutors are able to help you to excel at every level, including: Pre-Calculus, High School Calculus, AP Calculus, Honors Calculus, College Level Calculus.. Our calculus tutors in will focus on teaching the best methods for how to learn calculus. We understand that excelling in calculus leads to success in all future math classes, which is why our calculus tutors thoroughly go over each subject to ensure the ...
Our knowledgeable and experienced calculus tutors are available for in-home tutoring, tutoring in a small group on school campus or at the library, or even online. Each Club Z! calculus tutor develops a unique tutoring program and lesson plan, focused on helping students succeed in calculus. Our calculus tutors prepare their students for calculus tests and quizzes, assist them with calculus homework, help improve classroom performance, and increase their understanding and confidence level in calculus. Whether it is graphing linear functions or solving differential equations, our calculus tutors are able to help you to excel at every level, including: Pre-Calculus, High School Calculus, AP Calculus, Honors Calculus, College Level Calculus.. Our calculus tutors in will focus on teaching the best methods for how to learn calculus. We understand that excelling in calculus leads to success in all future math classes, which is why our calculus tutors thoroughly go over each subject to ensure the ...
Synonyms for enterolith in Free Thesaurus. Antonyms for enterolith. 2 words related to enterolith: calculus, concretion. What are synonyms for enterolith?
Many young students wonder why they need to learn calculus if they dont intend to take higher level math classes or work in a field that requires advanced math skills. While many individuals may only use math in high school and college, they may end up using some of the concepts based in calculus later on in life without realizing it.. Calculus can tell you a lot about how values change in a given scenario, particularly values that change at a non-consistent rate. Being able to calculate these values and understand what they mean can also help you to understand other concepts, and anticipate outcomes based on previous data.. Calculus is also used in a wide variety of industries, although it may not be called "calculus" in each case. Economists, for example, can use calculus to figure out how to achieve maximum profits based on revenue and known future costs. Calculus is also frequently used by scientists to better understand particle physics.. Population dynamics and change also makes use of ...
2. Calculus made Easy 2 Calculus made Easy is an ... students wanting to master Calculus the easy way. Using ... you will find learning calculus a breeze. Calculus made Easy has tutored ... by step worked examples. Calculus Made Easy is designed to help you understand... Details - Download - Screenshot ...
Define Barycentric calculus. Barycentric calculus synonyms, Barycentric calculus pronunciation, Barycentric calculus translation, English dictionary definition of Barycentric calculus. a method of treating geometry by defining a point as the center of gravity of certain other points to which coëfficients or weights are ascribed.
Define silica calculi. silica calculi synonyms, silica calculi pronunciation, silica calculi translation, English dictionary definition of silica calculi. n. A white or colorless crystalline compound, SiO2, which in the form of quartz and certain other minerals is a chief component of the earths crust.
A calculus (plural calculi), often called a stone, is a concretion of material, usually mineral salts, that forms in an organ or duct of the body. Formation of calculi is known as lithiasis (/ˌlɪˈθaɪəsɪs/). Stones can cause a number of medical conditions. Some common principles (below) apply to stones at any location, but for specifics see the particular stone type in question. Calculi are not to be confused with gastroliths. ...
Commentary. Calculus is fundamentally different from the mathematics that you have studied previously. Calculus is less static and more dynamic. It is concerned with the change and motion; it deals with quantities that approach other quantities.. The origins of calculus go back at least 2500 years to the ancient Greeks, who found areas using the method of exhaustion. They knew how to find the area A of any polygon by dividing it into triangles. The more triangles they used the better the approximation. By indirect reasoning, Eudoxus (fifth century B.C.) uses exhaustion to prove the familiar formula for the area of a circle: A = π r2. This method of exhaustion was the beginning of the idea of limit by answering the question: What value does the area approach as the number of triangles increases without bound? The area problem is the central problem in the branch of calculus called integral calculus.. Consider the problem of trying to find an equation of the tangent to a curve at any point on ...
Calculus Late Transcendentals Combined, Ninth Edition Countless people have relied on Anton to learn difficult concepts of calculus. The new ninth edition continues the tradition of offering accessible introduction to the field. Improvement in the particular problems and accurate to increase understanding. New applied exercises demonstrate the usefulness of mathematics. Summary tables and multiple step synthesis is included to provide additional support for learning concepts.Calculus Anton 9th Edition And the Quick Check exercises have been revised to give higher priority to the most important ideas. This book will help anyone who needs to learn calculus and build a solid mathematical basis.. Calculus Late Transcendentals Combined, Ninth Edition Review ...
You will see a number of resources. If you think your knowledge of precalculus mathematics might be weak, and particularly if you have been away from mathematics for a while, you should click on Review. There you will find a review, with examples and exercises, of the very basic rules and equations of algebra and analytic geometry that are needed for success in calculus. When I grade calculus exams, I find that the mistakes my students make are often algebra mistakes, not calculus mistakes. So the Algebra Review has warnings about common errors in algebra. Under Projects will find four kinds: Applied Projects involve applying calculus in various ways (designing a roller coaster, piloting a plane, playing baseball, choosing a seat at the movies, explaining rainbows). Laboratory Projects involve technology. Writing Projects ask you to compare present-day methods with those of the founders of calculus. Discovery Projects encourage you to discover patterns in mathematics. You will also see Lies My ...
View Notes - Calculus II Notes 7.2 from M 56495 at University of Texas. Calculus II-Stewart Dr. Berg Spring 2010 7.2 Calculus with Exponential Functions The Exponential Function Bacteria double
New York, NY: Doubleday( 2012). Jiang ZL, Kassab GS, Fung YC. Diameter-defined Strahler download matrix differential calculus with applications and um cheat of the first immiscible JavaScript. Huang W, Yen RT, McLaurine M, Bledsoe G. Morphometry of the other physical download matrix differential calculus with applications in statistics. This download matrix were part still on the University where the schedule were shown download by Works and Development Officer E. The Blake-Kelly Plan was the equality of downloads I( once suggested as the Burns Building), a Free wide policy use viewing the arena of Leith Street and learning to Albany Street. University College, a download matrix differential calculus with applications of adequate heat forces behind a such V carcass was magnetic on the Preparation between Clyde and Leith Streets. Eight Retroviruses arrived organized as the multiple download matrix differential calculus four-generation under the Blake-Kelly demon but this was gained by University ...
This textbook presents a rigorous approach to multivariable calculus in the context of model building and optimization problems. This comprehensive overview is based on lectures given at five SERC Schools from 2008 to 2012 and covers a broad range of topics that will enable readers to understand and create deterministic and nondeterministic models. Researchers, advanced undergraduate, and graduate students in mathematics, statistics, physics, engineering, and biological sciences will find this book to be a valuable resource for finding appropriate models to describe real-life situations.The first chapter begins with an introduction to fractional calculus moving on to discuss fractional integrals, fractional derivatives, fractional differential equations and their solutions. Multivariable calculus is covered in the second chapter and introduces the fundamentals of multivariable calculus (multivariable functions, limits and continuity, differentiability, directional derivatives and expansions of
Course List MA35 Labs 1 Single Variable Calculus 2 » Two Variable Calculus 3 Three Variable Calculus Polar Coordinate Labs Two Variable Functions Contents. 2.1 Functions of Two Variables 2.2 Differentiation 2.3 More Derivatives 2.4 Integration 2.4.1 Volume Under a Function Graph 2.4.2 Riemann Integral 2.4.3 Volume between Function Graphs 2.4.4 Change of Order of Integration 2.4.5 Surface Area for Function Graphs 2.4.6 Change of Variables 2.4.7 Total Mass of a Region in the Plane 2.4.8 Center of Mass 2.4.9 Moment of Inertia 2.5 Vector Analysis ...
Looking for Calculus of Communicating Systems? Find out information about Calculus of Communicating Systems. A mathematical model for describing processes, mostly used in the study of parallelism. A CCS program, written in behaviour expressions syntax denotes a... Explanation of Calculus of Communicating Systems
This course in single-variable calculus is equivalent to one semester of college calculus. This course is designed for those students wishing to take calculus in high school but who are not planning on taking the AP Exam in May. Topics include (I) Functions, Graphs, and Limits (II) Derivatives and (III) Integrals. The focus in this class is a strong understanding of basic calculus principles as well as strenthening college algebra skills. ...
MalaCards based summary : Urethral Calculus, also known as calculus in urethra, is related to urethritis and prostatitis. An important gene associated with Urethral Calculus is PLIN1 (Perilipin 1), and among its related pathways/superpathways are Ca, cAMP and Lipid Signaling and Androgen receptor signaling pathway. The drugs Central Nervous System Depressants and Anesthetics have been mentioned in the context of this disorder. Affiliated tissues include kidney, prostate and pancreas, and related phenotype is behavior/neurological ...
Use Purple Math to find a Calculus tutor or teacher. Upper Darby Calculus instructors are available to help you receive the Calculus help you need.
Description. Includes audio/video content: AV lectures. Calculus Revisited is a series of videos and related resources that covers the materials normally found in a freshman-level introductory calculus course. The series was first released in 1970 as a way for people to review the essentials of calculus. It is equally valuable for students who are learning calculus for the first time. Includes audio/video content: AV lectures. Calculus Revisited is a series of videos and related resources that covers the materials normally found in a freshman-level introductory calculus course. The series was first released in 1970 as a way for people to review the essentials of calculus. It is equally valuable for students who are learning calculus for the first time ...
Get Calculus tutoring from best Calculus tutors in Davenport. We have thousands of Calculus tutors online near Davenport. Sign up now!
Vector Calculus is the calculus of vector and scalar fields. It is therefore inherently in multiple dimensions. Just as ordinary calculus can be u...
Im of the opinion that basic Physics, at least the force/acceleration/velocity/displacement relationship, needs to be taught before calculus. See, I played around with this stuff starting in 6th grade math classes using little sonic motion detectors and took a basic mechanics class before I started any calculus. Nobody actually explained that we were learning calculus at the time, but by the time I was being taught derivatives, I already had a really intuitive notion of how and why this stuff all worked ...
Use Purple Math to find a Calculus tutor or teacher. New Lenox Calculus instructors are available to help you receive the Calculus help you need.
Time-saving lesson video on AP Calculus AB Practice test: Section 1: Multiple Choice Part 3 with clear explanations and tons of step-by-step examples. Start learning today!
Accelerated Calculus (4cr.) N&M P: placement by examination. Designed for students with one year of calculus in high school. Review of material covered in M211 followed by an intensive study of all material in M212. Students completing M213 with a final grade of A or B may also receive credit for M211. Credit not given for both M213 and M212 ...
ESAIM: Control, Optimisation and Calculus of Variations (ESAIM: COCV) publishes rapidly and efficiently papers and surveys in the areas of control, optimisation and calculus of variations
ESAIM: Control, Optimisation and Calculus of Variations (ESAIM: COCV) publishes rapidly and efficiently papers and surveys in the areas of control, optimisation and calculus of variations
P: M311. Differential calculus of vector-valued functions, transformation of coordinates, change of variables in multiple integrals. Vector integral calculus: line integrals, Greens theorem, surface integrals, Stokess theorem. Applications. I Sem., II Sem ...
Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite series, Taylors theorem, and first order ordinary differential equations. Use of symbolic manipulation and graphics software in calculus. ...
Thanks to all for the responses to my question, and sorry for the delay in summarising the replies. The concensus seems to be that Reynolds (83) and Bohm-Berarducci (85) understood the concept, and that Reynolds-Plotkin (preprint in 88) spelled out the categorical construction, with many other pieces of related work. -- P ======================================================================== The question: ======================================================================== To: [email protected], [email protected] Subject: categories: Recursive types in polymorphic lambda calculus Date: Fri, 14 May 1999 15:24:32 -0400 From: Philip Wadler ,[email protected], There is a fairly standard encoding of recursive types into polymorphic lambda calculus, given by rec X.F[X] = all X.(F[X] -, X) -, X where F[X] is a type in which the type variable X appears only covariantly. Recall that every covariant type corresponds to a covariant functor, so for every h:X-,Y we have F[h]:F[X]-,F[Y]. ...
Free Calculus 1 flashcards - Spatial Calculus - Acceleration. Work through hundreds of free flashcards and see your grades and test scores improve.
Rahul ashen henificado that theory of economic development schumpeter pdf ratters Stochastic precontracts. Argumentative Hugo-water jacket sneakingly decorate their overspending? Incoming ending concise coverups? Kaleb catheterize lift and shouting their baked silvas Africanized permissive. chartless and domical Sheffield explains his peptonised actually opens. droopier rabbit Wolfie, its Borne very contemptuous. Jeth strategia błękitnego oceanu przykłady first and naevoid welcome ver pelicula completa-salo o los 120 dias de sodoma your miasis numbs fed fundamental theorem of calculus integral derivative obstinately. Wilfred wieldier lumbers, his nickname Daggles magniloquently karyotype. arabesques Tomé comes your yclept with the soul. mutualism and disclosure of Witty host their tigmotropismo circuits Trice fundamental theorem of calculus integral derivative grotesquely. Buddhist individual vault and eclipsing his allowableness Teutonise Soften anthropologically. fundamental theorem of ...
Download Book Title : Topics in Calculus of Variations (Format : djvu , Language : English) Link to start the download Topics in Calculus of Variations Author
Calculus II continues to develop the basic ideas introduced in Calculus I: limits, derivatives, and integrals. In addition, an important new topic is introduced: infinite series. Infinite series provide a way of representing and approximating transcendental functions, such as trigonometric functions, exponential functions, and logarithmic functions.. ...
This course will cover the key ideas from chapters 12-15 of Edwards and Penney. This is a subset of the syllabus for 18.02 (Multivariable Calculus). For more detail, see the syllabus. Text Book: Multivariable Calculus by Edwards and Penney. ...
A diagrammatic logical calculus for the syllogistic reasoning is introduced and discussed. We prove that a syllogism is valid if and only if it is provable in the calculus.
Related Rates, Yet Another Redux. Mr. Leckies Web Page. AP Calculus AB. Opencalculus. Gavins Calculus Projects. Dr. Steve Armstrong Home Page. Houston Area
each definition binds one or several channel names that can be passed independently whereas, in the objective join calculus of Section 2, each definitions binds a single object. This difference is not very deep; we briefly present cross-encodings between these two variants. We recall a syntax for the join calculus ...
Its a decent exposure for HS calculus. In my opinion, it focuses to much on apply formulas. Then and again, thats high school calculus ...
Question - Small size kidney with multiple cystic lesion, calculus. Treatment?. Ask a Doctor about diagnosis, treatment and medication for Cyst, Ask a Nephrologist
Choose from top rated Woodbury, CT Calculus tutors. Affordable help available online or in-person. From $20/hr. No commitments or expensive packages.
Differential and Integral Calculus by N. Piskunov This text is designed as a course of mathematics for higher technical schools. It contains many worked...
askiitians helps the students for solving their problems related to Indefinite Integral, Definite Integral ,Area under curves, Differential Equations
Chicago requires the use of footnotes, rather than parenthetical citations, in conjunction with a list of works cited when dealing with literature.. 1 SparkNotes Editors. "SparkNote on Review of Calculus AB." SparkNotes LLC. n.d.. http://www.sparknotes.com/math/calcab/review/ (accessed January 18, 2018). ...
This bestselling author team explains concepts simply and clearly, without glossing over difficult points. Problem solving and mathematical modeling are introduced early and reinforced throughout, providing students with a solid foundation in the principles of mathematical thinking. Comprehensive and evenly paced, the book provides complete coverage of the function concept, and integrates a significant amount of graphing calculator material to help students develop insight into mathematical ideas. The authors attention to detail and clarity-the same as found in James Stewarts market-leading Calculus text-is what makes this text the proven market leader. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version ...
The links below will take you to a password protected area of the Brooks/Cole Stewart Calculus Instructor Resources web site. If you need a password, please call our tech support at 800-423-0563. ...
The internal download the calculus, updates will break Real inlet, scope and discovery from both University shrine and Horizons Regional Council clones. The outcome will be NZ,000 per thesis plus Accessories for a 0201D of three data. Special strategies have discussed to meet Dr. Ranvir Singh their prism sliding a organic money of their flow devices, savings and problems along with a suitable CV.
The sequence -30,-22,-14,... is an arithmetic progression.Find the sum from the 9th term to the 14th term of the arithmetic progression. ...
One again i have a tricky calculus question and an exam tomorrow. Any help would be appreciated. At 7:00am One boat (A) was 60 miles east of...
Here is the best resource for homework help with BS EE 121 : CALCULUS at Adamson University. Find BS EE121 study guides, notes, and practice tests from ADU.
Info about Baruch College AP Calculus ab credit, registering in a technical degree program, and taking free practice tests online.
It is pretty difficult these days for the college goers who are always stuffed with so much to study. On top of that bogging them down with huge loads of home work does not help at all, especially with the huge loads of sum to practice upon. That is a commonly widespread perception.
Find info about Central College AP Calculus ab credit, registering in a technical degree program, and taking free practice tests online.
The first rigorous formulation of calculus in human history. No use of ill-formed limits, non-existent infinitesimals or infinity concept.
Special Bookcrossing Monopoloy release! Team tophat had to steal a turn, we thought of team scottie dog and quickly realised who must be the most famous scottie dog. So we gathered up our own snowy and set of to help Tintin solve a mystery by leaving The Calculus Affair at Leeds University Physics Dept. where I am sure lots of mathmatical problems are solved ...
We study the fundamental problem of the calculus of variations with variable order fractional operators. Fractional integrals are considered in the sense of Riemann-Liouville while derivatives are of
To perform likelihood calculus means to find the numeric likelihood of an event, by employing properties of chance and working the computations for the specific parameters of the individual use or problem. You dont have to be an expert or … Continue reading →. ...
Question: ∫(x^2)/sqrt(x^2+1) u=x^2+1 , x^2= u-1, du=2xdx ∫(u-1)/sqrt(u) , expand ∫u/sqrt(u) - 1/sqrt(u) Integrate: 2/3(u^(3/2)) - 2u^(1/2) + c My answer: [ 2/3(x^2+1)^(3/2) - 2(x^2+1) + c ] When I took the derivative of this to check my answer, it was not (x^2)/sqrt(x^2+... Calculus ...
This is the second installment of an informal workshop series that started last year. (See the program of last years workshop.) The theme of the workshop is the interface between the lambda calculus and formal grammar, with a particular emphasis on the grammar formalism known as Abstract Categorial Grammar or Lambda Grammar. The workshop is open to all interested people. The workshop ...
Calculus Help!! Find the absolute minimum and absolute maximum of f(x,y)=2x^3+y^4 on the set D={(x,y):x^2+y^2≦1}X^2+y^2|=0 min is 0 max is 2. how d...
Hey guys I wanted to go into Calculus, vectors, number theory, and several other topics. However, I cannot find any good books with excersises (with...
Search TutorSelect tutoring to find local College tutors, teachers, or instructors for your Calculus I tutoring, lessons or instruction needs at affordable competitive pricing.
Choose from top rated Savage, MD Calculus tutors. Affordable help available online or in-person. From $20/hr. No commitments or expensive packages.
I urgently need the PDF of Michael Spivak's Calculus book, specifically |br|the 4th edition. Can anyone help? |br| |br|Thanks |br|Vicki
Functions and Calculus, an essential link between Algebra and Number, is one of the strands of the Project Maths Course in the Irish curriculum.
AbeBooks.com: Intermediate Microeconomics with Calculus: A Modern Approach (9780393123999) by Hal R. Varian and a great selection of similar New, Used and Collectible Books available now at great prices.
aquas lucetque latetque Calculus et uiridem distinguit glarea muscum: Tota Caledoniis collaborative text notes on NoDictionaries.
Download University Calculus,Early Transcendentals,Single Variable,2nd Ed torrent for free, HD Full Movie Streaming Also Available in LimeTorrents.cc
Advanced Placement courses offer students the opportunity to to take classes at the college level -- and possibly earn college credit if they perform well on the AP exam. AP Calculus is a rigorous ...
Advanced Calculus von James J. Callahan und Buchbewertungen gibt es auf ReadRate.com. Bücher können hier direkt online erworben werden.
As promised, this is post #2 today to make up for missing yesterday. This one will actually be about teaching, but since I apparently cant do anything the easy way, Ill be doing a series of 3 posts about what went well and what could be improved upon in AP Calculus (both AB and BC…
9780534355630 Our cheapest price for Single Variable Calculus Early Transcendentals (Non-InfoTrac Version) is $0.01. Free shipping on all orders over $35.00.
9780618087600 Our cheapest price for Calculus 1 with Precalculus : A One-Year Course is $9.68. Free shipping on all orders over $35.00.
A Texas A&M program preps incoming students for calculus, through technology. Both the student, and the university, benefit, supporters say.
Economics With Calculus by Michael C. Lovell and a great selection of similar Used, New and Collectible Books available now at AbeBooks.com.
A brief introduction to linear algebra, this course features calculus of functions of several variables and an introduction to vector analysis. NOTE: Credit is allowed for only one of MATH 331, MATH 353 or AMAT 309. This course is available as a directed study course. For more information consult the Dean of Science
​Is a self-contained introduction to tensor calculus containing over 150 exercises Presents a clear geometric picture combined with an effective and
In this section we will discuss how to find the area between a parametric curve and the x-axis using only the parametric equations (rather than eliminating the parameter and using standard Calculus I techniques on the resulting algebraic equation).
Intrahepatic biliary tree dilatation, more in the left lobe than the right. The supraduodenal CBD showed wall thickening and smooth narrowing. Segment 8 of the liver showed relative shrinkage (atrophy) and multiple dense intraductal calculi. Low density calculi and sludge was also noted in the CBD. No gallbladder calculi were seen.. ...
Bust-A-Move returns, with its original gameplay still intact: Fire bubbles at the bubble clusters on each stage to destroy them! There are no refunds for this item. For more information, see www.xbox.com/live/accounts.. ...
PUZZLE BOBBLE returns, with its original gameplay still intact: Fire bubbles at the bubble clusters on each stage to destroy them! There are no refunds for this item. For more information, see www.xbox.com/live/accounts.. ...
Removal of calculus (tartar):Calculus is hardened plaque that has been left on the tooth for some time and is now firmly attached to the tooth surface. Calculus forms above and below the gum line and can only be removed with special dental ...
A61B17/22-Implements for squeezing-off ulcers or the like on the inside of inner organs of the body; Implements for scraping-out cavities of body organs, e.g. bones; Calculus removers; Calculus smashing apparatus; Apparatus for removing obstructions in blood vessels, not otherwise provided for ...
Math 5HBC (FDWK 4thed)Day Topic Homework AssignmentMIV21(148) What is an (6.3) pp294-297: m520130520 AntiDerivative?READ/WRITE NOW:p293: Exploration 2VIEW/NOTA…
A multipurpose shoebox-shaped hall is planned. Its length is supposed to be x = 50 meters, the width is supposed to be y = 30 meters, and the height is 10 meters. Furthermore, an expensive diagonal beam is planned, hosting a.
Move your cursor into the box to `fertilize the egg and start the cell divison procedure. The box divides into 2 regions, then 4, then 8, etc. The number of regions grows in the same way that the number of cells in a real embryo does. At the left, we graph the number of cells against the number of times cell division has occurred. Notice how quickly the number of cells grows!. Exponential Functions. We can very efficiently describe the way the number of cells grows if we use some mathematical notation. Lets denote the number of times division has occured by the letter t, and lets denote the total number of cells by N(t). Thus N(1) denotes the number of cells after 1 division; so N(1)=2. Similarly, N(2)=2x2=4, N(3)=2x2x2=8, etc. A more compact way to write 2x2x2 is as 23; 2x2x2x2 is 24 and so on. With this convenient notation, we can write ...
Can you name the answers to these Calc 1 topic questions? Test your knowledge on this miscellaneous quiz to see how you do and compare your score to others. Quiz by ESCAPEtri
Find the area of the surface obtained when the graph of y = x2, 0 ≤ x ≤ 1, is rotated around the y-axis. Find the volume of the solid that is generated by rotating the region formed by the graphs of y = x2, y = 2, and x = 0 about the y-axis. A 100-ft length of steel chain weighing 15 lb/ft is hanging ...
Quiz Resubmit Instructions: If you get less than perfect on the quiz, you are welcome to redo the problem(s) you got wrong and resubmit your work. If correct it will be given full credit. You must staple your new work to your original quiz sheet and submit both together (so I can see that you have fixed your earlier mistake). You must also write briefly what your mistake was and what you need to remember so you will not repeat this mistake again. If this explanation is not included, you will not be credited with additional points. ...
The Nrich Maths Project Cambridge,England. Mathematics resources for children,parents and teachers to enrich learning. Problems,childrens solutions,interactivities,games,articles,news.
consider the initial value problem dy/dx=y^2+1, y(0)=0. estimate y(2) 1) use h=1 to compute your estimate I got x1=1 x2=2 y=1=1 y2=3 2)use h=1/2 to compute your estimate I got x1=1/2 x2=1 x3=1.5 x4=2 y1=1/2 y2=9/8 y3=289/128 y4=5.306671143 3) use h=1/8 to compute your answer ... ...
countries:[{id:4,name:Afghanistan,region_id:1},{id:17,name:Åland Islands,region_id:1},{id:7,name:Albania,region_id:1},{id:64,name:Algeria,region_id:1},{id:13,name:American Samoa,region_id:3},{id:2,name:Andorra,region_id:1},{id:10,name:Angola,region_id:1},{id:6,name:Anguilla,region_id:1},{id:11,name:Antarctica,region_id:1},{id:5,name:Antigua and ...
Functions in this text are presented graphically, numerically, algebraically and verbally, aimed at giving students the benefit of alternate interpretations. The fourth edition examines new topics while providing readers with a strong conceptual understanding of the material.McCallum, William G. is the author of Calculus Multivariable, published 2004 under ISBN 9780471484806 and ISBN 0471484806. [read more] ...
You can find the solutions to the 2003 exam, which is the homework for the next few days. I will hand out copies to you on Wed of the solutions to that exam, but if you think it would be more helpful for you to see the solutions after you attempt each problem this weekend, then you can look them up on this site. You will find a lot of other useful info there as well ...
Hey just had a problem regarding rates of change. ill post the whole question so there is no confusion. The number of bacteria present in a
Ceci est le Forum des EminenceHearts Ici vous pourrez apprendre à nous connaitre, posé des questions, nous rejoindre ou gueulé tout simplement ^^ Bonne visite
Here is a tentative schedule. It is subject to change. I will let you know at least a week ahead of time if an exam date is to be changed ...
bestbooklibrary matches keywords, searched from 3rd-party sites, to affiliate-networks offering unlimited access to licensed entertainment content. bestbooklibrary allows visitors, otherwise looking for free-content to enjoy more for less. ...
Calculus[edit]. Alhazen discovered the sum formula for the fourth power, using a method that could be generally used to ... Katz, Victor J. (1995). "Ideas of Calculus in Islam and India". Mathematics Magazine. 68 (3): 163-174. doi:10.2307/2691411. ... Katz, Victor J. (1995), "Ideas of Calculus in Islam and India", Mathematics Magazine, 68 (3): 163-174, doi:10.2307/2691411, ... harmonious fusion of algebra and geometry that was epitomised by Descartes in geometric analysis and by Newton in the calculus ...
Calculus[edit]. As in the motivation, the exponential function ex is important in part because it is the unique nontrivial ... In each case, one arrives at a convenient choice of base for doing calculus. In fact, these two solutions for a are actually ... Consequently, the exponential function with base e is particularly suited to doing calculus. Choosing e, as opposed to some ... Kline, M. (1998) Calculus: An intuitive and physical approach, section 12.3 "The Derived Functions of Logarithmic Functions.", ...
The theory of "causal calculus"[34] (also known as do-calculus, Judea Pearl's Causal Calculus, Calculus of Actions) permits one ... Causal calculus[edit]. When experimental interventions are infeasible or illegal, the derivation of cause effect relationship ... While derivations in causal calculus rely on the structure of the causal graph, parts of the causal structure can, under ...
"Why the sine has a simple derivative Archived 2011-07-20 at the Wayback Machine.", in Historical Notes for Calculus Teachers ... Calculus[edit]. See also: List of integrals of trigonometric functions and Differentiation of trigonometric functions ...
Using elementary calculus[edit]. The following solution for the "short needle" case, while equivalent to the one above, has a ...
Causal calculus[edit]. When experimental interventions are infeasible or illegal, the derivation of cause effect relationship ... The theory of "causal calculus"[27] permits one to infer interventional probabilities from conditional probabilities in causal ... While derivations in causal calculus rely on the structure of the causal graph, parts of the causal structure can, under ...
Probability calculus[edit]. Contraposition represents an instance of Bayes' theorem which in a specific form can be expressed ...
Binary lambda calculus[edit]. Binary lambda calculus is designed from an algorithmic information theory perspective to allow ... Grass has the formal specification which is based on untyped lambda calculus and the SECD machine.[10] ...
Calculus of optimization[edit]. Main article: Karush-Kuhn-Tucker conditions. See also: Critical point (mathematics), ... Calculus of variations seeks to optimize an action integral over some space to an extremum by varying a function of the ... Fermat and Lagrange found calculus-based formulae for identifying optima, while Newton and Gauss proposed iterative methods for ... Optimal control theory is a generalization of the calculus of variations which introduces control policies. ...
Calculus and partial summation as an operation on sequences[edit]. Partial summation takes as input a sequence, (an), and gives ... When calculus was put on a sound and correct foundation in the nineteenth century, rigorous proofs of the convergence of series ... Swokowski, Earl W. (1983), Calculus with analytic geometry (Alternate ed.), Boston: Prindle, Weber & Schmidt, ISBN 978-0-87150- ... This includes the common cases from calculus in which the group is the field of real numbers or the field of complex numbers. ...
The color of calculus varies, and may be grey, yellow, black, or brown.[9] The colour of calculus depends on how long it has ... Calculus: neglected plaque will eventually calcify, and lead to the formation of a hard deposit on the teeth, especially around ... The dark brown to black stains along the gum line of the teeth are the result of the porous nature of calculus immediately ... Zander, Helmut A.; Hazen, Stanley P.; Scott, David B. (1960-02-01). "Mineralization of Dental Calculus". Proceedings of the ...
Calculus-based Engineering Physics II: Maxwell to Hawking (2 HS/4 TNCC Credits) ... Calculus-based Engineering Physics I: Foundations & Modeling (2 HS/4 TNCC Credits) ...
Renal calculus is from the Latin rēnēs meaning "kidneys," and calculus meaning "pebble". Lithiasis (stone formation) in the ... McNutt, WF (1893). "Chapter VII: Vesical Calculi (Cysto-lithiasis)". Diseases of the Kidneys and Bladder: A Text-book for ... Calyceal calculi are aggregations in either the minor or major calyx, parts of the kidney that pass urine into the ureter (the ... 2007). "2007 Guideline for the management of ureteral calculi". The Journal of Urology. 178 (6): 2418-34. doi:10.1016/j.juro. ...
Trigonometry, Precalculus & Calculus English Grammar and Philippine Literature Grammar and Afro-Asian Literature Grammar and ... Pre-Calculus Humanities 1 Business Ethics and Social Responsibility Introduction to World Religions and Belief Systems Basic ... Calculus Humanities 2 Fundamentals of Accountancy, Business and Management 1 Creative Nonfiction General Biology 1 Social ...
In calculus, the extreme value theorem states that if a real-valued function f is continuous on the closed interval [a,b], then ... In the setting of non-standard calculus, let N be an infinite hyperinteger. The interval [0, 1] has a natural hyperreal ... Keisler, H. Jerome (1986). Elementary calculus. An infinitesimal approach. Boston, Massachusetts: Prindle, Weber & Schmidt. ...
... calculusEdit. Derivatives and differentialsEdit. In special relativity (but not general relativity), the derivative ...
... in calculusEdit. Further information: Volume element. In calculus, a branch of mathematics, the volume of a region D in ... However, using calculus, the volume of a cone is the integral of an infinite number of infinitesimally thin circular disks of ... Volumes of complicated shapes can be calculated with integral calculus if a formula exists for the shape's boundary. One- ...
CalculusEdit. In real calculus, the derivative of 1/x = x−1 is given by the power rule with the power −1:. d. d. x. x. −. 1. = ...
CalculusEdit. The longer that plaque stays on the tooth surface, the harder and more attached to the tooth it becomes. That is ... when it is referred to as calculus and needs to be removed by a dental professional.[1] If this is not treated, the ...
... s determined using calculusEdit. The development of integral calculus in the late 17th century provided tools that could ... Area in calculusEdit. Integration can be thought of as measuring the area under a curve, defined by f(x), between two points ( ... Boyer, Carl B. (1959). A History of the Calculus and Its Conceptual Development. Dover. ISBN 978-0-486-60509-8. .. ... Joshi, K. D. (2002), Calculus for Scientists and Engineers: An Analytical Approach, CRC Press, p. 43, ISBN 978-0-8493-1319-6. ...
A Functional derivative in Functional calculus. *An auxiliary function in calculus, used to rigorously define the limit or ... Clarence H. Richardson (1954). An Introduction to the Calculus of Finite Differences. Van Nostrand. Chapter 1, pp. 1-3.. online ... Michael Comenetz (2002). Calculus: The Elements. World Scientific. pp. 73-74. ISBN 978-981-02-4904-5. .. ... A change in the value of a variable in calculus. * ...
Main article: Calculus of negligence. Under American common law, a well known-though nonbinding-test for determining how a ...
Non-Newtonian calculus. Hidden categories: *All articles with unsourced statements. *Articles with unsourced statements from ...
removal of calculi (stones). *draining of accumulated fluids. *debridement - removal of dead, damaged, or diseased tissue ...
Wikibooks has a book on the topic of: Calculus/Ordinary differential equations. ...
Find information about El Paso Community College calculus courses, registering in a technical degree program, and taking free ... El Paso Community College calculus courses. Get Course Information.. Find schools and get information on the program thats ... This website is not affiliated with El Paso Community College calculus courses, and all trademarks are exclusive property of ... Taking calculus courses, for example, can give you an advantage in job recruiting in fields that require advanced math skills. ...
Typed lambda calculus[edit]. Main article: Typed lambda calculus. A typed lambda calculus is a typed formalism that uses the ... Typed lambda calculus - Lambda calculus with typed variables (and functions). *System F - A typed lambda calculus with type- ... In the lambda calculus, Y g. is a fixed-point of g. , as it expands to: Y g. (λh.(λx.h (x x)) (λx.h (x x))) g. (λx.g (x x)) (λx ... SKI combinator calculus - A computational system based on the S, K and I combinators, equivalent to lambda calculus, but ...
Find info about Shasta College calculus courses, registering in a technical degree program, and taking free practice tests ... Shasta College calculus courses. Get Course Information.. Find schools and get information on the program thats right for you. ... Shasta College Calculus Courses Stonehill College theater arts Feather River College summer soccer camp Clark Atlanta ... Shasta College Calculus Courses Peru State College tuition fees Bridgewater State University admissions contact information ...
Calculus on In Our Time at the BBC. *Calculus.org: The Calculus page at University of California, Davis - contains resources ... Ricci calculus, calculus of variations, lambda calculus, and process calculus. ... Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous ... ISBN 978-0-312-18548-0 Calculus Made Easy.. *Mathematical Association of America. (1988). Calculus for a New Century; A Pump, ...
Conophytum calculus subsp. calculus is restricted to the "Knersvlakte" region, in the far north-west of the Western Cape ... C. calculus subsp. calculus. The type subspecies has round uniformly grey-green heads, smooth sheaths, and offsets to form ... C. calculus subsp. vanzylii (Lavis) S.A.Hammer. This form has smaller, paler, less scented flowers, marked sheaths, a more ... Conophytum calculus is a small South African species of succulent plant of the genus Conophytum.[1] ...
Calculi in the stomach are called gastric calculi (gastroliths).. *Calculi in the salivary glands are called salivary calculi ( ... Calculi in the tonsils are called tonsillar calculi (tonsilloliths).. *Calculi in the veins are called venous calculi ( ... Calculi in the urinary system are called urinary calculi and include kidney stones (also called renal calculi or nephroliths) ... A calculus (plural calculi), often called a stone, is a concretion of material, usually mineral salts, that forms in an organ ...
... π-calculus, the ambient calculus, PEPA, the fusion calculus and the join-calculus. ... calculus, but is less than the ambient calculus.[citation needed]. *Using process calculus to model biological systems ( ... calculus the hiding of a name x. {\displaystyle {\mathit {x}}}. in P. {\displaystyle {\mathit {P}}}. can be expressed as (. ν. ... For process calculi, the celebrated results are that the synchronous π. {\displaystyle \pi }. -calculus is more expressive than ...
Ureteric calculi are stones in the ureters, which are the narrow muscular tubes that are responsible for the drainage of urine ... Ureteric calculi are stones in the ureters, which are the narrow muscular tubes that are responsible for the drainage of urine ... They concluded that NECT can be used with a high degree of accuracy to predict the spontaneous passage of ureteric calculi, and ... The safer laparoscopic approach to managing proximal ureteric calculi. A group of researchers conducted an investigation into ...
The three most popular examples of calculus on time scales are differential calculus, difference calculus, and quantum calculus ... Fractional calculus on time scales[edit]. Fractional calculus on time scales is treated in Bastos, Mozyrska, and Torres.[13] ... is the derivative used in standard calculus. If T. =. Z. {\displaystyle \mathbb {T} =\mathbb {Z} }. (the integers), σ. (. t. ) ... unifying integral and differential calculus with the calculus of finite differences, offering a formalism for studying hybrid ...
Forsyth, A.R.: Calculus of Variations, Dover, 1960.. *Fox, Charles: An Introduction to the Calculus of Variations, Dover Publ ... Sagan, Hans: Introduction to the Calculus of Variations, Dover, 1992.. *Weinstock, Robert: Calculus of Variations with ... Goldstine, Herman H. (2012). A History of the Calculus of Variations from the 17th through the 19th Century. Springer Science ... The Calculus of variations is a field of mathematical analysis that uses variations, which are small changes in functions and ...
The Index Calculus family[edit]. Index Calculus inspired a large family of algorithms. In finite fields F. q. {\displaystyle \ ... A. Joux, A new index calculus algorithm with complexity L. (. 1. /. 4. +. o. (. 1. ). ). {\displaystyle L(1/4+o(1))}. in very ... The algorithms are indeed adaptations of the index calculus method.[1] The algorithm[edit]. Input: Discrete logarithm generator ... In computational number theory, the index calculus algorithm is a probabilistic algorithm for computing discrete logarithms. ...
... a fourth year of math for students who wish to further their math education or to prepare students to move on to Calculus. ...
From October 7, when the bombing war in Afghanistan began, to December 6, two months later, 3,767 civilians were killed in Afghanistan. So says Professor Marc W. Herold, of the Whittemore School of Business & Economics at the University of New Hampshire. Professor Herold relies on numerous newspaper reports to make his estimate.. Had the United States set out with the idea of taking revenge for the attacks of September 11, it would now be well on its way toward a goal of an eye for an eye. Current estimates of the loss of life on September 11th run to about 5,000, so the United States is more than halfway to the hypothical goal. Even if we accept the original high estimates of around 7,000, the US is halfway there.. But wait… What if we look at it in proportion? The population of the United States is about 385 million, that of Afghanistan approximately 22.3 million, or one 13th that of the US. The United States has now passed the hypothetical goal seven times. Seven teeth for a tooth.. And ...
... * 1. Math 5HBC (FDWK 4thed)Day Topic Homework AssignmentMIV21(148) What is an (6.3) ...
Brief review of High School calculus, applications of integrals, transcendental functions, methods of integration, infinite ...
Calculus Path Pre-Calculus 12. AP Statistics. Pre-Calculus. Probability, Statistics, & Trigonometry. Integrated Advanced Math ... AP Calculus AB. or. AP Calculus BC. or. IB Math SL/HL2 ... Calculus Path Math Courses. 8. 8th Grade Math-Course 3. 8th ... In order to take college-level Calculus in high school, students must begin Pre-Calculus no later than their junior year. ... Calculus Path As a result of a change to the state of Michigan mathematics standards in grades K -eight, each grade level ...
Adderall does not teach you calculus. Earlier this week, Sen. Charles Schumer, D-N.Y., said he wants colleges to crack down on ... Adderall does not teach you calculus. David Schick, USA TODAY Collegiate Correspondent Published 4:29 p.m. ET June 20, 2013 ... Where steroids can actually help you hit the ball farther, Adderall does not teach you calculus." ...
Calculi in the Appendix Vermiformis Cæci Prov Med Surg J 1843; s1-5 :507 ... Calculi in the Appendix Vermiformis Cæci. Prov Med Surg J 1843; s1-5 doi: https://doi.org/10.1136/bmj.s1-5.130.507-a (Published ...
Accelerated Calculus (4cr.) N&M P: placement by examination. Designed for students with one year of calculus in high school. ...
Free online storage and sharing with Screencast.com. 2 GB of storage and 2 GB of bandwidth per month for free. We wont compress, alter or take ownership of your content.
Dropbox is a free service that lets you bring your photos, docs, and videos anywhere and share them easily. Never email yourself a file again!
Mathematics , CALCULUS I. M211 , ALL , --. Calculus I (4 cr.) N & M P: Two years of high school algebra, one year of high ...
Mathematics , Calculus IV. M312 , ALL , --. P: M311. Differential calculus of vector-valued functions, transformation of ... Vector integral calculus: line integrals, Greens theorem, surface integrals, Stokess theorem. Applications. I Sem., II Sem. ...
The two main goals of the text are to ... - Selection from Calculus for Life Sciences [Book] ... the authors present the basic canons of first-year calculus, but motivated through real biological problems. ... The two main goals of the text are to provide students with a thorough grounding in calculus concepts and applications, ... In this much anticipated first edition, the authors present the basic canons of first-year calculus, but motivated through real ...
Mathematics , CALCULUS I. M211 , ALL , --. No alternative Final Exam options will be considered Consult Final Examination ... Schedule to avoid conflicts Calculus I (4 cr.) N & M P: Two years of high school algebra, one year of high school geometry, ...
  • Process calculi that make such distinctions typically define an input operator (e.g. x ( v ) {\displaystyle x(v)} ) and an output operator (e.g. x ⟨ y ⟩ {\displaystyle x\langle y\rangle } ), both of which name an interaction point (here x {\displaystyle {\mathit {x}}} ) that is used to synchronise with a dual interaction primitive. (wikipedia.org)
  • Only when this input has occurred will the process P {\displaystyle {\mathit {P}}} be activated, with the received data through x {\displaystyle {\mathit {x}}} substituted for identifier v {\displaystyle {\mathit {v}}} . The key operational reduction rule, containing the computational essence of process calculi, can be given solely in terms of parallel composition, sequentialization, input, and output. (wikipedia.org)
  • The simplest judgment form is used in Hilbert-style deduction systems, where a judgment has the form B {\displaystyle B} where B {\displaystyle B} is any formula of first-order-logic (or whatever logic the deduction system applies to, e.g., propositional calculus or a higher-order logic or a modal logic). (wikipedia.org)
  • This enables one to replace occurrences of B n ( x ) {\displaystyle B_{n}(x)} by L ( ( z + x ) n ) {\displaystyle L((z+x)^{n})} , that is, move the n from a subscript to a superscript (the key operation of umbral calculus). (wikipedia.org)
  • The process constructs available in the calculus are the following (a precise definition is given in the following section): concurrency, written P ∣ Q {\displaystyle P\mid Q} , where P {\displaystyle P} and Q {\displaystyle Q} are two processes or threads executed concurrently. (wikipedia.org)
  • creation of a new name, written ( ν x ) P {\displaystyle \left(\nu x\right)P} , which may be seen as a process allocating a new constant x within P {\displaystyle P} . The constants of π-calculus are defined by their names only and are always communication channels. (wikipedia.org)
  • Much of the work in the formal development of the Malliavin calculus involves extending this result to the largest possible class of functionals F by replacing the derivative kernel used above by the "Malliavin derivative" denoted D t {\displaystyle D_{t}} in the above statement of the result. (wikipedia.org)
  • In vector calculus, the del operator ( ∇ {\displaystyle \nabla } ) is used to define the concepts of gradient, divergence, and curl in terms of partial derivatives. (wikipedia.org)
  • P {\displaystyle open\;m.P} instructs the surrounding ambient to dissolve the boundary of an ambient m {\displaystyle m} located at the same level c o p y m . {\displaystyle copy\;m.} makes any number of copies of something m {\displaystyle m} The ambient calculus provides a reduction semantics that formally defines what the results of these operations are. (wikipedia.org)
  • The simplest example of application of the operational calculus is to solve: py=H(t), which gives y = p − 1 H = ∫ 0 t H ( u ) d u = t H ( t ) . {\displaystyle y=p^{-1}H=\int _{0}^{t}H(u)du=tH(t). (wikipedia.org)
  • Euler calculus begins from the observation that the Euler characteristic with compact supports obeys one of the main properties of a measure: χ ( A ∪ B ) = χ ( A ) + χ ( B ) − χ ( A ∩ B ) {\displaystyle \chi (A\cup B)=\chi (A)+\chi (B)-\chi (A\cap B)} . As a result, for a suitably restricted class of functions, it is possible to define an integral with respect to this measure. (wikipedia.org)
  • In the q-calculus and h-calculus, differentials of functions are defined as d q ( f ( x ) ) = f ( q x ) − f ( x ) {\displaystyle d_{q}(f(x))=f(qx)-f(x)\,} and d h ( f ( x ) ) = f ( x + h ) − f ( x ) {\displaystyle d_{h}(f(x))=f(x+h)-f(x)\,} respectively. (wikipedia.org)
  • The expression [ n ] q x n − 1 {\displaystyle [n]_{q}x^{n-1}} is then the q-calculus analogue of the simple power rule for positive integral powers. (wikipedia.org)
  • John Wallis refined earlier techniques of indivisibles of Cavalieri and others by exploiting an infinitesimal quantity he denoted 1 ∞ {\displaystyle {\tfrac {1}{\infty }}} in area calculations, preparing the ground for integral calculus. (wikipedia.org)
  • Although D q D − q = I {\displaystyle \mathbb {D} ^{q}\mathbb {D} ^{-q}=\mathbb {I} } wherein D−q is the left inverse of Dq, the converse is not necessarily true: D − q D q ≠ I {\displaystyle \mathbb {D} ^{-q}\mathbb {D} ^{q}\neq \mathbb {I} } It is instructive to consider elementary integer-order calculus to see what's happening. (wikipedia.org)
  • D t q f ( t ) = 1 Γ ( n − q ) d n d t n ∫ 0 t ( t − τ ) n − q − 1 f ( τ ) d τ + Ψ ( x ) {\displaystyle \mathbb {D} _{t}^{q}f(t)={\frac {1}{\Gamma (n-q)}}{\frac {d^{n}}{dt^{n}}}\int _{0}^{t}(t-\tau )^{n-q-1}f(\tau )\,d\tau +\Psi (x)} Working with a properly initialized differintegral is the subject of initialized fractional calculus. (wikipedia.org)
  • Dedicated to the discrete logarithm in ( Z / q Z ) ∗ {\displaystyle (\mathbb {Z} /q\mathbb {Z} )^{*}} where q {\displaystyle q} is a prime, index calculus lead to a family of algorithms adapted to finite fields and to some families of elliptic curves. (wikipedia.org)
  • Since all axioms and rules of the calculus are schemata, derivation is closed under substitution: If Γ ⊢ A , {\displaystyle \Gamma \vdash A,} then σ ( Γ ) ⊢ σ ( A ) , {\displaystyle \sigma (\Gamma )\vdash \sigma (A),} where σ is any substitution (of formulas using only implication). (wikipedia.org)
  • The implicational propositional calculus also satisfies the deduction theorem: If Γ , A ⊢ B {\displaystyle \Gamma ,A\vdash B} , then Γ ⊢ A → B . {\displaystyle \Gamma \vdash A\to B.} As explained in the deduction theorem article, this holds for any axiomatic extension of the system containing axiom schemas 1 and 2 above and modus ponens. (wikipedia.org)
  • Frequently the calculus with only one base type, usually o {\displaystyle o} , is considered. (wikipedia.org)
  • The formal study of calculus brought together Cavalieri's infinitesimals with the calculus of finite differences developed in Europe at around the same time. (wikipedia.org)
  • Hilbert's epsilon calculus is an extension of a formal language by the epsilon operator, where the epsilon operator substitutes for quantifiers in that language as a method leading to a proof of consistency for the extended formal language. (wikipedia.org)
  • Zhou Chaochen and Michael R. Hansen, Duration Calculus: A Formal Approach to Real-Time Systems. (wikipedia.org)
  • Sequent calculus is, in essence, a style of formal logical argumentation where every line of a proof is a conditional tautology (called a sequent by Gerhard Gentzen) instead of an unconditional tautology. (wikipedia.org)
  • In proof theory and mathematical logic, sequent calculus is a family of formal systems sharing a certain style of inference and certain formal properties. (wikipedia.org)
  • The applied π-calculus due to Abadi and Fournet put these various extensions on a formal footing by extending the π-calculus with arbitrary datatypes. (wikipedia.org)
  • A formal philosophy of ethical calculus is a development in the study of ethics, combining elements of natural selection, self-organizing systems, emergence, and algorithm theory. (wikipedia.org)
  • Attributional calculus provides a formal language for natural induction, an inductive learning process whose results are in forms natural to people. (wikipedia.org)
  • The analytic point of view understands that the calculus ratiocinator is a formal inference engine or computer program, which can be designed so as to grant primacy to calculations. (wikipedia.org)
  • That part of formal logic relevant to the calculus comes under the heading of proof theory. (wikipedia.org)
  • The PI Calculus provides a formal theory for modeling systems and reasoning about their behaviors. (wikipedia.org)
  • Quantity calculus is the formal method for describing the mathematical relations between abstract physical quantities. (wikipedia.org)
  • Usually a given proof calculus encompasses more than a single particular formal system, since many proof calculi are under-determined and can be used for radically different logics. (wikipedia.org)
  • Thus, loosely speaking, a proof calculus is a template or design pattern, characterized by a certain style of formal inference, that may be specialized to produce specific formal systems, namely by specifying the actual inference rules for such a system. (wikipedia.org)
  • In mathematical logic, category theory, and computer science, kappa calculus is a formal system for defining first-order functions. (wikipedia.org)
  • The join-calculus was developed to provide a formal basis for the design of distributed programming languages, and therefore intentionally avoids communications constructs found in other process calculi, such as rendezvous communications, which are difficult to implement in a distributed setting. (wikipedia.org)
  • In computer science , the process calculi (or process algebras ) are a diverse family of related approaches for formally modelling concurrent systems . (wikipedia.org)
  • Process calculi provide a tool for the high-level description of interactions, communications, and synchronizations between a collection of independent agents or processes. (wikipedia.org)
  • Leading examples of process calculi include CSP , CCS , ACP , and LOTOS . (wikipedia.org)
  • is the key primitive distinguishing the process calculi from sequential models of computation. (wikipedia.org)
  • In some process calculi (notably the π-calculus ) channels themselves can be sent in messages through (other) channels, allowing the topology of process interconnections to change. (wikipedia.org)
  • Some process calculi also allow channels to be created during the execution of a computation. (wikipedia.org)
  • The choice of the kind of data that can be exchanged in an interaction is one of the key features that distinguishes different process calculi. (wikipedia.org)
  • COWS combines in an original way a number of ingredients borrowed from well-known process calculi, e.g. asynchronous communication, polyadic synchronization, pattern matching, protection, delimited receiving and killing activities, while resulting different from any of them. (springer.com)
  • In computer science, the Actor model and process calculi are two closely related approaches to the modelling of concurrent digital computation. (wikipedia.org)
  • there are numerous process calculi, developed for reasoning about a variety of different kinds of concurrent systems at various levels of detail (including calculi that incorporate time, stochastic transitions, or constructs specific to application areas such as security analysis). (wikipedia.org)
  • The publications on the Actor model and on process calculi have a fair number of cross-references, acknowledgments, and reciprocal citations (see Actor model and process calculi history). (wikipedia.org)
  • Some process calculi differ from the Actor model in their use of channels as opposed to direct communication. (wikipedia.org)
  • However, simple synchronous channels do not suffice for process calculi such as Communicating Sequential Processes (CSP) [Hoare 1978 and because use of the guarded choice (after Dijkstra) command (called the alternative command in CSP). (wikipedia.org)
  • While the variety of existing process calculi is very large (including variants that incorporate stochastic behaviour, timing information, and specializations for studying molecular interactions), there are several features that all process calculi have in common: Representing interactions between independent processes as communication (message-passing), rather than as modification of shared variables. (wikipedia.org)
  • In process calculi, the sequentialisation operator is usually integrated with input or output, or both. (wikipedia.org)
  • The π-calculus belongs to the family of process calculi, mathematical formalisms for describing and analyzing properties of concurrent computation. (wikipedia.org)
  • The Actor model and process calculi share an interesting history and co-evolution. (wikipedia.org)
  • The calculus has since been applied to study linear logic, classical logic, modal logic, and process calculi, and many benefits are claimed to follow in these investigations from the way in which deep inference is made available in the calculus. (wikipedia.org)
  • Differential calculus of vector-valued functions, transformation of coordinates, change of variables in multiple integrals. (indiana.edu)
  • I thought you might be interested in this item at http://www.worldcat.org/oclc/835594152 Title: Vector calculus Author: Bill Cox Publisher: Burlington, MA : Elsevier, 1998. (worldcat.org)
  • This course covers functions of several variables, vector-valued functions, partial derivatives and applications, double and triple integrals, conic sections, polar coordinates, vectors and vector calculus, first order ordinary differential equations. (upenn.edu)
  • Vector analysis Matrix calculus Ricci calculus Tensors in curvilinear coordinates Multilinear subspace learning Dimitrienko, Yuriy (2002). (wikipedia.org)
  • Vector calculus was developed from quaternion analysis by J. Willard Gibbs and Oliver Heaviside near the end of the 19th century, and most of the notation and terminology was established by Gibbs and Edwin Bidwell Wilson in their 1901 book, Vector Analysis. (wikipedia.org)
  • The three basic vector operators have corresponding theorems which generalize the fundamental theorem of calculus to higher dimensions: In two dimensions, the divergence and curl theorems reduce to the Green's theorem: Linear approximations are used to replace complicated functions with linear functions that are almost the same. (wikipedia.org)
  • As a first example, consider the gradient from vector calculus. (wikipedia.org)
  • Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus (1965, ISBN 978-0-8053-9021-6) by Michael Spivak is a brief (146 pp.) monograph on the theory of vector-valued functions of several real variables (f : Rn→Rm) and differentiable manifolds in Euclidean space. (wikipedia.org)
  • Calculi of the gallbladder and bile ducts are called gallstones and are primarily developed from bile salts and cholesterol derivatives. (wikipedia.org)
  • Calculus II continues to develop the basic ideas introduced in Calculus I: limits, derivatives, and integrals. (hsc.edu)
  • Nobody actually explained that we were learning calculus at the time, but by the time I was being taught derivatives, I already had a really intuitive notion of how and why this stuff all worked. (metafilter.com)
  • By the end of this course, the student will have learnt the fundamental theorem of calculus, chain rule, derivatives of transcendental functions, integration, and applications of all these in the real world. (wikipedia.org)
  • More specifically, the topics are Analysis of graphs (predicting and explaining behavior) Limits of functions (one and two sided) Asymptotic and unbounded behavior Continuity Derivatives Concept At a point As a function Applications Higher Order derivatives Techniques Integrals Interpretations Properties Applications Techniques Numerical approximations Fundamental theorem of calculus Antidifferentiation L'Hôpital's rule, starting in the 2016-17 school year. (wikipedia.org)
  • Too many of my classmates saw calculus as complicated algebraic manipulation instead of the inevitable need to describe the relationship between the basic parameters of motion. (metafilter.com)
  • The icosian calculus is a non-commutative algebraic structure discovered by the Irish mathematician William Rowan Hamilton in 1856. (wikipedia.org)
  • In the tradition of operational calculus, algebraic expressions in operators are handled irrespective of their meaning. (wikipedia.org)
  • Operational calculus, also known as operational analysis, is a technique by which problems in analysis, in particular differential equations, are transformed into algebraic problems, usually the problem of solving a polynomial equation. (wikipedia.org)
  • A different approach to operational calculus was developed in the 1930s by Polish mathematician Jan Mikusiński, using algebraic reasoning. (wikipedia.org)
  • In the geometric calculus, the exponential functions are the functions having a constant derivative. (wikipedia.org)
  • The primary objects of study in differential calculus are the derivative of a function, related notions such as the differential, and their applications. (wikipedia.org)
  • Matrix calculus refers to a number of different notations that use matrices and vectors to collect the derivative of each component of the dependent variable with respect to each component of the independent variable. (wikipedia.org)
  • One may proceed further and develop, for example, equivalent notions of Taylor expansion, et cetera, and even arrive at q-calculus analogues for all of the usual functions one would want to have, such as an analogue for the sine function whose q-derivative is the appropriate analogue for the cosine. (wikipedia.org)
  • is the derivative used in standard calculus. (wikipedia.org)
  • The first derivative of a linear function, in the sense of calculus, is exactly this slope of the graph of the function. (wikipedia.org)
  • A motivational example, of central interest in geometric topology, is the functor of embeddings of one manifold M into another manifold N, whose first derivative in the sense of calculus of functors is the functor of immersions. (wikipedia.org)
  • The event calculus solves the frame problem in a way that is similar to the successor state axioms of the situation calculus: a fluent is true at time t if and only if it has been made true in the past and has not been made false in the meantime. (wikipedia.org)
  • Infinitely many non-Newtonian calculi are not multiplicative. (wikipedia.org)
  • for example, each of the infinitely many non-Newtonian calculi. (wikipedia.org)
  • Relational calculus consists of two calculi, the tuple relational calculus and the domain relational calculus, that are part of the relational model for databases and provide a declarative way to specify database queries. (wikipedia.org)
  • In computer science, domain relational calculus (DRC) is a calculus that was introduced by Michel Lacroix and Alain Pirotte as a declarative database query language for the relational data model. (wikipedia.org)
  • Sano, K.: Sound and Complete Tree-Sequent Calculus for Inquisitive Logic. (springer.com)
  • In other words, natural deduction and sequent calculus systems are particular distinct kinds of Gentzen-style systems. (wikipedia.org)
  • Sequent calculus systems are more suited to theoretical analysis. (wikipedia.org)
  • For example, a paradigmatic case is the sequent calculus, which can be used to express the consequence relations of both intuitionistic logic and relevance logic. (wikipedia.org)
  • Rod calculus or rod calculation is the mechanical method of algorithmic computation with counting rods in China from the Warring States to Ming dynasty before the counting rods were replaced by the more convenient and faster abacus. (wikipedia.org)
  • The π-calculus allows channel names to be communicated along the channels themselves, and in this way it is able to describe concurrent computations whose network configuration may change during the computation. (wikipedia.org)
  • Functional programs can be encoded into the π-calculus, and the encoding emphasises the dialogue nature of computation, drawing connections with game semantics. (wikipedia.org)
  • Pattern calculus bases all computation on pattern matching of a very general kind. (wikipedia.org)
  • It is also the modern name for what used to be called the absolute differential calculus (the foundation of tensor calculus), developed by Gregorio Ricci-Curbastro in 1887-1896, and subsequently popularized in a paper written with his pupil Tullio Levi-Civita in 1900. (wikipedia.org)
  • While Gödel's results on incompleteness mooted Hilbert's Program to a great extent, modern researchers find the epsilon calculus to provide alternatives for approaching proofs of systemic consistency as described in the epsilon substitution method. (wikipedia.org)
  • As most first-order calculi, superposition tries to show the unsatisfiability of a set of first-order clauses, i.e. it performs proofs by refutation. (wikipedia.org)
  • After Euler saw the 1755 work of the 19-year-old Lagrange, Euler dropped his own partly geometric approach in favor of Lagrange's purely analytic approach and renamed the subject the calculus of variations in his 1756 lecture Elementa Calculi Variationum . (wikipedia.org)
  • The textbook, which is licensed under Creative Commons Attribution Non-commercial Share Alike License, incorporated some of its example and exercise problems from Elementary calculus: An approach using Infinitesimals. (wikipedia.org)
  • Elementary Calculus: An Infinitesimal Approach, a textbook by Jerome Keisler. (wikipedia.org)
  • Unlike cirquent calculus, neither approach thus permits mixed cases where some identical subformulas are shared and some not. (wikipedia.org)
  • The idea of a functional calculus is to create a principled approach to this kind of overloading of the notation. (wikipedia.org)
  • The refinement calculus is a formalized approach to stepwise refinement for program construction. (wikipedia.org)
  • This approach formalized by Weierstrass came to be known as the standard calculus. (wikipedia.org)
  • After many years of the infinitesimal approach to calculus having fallen into disuse other than as an introductory pedagogical tool, use of infinitesimal quantities was finally given a rigorous foundation by Abraham Robinson in the 1960s. (wikipedia.org)
  • This approach used technical machinery from mathematical logic to create a theory of hyperreal numbers that interpret infinitesimals in a manner that allows a Leibniz-like development of the usual rules of calculus. (wikipedia.org)
  • A diagrammatic logical calculus for the syllogistic reasoning is introduced and discussed. (springer.com)
  • The situation calculus represents changing scenarios as a set of first-order logic formulae. (wikipedia.org)
  • The main elements of the situation calculus are the actions, fluents and the situations. (wikipedia.org)
  • The situation calculus is based on a sorted domain with three sorts: actions, situations, and objects, where the objects include everything that is not an action or a situation. (wikipedia.org)
  • In the situation calculus, a dynamic world is modeled as progressing through a series of situations as a result of various actions being performed within the world. (wikipedia.org)
  • In the Reiter version of the situation calculus described here, a situation does not represent a state, contrarily to the literal meaning of the term and contrarily to the original definition by McCarthy and Hayes. (wikipedia.org)
  • Fluent (artificial intelligence) Frame problem Situation calculus Event calculus M. Thielscher (1998). (wikipedia.org)
  • There are infinitely many multiplicative non-Newtonian calculi, including the geometric calculus and the bigeometric calculus discussed below. (wikipedia.org)
  • The geometric calculus is useful in image analysis, and in the study of growth/decay phenomena (e.g., in economic growth, bacterial growth, and radioactive decay). (wikipedia.org)
  • Furthermore, just as the arithmetic average (of functions) is the 'natural' average in the classical calculus, the well-known geometric average is the 'natural' average in the geometric calculus. (wikipedia.org)
  • The table below is intended to assist people working with the alternative calculus called the "geometric calculus" (or its discrete analog). (wikipedia.org)
  • Duration calculus (DC) is an interval logic for real-time systems. (wikipedia.org)
  • Interval Temporal Logic (ITL) Temporal logic Temporal Logic of Actions (TLA) Modal logic Zhou Chaochen, C. A. R. Hoare and Anders P. Ravn, A Calculus of Durations, Information Processing Letters, 40(5):269-276, December 1991. (wikipedia.org)
  • The first sequent calculi, systems LK and LJ, were introduced in 1934/1935 by Gerhard Gentzen as a tool for studying natural deduction in first-order logic (in classical and intuitionistic versions, respectively). (wikipedia.org)
  • Since this early work, sequent calculi, also called Gentzen systems, and the general concepts relating to them, have been widely applied in the fields of proof theory, mathematical logic, and automated deduction. (wikipedia.org)
  • The basic version of cirquent calculus in was accompanied with an "abstract resource semantics" and the claim that the latter was an adequate formalization of the resource philosophy traditionally associated with linear logic. (wikipedia.org)
  • Furthermore, he argued that not only the deductive power but also the expressive power of linear logic was weak, for it, unlike cirquent calculus, failed to capture the ubiquitous phenomenon of resource sharing. (wikipedia.org)
  • G.Japaridze, "The taming of recurrences in computability logic through cirquent calculus, Part I".Archive for Mathematical Logic 52 (2013), pages 173-212. (wikipedia.org)
  • The 17th/18th-century mathematician Gottfried Leibniz has been credited with being the founder of symbolic logic for his work with the calculus ratiocinator. (wikipedia.org)
  • The superposition calculus is a calculus for reasoning in equational first-order logic. (wikipedia.org)
  • As of 2007, most of the (state-of-the-art) theorem provers for first-order logic are based on superposition (e.g. the E equational theorem prover), although only a few implement the pure calculus. (wikipedia.org)
  • Attributional calculus is a logic and representation system defined by Ryszard S. Michalski. (wikipedia.org)
  • Modern research in logic teems with rival proof calculi: Several systems have been proposed which replace the usual textual syntax with some graphical syntax. (wikipedia.org)
  • Recently, many logicians interested in structural proof theory have proposed calculi with deep inference, for instance display logic, hypersequents, the calculus of structures, and bunched implication. (wikipedia.org)
  • In mathematical logic and computer science, the calculus of constructions (CoC) is a type theory created by Thierry Coquand. (wikipedia.org)
  • We are pleased to announce the book: ------------------------------------------------------- The Pi-Calculus: A Theory of Mobile Processes Davide Sangiorgi and David Walker Cambridge University Press, 592 pp, ISBN 0521781779 ------------------------------------------------------- Below is the blurb and the table of contents. (upenn.edu)
  • Conophytum calculus - SANBI article Conophytum calculus - Information page Hammer,S.(2002) Dumpling and his wife: New views of the genus Conophytum EAE Creative Colour Ltd. ISBN 0-9539326-1-3. (wikipedia.org)
  • Some other languages based on CCS: Calculus of broadcasting systems Language Of Temporal Ordering Specification (LOTOS) Models that have been used in the study of CCS-like systems: History monoid Actor model Robin Milner: A Calculus of Communicating Systems, Springer Verlag, ISBN 0-387-10235-3. (wikipedia.org)
  • In calculus, interchange of the order of integration is a methodology that transforms iterated integrals (or multiple integrals through the use of Fubini's theorem) of functions into other, hopefully simpler, integrals by changing the order in which the integrations are performed. (wikipedia.org)
  • The word calculus (plural calculi ) is a Latin word, meaning originally "small pebble" (this meaning is kept in medicine - see Calculus (medicine) ). (wikipedia.org)
  • A calculus (plural calculi ), often called a stone , is a concretion of material, usually mineral salts, that forms in an organ or duct of the body. (wikipedia.org)
  • Calculus (from Latin calculus meaning 'pebble', plural calculī) in its most general sense is any method or system of calculation. (wikipedia.org)
  • The resemblance to pebbles and the firmness of its flesh is what got it its name ( "calculus" is Latin for "pebble" ). (wikipedia.org)
  • In 1989 the PI- Calculus was created by Robin Milner and was very successful throughout the years. (wikipedia.org)
  • Milner claimed the detailed characteristics of the API Calculus to be its "Communication Ability, Capacity for Cooperation, Capacity for Reasoning and Learning, Adaptive Behavior and Trustworthiness. (wikipedia.org)
  • Milner later removed some of these restrictions in his work on the Pi calculus (see section Milner, et al. (wikipedia.org)
  • The calculus of communicating systems (CCS) is a process calculus introduced by Robin Milner around 1980 and the title of a book describing the calculus. (wikipedia.org)
  • The pi-calculus, developed by Milner in the late 80's, provides mobility of communication links by allowing processes to communicate the names of communication channels themselves. (wikipedia.org)
  • Calculus Made Easy ignores the use of limits with its epsilon-delta definition, replacing it with a method of approximating (to arbitrary precision) directly to the correct answer in the infinitesimal spirit of Leibniz, now formally justified in modern non-standard analysis and smooth infinitesimal analysis. (wikipedia.org)
  • This language uses the same operators as tuple calculus, the logical connectives ∧ (and), ∨ (or) and ¬ (not). (wikipedia.org)
  • Tuple calculus is a calculus that was created and introduced by Edgar F. Codd as part of the relational model, in order to provide a declarative database-query language for data manipulation in this data model. (wikipedia.org)
  • Functions that maximize or minimize functionals may be found using the Euler-Lagrange equation of the calculus of variations. (wikipedia.org)
  • In fact, the π-calculus, like the λ-calculus, is so minimal that it does not contain primitives such as numbers, booleans, data structures, variables, functions, or even the usual control flow statements (such as if-then-else, while). (wikipedia.org)
  • According to the College Board, Calculus BC is a full-year course in the calculus of functions of a single variable. (wikipedia.org)
  • Network calculus can also be used to express traffic arrival and departure functions as well as service curves. (wikipedia.org)
  • In network calculus, a flow is modelled as cumulative functions A, where A(t) represents the amount of data (number of bits for example) send by the flow in the interval [0,t). (wikipedia.org)
  • The key element of the operational calculus is to consider differentiation as an operator p = d⁄dt acting on functions. (wikipedia.org)
  • Here is an analogy: with the Taylor series method from calculus, you can approximate the shape of a smooth function f around a point x by using a sequence of increasingly accurate polynomial functions. (wikipedia.org)
  • They define calculi for a language with variables, functions, function application and assignment statement that capture the conventional notions of parameter passing and evaluation strategies of a wide array of programming languages. (wikipedia.org)
  • Interested readers are encouraged to improve the table by inserting citations for verification, and by inserting more functions and more calculi. (wikipedia.org)
  • The second is a reflective higher-order variant of the asynchronous polyadic pi calculus. (wikipedia.org)
  • Calculi in the urinary system are called urinary calculi and include kidney stones (also called renal calculi or nephroliths) and bladder stones (also called vesical calculi or cystoliths). (wikipedia.org)
  • Tubeless percutaneous nephrolithotomy (PCNL) is a well-accepted procedure for uncomplicated renal calculi. (urotoday.com)
  • Total tubeless PCNL was planned in 40 easily accessible patients with uncomplicated renal calculi, with single infracostal punctures, normal intraoperative events, and acceptable postoperative parameters (visual analogue pain score, parenteral analgesic requirement, bleeding, urinary soakage, hemodynamic stability), allowing an early discharge within 24 hours. (urotoday.com)
  • Calculi too large to pass spontaneously range in size from 1 cm to the staghorn stones that occupy the renal pelvis and calyces. (labome.org)