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.
Rayleigh has been modified to form a new constituency of Rayleigh and Wickford which was first contested in 2010. The 1997 ... "Election Data 1997". Electoral Calculus. Archived from the original on 15 October 2011. Retrieved 18 October 2015. C. Rallings ... "Election Data 2001". Electoral Calculus. Archived from the original on 15 October 2011. Retrieved 18 October 2015. " ... Electoral Calculus. Archived from the original on 15 October 2011. Retrieved 18 October 2015. " ...
Differential Forms, and Variational Principles. Dover. ISBN 978-0-486-65840-7. Synge J.L., Schild A. (1949). Tensor Calculus. ... Four-gradient Ricci calculus Synge J.L., Schild A. (1949). Tensor Calculus. pp. 87-89-90. Bishop, R.L.; Goldberg, S.I. (1968), ... Tensor Calculus, Schaum's Outlines, McGraw Hill (USA), ISBN 0-07-033484-6 T. Frankel (2012), The Geometry of Physics (3rd ed ...
Differential Forms, and Variational Principles. Dover. ISBN 978-0-486-65840-7. Synge J.L., Schild A. (1949). Tensor Calculus. ... A pure tensor of V ⊗ W is one that is of the form v ⊗ w It could be written dyadically aibj, or more accurately aibj ei ⊗ fj, ... Ricci calculus The earliest foundation of tensor theory - tensor index notation. Tensor order The components of a tensor with ... The wedge product is the anti-symmetric form of the ⊗ operation. The quotient space of T(V) on which it becomes an internal ...
These two latter areas formed one constituency prior to the 2000 review. The new town of Cumbernauld is approximately 15 miles ... Leigh Rayment's Historical List of MPs - Constituencies beginning with "C" (part 6) "Election Data 2015". Electoral Calculus. ... "Election Data 2010". Electoral Calculus. Archived from the original on 17 October 2015. Retrieved 17 October 2015. "Election ... Data 2005". Electoral Calculus. Archived from the original on 15 October 2011. Retrieved 18 October 2015. ...
... calculus of constructions and its derivatives. Automath; ST type theory; some forms of combinatory logic; others defined in the ... Many systems of type theory, such as the simply-typed lambda calculus, intuitionistic type theory, and the calculus of ... it is called a normal form. A system of type theory is said to be strongly normalizing if all terms have a normal form and any ... Simply typed lambda calculus which is a higher-order logic; intuitionistic type theory; system F; LF is often used to define ...
It was then merged with part of the constituency of Newham South to form the new constituency of West Ham. The London Borough ... "Election Data 1987". Electoral Calculus. Archived from the original on 15 October 2011. Retrieved 28 June 2017. "Election Data ... Leigh Rayment's Historical List of MPs - Constituencies beginning with "N" (part 1) "Election Data 1983". Electoral Calculus. ... 1992". Electoral Calculus. Archived from the original on 15 October 2011. Retrieved 28 June 2017. "Politics Resources". ...
... and Green's theorem from vector calculus. If a k-form is thought of as measuring the flux through an infinitesimal k- ... The exterior derivative of this (n − 1)-form is the n-form d ω V = div ⁡ V ( d x 1 ∧ d x 2 ∧ ⋯ ∧ d x n ) . {\displaystyle d\ ... A smooth function f : M → ℝ on a real differentiable manifold M is a 0-form. The exterior derivative of this 0-form is the 1- ... The exterior derivative of a differential form of degree k is a differential form of degree k + 1. If f is a smooth function (a ...
... such that the first fundamental form is of the form d s 2 = ( f 1 ( x ) + f 2 ( y ) ) ( d x 2 + d y 2 ) . {\displaystyle ds^{2 ... Gelfand, I.M. & Fomin, S.V. (2000). Calculus of variations. Dover. ISBN 0-486-41448-5. (Translated from the Russian by R. ... big (}f_{1}(x)+f_{2}(y){\big )}\left(dx^{2}+dy^{2}\right).\,} Sometimes a metric of this form is called a Liouville metric. ...
This constituency was formed in 2005 from parts of the old Paisley North and Renfrewshire West constituencies. UK Parliamentary ... "Election Data 2005". Electoral Calculus. Archived from the original on 15 October 2011. Retrieved 18 October 2015. Leigh ... http://www.tusc.org.uk/txt/320.pdf "Election Data 2010". Electoral Calculus. Archived from the original on 17 October 2015. ... Electoral Calculus. Archived from the original on 17 October 2015. Retrieved 17 October 2015. ...
Simply-typed lambda calculus (Input: Terms in the eta-long beta-normal form. Output: higher-order patterns): Baumgartner, ... Calculus of constructions: Pfenning, Frank (Jul 1991). "Unification and Anti-Unification in the Calculus of Constructions" (PDF ...
Other equivalent forms for the Hessian are given by Hess ( f ) ( X , Y ) = ⟨ ∇ X grad f , Y ⟩ {\displaystyle {\mbox{Hess}}(f)(X ... Callahan, James J. (2010). Advanced Calculus: A Geometric View. Springer Science & Business Media. p. 248. ISBN 978-1-4419-7332 ... Neudecker, Heinz; Magnus, Jan R. (1988). Matrix Differential Calculus with Applications in Statistics and Econometrics. New ... Jacobian matrix Hessian equations Binmore, Ken; Davies, Joan (2007). Calculus Concepts and Methods. Cambridge University Press ...
Sunderland North, as can be inferred from the name, formed the northern part of the City of Sunderland. At the 2010 general ... "Election Data 1987". Electoral Calculus. Archived from the original on 15 October 2011. Retrieved 18 October 2015. "Election ... "Election Data 1997". Electoral Calculus. Archived from the original on 15 October 2011. Retrieved 18 October 2015. "Election ... "Election Data 2005". Electoral Calculus. Archived from the original on 15 October 2011. Retrieved 18 October 2015. ...
Pitman, "Special Forms in Lisp", p. 179. Steele and Gabriel, "The Evolution of Lisp", pp. 245-248 Wand, "The Theory of Fexprs ... John N. Shutt, "vau-calculi and the theory of fexprs", talk, New England Programming Languages and Systems Symposium Series ( ... At the 1980 Conference on Lisp and Functional Programming, Kent Pitman presented a paper "Special Forms in Lisp" in which he ... Kent M. Pitman, "Special Forms in Lisp", Proceedings of the 1980 ACM Conference on Lisp and Functional Programming, 1980, pp. ...
In single-variable calculus, we drop some information. We retain only the linear map, in the form of a scalar multiplying agent ... The usual fundamental theorem of calculus for single-variable calculus has the following local generalization. If a g {\ ... form on any smooth manifold, all the terms in this equation make sense, so for any such form we can ask whether or not it ... form on G {\displaystyle G} (cf. Lie algebra valued form) defined by ω G ( X g ) = ( T g L g ) − 1 X g {\displaystyle \omega _{ ...
Calculus: Conceived of differential calculus. Discovered the derivative. Discovered the differential coefficient. Developed ... they formed the last of the exclusively oral literature. They were expressed in a highly compressed mnemonic form, the sūtra ( ... Their discovery of these three important series expansions of calculus-several centuries before calculus was developed in ... To form the next layer, the same formula was used, but the bricks were arranged transversely. The process was then repeated ...
Perloff (2008). Microeconomics Theory & Applications with Calculus. Pearson. p. 193. Hirschey (2003) p. 238.[full citation ... "A theorem on homogeneous functions and extended Cobb-Douglas forms". Proc. Natl. Acad. Sci. 73 (10): 3747-3748. ...
For a curve given by the equation F(x, y)=0, if the equation of the tangent line at R=(x0, y0) is written in the form cos ⁡ α x ... Differential and integral calculus: with applications by George Greenhill (1891) p326 ff. (Google books) J. Dennis Lawrence ( ... It is the roulette formed by a circle rolling around a circle with the same radius. We also have shown that the catacaustic of ... Benjamin Williamson (1899). An elementary treatise on the differential calculus. Logmans, Green, and Co. pp. 227 ff. ...
Stack memory: An automaton may also contain some extra memory in the form of a stack in which symbols can be pushed and popped ... Boolean differential calculus Yan, Song Y. (1998). An Introduction to Formal Languages and Machine Computation. Singapore: ... An automaton can be defined in a symbolic language or its specification may be entered in a predesigned form or its transition ... one can show that such variable automata homomorphisms form a mathematical group. In the case of non-deterministic, or other ...
The formation rules of a propositional calculus may, for instance, take a form such that; if we take Φ to be a propositional ... A predicate calculus will usually include all the same rules as a propositional calculus, with the addition of quantifiers such ... A formal system (also called a logical calculus, or a logical system) consists of a formal language together with a deductive ... In mathematical logic, formation rules are rules for describing which strings of symbols formed from the alphabet of a formal ...
Introduction to the calculus of variations; Imperial College Press, London (2004), 2nd ed. (2009), 3rd ed (2014); According to ... PDF The pullback equation for differential forms; with G. Csato et O. Kneuss, Birkhaüser, PNLDE Series, New York, 83 (2012). ... He is a specialist of the calculus of variations and of partial differential equations. He has written several articles and ... 922 (1982). PDF According to WorldCat, the book is held in 419 libraries Direct methods in the calculus of variations; Springer ...
Unit vectors are formed as shown in the image at right, both tangential and normal to the path. This coordinate system ... An Elementary Course of Infinitesimal Calculus. University Press. p. 406. ISBN 1-108-00534-9. Guang Chen; Fook Fah Yap (2003). ... Thus, uρ and uθ form a local Cartesian coordinate system attached to the particle, and tied to the path traveled by the ... ISBN 81-203-2189-8. Shigeyuki Morita (2001). Geometry of Differential Forms. American Mathematical Society. p. 1. ISBN 0-8218- ...
This constituency was formed in 2005 from parts of the old Clydesdale, Hamilton North and Bellshill and Hamilton South ... Leigh Rayment's Historical List of MPs - Constituencies beginning with "L" (part 1) "Election Data 2015". Electoral Calculus. ... BBC - Election 2010 - Lanark & Hamilton East "Election Data 2005". Electoral Calculus. Archived from the original on 15 October ... Electoral Calculus. Archived from the original on 17 October 2015. Retrieved 17 October 2015. ...
Easingwold, Thirsk and surrounding villages joined rural Ryedale to form a new Thirsk and Malton constituency. Bedale rejoined ... "Election Data 2001". Electoral Calculus. Archived from the original on 15 October 2011. Retrieved 18 October 2015. "Election ... Data 1997". Electoral Calculus. Archived from the original on 15 October 2011. Retrieved 18 October 2015. Coordinates: 54°05′53 ... " "Election Data 2005". Electoral Calculus. Archived from the original on 15 October 2011. Retrieved 18 October 2015. " ...
This textbook in multivariate calculus introduces the exterior algebra of differential forms adroitly into the calculus ... The exterior algebra is also used in multivariable calculus, as the differential forms of higher degree belong to the exterior ... If ei, i = 1, 2, ..., n, form an orthonormal basis of V, then the vectors of the form e i 1 ∧ ⋯ ∧ e i k , i 1 < ⋯ < i k , {\ ... It was thus a calculus, much like the propositional calculus, except focused exclusively on the task of formal reasoning in ...
This form is, in reality, a microcrystalline agglomerate that takes the shape of a biconcave disc. Weddellite crystals are ... Together, whewellite and weddellite are the most common renal calculi. Weddellite occurs as authigenic crystals in sea floor ... Weddellite (CaC2O4·2H2O) is a mineral form of calcium oxalate named for occurrences of millimeter-sized crystals found in ... Occasionally, weddellite partially dehydrates to whewellite, forming excellent pseudomorphs of grainy whewellite after ...
Space forms A Riemannian manifold is a space form if its sectional curvature is equal to a constant K. The Riemann tensor of a ... ISBN 0-691-08542-0. Synge J.L., Schild A. (1949). Tensor Calculus. first Dover Publications 1978 edition. pp. 83; 107. ISBN 978 ... ISBN 0-691-01146-X. Lovelock, David; Rund, Hanno (1989) [1975]. Tensors, Differential Forms, and Variational Principles. Dover ... and by contracting with the metric twice we find the explicit form: R a b c d = K ( g a c g d b − g a d g c b ) {\displaystyle ...
Chernoff-Hoeffding Theorem (additive form)[edit]. Let q = p + ε. Taking a = nq in (1), we obtain:. Pr. (. 1. n. ∑. X. i. ≥. q. ... Therefore, we can easily compute the infimum, using calculus:. d. d. t. (. p. e. (. 1. −. q. ). t. +. (. 1. −. p. ). e. −. q. t ... Multiplicative form (relative error)[edit]. Multiplicative Chernoff Bound. Suppose X1, ..., Xn are independent random variables ... Multiplicative form[edit]. Set Pr(Xi = 1) = pi. According to (1), ... Additive form (absolute error)[edit]. The following Theorem is ...
The constituency was formed by the division of Lanarkshire constituency. The constituency was split in 1997 to form Hamilton ... "Election Data 1987". Electoral Calculus. Archived from the original on 15 October 2011. Retrieved 28 June 2017. "Election Data ... Electoral Calculus. Archived from the original on 15 October 2011. Retrieved 28 June 2017. " ... 1992". Electoral Calculus. Archived from the original on 15 October 2011. Retrieved 28 June 2017. ...
... forming calculus. Certain types of chemicals called pyrophosphates help to decrease calculus buildup by stopping the growth of ... Coral Dental calculus is the other name is dirt in his mouth attached to the teeth in the long term so that over time will ... To remove calculus or tartar should not be done alone or using an object or chemical drugs that are not clear. To clean the ... For calculus did not return to our teeth, we can do some tartar precautions as follows below:. 1. Diligent brushing your teeth ...
Percutaneous nephrolithotomy under ultrasound guidance for treatment of renal calculi and upper ureteral calculi ... Stone is how to form? Why repeated attacks? Uric acid stones in metabolic stones ... Since its inception, ESWL has become the first choice for the treatment of urinary calculi because of its non-invasive, safe ... Figure 35 pattern of ureteral calculi before and after lithotripsy. There are several types of extracorporeal shock wave ...
Also, assume we have closed forms the derivatives: $a_1^{(n)}$ and $b_1^{(n)}$ in terms of $n$. ... Not the answer youre looking for? Browse other questions tagged calculus matrices recurrence-relations differential-operators ... I expect there to be a closed form solution for this case, however, I have trouble deriving it. ... How to solve a form of tridiagonal system of equations (with fringes?) ...
Normal forms and confluence[edit]. Main article: Normalization property (abstract rewriting). For the untyped lambda calculus, ... 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 ...
Calculus I : differentiation and integration, [author, Said Hamilton ; editor, Linda Hamilton] Borrow it Toggle Dropdown * Peru ... Calculus,/a,,/span, - ,span property=offers typeOf=Offer,,span property=offeredBy typeof=Library ll:Library resource= ... Calculus,/a,,/span, - ,span property=offers typeOf=Offer,,span property=offeredBy typeof=Library ll:Library resource= ... Calculus. Local Identifier. http://link.peru.lib.in.us/resource/KqWK9v0BQQc/ Network Identifier. http://library.link/resource/ ...
Vector calculus. [Bill Cox] -- Building on previous texts in the Modular Mathematics series, in particular Vectors in Two or ... Three Dimensions and Calculus and ODEs, this book introduces the student to the concept of vector ... ... Genre/Form:. Electronic books. Additional Physical Format:. Print version:. Cox, Bill, 1945-. Vector calculus.. Burlington, MA ... Calculus and ODEs, this book introduces the student to the concept of vector calculus. It provides an overview of some of the ...
Calculus-Applications of Derivatives: Applied Optimization. [Films Media Group,; KM Media,;] -- Minimize the cost of a ... Genre/Form:. Educational films. Internet videos. Additional Physical Format:. Digital transfer of (manifestation):. KM Media, ... schema:alternateName "Calculus-Applications of Derivatives: Applied Optimization" ;. schema:contentRating "9-12." ;. schema: ... Dimensions of a Rectangle that Minimize its Perimeter : Calculus-Applications of Derivatives: Applied Optimization. Author:. ...
In patients who form group I calculi, with neither hypercalciuria nor high urinary phosphate concentrations, the urine may ... The calculi forming these round objects exhibited an uneven compact surface composed of closely connected rounded structures. ... Calculi of patients with high urinary phosphate concentrations are formed at urinary supersaturation with respect to ... Each calculus, however, contained spheres of only one type, i.e., either all smooth or all spiky. Group I and II calculi had ...
Forming good men and good citizens since 1776.. Hampden-Sydney, VA 23943 (434) 223-6000 Contact the College ... Calculus II continues to develop the basic ideas introduced in Calculus I: limits, derivatives, and integrals. In addition, an ...
Relationships between them form positional parameters. The calculus of predispositions primarily deals with analyzing the ... This calculus is based on a weight function, which represents a variation on the well-known criterion of optimality for local ... Calculus of predispositions is a basic part of predispositioning theory and belongs to the indeterministic procedures. "The key ... "In order to quantify the evaluation of a position we need new techniques, which I have grouped under the heading of calculus of ...
The untyped lambda calculus is implemented by performing reductions on a lambda term, until the term is in normal form. The ... Later the lambda calculus was resurrected as a definition of a programming language. Lambda calculus is the model and ... This is not a criticism of pure lambda calculus, and lambda calculus as a pure system is not the primary topic here. The ... "Lecture Notes on Lambda Calculus (PDF)" (PDF). p. 6. "Lambda calculus - intensionality". Stanford. p. 1.2 Intensionality. ...
Pre-Calculus Help Forum: Pre-calculus does not involve calculus, but explores topics that will be applied in calculus ... Pre-Calculus Forum. Pre-Calculus Help Forum: Pre-calculus does not involve calculus, but explores topics that will be applied ... calculus 1with pre calculus pg 341. , precalculus page 251. , content. , precalculus with limits answers page 1. , pre calculus ... This forum is for PRE-Calculus. READ BEFORE POSTING Jameson 2 Pages •. 1 2 ...
Form a matrix whose rows are the relations. *Obtain the reduced echelon form of the matrix *The first element in the last ... 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 ...
This course provides the calculus content oriented toward applications in computer and communication networks courses. The ... The course exposes students to the fundamental concepts of differential calculus and integral calculus. Coursework emphasizes ... This course provides the calculus content oriented toward applications in computer and communication networks courses. ... FORMS * PUBLICATIONS FOR FUTURE STUDENTS * STUDENT RECORDS * STUDENT LIFE * STUDENT LIFE * STUDENT SERVICES *. Student Services ...
of the form p. ⁢. (. λ. ). :=. ∑. c. n. ,. m. ⁢. λ. n. ⁢. λ. ¯. m. , we have p. ⁢. (. x. ). =. ∑. c. n. ,. m. ⁢. x. n. ⁢. (. x ... be a polynomial of the form p. ⁢. (. λ. ). :=. ∑. c. n. ,. m. ⁢. λ. n. ⁢. λ. ¯. m. . Notice that p. =. ∑. c. n. ,. m. ⁢. id. n ... continuous functional calculus. Let B. ⁢. (. H. ). be the algebra. of bounded operators. over a complex Hilbert space. H. . Let ... The continuous functional calculus is a functional calculus. which enables the expression ...
... form the diff. eq. of the family of curves represented by, c(y+c) 2 =x 3 ;where c is any arbitrary . Answer this question and ... Other Related Questions on Differential Calculus the diffrential equation satisfied by all the circles with centres on the line ...
Single Variable Calculus. Its time to redo calculus! Previously, all the calculus we have done is meant for functions with a ... a novel synthesis of discrete and continuous forms of Calculus; 3) an emphasis on the conceptual over the computational; and 4 ... A Calculus for Sequences. Its time to redo calculus! Previously, all the calculus we have done is meant for functions with a ... Discrete Calculus. To view this video please enable JavaScript, and consider upgrading to a web browser that supports HTML5 ...
Evaluation form. Weighting. Examination aids. Date. Time. Room *. Autumn. ORD. Written examination. 100/100. C 2017-12-13 09:00 ... The courses TMA4100/05/10/15 Calculus 1/2/3; or the courses MA1101/2/3 and MA1201/2; or equivalent. ...
... was written for the one- or two-semester applied calculus course for life ... Calculus with Applications for the Life Sciences (BOK) Margaret Lial, Nathan P. Ritchey, Raymond N. Greenwell ... Finite Mathematics and Calculus with Applications (BOK) Margaret Lial, Nathan P. Ritchey, Raymond N. Greenwell ... Calculus with Applications for the Life Sciences (BOK) Margaret Lial, Raymond N. Greenwell, Nathan P. Ritchey Del ...
Textbook solution for Calculus 10th Edition Ron Larson Chapter 11.2 Problem 99E. We have step-by-step solutions for your ... Convert the expressions in Exercises 6584 to power form. 18xx23x35. Finite Mathematics and Applied Calculus (MindTap Course ... Diagonal of a Cube Find the component form of the unit vector v in the direction of the diagonal of the cube shown in the ... To calculate: The component form of unit vector v in the direction of diagonal of cubeshown in figure. ...
... presents applications of fractional calculus, integral and differential equations of non-integer orders in describing systems ... Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles, Fields and Media ... Fractional Exterior Calculus and Fractional Differential Forms. Tarasov, Vasily E.. Pages 265-291 ... Applications of Fractional Calculus to Dynamics of Particles, Fields and Media. Authors. * Vasily E. Tarasov ...
... forms of periodontitis. Salivary levels of IL-6 and IL-17 were determined using enzyme-linked immunosorbent assay (ELISA) ... Therefore, a study was designed to determine levels of salivary IL-6 and IL-17 in patients with calculus associated chronic ... The levels of salivary IL-6 and IL-17 were increased significantly in calculus associated CP patients as compared to healthy ... cross-sectional study that is comprised of 41 healthy controls and 41 calculus associated chronic periodontitis patients (CP ...
... they form this surface. And of course, you can plot much more complicated functions. So, this one, well, if you can read very ... But, calculus, really, is about studying functions. Now, were going to actually move on to studying functions of several ... horizontal planes have equations of a form z equals some constant, z equals zero, z equals one, z equals two, and so on. So, ...
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