###### Calculi

###### Urinary Calculi

###### Ureteral Calculi

###### Kidney Calculi

###### Urinary Bladder Calculi

###### Dental Calculus

###### 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

###### Nephrostomy, Percutaneous

###### Salivary Gland Calculi

###### Urolithiasis

###### Calcium Oxalate

###### Gallstones

###### Cholelithiasis

###### Urologic Surgical Procedures

###### 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

###### Colic

###### 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

###### Diverticulum

###### Hydronephrosis

###### Holmium

###### Apatites

###### Lithiasis

###### Cystic Duct

###### Pyelonephritis, Xanthogranulomatous

###### Cholangiography

###### Bile Duct Diseases

###### Oxalates

###### Oxalic Acid

###### Triazines

###### 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

###### 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

###### Periodontal Index

###### Uric Acid

###### 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)

###### Dental Pellicle

###### Oral Hygiene Index

###### Endoscopes

###### Nephrocalcinosis

###### Cholangiopancreatography, Endoscopic Retrograde

###### Urethral Obstruction

###### Dental Plaque

###### Nigella sativa

###### Pedaliaceae

###### Potassium Citrate

###### Knowledge of Results (Psychology)

###### Tooth Discoloration

###### Anuria

###### 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

###### Ultrasonography

###### 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.

###### Cholecystectomy, Laparoscopic

###### 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.

###### Urinalysis

###### Spectrophotometry, Infrared

###### Root Planing

###### Pyelonephritis

###### Alcian Blue

###### 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

###### Metabolic Diseases

###### Treatment Outcome

###### Calcium Carbonate

###### Dental Scaling

###### Urinary Tract Infections

###### Cholecystitis

###### Propantheline

###### 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.

###### Crystallization

###### Gallbladder

###### Pancreatic Ducts

###### Gingival Hemorrhage

###### Sphincter of Oddi

###### Cholangiopancreatography, Magnetic Resonance

###### Urinary Bladder

###### Common Bile 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.

###### Citric Acid

###### 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

###### Urinary Bladder Neck Obstruction

###### Retroperitoneal Space

###### Ureter

###### Radiography, Abdominal

###### Durapatite

###### Optical Fibers

###### Powder Diffraction

###### Sulfadiazine

###### Oral Hygiene

###### Postoperative Complications

###### Gallbladder Diseases

###### Kidney

###### Tomography, X-Ray Computed

###### 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

###### Oral Health

###### Cystine

###### Ampulla of Vater

###### Silicon

###### Phosphorus

###### 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

###### Prospective Studies

###### 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)###### Fibrocalculous pancreatic diabetes and obesity<...

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OCLC 319729593.CS1 maint: numeric names: authors list (link) Adams, Robert A.; Essex, Christopher (2009).

**Calculus**: A Complete ... OCLC 144526840.CS1 maint: numeric names: authors list (link) 1941-, Larson, Ron (2010).**Calculus**. Edwards, Bruce H., 1946- (9th ... OCLC 799468131.CS1 maint: others (link) 1941-, Stewart, James (2008).**Calculus**: early transcendentals (6th ed.). Belmont, CA: ...###### Umbilic torus

**Calculus**. Ed. Charles Hartford. 6th ed. Boston: Houghton Mifflin Company, 1998. Helaman Ferguson, "Two Theorems, Two Sculptures ...

###### Area

**Calculus**. I: One-Variable

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###### Weierstrass substitution

Michael Spivak,

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... for terms of the lambda

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The undecidability of typability in the lambda-pi-

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The nested sequent

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Typed lambda

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The

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###### Fundamental theorem3

- These two branches are related to each other by the fundamental theorem of calculus, and they make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit. (wikipedia.org)
- They understand the foundation of the Fundamental Theorem of Calculus. (ti.com)
- vector fields, line integrals, flux integrals and integration theorems generalizing the Fundamental Theorem of Calculus. (princeton.edu)

###### Integral calculus12

- It was on the subject of integral calculus and contained many of Euler's discoveries about differential equations. (wikipedia.org)
- the former concerns instantaneous rates of change, and the slopes of curves, while integral calculus concerns accumulation of quantities, and areas under or between curves. (wikipedia.org)
- The ancient period introduced some of the ideas that led to integral calculus, but does not seem to have developed these ideas in a rigorous and systematic way. (wikipedia.org)
- From the age of Greek mathematics, Eudoxus (c. 408-355 BC) used the method of exhaustion, which foreshadows the concept of the limit, to calculate areas and volumes, while Archimedes (c. 287-212 BC) developed this idea further, inventing heuristics which resemble the methods of integral calculus. (wikipedia.org)
- According to Student PIRGS, this is "am introductory level single variable calculus book, covering standard topics in differential and integral calculus, and infinite series. (merlot.org)
- The course exposes students to the fundamental concepts of differential calculus and integral calculus. (centennialcollege.ca)
- 6. Integral Calculus. (doverpublications.com)
- The remainder of the Sullivan book, 320 pages, provides an overview of differential and integral calculus up through partial differentiation. (maa.org)
- The Himonas book is also an overview of differential and integral calculus, with very little in the way of theory. (maa.org)
- One could use these "indivisibles," he said, to calculate length, area and volume-an important step on the way to modern integral calculus. (scientificamerican.com)
- Editors' note: Countless students learn integral calculus-the branch of mathematics concerned with finding the length, area or volume of an object by slicing it into small pieces and adding them up. (scientificamerican.com)
- His "method of indivisibles" became a forerunner of integral calculus-but not before surviving attacks from Swiss mathematician Paul Guldin, ostensibly for empirical reasons. (scientificamerican.com)

###### Multivariable calculus1

- The book also includes multivariable calculus, though there is a single variable version. (merlot.org)

###### Single variable calculus1

- In addition to a strong background of single-variable calculus and precalclulus, students should have a serious interest in thinking rigorously about problems involving space and time. (princeton.edu)

###### Lambda32

- Lambda calculus (also written as λ-calculus ) is a formal system in mathematical logic for expressing computation based on function abstraction and application using variable binding and substitution . (wikipedia.org)
- Lambda calculus consists of constructing lambda terms and performing reduction operations on them. (wikipedia.org)
- Lambda calculus is Turing complete , that is, it is a universal model of computation that can be used to simulate any Turing machine . (wikipedia.org)
- Lambda calculus may be untyped or typed . (wikipedia.org)
- In typed lambda calculus, functions can be applied only if they are capable of accepting the given input's "type" of data. (wikipedia.org)
- in the simply typed lambda calculus it is, for example, a theorem that every evaluation strategy terminates for every simply typed lambda-term, whereas evaluation of untyped lambda-terms need not terminate. (wikipedia.org)
- One reason there are many different typed lambda calculi has been the desire to do more (of what the untyped calculus can do) without giving up on being able to prove strong theorems about the calculus. (wikipedia.org)
- [5] Lambda calculus has played an important role in the development of the theory of programming languages . (wikipedia.org)
- Functional programming languages implement the lambda calculus. (wikipedia.org)
- Lambda calculus is also a current research topic in Category theory . (wikipedia.org)
- The lambda calculus was introduced by mathematician Alonzo Church in the 1930s as part of an investigation into the foundations of mathematics . (wikipedia.org)
- Subsequently, in 1936 Church isolated and published just the portion relevant to computation, what is now called the untyped lambda calculus. (wikipedia.org)
- [11] In 1940, he also introduced a computationally weaker, but logically consistent system, known as the simply typed lambda calculus . (wikipedia.org)
- Until the 1960s when its relation to programming languages was clarified, the lambda calculus was only a formalism. (wikipedia.org)
- Thanks to Richard Montague and other linguists' applications in the semantics of natural language, the lambda calculus has begun to enjoy a respectable place in both linguistics [13] and computer science. (wikipedia.org)
- There is a bit of controversy over the reason for Church's use of the Greek letter lambda (λ) as the notation for function-abstraction in the lambda calculus, perhaps in part due to conflicting explanations by Church himself. (wikipedia.org)
- It is therefore used for naming specific methods of calculation and related theories, such as propositional calculus, Ricci calculus, calculus of variations, lambda calculus, and process calculus. (wikipedia.org)
- In pure lambda calculus , there are no constants . (planetmath.org)
- This question is a bit off topic, but I hope it is of sufficient interest [because of lambda calculus] to this group anyway. (upenn.edu)
- My favorites would be lambda calculus, RAM's, and imperative language models (e.g., the LOOP language). (upenn.edu)
- Occasionally, a book will cover the RAM model as a side-light, but I have been unable to find a book, for example, that covers lambda calculus. (upenn.edu)
- Though of course the lambda calculus was contemporaneous - or even earlier than - Turing machines. (upenn.edu)
- It covers the basic theory of pi-calculus, typed pi-calculi, higher-order processes, the relationship between pi-calculus and lambda-calculus, and applications of pi-calculus to object-oriented design and programming. (upenn.edu)
- We present the notion of recognizability in the simply typed lambda-calculus by showing the equivalence between intersection types and finite standard models. (labri.fr)
- We then show this notion of recognizability does not coincide with locally finite congruences of the lambda-calculus. (labri.fr)
- The Simple Yuser-friendly Lambda Visualization Interaction Application (SYLVIA) is a unique way to manipulate untyped lambda calculus expressions, by representing them as boxes connected by wires. (haskell.org)
- There's finally a lambda calculus lecture series on YouTube. (msdn.com)
- I looked through their lectures, and they have some very interesting ones, but I don't see anything on lambda calculus. (msdn.com)
- but I don't see anything in particular on lambda calculus. (msdn.com)
- Bart De Smet's posts on lambda calculus are also very good http://community.bartdesmet.net/blogs/bart/archive/2009/08/17/mis-using-c-4-0-dynamic-type-free-lambda-calculus-church-numerals-and-more.aspx . (msdn.com)
- Well, I am since lambda calculus is the essence of all functional programming. (msdn.com)
- It's just that in this case I'm particularly interested in the nitty gritty details of the simplest possible programming language, which is lambda calculus. (msdn.com)

###### Propositional calculus1

- The following outlines a standard propositional calculus. (planetmath.org)

###### Gottfried Wilhelm2

- Infinitesimal calculus was developed independently in the late 17th century by Isaac Newton and Gottfried Wilhelm Leibniz. (wikipedia.org)
- Modern calculus was developed in 17th-century Europe by Isaac Newton and Gottfried Wilhelm Leibniz (independently of each other, first publishing around the same time) but elements of it appeared in ancient Greece, then in China and the Middle East, and still later again in medieval Europe and in India. (wikipedia.org)

###### Derivatives5

- The coverage is up through vector calculus, partial derivatives and multiple integrals. (maa.org)
- Calculus II continues to develop the basic ideas introduced in Calculus I: limits, derivatives, and integrals. (hsc.edu)
- Calculus I is the study of limits, rates of change of a function, derivative of algebraic and trigonometric functions, applications of derivatives, integration and applications of the definite integral. (bucks.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)
- There are higher derivatives in vector calculus as well. (everything2.com)

###### 20181

- Starting in Fall, 2018, we will restructure our calculus sequence from the current sequence of four three-credit courses to the new sequence of three four-credit courses to better align with other schools in Virginia, including the Virginia Community College System. (radford.edu)

###### Geometry3

- Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations. (wikipedia.org)
- Am I ready for Calculus and Analytic Geometry? (physicsforums.com)
- The topics of Schubert varieties and the intersection theory of Schubert calculus are at the crossroads of algebraic geometry, representation theory, symplectic geometry and combinatorics. (utoronto.ca)

###### Theorems1

- The Anton book is a traditional calculus book with formal theorems and explanations of the theoretical background of how calculus works. (maa.org)

###### Differential equations1

- Calculus, including integration, differentiation, and differential equations are insufficient to model stochastic phenomena like noise disturbances of signals in engineering, uncertainty about future stock prices in finance, and microscopic particle movement in natural sciences. (gu.se)

###### Early Transcendentals3

- Calculus: Early Transcendentals , originally by D. Guichard, has been redesigned by the Lyryx editorial team. (merlot.org)
- You just viewed Calculus: Early Transcendentals . (merlot.org)
- Calculus: Early Transcendentals , 8th Edition, by Howard Anton, Irl Bivens and Stephen Davis. (maa.org)

###### Infinitesimal2

- Calculus uses methods originally based on the summation of infinitesimal differences. (wikiversity.org)
- This is entirely analogous to ordinary function calculus, where the infinitesimal change in the value of a function is df/dx * dx, and the total change over an interval is ∫ df/dx * dx = ΔF. (everything2.com)

###### Renal5

- 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)
- Renal sonogram demonstrates an echogenic shadowing calculus in the renal collecting system with hydronephrosis. (medscape.com)
- Contrast-enhanced CT scan demonstrates an opaque staghorn calculus filling the left renal collecting system. (medscape.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)

###### Robin Milner2

- 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 Robin Milner, Joachim Parrow, and David Walker in the late 80's extends CCS with mobility of communication links, by allowing processes to communicate the names of communication channels themselves. (wikipedia.org)

###### Absolute differen1

- Fundamental introduction for beginning student of absolute differential calculus and for those interested in applications of tensor calculus to mathematical physics and engineering. (google.com)

###### Process calculi5

- I'll take this opportunity to mention Orc , a language in the process calculi tradition that I really like. (lambda-the-ultimate.org)
- Unlike some other process calculi, Orc does not make unreasonable assumptions (like mobility) about what properties are implementable in a distributed system. (lambda-the-ultimate.org)
- I couldn't really figure out how to get transactions into a process calculi with multiple named input channels. (lambda-the-ultimate.org)
- It's probably worth noting that Montanari and Zavatarro (both authors on one or more of the references mentioned in the original post) have also done work on developing formalizations of the actor model based on process calculi. (lambda-the-ultimate.org)
- As time permits, the latter part of the course will explore type systems for process calculi and the current research on designing programming languages that make it easier to reason about process behavior, for instance to rule out dead lock. (upenn.edu)

###### Moral Calculus1

- So now let's consider the moral calculus surrounding Medicaid expansion from the perspective of taxpayers and society in general. (forbes.com)

###### Ureteric calculi5

- Ureteric calculi are stones in the ureters, which are the narrow muscular tubes that are responsible for the drainage of urine from the kidneys to the bladder. (news-medical.net)
- Stone size can predict the spontaneous passage of ureteric calculi. (news-medical.net)
- Also implicated in the etiopathogenesis of ureteric calculi are heredity, diet, anatomical abnormalities of the urinary tract and chronic urinary tract infections (UTIs). (news-medical.net)
- Hormonal imbalances and metabolic derangements, as well as hot/ dry climates, are also linked to ureteric calculi. (news-medical.net)
- They concluded that NECT can be used with a high degree of accuracy to predict the spontaneous passage of ureteric calculi, and that size combined with location of the stone are the most important parameters in this prediction. (news-medical.net)

###### Limits1

- In mathematics education, calculus denotes courses of elementary mathematical analysis, which are mainly devoted to the study of functions and limits. (wikipedia.org)

###### Formal5

- 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)
- As a general consideration, a calculus is a formal system that consists of a set of syntactic expressions, a distinguished subset of these expressions, plus a set of transformation rules that define a binary relation on the space of expressions. (planetmath.org)
- Although it is possible to construct an abstract formal calculus that has no immediate practical use and next to nothing in the way of obvious applications, the very name calculus indicates that this species of formal system owes its origin to the utility of its prototypical members in practical calculation. (planetmath.org)
- Generally speaking, any mathematical calculus is designed with the intention of representing a given domain of formal objects, and typically with the aim of facilitating the computations and inferences that need to be carried out in this representation . (planetmath.org)
- Thus some idea of the intended denotation , the formal objects that the formulas of the calculus are intended to denote, is given in advance of developing the calculus itself. (planetmath.org)

###### Algebra3

- Anybody who has taken Algebra 1 and has ever ridden in a car or pushed a toy train down a track can understand the basic concepts behind calculus. (metafilter.com)
- Obviously, a deep understanding of vector calculus requires a knowledge of the basics of vector algebra . (everything2.com)
- The spi-calculus is basically a pure process algebra spiced up with security primitives, and the applied pi-calculus can be seen as a generalisation of the spi-calculus where you allow arbitrary data signatures. (uu.se)

###### Chemistry4

- Chemistry vs Ap Calculus Ab? (yahoo.com)
- I now have Ap Calculus Ab and i was just wondering if it is as hard or harder than Chemistry. (yahoo.com)
- Many students find physical chemistry difficult not because the concepts are hard, but because they have to apply the calculus and physics they learned previously to problems in chemistry. (washington.edu)
- When freshmen and sophomores merely memorize calculus and physics for their exams rather than truly learning the material, they have difficulty later in senior-level physical chemistry courses. (washington.edu)

###### Derivative1

- The main operational difference between function calculus and vector calculus is that the standard derivative d/dx is replaced with the differential operator ∇, pronounced ' del ' or in the olden days' nabla . (everything2.com)

###### 17th-century1

- What few realize is that their calculus homework originated, in part, in a debate between two 17th-century scholars. (scientificamerican.com)

###### Symbolic3

- Use of symbolic manipulation and graphics software in calculus. (upenn.edu)
- In addition, the algorithm that decides the Mu-Calculus is used for symbolic (BDD-based) model-checking, a technique that has greatly extended the applicability of model-checking. (neu.edu)
- The Psi-calculi are in themselves unsuitable for some kinds of automated reasoning, and because of this we have developed a symbolic semantics for Psi-calculi. (uu.se)

###### Rigorous2

- Rigorous undergraduate treatment introduces calculus at the basic level, using infinitesimals and concentrating on theory rather than applications. (doverpublications.com)
- The two-part treatment offers a rigorous presentation of tensor calculus as a development of vector analysis as well as discussions of the most important applications of tensor calculus. (doverpublications.com)

###### Applications3

- The two main goals of the text are to provide students with a thorough grounding in calculus concepts and applications, analytical techniques, and numerical methods and to have students understand how, when, and why calculus can be used to model biological phenomena. (oreilly.com)
- Calculus: Ideas & Applications , by Alex Himonas and Alan Howard. (maa.org)
- With an informal, engaging tone and sound applications, The Calculus of Happiness facilitates financial literacy. (princeton.edu)

###### SageMath3

- Welcome to the SageMath Calculus Tutorial! (sagemath.org)
- No previous experience with SageMath or calculus is necessary, though you will need to either download SageMath or work online at CoCalc in order to participate actively in the following lessons. (sagemath.org)
- SageMath Calculus Tutorial - Last Visited , then select "Bookmark This Link" or your browser's equivalent. (sagemath.org)

###### AntiDerivatives1

- 4R2012 Calculus Unit5 AntiDerivatives! (slideshare.net)

###### Ureteral3

- Nonenhanced CT image shows an obstructing left proximal ureteral calculus with a slight soft-tissue rim around the stone (ie, rim sign). (medscape.com)
- We investigated the characteristics and diagnosis of primary asymptomatic ureteral calculi. (nih.gov)
- De novo asymptomatic ureteral calculi do exist. (nih.gov)

###### Functions2

- calculus) was invented in the 1930s by Alonzo Church, as a form of mathematical logic dealing primarly with functions and the application of functions to their arguments . (planetmath.org)
- 12. Standard Calculus and Sequences of Functions. (doverpublications.com)

###### Bisimulation1

- We have developed Hennessy-Milner style modal logics for general nominal transition systems (of which the Psi-calculi form an example), and showed adequacy for both strong and weak bisimulation. (uu.se)

###### Trigonometry1

- If you would first like to brush up on some pre-calculus and trigonometry concepts, this review may be of help. (sagemath.org)

###### Urinary2

- The goals of imaging of urinary calculi are to determine the presence of stones witin the urinary tract, evaluate for complications, estimate the likelihood of stone passage, confirm stone passage, assess the stone burden, and evaluate disease activity. (medscape.com)
- Ultrasonography (US) use for initial evaluation of suspected urinary calculi is common outside the United States. (medscape.com)

###### Students9

- In order to take college-level Calculus in high school, students must begin Pre-Calculus no later than their junior year. (google.com)
- Designed for students with one year of calculus in high school. (indiana.edu)
- There are likely to be more, better prepared students here than in your high school, but remember that you are trying to learn Calculus and not competing with other students. (unl.edu)
- In my opinion, students are there to learn calculus and should already know what a function is. (maa.org)
- Presenting Newton's problem to students and then proposing Calculus as the solution seems so much better than the reverse. (metafilter.com)
- For many students, calculus is more like an afterbirth. (metafilter.com)
- MATH 171 will be for all students starting the calculus sequence for the first time. (radford.edu)
- This classic introductory text, geared toward undergraduate students of mathematics, is the work of an internationally renowned authority on tensor calculus. (doverpublications.com)
- He himself built a tool - using Markov chains - that set students new calculus problems in function of their past performance He argues that at present MOOCs may not be very good at teaching people. (scoop.it)

###### Courses5

- Info concerning El Paso Community College calculus courses, registering for required degree courses, and taking free tests online. (calculuscourse.org)
- Taking calculus courses, for example, can give you an advantage in job recruiting in fields that require advanced math skills. (calculuscourse.org)
- Get info about Shasta College calculus courses, registering for elective courses, and taking tests for free online. (calculuscourse.org)
- This sequence of courses is the Calculus Path and is shown in the right column of the chart below. (google.com)
- Calculus courses are sequential, so the stuff you see in 191, for example, will enable you to make sense of a lot of the stuff you will see in 192. (unl.edu)

###### Precalculus1

- Using only high-school-level math (precalculus with a dash of calculus), Fernandez guides us through several of the surprising results, including an easy rule of thumb for choosing foods that lower our risk for developing diabetes (and that help us lose weight too), simple "all-weather" investment portfolios with great returns, and math-backed strategies for achieving financial independence and searching for our soul mate. (princeton.edu)

###### Processes1

- 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)

###### Graphs1

- im not gonna complain, i got 95-99 averages throughout all 4 hs semesters on those 2 classes, but AP calculus has alot of annoying word problems and analyzing graphs. (yahoo.com)

###### Mathematical tools1

- The pi-calculus provides a conceptual framework for understanding mobility, and mathematical tools for expressing systems and reasoning about their behaviours. (upenn.edu)

###### Physics1

- I'm of the opinion that basic Physics, at least the force/acceleration/velocity/displacement relationship, needs to be taught before calculus. (metafilter.com)

###### Theoretical1

- 2007) Calculus I - Theoretical focus. (wikiversity.org)

###### Kidney2

- Scout intravenous urogram shows a smooth, dense, round calculus in the left kidney. (medscape.com)
- Calculi occurring in the KIDNEY. (labome.org)

###### Vectors1

- 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 calculus. (worldcat.org)

###### Approach1

- Brief Calculus:An Applied Approach , 8th Edition, by Michael Sullivan. (maa.org)

###### Book5

- Wikibooks has a book on the topic of Calculus . (wikiversity.org)
- The explanations are adequate for the purpose, but the book is suitable only for the most basic overview of calculus. (maa.org)
- Since there are so many calculus books and the coverage in them is so similar, I cannot say that this book is outstanding. (maa.org)
- This book presents the pi-calculus, a theory of mobile systems. (upenn.edu)
- The book serves both as a reference for the theory and as an extended demonstration of how to use pi-calculus to describe systems and analyse their properties. (upenn.edu)