teapot , an iconic model in 3D computer graphics created by Martin Newell computer scientist Martin Newell in 1975. Computer graphics is a sub field of computerscience which studies methods for digitally ... Processing , http www.eg.org events Symposium on Rendering, and Symposium on Computer Animation . As in the rest of computerscience, conference publications in computer graphics are generally more ...dablink This article is about the scientific discipline of computer graphics. For other uses see Computer ... computer graphics three dimensional computer graphics , it also encompasses 2D computer graphics two dimensional graphics and image processing . Overview Computer graphics studies the manipulation .... Computer graphics is often differentiated from the field of visualization graphic visualization , although ... visualization Computer vision Image processing Computational geometry Computational topology Applied mathematics Applications of computer graphics include Special effect Special effects Visual effects Video game Video games Digital art History One of the first displays of computer animation ... and journals where the most significant results in computer graphics are published. Among them ... An extensive history of computer graphics can be found at http accad.osu.edu waynec history lessons.html this page . ref Subfields in computer graphics A broad classification of major subfields in computer ... geometric quantities for the discrete surfaces used in computer graphics. ref name columbia ddg ... with light . See Rendering computer graphics for more information. Transport light transport theory ... in computer graphics multicol Jim Blinn Jack E. Bresenham Loren Carpenter Edwin Catmull Robert L. Cook Paul Debevec Ronald Fedkiw Ron Fedkiw James D. Foley multicol break David Forsyth computer ... Williams multicol end See also multicol 3D computer graphics Cloth modeling Computer facial animation ... reflist Further reading James D. Foley Foley et al . Computer Graphics Principles and Practice . Shirley ... more details
File Nearest integer.svg thumb 300px A plot of the nearest integer function, rounding to the nearest even integer In computerscience , the nearest integer function of real number x denoted variously by math x math , ref MathWorld title Nearest Integer Function urlname NearestIntegerFunction accessdate 2008 08 15 ref math lfloor x rceil math , math Vert x Vert math , ref cite book author J.W.S. Cassels title An introduction to Diophantine approximation series Cambridge Tracts in Mathematics and Mathematical Physics volume 45 publisher Cambridge University Press year 1957 page 1 ref nint x , or Round x , is a function mathematics function which returns the nearest integer to x . To avoid ambiguity when operating on half integer s, a rounding rule must be chosen. On most computer implementations, the selected rule is to round half integers to the nearest even number even integer for example, math 1.25 1 math math 1.50 2 math math 1.75 2 math math 2.25 2 math math 2.50 2 math math 2.75 3 math math 3.25 3 math math 3.50 4 math math 3.75 4 math math 4.50 4 math etc. This is in accordance with the IEEE 754 standards and helps reduce bias in the result. There are many other possible rules for rounding Tie breaking tie breaking when rounding a half integer include rounding up, rounding down, rounding to or away from zero, or random rounding up or down. See also Floor and ceiling functions References references Category Mathematical notation Category Elementary special functions Category Parity Category Article Feedback 5 th ... more details
File IP polytope with LP relaxation.png right thumb 300px The red dots are the integer lattice points within the blue polygon, the latter representing a two dimensional linear program Study of integer points in convex polyhedra ref In some contexts convex polyhedra are called simply polyhedra . ref is motivated by the questions, such as how many nonnegative integer valued solutions does a system of linear equations with nonnegative coefficients have or how many solutions does an integer linear program have . Counting integer points in polyhedra or other questions about them arise in representation theory , commutative algebra , algebraic geometry , statistics , and computerscience . ref http math.sfsu.edu beck src06.html Integer points in polyhedra. Geometry, Number Theory, Representation Theory, Algebra, Optimization, Statistics , ACM SIAM Joint Summer Research Conference, 2006 ref The set of integer points, or, more generally, the set of points of an affine lattice , in a polyhedron is called Z polyhedron , ref The term Z polyhedron is also used as a synonym to convex lattice polytope , the convex hull of finitely many points in an affine lattice. ref from the mathematical notation math mathbb Z math or Z for the set of integer numbers. ref Computations on Iterated Spaces in The Compiler Design Handbook Optimizations and Machine Code Generation, CRC Press 2007, 2nd edition, ISBN 142004382X, http books.google.com books?id 1kqAv uDEPEC&pg PT465&dq 22Z polyhedron 22 v onepage&q 22Z polyhedron 22&f false p.15 7 ref Properties For a lattice &Lambda , Minkowski s theorem relates ... to loop optimization , the set of the executions of the loop body is viewed as the set of integer ... References and notes reflist Further reading Integer Points In Polyhedra Geometry, Number Theory, Algebra, Optimization Proceedings of an AMS IMS SIAM Joint Summer Research Conference on Integer ... Barvinok , Integer Points in Polyhedra , 2008, ISBN 3037190523 Category Lattice points Category Linear ... more details
for finding integer relations among real numbers. Preliminary version STACS 1986 Symposium Theoret. Aspects ComputerScience Lecture Notes ComputerScience 210 1986 , p. 105 118. SIAM J. Computing ...An integer relation between a set of real numbers x sub 1 sub , x sub 2 sub , ..., x sub n sub is a set ... 2 cdots a nx n 0. , math An integer relation algorithm is an algorithm for finding integer relations. Specifically, given a set of real numbers known to a given precision, an integer relation algorithm will either find an integer relation between them, or will determine that no integer relation exists ... of its coefficients would always find an integer relation for sufficiently large coefficients. Results of interest occur when the size of the coefficients in an integer relation is small compared ... of the Euclidean algorithm can determine whether there is an integer relation between any two ... fraction expansion of x sub 1 sub x sub 2 sub if there is an integer relation between the numbers ... Ferguson and R.W. Forcade . ref MathWorld urlname IntegerRelation title Integer Relation ref ..., Numerically Stable Integer Relation Algorithm by Helaman R. P. Ferguson and David H. Bailey RNR ... Editors Name Top 10 Algorithms journal SIAM News volume 33 issue 4 ref Applications Integer relation ... number x is likely to be algebraic number algebraic , by searching for an integer relation between a set of powers of x 1, x , x sup 2 sup , ..., x sup n sup . The second application is to search for an integer ... to a high degree of precision usually at least 100 significant figures , and then use an integer relation algorithm to search for an integer relation between this value and a set of mathematical constants. If an integer relation is found, this suggests a possible closed form expression for the original ... of confidence that any integer relation that is found is not just a Almost integer numerical artifact . A notable success of this approach was the use of the PSLQ algorithm to find the integer relation ... more details
Unreferenced date March 2007 In computerscience , precision of a numerical quantity is a measure of the detail in which the quantity is expressed. This is usually measured in bits, but sometimes in decimal digits. It is related to precision arithmetic precision in mathematics , which describes the number of digits that are used to express a value. Rounding error further2 Floating point Precision is often the source of rounding error s in computation . The number of bits used to store a number will often cause some loss of accuracy. An example would be to store sin 0.1 in IEEE single precision floating point standard. The error is then often magnified as subsequent computations are made to the data it can also be reduced . See also Integercomputerscience Arbitrary precision arithmetic Precision arithmetic IEEE754 IEEE floating point standard Category Computer data ja ... more details
types Integercomputerscience int , boolean data type boolean , Double precision double Class computer ...Advanced Placement Advanced Placement ComputerScience also called AP Comp Sci , APCS or AP Java is the name ... school students as an opportunity to earn college credit for a college level computerscience course. AP ComputerScience A ref http apcentral.collegeboard.com apc public courses teachers corner 4483.html AP ComputerScience A Home Page , The College Board ref is meant to be the equivalent of a first semester course in computerscience, while AP ComputerScience AB ref http apcentral.collegeboard.com apc public courses teachers corner 8153.html AP ComputerScience AB Home Page , The College ... language Java . AP ComputerScience AB was discontinued following the May 2009 exam administration ... Science AB Home Page ref The current Chief Reader for AP ComputerScience 2008 2012 is Dr. Jody Paul, ref Paul, Jody, http www.jodypaul.com www.jodypaul.com ref Associate Professor of ComputerScience at Metropolitan State College of Denver . AP ComputerScience A Advanced Placement ComputerScience ... are not covered to the extent that they are covered in AP ComputerScience AB. AP ComputerScience AB Discontinued Advanced Placement ComputerScience AB included all the topics of AP ComputerScience ... . For example, binary trees were studied in AP ComputerScience AB but not in AP ComputerScience A. The use of Recursion computerscience recursive data structures and dynamic allocation dynamically allocated structures was fundamental to AP ComputerScience AB. Due to low numbers of students taking AP ComputerScience AB, it was discontinued after the 2008 2009 year. ref Cech, Scott J ... ref cite web url http apcentral.collegeboard.com apc public repository ap computerscience course description.pdf title ComputerScience A Course Description format PDF pages 8 10 publisher College ... apc public repository ap09 compsci coursedesc.pdf title ComputerScience A ComputerScience AB Course ... more details
The following outline is provided as an overview of and topical guide to computerscienceComputerscience also called computing science &ndash study of the theoretical foundations of information and computation ... system for computerscience is the ACM Computing Classification System devised by the Association for Computing Machinery . The ACM computerscience body of knowledge is a recommended curriculum for a university level computerscience course. Subfields Mathematical foundations Mathematical ... systems Concurrency computerscience Concurrency The theory and practice of simultaneous computation ... structures and properties Bioinformatics and Computational biology The use of computerscience ... computerscience Computability theory What is calculable with the current models of computers. Proofs ... quantum superposition of bits. History main History of computerscience Vocations Programmer Software ... data structure Array List computing List Tree data structure Tree String computerscience String Matrix computerscience Databases Database Other Abstraction computerscience Abstraction Big O notation Closure computerscience Closure Compiler Programming paradigms Object oriented programming Object oriented programming Class computerscience Class Inheritance computerscience Inheritance Object computer ... portal Computerscience Cognitive science External links sisterlinks Computerscience dmoz Computers ComputerScience http www.acm.org education curricula ComputerScience2008.pdf Association for Computing Machinery ACM report on a recommended computerscience curriculum 2008 http www.lecturefox.com computerscience Directory of free university lectures in ComputerScience http liinwww.ira.uka.de bibliography Collection of ComputerScience Bibliographies http se.ethz.ch meyer gallery Photographs ... 2007 2006fall cs1 UCLA ComputerScience 1 Freshman ComputerScience Seminar Section 1 http webcast.berkeley.edu ... Category Outlines Computerscience Category Computerscience Outline Category Computing lists Computer ... more details
of computer program s. An expression programming expression is said to be referentially transparent if it can be replaced with its Value computerscience value without changing the behavior of a program ... to reason about program behavior. This can help in proving correctness computerscience correctness , simplifying an algorithm , assisting in modifying code without breaking it, or optimization computerscience optimizing code by means of memoization , common subexpression elimination or parallelization ... are discarded and their side effect computerscience side effect s are insignificant. Take a function that takes no parameters and returns input from the computer keyboard keyboard . A call to this function ... scope programming scope d variable, or a lexical closure computerscience closure to help it compute ... effect computerscience side effects . code today code is not transparent, as if you evaluate ... for optimization computerscience optimization . See also Idempotence Computerscience meaning Idempotence in computerscience References cite journal first1 Harald last1 S ndergaard first2 ... Transparency human computer interaction transparent , in programming this is not always the case ... opaque, and the other which is referentially transparent pre globalValue 0 integer function rq integer x begin globalValue globalValue 1 return x globalValue end integer function rt integer ..., say we wish to reason about the following statement integer p rq x rq y rq x rq x One may be tempted to simplify this statement to integer p rq x rq y 0 integer p rq x 0 integer p rq x However ... the statement to integer a globalValue integer p x a 1 y a 2 x a 3 x a 4 globalValue globalValue 4 integer a globalValue integer p x a 1 y a 2 x a 3 x a 4 globalValue globalValue 4 integer a globalValue integer p x a 1 y a 2 1 globalValue globalValue 4 integer a globalValue integer p x a 1 y a 2 globalValue globalValue 4 integer p x y 1 globalValue globalValue 4 This takes more steps and requires ... more details
saved book title Computerscience subtitle cover image cover color Computerscience Main article Computerscience Supporting article History of computerscience Category Wikipedia books on computerscienceComputerscience ... more details
In theoretical computerscience , correctness of an algorithm is asserted when it is said that the algorithm is correct with respect to a program specification specification . Functional correctness refers to the input output behaviour of the algorithm i.e., for each input it produces the correct output . A distinction is made between total correctness , which additionally requires that the algorithm terminates, and partial correctness , which simply requires that if an answer is returned it will be correct. Since there is no general solution to the halting problem , a total correctness assertion may lie much deeper. A termination proof is a type of mathematical proof that plays a critical role in formal verification because total correctness of an algorithm depends on termination. For example, successively searching through integer s 1, 2, 3, to see if we can find an example of some phenomenon &mdash say an odd perfect number &mdash it is quite easy to write a partially correct program using long division by two to check n as perfect or not . But to say this program is totally correct would be to assert something Perfect number Odd perfect numbers currently not known in number theory . A proof would have to be a mathematical proof, assuming both the algorithm and specification are given formally. In particular it is not expected to be a correctness assertion for a given program implementing the algorithm on a given machine. That would involve such considerations as limitations on computer memory . A deep result in proof theory , the Curry Howard correspondence , states that a proof ... Design by contract Program analysis computerscience Model checking Compiler correctness Program derivation Computing stub Category Formal methods terminology Category Theoretical computerscience de Korrektheit Informatik es Correctitud ja ... formal system for reasoning rigorously about the correctness of computer programs. It can only show ... more details
In number theory , the integer square root isqrt of a positive integer n is the positive integer m which is the floor and ceiling functions greatest integer less than or equal to the square root of n , math mbox isqrt n lfloor sqrt n rfloor. math For example, math mbox isqrt 27 5 math because math 5 cdot 5 25 le 27 math and math 6 cdot 6 36 27 math . Algorithm One way of calculating math sqrt n math and math mbox isqrt n math is to use Newton s method to find a solution for the equation math x 2 n 0 math , giving the Recursion recursive formula math x k 1 frac 1 2 left x k frac n x k right , quad k ge 0, quad x 0 0. math The sequence math x k math Limit mathematics converges Rate of convergence quadratically to math sqrt n math as math k to infty math . It can be proven that if math x 0 n math is chosen as the initial guess, one can stop as soon as math x k 1 x k 1 math to ensure that math lfloor x k 1 rfloor lfloor sqrt n rfloor. math Domain of computation Although math sqrt n math is irrational number irrational for almost all math n math , the sequence math x k math contains only rational number rational terms when math x 0 math is rational. Thus, with this method it is unnecessary to exit the field mathematics field of rational numbers in order to calculate math mbox isqrt n math , a fact which has some theoretical advantages. Stopping criterion One can prove that math c 1 math is the largest possible number for which the stopping criterion math x k 1 x k c math ensures math lfloor x k 1 rfloor lfloor sqrt n rfloor math in the algorithm above. Since actual computer calculations involve roundoff errors, a stopping constant less than 1 should be used, e.g. math x k 1 x k 0.5. math See also Methods of computing square roots External links http mathcentral.uregina.ca RR database RR.09.95 grzesina1.html A geometric view of the square root algorithm number theoretic algorithms Category Number theoretic algorithms Category Number theory Category Root finding algorithms ... more details
In mathematics , an integer valued polynomial also known as a numerical polynomial P t is a polynomial whose value P n is an integer for every integer n . Every polynomial with integer coefficient s is integer valued, but the converse is not true. For example, the polynomial math frac 1 2 t 2 frac 1 2 t math takes on integer values whenever t is an integer. That is because one of n and n 1 must be an even number . The values this polynomial takes are the triangular number s. Integer valued polynomials are objects of study in their own right in algebra, and frequently appear in algebraic topology . cn date March 2012 Classification In fact integer valued polynomials can be described fully. Inside the polynomial ring Q t of polynomials with rational number coefficients, the subring of integer valued polynomials is a free abelian group . It has as basis linear algebra basis the polynomials P sub k sub t t t &minus 1 ... t &minus k 1 k for k 0,1,2, ..., i.e., the binomial coefficient s. In other words, every integer valued polynomial can be written as a integer linear combination of binomial ... series binomial coefficients are integer valued polynomials, and conversely, the discrete difference of an integer series is an integer series, so the discrete Taylor series of an integer series generated by a polynomial has integer coefficients and is a finite series . Fixed prime divisors Integer .... For example, the polynomials P with integer coefficients that always take on even number values are just those such that P 2 is integer valued. Those in turn are the polynomials that may be expressed as a linear combination with even integer coefficients of the binomial coefficients. In questions ... n . Other rings Numerical polynomials can be defined over other rings and fields, in which case the integer ... Chabert first2 J L. title Integer valued polynomials series Mathematical Surveys and Monographs ... year 1997 issue 1 pages 65 75 doi 10.1112 S0024610796004395 References DEFAULTSORT Integer Valued Polynomial ... more details
Unreferenced date December 2009 Other uses Offset disambiguation Offset In computerscience , an offset within an Array data structure array or other data structure object is an integercomputerscienceinteger indicating the distance displacement from the beginning of the object up until a given element or point, presumably within the same object. The concept of a distance is valid only if all elements of the object are the same size typically given in Byte addressable bytes or Word addressable words . For example, given an array of characters A , containing tt abcdef tt , one can say that the element containing the letter tt c tt has an offset of 2 from the start of A . In assembly language In computer engineering and low level programming such as assembly language , an offset usually denotes the number of address locations added to a base address in order to get to a specific absolute address . In this original meaning of offset, only the basic address unit, usually the 8 bit byte , is used to specify the offset s size. In this context an offset is sometimes called a relative address . In IBM System 360 instructions, a 12 bit offset embedded within certain instructions provided a range of between 0 and 4096 bytes. For example within an unconditional branch instruction X 47F0Fxxx the xxx 12bit hexadecimal offset provided the byte offset from the base register 15 to branch to. An odd offset would cause a program check unless the base register itself also contained an odd address since instructions had to be aligned on half word boundaries to execute without a program or hardware interrupt . Talking more about the this, this is actually an indirect way to address to some memory location in a format of segment offset. For example, we want to refer to a memory location like F867. So we can do it in a way like this. First defining a segment like F000 and then the offset with 0867 ... DEFAULTSORT Offset ComputerScience Category Computer memory ar ca Offset inform tica de ... more details
A non integer representation uses non integer numbers as the radix , or bases, of a positional notation positional numbering system . For a non integer radix 1, the value of math x d n dots d 2d 1d 0.d 1 d 2 dots d m math is math x beta nd n cdots beta 2d 2 beta d 1 d 0 beta 1 d 1 beta 2 d 2 cdots beta m d m . math The numbers d sub i sub are non negative integers less than . This is also known as a expansion , a notion introduced by harvtxt R nyi 1957 and first studied in detail by harvtxt Parry 1960 . Every real number has at least one possibly infinite expansion. There are applications of expansions in coding theory harv Kautz 1965 and models of quasicrystal s harv Burdik Frougny Gazeau Krejcar 1998 . Construction expansions are a generalization of decimal expansion s. While infinite decimal expansions are not unique for example, 1.000... 0.999... , all finite decimal expansions .... Denote by nowrap x the floor function of x , that is, the greatest integer less than or equal to x , and let nowrap begin x x x nowrap end be the fractional part of x . There exists an integer k ... lexicographically largest string representing x . With an integer base, this defines the usual radix expansion for the number x . This construction extends the usual algorithm to possibly non integer ... 10 sub 1001111111110 sub 2 sub becomes 1000001010101010101010100 sub 2 sub . This means that every integer ... expansions is considerably more subtle than that of integer bases harv Glendinning Sidorov ... issn 0305 4470 volume 31 issue 30 pages 6449 6472 . citation series Lecture Notes in ComputerScience publisher Springer Berlin Heidelberg ISSN 0302 9743 volume 583 1992 title LATIN 92 doi 10.1007 ... integer base first Christiane last Frougny url http books.google.com books?id I3fC6batwokC&lpg PA154 ... title Unique representations of real numbers in non integer bases url http www.mrlonline.org mrl 2001 ... . External links mathworld title Base urlname Base DEFAULTSORT Non Integer Representation Category ... more details
Category Integer sequences Category Encyclopedias on science and mathematics Category Online encyclopedias ...infobox website name On Line Encyclopedia of Integer Sequences logo File OEISicon.svg 150px url http oeis.org oeis.org launch date start date 1996 author Neil Sloane The On Line Encyclopedia of Integer Sequences OEIS , also cited simply as Sloane s , is an online database of integer sequence s, created ... on integer sequences of interest to both professional mathematician s and recreational mathematics ... database of its kind. Each entry contains the leading terms of the sequence, Keyword computer ... to generate a Graph of a function graph or play a Computer music musical representation of the sequence ... Sloane started collecting integer sequences as a graduate student in 1965 to support his work in combinatorics ... in book form twice A Handbook of Integer Sequences 1973, ISBN 0 12 648550 X , containing 2,372 sequences in lexicographic order and assigned numbers from 1 to 2372. The Encyclopedia of Integer ... which may differ in their few initial terms in A Handbook of Integer Sequences as N numbers from N0001 ... work, Sloane founded the Journal of Integer Sequences in 1998. ref http www.cs.uwaterloo.ca journals JIS Journal of Integer Sequences ISSN 1530 7638 ref The database continues to grow at a rate ... of Integer Sequences ref In 2004, Sloane celebrated the addition of the 100,000th sequence to the database ... integer sequences, the OEIS also catalogs sequences of fraction mathematics fraction s, the digits of transcendental number s, complex number s and so on by transforming them into integer sequences ... such as 3.1415926535897... are catalogued under representative integer sequences such as decimal expansions ... integer sequences page 10 format PDF ref One of the earliest self referential sequences Sloane accepted ... integer, prefixed by A and zero padded on the left prior to November 2004 . The letter A stands ..., the ID numbers are not the same. The 1973 Handbook of Integer Sequences contained about 2400 sequences ... more details
In mathematics , a square free , or quadratfrei , integer is one divisor divisible by no square number perfect square , except 1. For example, 10 is square free but 18 is not, as it is divisible by 9 3 sup 2 sup . The smallest positive square free numbers are 1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 33, 34, 35, 37, 38, 39, ... OEIS id A005117 Ring theory generalizes the concept of being square free . Equivalent characterizations The positive integer n is square free if and only if in the canonical representation of a positive integer prime factorization of n , no prime number occurs more than once. Another way of stating the same is that for every prime divisor factor p of n , the prime p does not divide n p . Yet another formulation n is square free if and only if in every factorization n ab , the factors a and b are coprime . An immediate result of this definition is that all prime numbers are square free. The positive integer ... math frac zeta s zeta 2s prod p frac 1 p 2s 1 p s prod p 1 p s . math The positive integer n is square ... the classification of finitely generated abelian group s. The integer n is square free if and only ... Z k Z is a field if and only if k is a prime. For every positive integer n , the set ... structure Boolean algebra if and only if n is square free. The radical of an integer is always square ... numbers , Science in China Series A Mathematics 36 2 1993 , pp. 154 169. Cited in Pappalardi 2003 .... The converse is also true. Since every positive integer has a unique binary representation it is possible to reverse this encoding so that they may be decoded into a unique square free integer. Again, for example if we begin with the number 42, this time as simply a positive integer, we have its binary ... of Integer Sequences OEIS Erd s squarefree conjecture The central binomial coefficient math 2n choose ... DEFAULTSORT Square Free Integer Category Number theory Category Integer sequences bg ... more details
third party date February 2012 In probability and statistics , the generalized integer gamma distribution GIG is the distribution of the sum of independent Gamma distribution gamma distributed random variables , all with integer shape parameters and different rate parameters. A related concetpt is the generalized near integer gamma distribution GNIG Definition The random variable math X math has a gamma distribution with shape parameter math r math and Scale parameter Rate parameter rate parameter .... Then the random variable Y defined by math Y sum p j 1 X j math has a GIG generalized integer ... science article B6WK9 45J4Y1R 19 2 b439ff01637b5e9d2c682459a5b9c135 The Generalized Integer Gamma distribution a basis for distributions in Multivariate Statistics . Journal of Multivariate Analysis , 64 , 86 102. ref ref Coelho, C. A. 1999 . http www.sciencedirect.com science article ... near integer gamma distribution of depth math p 1 math is the distribution of the random variable ref name Coe04 Coelho, C. A. 2004 . http www.sciencedirect.com science article pii S0047259X03002112 The Generalized Near Integer Gamma distribution a basis for near exact approximations to the distributions ... integer real and where math lambda neq lambda j math math j 1, dots,p math . Properties The probability ... A mixture ofGeneralized Integer Gamma distributions as the exact distribution ofthe product of an odd ... http www.sciencedirect.com science article pii S0378375806002400 Study of the quality of several ... science article pii S037837580600228X Development and study of two near exact approximations to the distribution ... www.sciencedirect.com science article pii S0024379508003480 The advantage of decomposing elaborate ..., F. J. 2010 http www.sciencedirect.com science article pii S0047259X09001778 Near exact distributions ... science article pii S0047259X11000625 The distribution of the product of powers ... with using the generalized chi squared distribution , for which computer algorithms have been ... more details
In general topology , a branch of mathematics, the integer broom topology , is an example of a topology on the so called integer broom space X . ref name CEIT Citation first L. A. last Steen first2 J. A. last2 Seebach title Counterexamples in Topology publisher Dover year 1995 page 140 ISBN 048668735X ref To give a set X a topology means to say which subset s of X are open set open in a manner that satisfies certain axioms ref name CEIT2 Citation first L. A. last Steen first2 J. A. last2 Seebach title Counterexamples in Topology publisher Dover year 1995 page 3 ISBN 048668735X ref The union mathematics union of open sets is an open set. The finite intersection mathematics intersection of open sets is an open set. X and the empty set are open sets. Definition of the integer broom space File Integer Broom Plot FBN.gif thumb center A subset of the integer broom center The integer broom space X is a subset of the plane R sup 2 sup . Assume that the plane is parametrised by polar coordinates . The integer broom contains the origin and the points nowrap 1 n ,&theta R sup 2 sup such that n is a non negative integer , and nowrap 1 &theta 1 k k N and k 1 . ref name CEIT The image on the right gives an illustration for nowrap 1 0 n 5 and nowrap 1 1 15 &theta 1 . Geometrically, the space consists of a series of convergent sequence s. For a fixed n , we have a sequence of points lying on circle with centre 0,0 and radius n that converges to the point n ,0 . Definition of the integer broom topology We deine a topology on X be means of a product topology . The Integer Broom space is given by the polar coordinates math n, theta in n in Z n ge 0 times theta 1 k k in Z, k ge 1 , . math Let us write nowrap 1 n ,&theta U &thinsp × &thinsp V for simplicity. The Integer Broom topology ... from R . ref name CEIT Properties The integer broom space, together with the integer broom topology ... 1995 pages 200 201 ISBN 048668735X ref References reflist DEFAULTSORT Integer Broom topology Category ... more details
unreferenced date October 2006 A resource , or system resource , is any physical or virtual component of limited availability within a computer system. Every device connected to a computer system is a resource. Every internal system component is a resource. Virtual system resources include Computer file files , network connections and memory areas. Major resource types Central processing unit CPU time Random access memory and virtual memory Hard disk space Computer networking Network throughput Power management Electrical power External Peripheral Devices Input output operations Resource management A resource handle is an identifier for a resource that is currently being accessed. Resource handles can be opaque, in which case they are often integer numbers, or they can be pointer computer programming pointer s that allow access to further information. Common resource handles are file descriptor s and Internet socket socket s. A situation when a computer program allocates a resource and fails to deallocate it after use is called a resource leak . Resource tracking is the ability of an operating system , virtual machine or other program to terminate the access to a resource that has been allocated but not deallocated after use. When implemented by a virtual machine this is often done in the form of Garbage collection computer science garbage collection . Without resource tracking programmers must take care of proper manual resource deallocation. They may also use the RAII technique to automate this task. Access to memory areas is often controlled by Semaphore programming semaphore s, which allows a pathological situation called a deadlock , when different Thread computer science thread s or Process computing processes try to allocate resources already allocated by each other. A deadlock usually leads to a program becoming partially or completely unresponsive. Access to resources is also sometimes regulated by Queue data structure queuing in the case of computing time ... more details
Multiple issues refimprove July 2007 orphan February 2009 A scale factor is used in computerscience when a real world set of numbers needs to be represented on a different scale in order to fit a specific Computer numbering formats number format . For instance, a 16 bit signedness unsigned integer uint16 can only hold a value as large as 65,535 sub 10 sub . If uint16 s are to be used to represent values from 0 to 131,070 sub 10 sub , then a scale factor of 1 2 would be introduced. Notice that while the scale factor extends the range, it also decreases the Precision computerscience precision . In this example, for instance, the number 3 could not be represented because a stored 1 represents a real world 2, and a stored 2 represents a real world 4. Uses Certain number formats may be chosen ..., not lose any Precision computerscience precision , we need to multiply these numbers by 10 sup 3 sup , or 1,000, giving us integer values of pre 15400, 133, 4650, 1000, 8001 pre also note that these numbers .... DEFAULTSORT Scale Factor ComputerScience Category Theory of computation ..., 16. Integer values to Fractional Certain processors, particularly Digital signal processor DSPs ... is less than the same number of bits would provide to an integer. For instance, in an 8 bit field, an unsigned integer can store values from nowiki 0, 255 nowiki but an unsigned fixed point with 5 fractional bits only has 4 bits left over for the integer value, and so can only store integer values from ... sup 8 sup 256, because the fixed point field can also store 16 fractional values for each integer value ... 8 bit fixed point format with 4 fractional bits, and 4 integer bits. As mentioned, the highest integer ... representations of real data in 8 bit unsigned fixed point fields with 4 integer bits and 4 fractional ..., since 8 bits can have 256 unique configurations. In the example given Integer values to Fractional ... moves. On the other hand, when you divide by a number that is NOT an integer power of 2, you are changing ... more details
The term Theoretical ComputerScience may refer to The field of theoretical computerscience . Theoretical ComputerScience journal , a journal covering this field. disambig ... more details
In computerscience , and in particular functional programming , a hylomorphism is a Recursion computerscience recursive function, corresponding to the function composition composition of an anamorphism which first builds a set of results also known as unfolding and a catamorphism which then fold higher order function folds these results into a final return value . Fusion of these two recursive computations into a single recursive pattern then avoids building the intermediate data structure. This is a particular form of the optimizing program transformation techniques collectively known as deforestation computerscience deforestation . The categorical dual of a hylomorphism is called a metamorphism , and is a catamorphism followed by an anamorphism. Formal definition A hylomorphism math h A rightarrow C math can be defined in terms of its separate anamorphic and catamorphic parts. The anamorphic part can be defined in terms of a arity unary function math g A rightarrow B times A math defining the list of elements in math B math by repeated application unfolding , and a predicate mathematics predicate math p A rightarrow text Boolean math providing the terminating condition. The catamorphic part can be defined as a combination of an initial value math c in C math for the fold and a binary Operation mathematics operator math oplus B times C rightarrow C math used to perform the fold. Thus a hylomorphism math h ,a begin cases c & mbox if p ,a b oplus ha & mbox otherwise end cases math where math b, a ga math may be defined assuming appropriate definitions of math p math , math g math , math h math . Notation An abbreviated notation for the above hylomorphism is math h c, oplus , g, p math . Hylomorphisms in practice Lists List computing Lists are common data structures, as they naturally ... function. source lang haskell factorial IntegerInteger factorial n n 0 1 n 0 n factorial n 1 source ... mathematics term of the Fibonacci sequence . source lang haskell fibonacci IntegerInteger fibonacci ... more details
In mathematics, and especially general topology , the prime integer topology and the relatively prime integer topology are examples of topology topologies on the set of positive integer whole number s, i.e. the set nowrap 1 Z sup sup 1, 2, 3, 4, &hellip . ref name CEIT Citation first L. A. last Steen first2 J. A. last2 Seebach title Counterexamples in Topology publisher Dover year 1995 ISBN 048668735X ref To give the set Z sup sup a topology means to say which subset s of Z sup sup are open , and to do so in a way that the following axiom s are met ref name CEIT Citation first L. A. last Steen first2 J. A. last2 Seebach title Counterexamples in Topology publisher Dover year 1995 ISBN 048668735X ref The union mathematics union of open sets is an open set. The finite intersection mathematics intersection of open sets is an open set. Z sup sup and the empty set are open sets. Construction Given two positive integers nowrap 1 a , b Z sup sup , define the following congruence class math U a b b na in mathbf Z , , n in mathbf Z math Then the relatively prime integer topology is the topology generated from the basis math mathfrak B U a b , , a,b in mathbf Z , a,b 1 math and the prime integer topology is the sub topology generated from the sub basis math mathfrak P U p b , , p,b in mathbf Z , p text is prime math The set of positive integers with the relatively prime integer topology or with the prime integer topology are examples of topological spaces that are Hausdorff space Hausdorff but not regular space regular . ref name CEIT See also F rstenberg s proof of the infinitude of primes References Reflist Category General topology it Topologia degli interi equispaziati ... more details
language, variables may only be able to store a specified datatype e.g. Integercomputerscienceinteger or string computerscience string . Alternatively, a datatype may be associated only with the current ..., a value computerscience value . The variable name is the usual way to Reference computerscience ... of the exact information it represents. Dubious Dubious date February 2012 A variable name in computer source code is an Identifier In computer languages identifier that can be Name binding bound to a Value computerscience value during Run time program lifecycle phase run time , and the value ... accessed or Assignment computerscience changed at any time. However, in Pure function ... programming lifetime due to the requirements of referential transparency computerscience referential ... of the variable, such as access permission, Lock computerscience locks , Semaphore programming ... computerscience closure . Unless the programming language features garbage collection computerscience garbage collection , a variable whose extent permanently outlasts its scope can result in a memory ... by modifying each other s variables. Doing so also prevents action at distance computerscience action ..., a value is represented by some Object computerscience data object , which is stored ... See also Identifier Namespace computerscience Unlike their mathematical counterparts, programming ...refimprove date November 2009 In computer programming , a variable is a memory location storage location ... . Variables in computer programming are frequently given long names to make them relatively descriptive ... of the variable itself. A variable name s scope affects its extent . Scope is a Scope computerscience Lexical scoping lexical aspect of a variable. Most languages define a specific scope for each ... be permissible for a variable binding to extend beyond its scope, as occurs in Lisp closure computerscience closures and C Local variable Static local variables static local variable s when execution ... more details
In mathematics , an integer sequence prime is a prime number found as a member of an integer sequence . For example, the 8th Delannoy number , 265729, is prime. A challenge in empirical mathematics is to identify large prime values in rapidly growing sequences. A common subclass of integer sequence primes are constant primes , formed by taking a constant real number and considering prefixes of its decimal representation, omitting the decimal point. For example, the first 6 decimal digits of the constant , approximately 3.14159265, form the prime number 314159, which is therefore known as a pi prime . Similarly, a constant prime based on e mathematical constant e is called an e prime . Other examples of integer sequence primes include Cullen prime &ndash a prime that appears in the sequence of Cullen numbers math a n n2 n 1 , . math Factorial prime &ndash a prime that appears in either of the sequences math a n n 1 math or math b n n 1 , . math Fermat prime &ndash a prime that appears in the sequence of Fermat numbers math a n 2 2 n 1 , . math Fibonacci prime &ndash a prime that appears in the sequence of Fibonacci number s. Lucas prime &ndash a prime that appears in the Lucas number s. Mersenne prime &ndash a prime that appears in the sequence of Mersenne numbers math a n 2 n 1 , . math Primorial prime &ndash a prime that appears in either of the sequences math a n n 1 math or math b n n 1 , . math Pythagorean prime &ndash a prime that appears in the sequence math a n 4n 1 , . math Woodall prime &ndash a prime that appears in the sequence of Woodall numbers math a n n2 n 1 , . math The On Line Encyclopedia of Integer Sequences includes many sequences corresponding to the prime subsequences of well known sequences, for example OEIS A001605 A001605 for Fibonacci number s that are prime. References MathWorld urlname IntegerSequencePrimes title Integer Sequence Primes MathWorld urlname ConstantPrimes title Constant Primes MathWorld urlname Pi Prime title Pi Prime MathWorld ... more details
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