1 e it math In probability theory and statistics , the discreteuniformdistribution is a discrete probability distribution probability distribution whereby a finite number of equally spaced values are equally ... discreteuniformdistribution would be a known, finite number of equally spaced outcomes equally ... n math that are equally spaced and equally probable, then it has a discreteuniformdistribution. The probability of any outcome math k i math is math 1 n math . A simple example of the discreteuniformdistribution is throwing a fair dice . The possible values of math k math are 1, 2, 3, 4, 5 ... permutation See rencontres numbers for an account of the probability distribution of the number of fixed points of a uniformly distributed random permutation . See also Delta distributionUniformdistribution continuous Notes reflist group notes References reflist ProbDistributions discrete finite Common univariate probability distributions DEFAULTSORT UniformDistributionDiscrete Category Discrete ... and their values added, the uniformdistribution no longer fits since the values from 2 to 12 do not have equal probabilities. The cumulative distribution function CDF can be expressed in terms of a degenerate distribution as math F k a,b,n 1 over n sum i 1 n H k k i math where the Heaviside step function math H x x 0 math is the CDF of the degenerate distribution centered at math x 0 math , using ... is described by saying that a sample of k observations is obtained from a uniformdistribution on the integers ... more details
Uniformdistribution may refer to Probability theory UniformdistributiondiscreteDiscreteuniformdistributionUniformdistribution continuous Continuous uniformdistribution Other Uniformdistribution modulo 1 , see Equidistributed sequence Uniformdistribution ecology , a type of species distributionDistribution of military uniform s disambig de Gleichverteilung eo Uniforma distribuo eu Banaketa uniforme argipena fr Loi uniforme nl Uniforme verdeling pl Rozk ad jednostajny ru vi Ph n b ng u nhi n u ... more details
Uniformdistribution is a Mathematics mathematical tool, mainly used in statistics . Uniformdistribution may also refer to Uniformdistribution continuous Uniformdistributiondiscrete disambig ... more details
The discrete phase type distribution is a probability distribution that results from a system of one or more inter related geometric distribution s occurring in sequence, or phases. The sequence in which each of the phases occur may itself be a stochastic process . The distribution can be represented by a random variable describing the time until absorption of an absorbing Markov chain with one absorbing ... block math T math . Definition. A distribution on math 0,1,2,... math is a discrete phase type distribution if it is the distribution of the first passage time to the absorbing state of a terminating ... time equivalent in the phase type distribution . Definition A terminating Markov chain is a Markov ... T math the upper left block of its transition matrix and math tau math the initial distribution. The distribution ... , T math or math mathrm DPH boldsymbol tau , T math . Its cumulative distribution function is math ... of process starting in the absorbing state is zero. The factorial moments of the distribution function ... is the appropriate dimension identity matrix . Special cases Just as the continuous time distribution is a generalisation of the exponential distribution, the discrete time distribution is a generalisation of the geometric distribution, for example Degenerate distribution , point mass at zero or the empty phase type distribution 0 phases. Geometric distribution 1 phase. Negative binomial distribution 2 or more identical phases in sequence. Mixed Geometric distribution 2 or more non identical phases, that each have a probability of occurring in a mutually exclusive, or parallel, manner. This is the discrete analogue of the Hyperexponential distribution , but it is not called the Hypergeometric distribution , since that name is in use for an entirely different type of discretedistribution. See also Phase type distribution Queueing model Queueing theory References M. F. Neuts. Matrix Geometric ... discrete infinite Category Discrete distributions Category Types of probability distributions ... more details
for the same reasons as Uniformdistributiondiscrete Estimation of maximum estimation for the discrete ... Rectangular function Uniformdistributiondiscrete References reflist External links http www.stud.feec.vutbr.cz ...Probability distribution name Uniform type density pdf image image Uniformdistribution PDF.png 350px PDF of the uniform probability distribution using the maximum convention at the transition points. BR small Using maximum convention small cdf image image Uniformdistribution CDF.png 350px CDF of the uniform ... mathrm e ita it b a math In probability theory and statistics , the continuous uniformdistribution ... uniformdistribution is math f x begin cases frac 1 b a & mathrm for a le x le b, 8pt 0 & mathrm for x ... function For n 2, the n th cumulant of the uniformdistribution on the interval ... of positive, finite measure, the uniform probability distribution on S can be specified by defining ... uniform Restricting math a 0 math and math b 1 math , the resulting distribution U 0,1 is called a standard uniformdistribution . One interesting property of the standard uniformdistribution is that if u sub 1 sub has a standard uniformdistribution, then so does 1 u sub 1 sub . This property ... has a standard uniformdistribution, then by the inverse transform sampling method, Y &minus ln ... with parameters 1 and n . Note this implies that the standard uniformdistribution is a special ... . Using the half maximum convention at the transition points, the uniformdistribution may be expressed ... and 1 if the null hypothesis is true. Sampling from a uniformdistribution There are many applications ... to the standard uniformdistribution. If u is a value sampled from the standard uniformdistribution, then the value a b &minus a u follows the uniformdistribution parametrised by a and b , as described above. Sampling from an arbitrary distribution Main Inverse transform sampling The uniform ... uniform random variable s into two independent normal distribution normally distributed random ... more details
one source date May 2010 In probability theory and directional statistics , a circular uniformdistribution is a probability distribution on the unit circle whose density is uniform for all angles. Description The pdf of the circular uniformdistribution is math f UC theta frac 1 2 pi . math In terms of the circular variable math z e i theta math the circular moments of the circular uniformdistribution .... math R langle z n rangle 0 , math Distribution of the mean The sample mean of a set of N measurements math z n e i theta n math drawn from a circular uniformdistribution is defined as math overline ... The sample mean for the circular uniformdistribution will be concentrated about zero, becoming more concentrated as N increases. The distribution of the sample mean for the uniformdistribution ... S math are constant. The distribution of the angle math P overline theta math is uniform math P overline theta frac 1 2 pi math and the distribution of math overline R math is given by ref name ... thumb 360px A 10,000 point Monte Carlo simulation of the distribution of the sample mean of a circular uniformdistribution for N 3 where math J 0 math is the Bessel ... information theory information entropy of the uniformdistribution is simply math H U int Gamma frac ... Monte Carlo simulation of the distribution of the mean for N 3 is shown in the figure. For certain ... . math For large N , the distribution of the mean can be determined from the central limit theorem ... variables i.i.d s, will be Normal distribution normally distributed with mean zero and variance ... of two normally distributed variables, will be Chi distribution Chi distributed with two degrees of freedom i.e. Rayleigh distribution Rayleigh distributed and variance math 1 2N math math lim N rightarrow ... math 2 pi math . This is the maximum entropy any circular distribution may have. See also Wrapped distribution References references ProbDistributions directional Category Continuous distributions ... more details
In applied mathematics, the non uniformdiscrete Fourier transform NDFT of a signal is a type of Fourier transform , related to a discrete Fourier transform or discrete time Fourier transform , but in which the input signal is not sampled at equally spaced intervals. As a result of this, the computed Discrete Fourier Transform can also consist of unevenly sampled frequency values. It is however also possible to compute uniformly sampled frequency values from an unevenly sampled input signal. External links http homepages.inf.ed.ac.uk rbf CVonline LOCAL COPIES PIRODDI1 NUFT NUFT.html Non Uniform Fourier Transform A Tutorial . http citeseerx.ist.psu.edu viewdoc download?doi 10.1.1.15.3781&rep rep1&type pdf Nonuniform fast Fourier transforms using min max interpolation http www user.tu chemnitz.de potts nfft guide html node2.html Notation, the NDFT and the NFFT http www user.tu chemnitz.de potts nfft guide3 html index.html NFFT 3.0 &ndash Tutorial Category Fourier analysis Category Transforms ... more details
Wiktionarypar discrete Wiktionarypar discreet Discrete in science is the opposite of continuity continuous something that is separate distinct individual. Discrete may refer to Discrete particle or quantum in physics, for example in quantum theory Discrete device , an electronic component with just one circuit element, either passive or active, other than an integrated circuit Discrete group , a group with the discrete topology Discrete mathematics , the study of structures without continuity Discrete optimization , a branch of optimization in applied mathematics and computer science Discrete probability distribution , a random variable that can be counted Discrete signal , a time series consisting of a sequence of quantities Discrete space , a simple example of a topological space Discrete time , non continuous time, which results in discrete time samples Discrete pitch music pitch , a pitch with a steady frequency, rather than an indiscrete gliding, glissando or portamento, pitch See also Autodesk Media and Entertainment Formerly known as Discreet . disambig cs Diskr tn eu Diskretu fr Discret lt Diskretumas nl Discreet pt Discreto sk Diskr tny ... more details
Other uses File Porfirio Diaz paint.jpg thumb right 250px Uniform of Porfirio D az , about 1900 A uniform ... the uniform. Other uniforms are trade dress ed such as the brown uniforms of United Parcel Service .... Workers required to wear a uniform include retailer workers, bank and post office workers, public ... corporate image but also has important effects on the employees required to wear the uniform. However the term uniform is misleading because employees are not always fully uniform in appearance and may ... is uniform only in the color of their appearance not in its features. Pratt & Rafaeli, 1997 described ... Nathan Farragut Twining in Dress Blue uniform Schools Main School uniform Uniforms are required in many .... Countries with mandatory school uniforms include Japanese school uniform Japan , korean school uniform ... Kingdom , among as many other places. In some countries, uniform types vary from school to school ... primary schools will have a uniform jumper and or polo shirt with the school name and logo. Sports See also Baseball uniform Jersey clothing In sports Most, if not all, professional sports teams also ... common. Security and armed forces Main Military uniform Military personnel or civilian officials generally wear several kinds of uniforms battledress , khakis dress uniform worn at ceremonies, official ... dress worn in the mess or at other formal occasions. everyday work uniform, often with abbreviated ... class of 2005 graduation and commissioning ceremony. Main Prison uniform Civilian officials main Diplomatic uniform From about 1800 to after the Second World War, diplomats from most countries and often ... s are often required by their employer s to wear a uniform. Uniform hygiene In some countries or regions such as the UK , Australia or Hong Kong , the laundry expenses of working uniform or clothing ... archive archivedate 27 February 2008 ref Scouting Portal Scouting The Scout uniform is a specific characteristic ... that they are members one with another of one World Brotherhood . The original uniform, which has ... more details
Infobox television episode Title For the Uniform Image Image USS Defiant leaving DS9 damaged.jpg 270px Caption USS Defiant almost hits Deep Space 9 on its departure from the station. Series Star Trek Deep Space Nine Season 5 Episode 13 Production 511 Airdate Start date 1997 02 03 Writer Peter Allan Fields Director Victor Lobl Music Dennis McCarthy composer Dennis McCarthy Guests Kenneth Marshall Michael Eddington Eric Pierpoint Sanders Aron Eisenberg Nog Prev The Begotten Next In Purgatory s Shadow Episode list List of Star Trek Deep Space Nine episodes List of Star Trek Deep Space Nine episodes NOTOC For the Uniform is the 111th episode of Star Trek Deep Space Nine , the 13th episode of the fifth season. It has an average fan rating of 4.3 5 on the official Star Trek website as of September, 2009. Plot Benjamin Sisko Sisko encounters Michael Eddington , his former Starfleet Security Chief, who betrayed him and joined the Maquis Star Trek Maquis . Obsessed with capturing the traitor, Sisko pursues him in the USS Defiant Defiant . But when Sisko gives the order to fire, the Defiant experiences a massive computer failure caused by Eddington. He leaves Sisko angry and humiliated, and facing a long trip home. The Defiant is towed back to Deep Space Nine space station Deep Space Nine , and Miles O Brien Star Trek O Brien begins the massive job of bringing the ship back on line. Adding insult to injury, Sisko learns that Captain Sanders of the Excelsior class starship Starship Malinche has been assigned to apprehend Eddington since Starfleet feels Sisko hasn t himself been able to do the job in the past eight months. But when he learns that Eddington attacked Cardassian colonies in the DMZ with a biogenic weapon, Sisko sees his chance. Despite the fact that the Defiant is not ready ... DVD set, volume 5 , disc 4, selection 1. External links wikiquote Star Trek Deep Space Nine For the Uniform .5B5.13.5D For the Uniform IMDb title id 0708544 TV.com episode 20926 memoryalpha StarTrek.com ... more details
in a certain sense. Definitions Given a set X the discrete topology on X is defined by letting every subset of X be open set open and hence also closed set closed , and X is a discrete topological space if it is equipped with its discrete topology the discreteuniform space uniformity on X is defined ... Entourage definition entourage , and X is a discreteuniform space if it is equipped with its discrete uniformity. the discrete metric space metric math rho math on X is defined by math rho x,y ... a metric space can be discrete, without the metric being uniformly discrete for example the usual metric on the set 1, 1 2, 1 4, 1 8, ... of real numbers. Properties The underlying uniformity on a discrete metric space is the discrete uniformity, and the underlying topology on a discreteuniform space is the discrete topology. Thus, the different notions of discrete space are compatible with one another. On the other hand, the underlying topology of a non discreteuniform or metric space can ... metric also, this space is not complete topology complete and hence not discrete as a uniform space ... form a basis topology basis for the discrete topology. A uniform space X is discrete if and only ... set finite . Every discreteuniform or metric space is complete space complete . Combining the above two facts, every discreteuniform or metric space is totally bounded space totally bounded ... continuous , and any function from a discreteuniform space to another uniform space is uniformly ...Refimprove date March 2011 In topology , a discrete space is a particularly simple example of a topological ... math . In this case math X, rho math is called a discrete metric space or a space of isolated point s . a set mathematics set S is discrete in a metric space math X,d math , for math S subseteq X math ... s. A set S is uniformly discrete in the metric space math X,d math , for math S subseteq X math ... space math E,d math is said to be uniformly discrete if there exists math r 0 math such that, for any ... more details
probability distribution such as the normal distribution normal . Discrete probability distributions ... , discrete probability distribution s, discrete Fourier transform s, discrete geometry , discrete ...For the mathematics journal Discrete Mathematics journal File 6n graf.svg thumb 250px Graph mathematics Graphs like this are among the objects studied by discrete mathematics, for their interesting graph ... in developing computer algorithm s. Discrete mathematics is the study of Mathematics mathematical Mathematical structure structures that are fundamentally discrete space discrete rather than ... , the objects studied in discrete mathematics such as integer s, Graph mathematics graphs , and statements in Mathematical logic logic ref Richard Johnsonbaugh, Discrete Mathematics , Prentice Hall ... title Discrete mathematics urlname DiscreteMathematics ref Discrete mathematics therefore excludes topics in continuous mathematics such as calculus and Mathematical analysis analysis . Discrete objects can often be enumeration enumerated by integers. More formally, discrete mathematics has been characterized as the branch of mathematics dealing with countable set s ref Norman L. Biggs , Discrete ... agreed, definition of the term discrete mathematics. ref Brian Hopkins, Resources for Teaching Discrete Mathematics , Mathematical Association of America, 2008. ref Indeed, discrete mathematics ... notions. The set of objects studied in discrete mathematics can be finite or infinite. The term finite mathematics is sometimes applied to parts of the field of discrete mathematics that deals with finite sets, particularly those areas relevant to business. Research in discrete mathematics ... which operate in discrete steps and store data in discrete bits. Concepts and notations from discrete mathematics are useful in studying and describing objects and problems in branches of computer ... ideas from discrete mathematics to real world problems, such as in operations research . Although the main ... more details
Discrete modelling is the discrete space discrete analogue of continuous modelling . In discrete modelling, discrete formulae are fit to data . A common method in this form of modelling is to use recurrence relation s. Mathapplied stub Category Applied mathematics ... more details
The phrase T distribution may refer to Student s t test in univariate statistics, Student s t distribution in univariate probability theory, Hotelling s T square distribution in multivariate statistics. Multivariate Student distribution . disambig Category Probability distributions ... more details
A discrete circuit is an electronic circuit built out of Discrete device discrete components , such as resistor s, transistor s, etc., instead of a single integrated circuit . Category Electronics terms electronics stub fr Circuit discret ... more details
wiktionarypar distribution tocright Distribution may refer to In mathematics, science, and technology In mathematics Distribution mathematics , generalized functions used to formulate solutions of partial differential equations Probability distribution , the probability of a particular values or value range of a variable Cumulative distribution function , in which the probability of a value is a function of that value Frequency distribution , a list of the values recorded in a sample Inner distribution and outer distribution , in coding theory Distribution differential geometry , a subset of the tangent ... state space Distribution of terms , a situation in which all members of a category are accounted ... elementary algebra In science Complementary distribution , in linguistics, a relationship between elements found in opposite environments Distribution pharmacology , the transfer of a drug within the body Distribution function , in physics, the number of particles per unit volume in phase space Population distribution , the geographical area in which a species lives Spectral power distribution , in color science, the power per unit area per unit wavelength of an illumination Trip distribution , part ... distribution , the final stage in the delivery of electricity Electronic brakeforce distribution , an automotive ... , the coordinated use of physically distributed computers for tasks or storage Software distribution, a bundle of a specific software already compiled and configured Linux distribution , one of several distributions built on the Linux kernel Distribution concurrency , the projection operator in a history monoid, a representation of the histories of concurrent computer processes Key distribution center , part of a cryptosystem intended to reduce the risks inherent in exchanging keys Content distribution , publishing and web design as method to provide information Digital distribution , publishing media digitally Distribution of elements in the distributed element model of electric circuits ... more details
Groups In mathematics , a discrete group is a group mathematics group G equipped with the discrete topology . With this topology G becomes a topological group . A discrete subgroup of a topological group G is a subgroup H whose relative topology is the discrete one. For example, the integer s, Z , form a discrete subgroup of the real numbers reals , R with the standard metric space metric topology , but the rational number s, Q , do not. Any group can be given the discrete topology. Since every map from a discrete space is continuous topology continuous , the topological homomorphisms between discrete ... of categories isomorphism between the category of groups and the category of discrete groups. Discrete groups can therefore be identified with their underlying non topological groups. With this in mind, the term discrete group theory is used to refer to the study of groups without topological ... when a topological group or Lie group is usefully endowed with the discrete topology, against nature ... only look at a single point to determine if the topological group is discrete. In particular, a topological group is discrete if and only if the singleton mathematics singleton containing the identity is an open set . A discrete group is the same thing as a zero dimensional Lie group uncountable discrete groups are not second countable so authors who require Lie groups to satisfy this axiom do not regard these groups as Lie groups . The identity component of a discrete group is just the trivial ... Hausdorff topology on a finite set is the discrete one, a finite Hausdorff topological group must necessarily be discrete. It follows that every finite subgroup of a Hausdorff group is discrete. A discrete subgroup H of G is cocompact if there is a compact subset K of G such that HK G . Discrete ... groups . A discrete normal subgroup of a connected space connected group G necessarily lies in the center group theory center of G and is therefore abelian group abelian . Other properties every discrete ... more details
In signal processing , discrete transforms are integral transform mathematical transforms , often linear transform s, of signals between discrete domains, such as between discrete time and discrete frequency. ref cite book title Television receivers edition author Jerry C. Whitaker publisher McGraw Hill Professional year 2001 isbn 9780071380423 page 147 url http books.google.com books?id n3hxYt1u8vwC&pg PA147&dq 22discrete transforms are 22&hl en v onepage&q 22discrete 20transforms 20are 22&f false ref Many common integral transform s used in signal processing have their discrete counterparts. For example, for the Fourier transform the counterpart is the discrete Fourier transform . In addition to spectral analysis of signals, discrete transforms play important role in data compression , detection theory signal detection , digital filter ing and correlation analysis. ref cite book title Signal coding and processing edition 2nd author Graham Wade publisher Cambridge University Press year 1994 isbn 9780521423366 page 332 url http books.google.com books?id CJswCy7 W8YC&pg PA332&dq 22discrete transforms are 22&hl en v onepage&q 22discrete 20transforms 20are 22&f false ref Transforms between a discrete domain and a continuous domain are not discrete transforms. For example, the discrete time Fourier transform and the Z transform , from discrete time to continuous frequency, and the Fourier series , from continuous time to discrete frequency, are outside the class of discrete transforms. Classical signal processing deals with one dimensional discrete transforms. Other application areas, such as image processing , computer vision , high definition television , visual telephony, etc. make use of two dimensional and in general, multidimensional discrete transforms. See also List of transforms Discrete transforms References reflist Category Digital signal processing Category Discrete transforms ... more details
Refimprove date September 2007 A discrete symmetry is a symmetry that describes non continuous changes in a system. For example, a square possesses discrete rotational symmetry, as only rotations by multiples of right angles will preserve the square s original appearance. Discrete symmetries sometimes involve some type of swapping , these swaps usually being called reflections or interchanges . In theoretical physics , a discrete symmetry is a symmetry under the transformations of a discrete group e.g. a topological group with a discrete topology whose elements form a finite or a countable set . physics stub Category Theoretical physics fa ... more details
regression bar In economics , discrete choice problems involve choices between two or more discrete alternatives ... . On the other hand, discrete choice analysis examines situations in which the potential outcomes are discrete, such that the optimum is not characterized by standard first order conditions. Loosely, regression analysis examines how much while discrete choice analysis examines which. However, discrete ... for Local Telephone Service A Fully Discrete Model of Residential Call Patterns and Service Choice , Rand Journal of Economics, Vol. 18, No. 1, pp109 123 ref Discrete choice models are statistical procedures ... Model , Transportation Research, Vol. 12, pp. 167 174. ref among numerous other applications. Discrete ... Nobel prize in 2000 for his pioneering work in developing the theoretical basis for discrete choice. Discrete choice models statistically relate the choice made by each person to the attributes of the person ... Marketing researchers use discrete choice models to study Consumer theory consumer demand and to predict ... problems. ref name cars Transportation planners use discrete choice models to predict demand for planned .... MIT catalogue ref The first applications of discrete choice models were in transportation planning, and much of the most advanced research in discrete choice models is conducted by transportation researchers. Energy forecasters and policymakers use discrete choice models for households and firms ..., No. 4, pp. 647 657 ref Environmental studies utilize discrete choice models to examine the recreators ... economists use discrete choice models to examine participation in the work force, occupation choice, and choice of college and training programs. ref name college Common Features of Discrete Choice Models Discrete choice models take many forms, including Binary Logit, Binary Probit, Multinomial Logit ... set is the set of alternatives that are available to the person. For a discrete choice model .... This third requirement distinguishes discrete choice analysis from regression analysis in which ... more details
Image Sampled.signal.svg right thumb Discrete sampled signal Image Digital.signal.svg right thumb Digital signal Discrete here means constituting a separate entity and is distinct from discreet a discreet signal is one not intended to be seen by others. A discrete signal or discrete time signal is a time series consisting of a sequence of qualities. In other words, it is a type series that is a function over a Domain mathematics domain of discrete integral. Unlike a continuous signal continuous time signal , a discrete time signal is a function of a continuous argument however, it may have been obtained by sampling information theory sampling from a continuous time signal, and then each value in the sequence is called a sample signal sample . When a discrete time signal obtained by sampling is a sequence corresponding to uniformly spaced times, it has an associated sampling rate the sampling rate is not apparent in the data sequence, and so needs to be associated as a separate data item. Acquisition Discrete signals may have several origins, but can usually be classified into one of two groups ref Digital Signal Processing Prentice Hall Pages 11 12 ref By acquiring values of an analog ... taking a certain elevator every day. Digital signals Image Discrete cosine.svg thumb right 350px Discrete cosine waveform with frequency of 50 Hz and a sampling rate of 1000 samples sec, easily satisfying ... signal is a discrete time signal for which not only the time but also the amplitude has been made discrete in other words, its samples take on only values from a discrete set. The process of converting a continuous valued discrete time signal to a digital discrete valued discrete time signal is known ... by an approximation selected from a given discrete set for example by truncating or rounding, but much ... . This process loses information, and so discrete valued signals are only an approximation of the converted continuous valued discrete time signal, itself only an approximation of the original continuous ... more details
A discrete system is a system with a countable number of states. Discrete systems may be contrasted with continuous systems, which may also be called analog systems. A final discrete system is often modeled with a directed graph mathematics graph and is analyzed for correctness and complexity according to computational theory . Because discrete systems have a countable number of states, they may be described in precise mathematical models . A computer is a finite state machine that may be viewed as a discrete system. Because computers are often used to model not only other discrete systems but continuous systems as well, methods have been developed to represent real world continuous systems as discrete systems. One such method involves sampling a continuous signal at discrete time intervals. See also Digital control Finite state machine Frequency spectrum Mathematical model Sample and hold Sample rate Sample time Z transform References cite book last Hopcroft first John E. coauthors Rajeev Motwani, Jeffrey D. Ullman title Introduction to Automata Theory, Languages, and Computation edition 2nd ed. publisher Addison Wesley location Reading Mass year 2001 isbn 0201441241 cite book last Benjamin C. Kuo title Digital Control Systems edition 2nd publisher Oxford University Press location USA year 1995 isbn 0195120647 Category Automata theory Category Models of computation Category Signal processing tech stub ... more details
In mathematics , especially category theory , a discrete category is a category whose only morphism s are the identity morphism s. It is the simplest kind of category. Specifically a category C is discrete if hom sub C sub X , X id sub X sub for all objects X hom sub C sub X , Y for all objects X Y Since by axioms, there is always the identity morphism between the same object, the above is equivalent to saying hom sub C sub X , Y is 1 when X Y and 0 when X is not equal to Y . Clearly, any class set theory class of objects defines a discrete category when augmented with identity maps. Any subcategory of a discrete category is discrete. Also, a category is discrete if and only if all of its subcategories are full category full . The limit category theory limit of any functor from a discrete category into another category is called a product category theory product , while the colimit is called a coproduct . References Robert Goldblatt 1984 . Topoi, the Categorial Analysis of Logic Studies in logic and the foundations of mathematics, 98 . North Holland. Reprinted 2006 by Dover Publications, and available http historical.library.cornell.edu cgi bin cul.math docviewer?did Gold010&id 3 online at http www.mcs.vuw.ac.nz rob Robert Goldblatt s homepage . Category Category theory es Categor a discreta nl Discrete categorie ... more details
object. Discrete geometry has large overlap with convex geometry and computational geometry , and is closely ... , discrete differential geometry , geometric graph theory , toric geometry , and combinatorial topology ... Kepler Kepler and Augustin Louis Cauchy Cauchy , modern discrete geometry has its origins ..., and Four colour theorem map colourings by Tait, Heawood, and Hadwiger. Topics in discrete ... Regular map graph theory Regular maps Lattice discrete subgroup Lattices and discrete group s Reflection group s Triangle group s Digital geometry Discrete differential geometry Geometric set partitioning and transversals See also Discrete and Computational Geometry Discrete mathematics Paul Erd s References cite book author Bezdek, Andr s Kuperberg, W. title Discrete geometry in honor of W ... 3 cite book author K roly Bezdek Bezdek, K roly title Classical Topics in Discrete Geometry publisher ... in discrete geometry publisher Springer location Berlin year 2005 isbn 0 387 23815 8 cite book last1 ..., Jacob E. and O Rourke, Joseph title Handbook of Discrete and Computational Geometry, Second Edition ... first Peter M. author link Peter M. Gruber title Convex and Discrete Geometry publisher Springer location Berlin year 2007 isbn 3 540 71132 5 cite book author Matou ek, Ji title Lectures on discrete ... Springer year 1997 isbn 3 540 61341 2 Mathematics footer Category Discrete geometry ar ... more details
Citations missing date March 2008 Expert subject mathematics date April 2009 Discrete optimization is a branch of Optimization mathematics optimization in applied mathematics and computer science . As opposed to continuous optimization , the Variable mathematics variables used in the optimization mathematics mathematical program or some of them are restricted to assume only discrete mathematics discrete values, such as the integers. Two notable branches of discrete optimization are combinatorial optimization , which refers to problems on graph mathematics graph s, matroid s and other discrete structures integer programming These branches are closely intertwined however since many combinatorial optimization problems can be modeled as integer programs e.g. Shortest path Linear programming formulation shortest path and conversely, integer programs can often be given a combinatorial interpretation. Category Mathematical optimization mathapplied stub eo Diskreta optimumigo pl Programowanie ca kowitoliczbowe ru zh ... more details
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