notability date January 2011 In database theory and database systems , a monotonic query is one whose result size does not decrease with the addition of new tuples in the database. Category Database theory database stub ... more details
Deadline monotonic priority assignment is a priority assignment policy used with fixed priority pre emptive scheduling . With deadline monotonic priority assignment, tasks are assigned priorities according to their deadlines the task with the shortest deadline being assigned the highest priority. This priority assignment policy is optimal for a set of periodic or sporadic tasks which comply with the following restrictive system model All tasks have deadlines less than or equal to their minimum inter arrival times or periods . All tasks have worst case execution time s WCET that are less than or equal to their deadlines. All tasks are independent and so do not block each others execution for example by accessing mutually exclusive shared resources . No task voluntarily suspends itself. There is some point in time, referred to as a critical instant, where all of the tasks become ready to execute simultaneously. Scheduling overheads switching from one task to another are zero. All tasks have zero release jitter the time from the task arriving to it becoming ready to execute . If restriction 7 is lifted, then deadline minus jitter monotonic priority assignment is optimal. If restriction 1. is lifted allowing deadlines greater than periods, then Audsley s optimal priority assignment algorithm may be used to find the optimal priority assignment. Deadline monotonic priority assignment is NOT optimal for fixed priority non pre emptive scheduling. A fixed priority assignment policy P is referred to as optimal if no task set exists which is schedulable using a different priority assignment policy which is not also schedulable using priority assignment policy P. Or in other words Deadline monotonic priority assignment DMPA policy is optimal if any process set, Q, that is schedulable by priority scheme, W, is also schedulable by DMPA ref name Burns Wellings cite book title Real Time ... algorithms de Deadline Monotonic Scheduling ... more details
nofootnotes date June 2008 A non monotonic logic is a formal logic whose Logical consequence consequence Relation mathematics relation is not Monotonicity of entailment monotonic . Most studied formal logics have a monotonic consequence relation, meaning that adding a formula to a theory never produces a reduction of its set of consequences. Intuitively, monotonicity indicates that learning a new piece of knowledge cannot reduce the set of what is known. A monotonic logic cannot handle various reasoning tasks such as Default logic reasoning by default consequences may be derived only because of lack of evidence of the contrary , abductive reasoning consequences are only deduced as most likely explanations and some important approaches to reasoning about knowledge the ignorance of a consequence must be retracted when the consequence becomes known and similarly belief revision new knowledge may contradict old beliefs . Default reasoning An example of a default assumption is that the typical bird flies. As a result, if a given animal is known to be a bird, and nothing else is known, it can be assumed to be able to fly. The default assumption must however be retracted if it is later learned ... should not be monotonic. Logics formalizing default reasoning can be roughly divided in two .... An abductive logic should not be monotonic because the most likely explanations are not necessarily ... a sprinkler was active , any logic that models explanations is non monotonic. Reasoning about knowledge If a logic includes formulae that mean that something is not known, this logic should not be monotonic ... in response to an addition of a new belief makes any logic for belief revision to be non monotonic ... and M. Schaerf 1993 A survey of complexity results for non monotonic logics Journal of Logic Programming ..., ed., The Blackwell Guide to Philosophical Logic . Blackwell. W. Lukaszewicz 1990 Non Monotonic Reasoning ... plato.stanford.edu entries logic nonmonotonic Non monotonic logic by G. Aldo Antonelli. Logic Category ... more details
In computer science , rate monotonic scheduling ref citation first1 C. L. last1 Liu authorlink1 Chung Laung Liu first2 J. last2 Layland title Scheduling algorithms for multiprogramming in a hard real time environment journal Journal of the ACM volume 20 issue 1 year 1973 pages 46 61 doi 10.1145 321738.321743 . ref is a scheduling algorithm used in real time operating system s with a static priority scheduling class. ref citation first1 Daniel P. last1 Bovet first2 Marco last2 Cesati title Understanding the Linux Kernel , http oreilly.com catalog linuxkernel chapter ch10.html 85347. ref The static priorities are assigned on the basis of the cycle duration of the job the shorter the cycle duration ... preemptive and have deterministic guarantees with regard to response times. Rate monotonic analysis .... Introduction A simple version of rate monotonic analysis assumes that threads have the following ... assigned according to the rate monotonic conventions tasks with shorter periods deadlines are given ... needs otherwise. Rate monotonic scheduling looks at a run modeling of all threads in the system and determines ... first1 J. last1 Lehoczky first2 L. last2 Sha first3 Y. last3 Ding contribution The rate monotonic ... monotonic priority assignment is optimal meaning that if any static priority scheduling algorithm can meet all the deadlines, then the rate monotonic algorithm can too. The deadline monotonic ... are identical in addition, deadline monotonic scheduling is optimal when deadlines are less ... real time operating system containing a working Rate Monotonic Scheduler. Dynamic priority ... a working Rate Monotonic Scheduler. Scheduling computing References references Further reading ... explained via the Mars Pathfinder Bug DEFAULTSORT Rate Monotonic Scheduling Category Scheduling algorithms Category Real time computing cs Rate monotonic scheduling de Rate Monotonic Scheduling fr Rate monotonic scheduling ko hu Rate Monotonic Scheduling ja sv Rate ... more details
wiktionarypar functionFunction may refer to Diatonic function , a term in music theory Function biology , explaining why a feature survived selection Function computer science , or subroutine, a portion of code within a larger program, performs a specific task Function engineering , related to the selected property of a system Function language , in linguistics, a way of achieving an aim using language Function mathematics , an abstract entity that associates an input to a corresponding output according to some rule Function model , a structured representation of the functions, activities or processes Function object , or functor or functionoid, a concept of object oriented programming Function Drinks , a beverage company based in Redondo Beach, California. A formal event such as a party or meeting See also Function hall Functional disambiguation Functionalism disambiguation Functor disambig bs Funkcija vor bg ca Funci desambiguaci cs Funkce da Funktion de Funktion et Funktsioon es Funci n eo Funkcio eu Funtzio argipena fr Fonction ko it Funzione lt Funkcija lmo Funziun nl Functie ja no Funksjon pl Funkcja ujednoznacznienie pt Fun o desambigua o ro Func ie dezambiguizare ru simple Function sk Funkcia sl Funkcija razlo itev sr sh Funkcija razvrstavanje sv Funktion olika betydelser th uk zh ... more details
Image VEST Core4 LowLevel.png thumbnail 320px right VEST 4 T function followed by a transposition layer In cryptography , a T function is a bijection bijective mapping that updates every bit of the state computer science state in a way that can be described as math x i x i f x 0, cdots, x i 1 math , or in simple words an update function in which each bit of the state is updated by a linear combination of the same bit and a function of a subset of its less significant bits. If every single less significant bit is included in the update of every bit in the state, such a T function is called triangular . Thanks to their bijectivity no collisions, therefore no entropy loss regardless of the used Boolean function s and regardless of the selection of inputs as long as they all come from one side of the output bit , T functions are now widely used in cryptography to construct block cipher s, stream cipher s, PRNG s and cryptographic hash function hash functions . T functions were first proposed in 2002 by Alexander Klimov A. Klimov and Adi Shamir A. Shamir in their paper A New Class of Invertible Mappings . Ciphers such as TSC 1 , TSC 3 , TSC 4 , ABC stream cipher ABC , Mir 1 and VEST are built with different types of T functions. Because arithmetic operation s such as addition , subtraction and multiplication are also T functions triangular T functions , software efficient word based T functions can be constructed by combining bitwise logic with arithmetic operations. Another important property of T functions based on arithmetic operations is predictability of their period mathematics period , which is highly attractive to cryptographers. Although triangular T functions are naturally vulnerable to guess and determine attacks, well chosen bitwise transposition mathematics transposition ... bit. Subsequent transposition of the output bits and iteration of the T function also do not affect ... and losing the T function bias of depending only on the less significant bits of the state. References ... more details
Orphan date February 2009 A unate function is a type of boolean function which has monotonic properties. They have been studied extensively in switching theory . A function math f x 1,x 2, ldots,x n math is said to be positive unate in math x i math if math f x 1,x 2, ldots,x i 1 ,1,x i 1 , ldots x n f bar x 1,x 2, ldots,x i 1 ,0,x i 1 , ldots,x n . , math Likewise, it is negative unate in math x i math if math f bar x 1,x 2, ldots,x i 1 ,0,x i 1 , ldots x n f x 1,x 2, ldots,x i 1 ,1,x i 1 , ldots,x n . , math If for every math x i math f is either positive or negative unate in the variable math x i math then it is said to be unate . A function is binate if it is not unate. For example the Logical disjunction function or with boolean values are used for true 1 and false 0 is positive unate. Category Logical syntax Compu lang stub positive unateness can also be considered as passing the same slope no change in the input and negative unate is passing the opposite slope.... non unate is dependence on more than one input of same or different slopes ... more details
In axiomatic set theory , a function f ordinal number Ord Ord is called normal or a normal function iff it is continuous function Continuous functions between partially ordered sets continuous with respect to the order topology and monotonicfunction strictly monotonically increasing . This is equivalent to the following two conditions For every infinite limit ordinal , f supremum sup f . For all ordinals , f f . Examples A simple normal function is given by f 1 note however that f 1 is not normal. If is a fixed ordinal, then the functions f , f and f sup sup for 1 are all normal. More important examples of normal functions are given by the aleph number s math f alpha aleph alpha math which connect ordinal and cardinal number s, and by the beth number s math f alpha beth alpha math . Properties If f is normal, then for any ordinal , f . ref harvnb Johnstone 1987 loc Exercise 6.9, p. 77 ref Proof If not, choose minimal such that f < . Since f is strictly monotonically increasing, f f < f , contradicting minimality of . Furthermore, for any non empty set S of ordinals, we have f sup S sup f S . Proof follows from the monotonicity of f and the definition of the supremum. For , set sup S and consider three cases if 0, then S 0 and sup f S f 0 if 1 is a successor ordinal successor , then there exists s in S with s , so that s . Therefore, f f s , which implies f sup f S if is a nonzero limit, pick any , and an s in S such that s possible since sup S . Therefore f f s so that f sup f S , yielding f sup f sup f S , as desired. Every normal function f has arbitrarily large fixed points see the fixed point lemma for normal functions for a proof. One can create a normal function g Ord Ord, called the derivative of f , where g is the th fixed point of f . ref harvnb Johnstone 1987 loc Exercise 6.9, p. 77 ref Notes reflist References citation first Peter last Johnstone authorlink ... more details
Any non negative measurable function math f colon X to mathbb R math is the pointwise limit of a monotonic ...In the mathematics mathematical field of real analysis , a simple function is a sufficiently nice see below for the formal definition real number real valued function over a subset of the real line which attains only a finite number of values. Some authors also require simple functions to be measurable function measurable as used in practice, they invariably are. A basic example of a simple function is the floor function over the half open interval 1,9 , whose only values are 1,2,3,4,5,6,7,8 . A more advanced example is the Dirichlet function over the real line, which takes the value 1 if x is rational and 0 otherwise. Thus the simple of simple function has a technical meaning somewhat at odds with common language. Note also that all step function s are simple. Simple functions are used as a first stage in the development of theories of integral integration , such as the Lebesgue integral , because it is very easy to create a definition of an integral for a simple function, and also, it is straightforward to approximate more general functions by sequences of simple functions. Definition Formally, a simple function is a finite linear combination of indicator function s of measurable set s. More precisely, let X , be a sigma algebra measurable space . Let A sub 1 sub , ..., A sub n sub be a sequence of measurable sets, and let a sub 1 sub , ..., a sub n sub be a sequence of real number real or complex number s. A simple function is a function math f X to mathbb C math of the form math f x sum k 1 n a k mathbf 1 A k x , math where math mathbf 1 A math is the indicator function ... simple functions are again simple functions, and multiplication by constant keeps a simple function ... measurable function defined over the measure space math X, Sigma, mu math as before. For each .... Royden . Real Analysis , 1968, Collier Macmillan. DEFAULTSORT Simple Function Category Measure theory ... more details
weakly monotonic there may be flat spots in its range. In either case, the quantile function is math ...See also quantile . In probability and statistics , the quantile function of the probability distribution ..., with that probability. The quantile function is one way of prescribing a probability distribution, and it is an alternative to the probability density function probability density or probability mass function mass function , the cumulative distribution function and the Characteristic function probability theory characteristic function . The derivative of the quantile function, namely the quantile density function, is yet another way of prescribing a probability distribution. It is the reciprocal of the pdf composed with the quantile function. Definition The quantile function, Q , of a probability distribution is the inverse function inverse of its cumulative distribution function cdf F . Assuming a continuous and strictly monotonic distribution function, math scriptstyle F colon R to 0,1 math , the quantile function returns the value below which random draws from the given ... function returns the minimum value of x for which the previous probability statement holds. Simple example For example, the quantile function for Exponential i.e. intensity and expected ... in principle by applying its quantile function to a sample from a uniform distribution. The demands ... site in External Links . Also see the entry on the probit function. Non composite rational approximations ... Student s T distribution Use of the inverse cumulative distribution function. journal Journal of Computational ... the sign function is 1 for positive arguments, 1 for negative arguments and zero at zero. It should not be confused with the trigonometric sine function. Non linear differential equations for quantile ... case of that available for any quantile function whose second derivative exists. In general the equation ... density function. The forms of this equation, and its classical analysis by series and asymptotic ... more details
log x . Examples of functions that are convex but not Monotonicfunction monotonically increasing include ...Image ConvexFunction.svg thumb 300px right Convex function on an interval. Image Epigraph convex.svg right thumb 300px A function in black is convex if and only if the region above its Graph of a function graph in green is a convex set . mergefrom Proper convex function discuss Talk Convex function Proper date March 2011 In mathematics , a real valued function mathematics function math f x math defined ... 1 t f x 2 . math A function is called strictly convex if math f tx 1 1 t x 2 t f x 1 1 t f x 2 , math for every math t , math , math 0 t 1 , math , and math x 1 not x 2 math . Note that the function must be defined over a convex set , otherwise the point math tx 1 1 t x 2 , math may not lie in the function domain. A function f is said to be strictly concave function concave if &minus f is strictly convex. Pictorially, a function is called convex if the function lies below or on the straight line ... is used A function is convex if its epigraph mathematics epigraph the set of points lying on or above the graph of a function graph is a convex set . These two definitions are equivalent, i.e., one holds if and only if the other one is true. Properties Suppose f is a function of one real number ... of the red line in the above drawing note also that the function R is symmetric in x,y . f is convex ... of convexity is quite useful to prove the following results. A convex function f defined on some open interval C is continuous function continuous on C and Lipschitz continuous on any ... . As a consequence, f is differentiable function differentiable at all but at most countable countably ... is shown in the examples section . A function is midpoint convex on an interval C if math f left ... weaker than convexity. For example, a real valued Lebesgue measurable function that is midpoint convex ...&pg PA12 p. 12 ref In particular, a continuous function that is midpoint convex will be convex ... more details
Nowhere monotonic continuous function proof of existence using the Baire category theorem ...dablink Weierstrass function may also refer to the Weierstrass elliptic function math wp math or the Weierstrass sigma function Weierstrass sigma, zeta, or eta functions . Image WeierstrassFunction.svg 300px right thumb Plot of Weierstrass Function over the interval &minus 2, 2 . Like fractal fractals , the function exhibits self similarity every zoom red circle is similar to the global plot. In mathematics , the Weierstrass function is a pathological mathematics pathological example of a real line real valued function mathematics function on the real line . The function has the property that it is continuous function continuous everywhere but differentiable nowhere. It is named after its discoverer Karl Weierstrass . Historically, the Weierstrass function is important because it was the first published 1872 to challenge the notion that every continuous function was differentiable except on a set of isolated points. Construction In Weierstrass original paper, the function was defined ... K nigliche Akademie der Wissenschaften on 18 July 1872. The proof that this function is continuous ... that the function is not differentiable at that point. To do this, we construct two sequences of points ... function must have a derivative, or that the set of points where it is not differentiable should ... to draw or visualise a continuous function whose set of nondifferentiable points is something other ... null set . When we try to draw a general continuous function, we usually draw the graph of a function which is Lipschitz and has other nice properties. The Weierstrass function could perhaps .... The function has detail at every level, so zooming in on a piece of the curve does not show it getting ... close, the function will not be monotone. Kenneth Falconer in his book The Geometry of Fractal Sets , observes that the Hausdorff dimension of the classical Weierstrass function is bounded above by math ... more details
, and it is quasiconvex. Any monotonicfunction is both quasiconvex and quasiconcave. More generally ...Image Quasiconvex function.png right thumb A quasiconvex function that is not convex. Image Nonquasiconvex function.png right thumb A function that is not quasiconvex the set of points in the domain of the function for which the function values are below the dashed red line is the union of the two red ... density function of the normal distribution is quasiconcave but not concave. In mathematics , a quasiconvex function is a real number real valued function mathematics function defined on an interval ... of the function and looking down at the remaining part of the domain, an observer always sees ... of unimodal ity for functions with a single real argument. Definition and properties A function math ... points does not give a higher a value of the function than do both of the other points, then f is quasiconvex ... a quasi convex function math f x math is to require that each sub levelset math S alpha f x f x leq ... value of the function than one of the other points does. A quasiconcave function is a function whose negative is quasiconvex, and a strictly quasiconcave function is a function whose negative is strictly quasiconvex. Equivalently a function math f math is quasiconcave if math f lambda x 1 lambda y ... ,f y big math Image Monotonicity example2.png right thumb A quasilinear function is both quasiconvex and quasiconcave. Image Quasi concave function graph.png right thumb The graph of a function that is both concave and quasi convex on the nonnegative real numbers. A strictly quasiconvex function has strictly convex lower contour set s, while a strictly quasiconcave function has strictly convex upper contour set s. A function that is both quasiconvex and quasiconcave is quasilinear . Applications ... than do the convex closures provided by Lagrangian function Lagrangian Lagrange duality dual problems ... , quasiconcave utility function s imply that consumers have convex preferences . Quasiconvex ... more details
In mathematics, omega function or &omega function may mean Pearson&ndash Cunningham function Lambert W function Wright Omega function mathdab ... more details
Barnes G function , related to the Gamma function Meijer G function , a generalization of the hypergeometric function Siegel G function , a class of functions in transcendence theory mathdab ... more details
is one to one and hence invertible if and only if it is either strictly monotonicfunction increasing ...Image Inverse Function.png thumb right A function and its inverse sup 1 sup . Because maps a to 3, the inverse sup 1 sup maps 3 back to a . In mathematics , if is a function mathematics function from a set A to a set B , then an inverse function for is a function from B to A , with the property that a round trip a function composition composition from A to B to A or from B to A to B returns each element of the initial set to itself. Thus, if an input x into the function produces an output y , then inputting y into the inverse function produces the output x , and vice versa. A function that has an inverse is called invertible the inverse function is then uniquely determined by ... can be determined to have an inverse if it is a one to one function. Definitions Image Inverse Functions ... be a function whose domain mathematics domain is the Set mathematics set X , and whose Range mathematics range is the set Y . Then is invertible if there exists a function g with domain Y and range ..., the function g is unique in other words, there can be at most one function g satisfying this property. That function g is then called the inverse of , denoted by sup 1 sup . Stated otherwise, a function is invertible if and only if its inverse relation is a function on the range Y , in which case the inverse relation is the inverse function. Not all functions have an inverse. For this rule ... a function with this property is called one to one, or information preserving, or an injective function injection . Example squaring and square root functions The function x x sup 2 sup may or may ... its output the sign of its input. Such a function is called non Injective function injective or information losing. Notice that neither the square root nor the principal square root function is the inverse of x sup 2 sup because the first is not Single valued function single valued , and the second ... more details
Riemann function may refer to one of the several function mathematics functions named after the mathematician Bernhard Riemann , including Riemann zeta function Thomae s function Riemann theta function . dab fr Fonction de Riemann ... more details
In mathematics , a zeta function is usually a function mathematics function analogous to the original example the Riemann zeta function math zeta s sum n 1 infty frac 1 n s . math Zeta functions include Airy zeta function , related to the zeros of the Airy function Artin Mazur zeta function Artin Mazur zeta function of a dynamical system Barnes zeta function Beurling zeta function of Beurling generalized primes Dedekind zeta function Dedekind zeta function of a number field Real analytic Eisenstein series Epstein zeta function Epstein zeta function of a quadratic form. Goss zeta function of a function field Hasse Weil zeta function Hasse Weil zeta function of a variety Hurwitz zeta function Hurwitz zeta function A generalization of the Riemann zeta function Ihara zeta function Ihara zeta function of a graph Igusa zeta function Igusa zeta function Jacobi zeta function This is related to elliptic functions and is not analogous to the Riemann zeta function. L function , a twisted zeta function. Lefschetz zeta function Lefschetz zeta function of a morphism Lerch zeta function Lerch zeta function A generalization of the Riemann zeta function Local zeta function of a characteristic p variety Matsumoto zeta function Minakshisundaram Pleijel zeta function of a Laplacian Motivic zeta function of a motive Mordell Tornheim zeta function of several variables Multiple zeta function Prime zeta function Like the Riemann zeta function, but only summed over primes. Riemann zeta function The archetypal example. Selberg zeta function Selberg zeta function of a Riemann surface Shintani zeta function Weierstrass zeta function This is related to elliptic functions and is not analogous to the Riemann zeta function. Witten zeta function of a Lie group Zeta function operator Zeta function of an operator See also Artin conjecture L functions Artin conjecture Birch and Swinnerton Dyer conjecture Riemann hypothesis and the generalized Riemann hypothesis . Selberg class S External links http www.maths.ex.ac.uk ... more details
In mathematics, by sigma function one can mean one of the following The Divisor function sum of divisors function sub a sub n , an arithmetic function . Weierstrass sigma function , related to elliptic functions Rado s sigma function, see busy beaver . mathdab de Teilersumme fr Fonction sigma ... more details
In mathematics , two different function mathematics functions are known as the pi or Pi function math pi x , math pi function &ndash the prime counting function math Pi x , math Pi function &ndash the Gamma function when offset to coincide with the factorial disambig th ... more details
The phrase Kernel function may refer to a kernel function , i.e., the kernel of an integral operator for that topic see kernel mathematics , or the kernel of a function . disambig ... more details
In mathematics , influence function is used to mean either a synonym for a Green s function Influence function statistics , the effect on an estimator of changing one point of the sample. disambig ... more details
In number theory , Dedekind function can refer to any of three functions, all introduced by Richard Dedekind Dedekind eta function Dedekind psi function Dedekind zeta function disambig de Dedekindsche Funktion ... more details
Partition function may refer to Partition function number theory Partition function mathematics , which generalizes its use in statistical mechanics and quantum field theory Partition function statistical mechanics Partition function quantum field theory disambig su Fungsi partisi ... more details
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