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An object-modeling language is a standardized set of symbols used to model a software system using an object-oriented framework. The symbols can be either informal or formal ranging from predefined graphical templates to formal object models defined by grammars and specifications.
A modeling language is usually associa... | Wikipedia/Object_modeling_language |
The energy systems language, also referred to as energese, or energy circuit language, or generic systems symbols, is a modelling language used for composing energy flow diagrams in the field of systems ecology. It was developed by Howard T. Odum and colleagues in the 1950s during studies of the tropical forests funded... | Wikipedia/Energy_Systems_Language |
Domain-specific modeling (DSM) is a software engineering methodology for designing and developing systems, such as computer software. It involves systematic use of a domain-specific language to represent the various facets of a system.
Domain-specific modeling languages tend to support higher-level abstractions than g... | Wikipedia/Domain-Specific_Modeling |
Algebraic modeling languages (AML) are high-level computer programming languages for describing and solving high complexity problems for large scale mathematical computation (i.e. large scale optimization type problems). One particular advantage of some algebraic modeling languages like AIMMS, AMPL, GAMS,
Gekko,
Math... | Wikipedia/Algebraic_modeling_language |
Object–role modeling (ORM) is used to model the semantics of a universe of discourse. ORM is often used for data modeling and software engineering.
An object–role model uses graphical symbols that are based on first order predicate logic and set theory to enable the modeler to create an unambiguous definition of an arb... | Wikipedia/Object-Role_Modeling |
Visual modeling is the graphic representation of objects and systems of interest using graphical languages. Visual modeling is a way for experts and novices to have a common understanding of otherwise complicated ideas. By using visual models complex ideas are not held to human limitations, allowing for greater complex... | Wikipedia/Visual_modeling |
Service Modeling Language (SML) and Service Modeling Language Interchange Format (SML-IF) are a pair of XML-based specifications created by leading information technology companies that define a set of XML instance document extensions for expressing links between elements, a set of XML Schema extensions for constrainin... | Wikipedia/Service_Modeling_Language |
Extended Enterprise Modeling Language (EEML) in software engineering is a modelling language used for enterprise modelling across a number of layers.
== Overview ==
Extended Enterprise Modeling Language (EEML) is a modelling language which combines structural modelling, business process modelling, goal modelling with... | Wikipedia/Extended_Enterprise_Modeling_Language |
General-purpose modeling (GPM) is the systematic use of a general-purpose modeling language to represent the various facets of an object or a system. Examples of GPM languages are:
The Unified Modeling Language (UML), an industry standard for modeling software-intensive systems
EXPRESS, a data modeling language for pr... | Wikipedia/General-purpose_modeling |
A transformation language is a computer language designed to transform some input text in a certain formal language into a modified output text that meets some specific goal.
Program transformation systems such as Stratego/XT, TXL, Tom, DMS, and ASF+SDF all have transformation languages as a major component. The trans... | Wikipedia/Transformation_language |
A framework-specific modeling language (FSML) is a kind of domain-specific modeling language which is designed for an object-oriented application framework.
FSMLs define framework-provided abstractions as FSML concepts and decompose the abstractions into features. The features represent implementation steps or choice... | Wikipedia/Framework-specific_modeling_language |
Rebeca (acronym for Reactive Objects Language) is an actor-based modeling language with a formal foundation, designed in an effort to bridge the gap between formal verification approaches and real applications. It can be considered as a reference model for concurrent computation, based on an operational interpretation ... | Wikipedia/Rebeca_Modeling_Language |
Business process modeling (BPM) is the action of capturing and representing processes of an enterprise (i.e. modeling them), so that the current business processes may be analyzed, applied securely and consistently, improved, and automated.
BPM is typically performed by business analysts, with subject matter experts co... | Wikipedia/Business_process_modeling |
The Architecture Analysis & Design Language (AADL) is an architecture description language standardized by SAE. AADL was first developed in the field of avionics, and was known formerly as the Avionics Architecture Description Language. It was funded in part by the US Army.
The Architecture Analysis & Design Language i... | Wikipedia/Architecture_Analysis_&_Design_Language |
WSML or Web Service Modeling Language is a formal language that provides a syntax and semantics for the Web Service Modeling Ontology (WSMO).
In other words, the WSML provides means to formally describe the WSMO elements as Ontologies, Semantic Web services, Goals, and Mediators.
The WSML is based on the logical forma... | Wikipedia/Web_Services_Modeling_Language |
Model-driven architecture (MDA) is a software design approach for the development of software systems. It provides a set of guidelines for the structuring of specifications, which are expressed as models. Model Driven Architecture is a kind of domain engineering, and supports model-driven engineering of software system... | Wikipedia/Model-driven_architecture |
Domain-specific modeling (DSM) is a software engineering methodology for designing and developing systems, such as computer software. It involves systematic use of a domain-specific language to represent the various facets of a system.
Domain-specific modeling languages tend to support higher-level abstractions than g... | Wikipedia/Domain-specific_modeling |
Model-based testing is an application of model-based design for designing and optionally also executing artifacts to perform software testing or system testing. Models can be used to represent the desired behavior of a system under test (SUT), or to represent testing strategies and a test environment. The picture on th... | Wikipedia/Model-based_testing |
EXPRESS is a standard for generic data modeling language for product data. EXPRESS is formalized in the ISO Standard for the Exchange of Product model STEP (ISO 10303), and standardized as ISO 10303-11.
== Overview ==
Data models formally define data objects and relationships among data objects for a domain of intere... | Wikipedia/EXPRESS_(data_modeling_language) |
A model transformation, in model-driven engineering, is an automated way of modifying and creating platform-specific model from platform-independent ones. An example use of model transformation is ensuring that a family of models is consistent, in a precise sense which the software engineer can define. The aim of using... | Wikipedia/Model_transformation |
The general algebraic modeling system (GAMS) is a high-level modeling system for mathematical optimization. GAMS is designed for modeling and solving linear, nonlinear, and mixed-integer optimization problems. The system is tailored for complex, large-scale modeling applications and allows the user to build large maint... | Wikipedia/General_Algebraic_Modeling_System |
Service-oriented modeling is the discipline of modeling business and software systems, for the purpose of designing and specifying service-oriented business systems within a variety of architectural styles and paradigms, such as application architecture, service-oriented architecture, microservices, and cloud computing... | Wikipedia/Service-oriented_modeling |
Business Process Model and Notation (BPMN) is a graphical representation for specifying business processes in a business process model.
Originally developed by the Business Process Management Initiative (BPMI), BPMN has been maintained by the Object Management Group (OMG) since the two organizations merged in 2005. Ver... | Wikipedia/Business_Process_Modeling_Notation |
In computer science, function-level programming refers to one of the two contrasting programming paradigms identified by John Backus in his work on programs as mathematical objects, the other being value-level programming.
In his 1977 Turing Award lecture, Backus set forth what he considered to be the need to switch to... | Wikipedia/Function-level_programming |
In computer science, Programming Computable Functions (PCF), or Programming with Computable Functions, or Programming language for Computable Functions, is a programming language which is typed and based on functional programming, introduced by Gordon Plotkin in 1977, based on prior unpublished material by Dana Scott. ... | Wikipedia/Programming_Computable_Functions |
The ACM Transactions on Programming Languages and Systems (TOPLAS) is a bimonthly, open access, peer-reviewed scientific journal on the topic of programming languages published by the Association for Computing Machinery.
== Background ==
Published since 1979, the journal's scope includes programming language design, ... | Wikipedia/ACM_Transactions_on_Programming_Languages_and_Systems |
A program transformation is any operation that takes a computer program and generates another program. In many cases the transformed program is required to be semantically equivalent to the original, relative to a particular formal semantics and in fewer cases the transformations result in programs that semantically di... | Wikipedia/Program_transformation |
In computer science and software programming, a value is the representation of some entity that can be manipulated by a program. The members of a type are the values of that type.
The "value of a variable" is given by the corresponding mapping in the environment. In languages with assignable variables, it becomes nece... | Wikipedia/Value_(computer_science) |
Programming language theory (PLT) is a branch of computer science that deals with the design, implementation, analysis, characterization, and classification of formal languages known as programming languages. Programming language theory is closely related to other fields including linguistics, mathematics, and software... | Wikipedia/Theory_of_programming |
A foreign function interface (FFI) is a mechanism by which a program written in one programming language can call routines or make use of services written or compiled in another one. An FFI is often used in contexts where calls are made into a binary dynamic-link library.
== Naming ==
The term comes from the specific... | Wikipedia/Foreign_function_interface |
In computing, external memory algorithms or out-of-core algorithms are algorithms that are designed to process data that are too large to fit into a computer's main memory at once. Such algorithms must be optimized to efficiently fetch and access data stored in slow bulk memory (auxiliary memory) such as hard drives or... | Wikipedia/External_memory_model |
A Kahn process network (KPN, or process network) is a distributed model of computation in which a group of deterministic sequential processes communicate through unbounded first in, first out channels. The model requires that reading from a channel is blocking while writing is non-blocking. Due to these key restriction... | Wikipedia/Kahn_process_networks |
In theoretical computer science, a nondeterministic Turing machine (NTM) is a theoretical model of computation whose governing rules specify more than one possible action when in some given situations. That is, an NTM's next state is not completely determined by its action and the current symbol it sees, unlike a deter... | Wikipedia/Nondeterministic_model_of_computation |
In mathematics, computer science and physics, a deterministic system is a system in which no randomness is involved in the development of future states of the system. A deterministic model will thus always produce the same output from a given starting condition or initial state.
== In physics ==
Physical laws that a... | Wikipedia/Deterministic_model |
In computer science, the cell-probe model is a model of computation similar to the random-access machine, except that all operations are free except memory access. This model is useful for proving lower bounds of algorithms for data structure problems.
== Overview ==
The cell-probe model is a modification of the ran... | Wikipedia/Cell-probe_model |
A computational model uses computer programs to simulate and study complex systems using an algorithmic or mechanistic approach and is widely used in a diverse range of fields spanning from physics, engineering, chemistry and biology to economics, psychology, cognitive science and computer science.
The system under stu... | Wikipedia/Computational_model |
In computational complexity theory, the decision tree model is the model of computation in which an algorithm can be considered to be a decision tree, i.e. a sequence of queries or tests that are done adaptively, so the outcome of previous tests can influence the tests performed next.
Typically, these tests have a smal... | Wikipedia/Decision_tree_model |
In computer science, the Robertson–Webb (RW) query model is a model of computation used by algorithms for the problem of fair cake-cutting. In this problem, there is a resource called a "cake", and several agents with different value measures on the cake. The goal is to divide the cake among the agents such that each a... | Wikipedia/Robertson–Webb_query_model |
The étale or algebraic fundamental group is an analogue in algebraic geometry, for schemes, of the usual fundamental group of topological spaces.
== Topological analogue/informal discussion ==
In algebraic topology, the fundamental group
π
1
... | Wikipedia/Algebraic_fundamental_group |
In mathematics, the Birch and Swinnerton-Dyer conjecture (often called the Birch–Swinnerton-Dyer conjecture) describes the set of rational solutions to equations defining an elliptic curve. It is an open problem in the field of number theory and is widely recognized as one of the most challenging mathematical problems... | Wikipedia/BSD_conjecture |
In mathematics, non-abelian class field theory is a catchphrase, meaning the extension of the results of class field theory, the relatively complete and classical set of results on abelian extensions of any number field K, to the general Galois extension L/K. While class field theory was essentially known by 1930, the ... | Wikipedia/Nonabelian_class_field_theory |
Freeform surface modelling is a technique for engineering freeform surfaces with a CAD or CAID system.
The technology has encompassed two main fields. Either creating aesthetic surfaces (class A surfaces) that also perform a function; for example, car bodies and consumer product outer forms, or technical surfaces for c... | Wikipedia/Freeform_surface_modeling |
Function Representation (FRep or F-Rep) is used in solid modeling, volume modeling and computer graphics. FRep was introduced in "Function representation in geometric modeling: concepts, implementation and applications" as a uniform representation of multidimensional geometric objects (shapes). An object as a point se... | Wikipedia/Function_representation |
In 3D computer graphics, a wire-frame model (also spelled wireframe model) is a visual representation of a three-dimensional (3D) physical object. It is based on a polygon mesh or a volumetric mesh, created by specifying each edge of the physical object where two mathematically continuous smooth surfaces meet, or by co... | Wikipedia/Wireframe_modeling |
In mathematics, an R-function, or Rvachev function, is a real-valued function whose sign does not change if none of the signs of its arguments change; that is, its sign is determined solely by the signs of its arguments.
Interpreting positive values as true and negative values as false, an R-function is transformed int... | Wikipedia/Rvachev_function |
In mathematics, specifically in topology,
the interior of a subset S of a topological space X is the union of all subsets of S that are open in X.
A point that is in the interior of S is an interior point of S.
The interior of S is the complement of the closure of the complement of S.
In this sense interior and closure... | Wikipedia/Exterior_(topology) |
Romulus is boundary representation (b-rep) solid modeling software, released first in 1978 by Ian Braid, Charles Lang, Alan Grayer, and the Shape Data team in Cambridge, England. It was the first commercial solid modeling kernel designed for straightforward integration into computer-aided design (CAD) software. Romulus... | Wikipedia/Romulus_(b-rep_solid_modeler) |
A node is a basic unit of a data structure, such as a linked list or tree data structure. Nodes contain data and also may link to other nodes. Links between nodes are often implemented by pointers.
== Nodes and trees ==
Nodes are often arranged into tree structures. A node represents the information contained in a s... | Wikipedia/Node_(computer_science) |
The Common Algebraic Specification Language (CASL) is a general-purpose specification language based on first-order logic with induction. Partial functions and subsorting are also supported.
== Overview ==
CASL has been designed by CoFI, the Common Framework Initiative (CoFI), with the aim to subsume many existing sp... | Wikipedia/Common_Algebraic_Specification_Language |
Attempto Controlled English (ACE) is a controlled natural language, i.e. a subset of standard English with a restricted syntax and restricted semantics described by a small set of construction and interpretation rules. It has been under development at the University of Zurich since 1995. In 2013, ACE version 6.7 was an... | Wikipedia/Attempto_Controlled_English |
UPPAAL is an integrated tool environment for modeling, validation and verification of real-time systems modeled as networks of timed automata, extended with data types (bounded integers, arrays etc.).
It has been used in at least 17 case studies since its release in 1995, including on Lego Mindstorms, for the Philips a... | Wikipedia/Uppaal_Model_Checker |
In its most common sense, methodology is the study of research methods. However, the term can also refer to the methods themselves or to the philosophical discussion of associated background assumptions. A method is a structured procedure for bringing about a certain goal, like acquiring knowledge or verifying knowledg... | Wikipedia/Methodology |
The B method is a method of software development based on B, a tool-supported formal method based on an abstract machine notation, used in the development of computer software.
== Overview ==
B was originally developed in the 1980s by Jean-Raymond Abrial in France and the UK. B is related to the Z notation (also orig... | Wikipedia/B-Method |
The Vienna Development Method (VDM) is one of the longest-established formal methods for the development of computer-based systems. Originating in work done at the IBM Laboratory Vienna in the 1970s, it has grown to include a group of techniques and tools based on a formal specification language—the VDM Specification L... | Wikipedia/Vienna_Development_Method |
SPIN is a general tool for verifying the correctness of concurrent software models in a rigorous and mostly automated fashion. It was written by Gerard J. Holzmann and others in the original Unix group of the Computing Sciences Research Center at Bell Labs, beginning in 1980. The software has been available freely sinc... | Wikipedia/SPIN_model_checker |
Methodism, also called the Methodist movement, is a Protestant Christian tradition whose origins, doctrine and practice derive from the life and teachings of John Wesley. George Whitefield and John's brother Charles Wesley were also significant early leaders in the movement. They were named Methodists for "the methodic... | Wikipedia/Methodism |
CoDel (Controlled Delay; pronounced "coddle") is an active queue management (AQM) algorithm in network routing, developed by Van Jacobson and Kathleen Nichols and published as RFC8289. It is designed to overcome bufferbloat in networking hardware, such as routers, by setting limits on the delay network packets experien... | Wikipedia/CAKE_(queue_management_algorithm) |
In computing, scheduling is the action of assigning resources to perform tasks. The resources may be processors, network links or expansion cards. The tasks may be threads, processes or data flows.
The scheduling activity is carried out by a mechanism called a scheduler. Schedulers are often designed so as to keep all ... | Wikipedia/Scheduling_algorithm |
In computer networking, integrated services or IntServ is an architecture that specifies the elements to guarantee quality of service (QoS) on networks. IntServ can for example be used to allow video and sound to reach the receiver without interruption.
IntServ specifies a fine-grained QoS system, which is often contra... | Wikipedia/Integrated_services |
In packet switching networks, traffic flow, packet flow or network flow is a sequence of packets from a source computer to a destination, which may be another host, a multicast group, or a broadcast domain. RFC 2722 defines traffic flow as "an artificial logical equivalent to a call or connection." RFC 3697 defines tra... | Wikipedia/Traffic_flow_(computer_networking) |
The generic cell rate algorithm (GCRA) is a leaky bucket-type scheduling algorithm for the network scheduler that is used in Asynchronous Transfer Mode (ATM) networks. It is used to measure the timing of cells on virtual channels (VCs) and or Virtual Paths (VPs) against bandwidth and jitter limits contained in a traffi... | Wikipedia/Generic_cell_rate_algorithm |
In theoretical computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm. Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, supposing that each elementary operation takes a... | Wikipedia/Polynomial-time_algorithm |
The Ramanujan tau function, studied by Ramanujan (1916), is the function
τ
:
N
→
Z
{\displaystyle \tau :\mathbb {N} \to \mathbb {Z} }
defined by the following identity:
... | Wikipedia/Ramanujan_tau_function |
In number theory, an additive function is an arithmetic function f(n) of the positive integer variable n such that whenever a and b are coprime, the function applied to the product ab is the sum of the values of the function applied to a and b:
f
(
a
b
)
=... | Wikipedia/Completely_additive_function |
In number theory, the sum of squares function is an arithmetic function that gives the number of representations for a given positive integer n as the sum of k squares, where representations that differ only in the order of the summands or in the signs of the numbers being squared are counted as different. It is denot... | Wikipedia/Sum_of_squares_function |
The Liouville lambda function, denoted by λ(n) and named after Joseph Liouville, is an important arithmetic function.
Its value is +1 if n is the product of an even number of prime numbers, and −1 if it is the product of an odd number of primes.
Explicitly, the fundamental theorem of arithmetic states that any positi... | Wikipedia/Liouville_function |
In arithmetic and algebra, the fifth power or sursolid of a number n is the result of multiplying five instances of n together:
n5 = n × n × n × n × n.
Fifth powers are also formed by multiplying a number by its fourth power, or the square of a number by its cube.
The sequence of fifth powers of integers is:
0, 1, 32... | Wikipedia/Fifth_power_(algebra) |
Graphemics or graphematics is the linguistic study of writing systems and their basic components, i.e. graphemes.
At the beginning of the development of this area of linguistics, Ignace Gelb coined the term grammatology for this discipline; later some scholars suggested calling it graphology to match phonology, but tha... | Wikipedia/Graphemics |
A cyclic number is a natural number n such that n and φ(n) are coprime. Here φ is Euler's totient function. An equivalent definition is that a number n is cyclic if and only if any group of order n is cyclic.
Any prime number is clearly cyclic. All cyclic numbers are square-free.
Let n = p1 p2 … pk where the pi are di... | Wikipedia/Cyclic_number_(group_theory) |
Gilbreath's conjecture is a conjecture in number theory regarding the sequences generated by applying the forward difference operator to consecutive prime numbers and leaving the results unsigned, and then repeating this process on consecutive terms in the resulting sequence, and so forth. The statement is named after ... | Wikipedia/Gilbreath's_conjecture |
In mathematics, the Mersenne conjectures concern the characterization of a kind of prime numbers called Mersenne primes, meaning prime numbers that are a power of two minus one.
== Original Mersenne conjecture ==
The original, called Mersenne's conjecture, was a statement by Marin Mersenne in his Cogitata Physico-Mat... | Wikipedia/Mersenne_conjectures |
Comptes rendus de l'Académie des Sciences (French pronunciation: [kɔ̃t ʁɑ̃dy də lakademi de sjɑ̃s], Proceedings of the Academy of Sciences), or simply Comptes rendus, is a French scientific journal published since 1835. It is the proceedings of the French Academy of Sciences. It is currently split into seven sections, ... | Wikipedia/Comptes_rendus_de_l'Académie_des_Sciences |
The Bunyakovsky conjecture (or Bouniakowsky conjecture) gives a criterion for a polynomial
f
(
x
)
{\displaystyle f(x)}
in one variable with integer coefficients to give infinitely many prime values in the sequence
f
(
... | Wikipedia/Bunyakovsky_conjecture |
Legendre's conjecture, proposed by Adrien-Marie Legendre, states that there is a prime number between
n
2
{\displaystyle n^{2}}
and
(
n
+
1
)
... | Wikipedia/Legendre's_conjecture |
In number theory, Brocard's conjecture is the conjecture that there are at least four prime numbers between (pn)2 and (pn+1)2, where pn is the nth prime number, for every n ≥ 2. The conjecture is named after Henri Brocard. It is widely believed that this conjecture is true. However, it remains unproven as of 2025.
T... | Wikipedia/Brocard's_conjecture |
In number theory, the Pólya conjecture (or Pólya's conjecture) stated that "most" (i.e., 50% or more) of the natural numbers less than any given number have an odd number of prime factors. The conjecture was set forth by the Hungarian mathematician George Pólya in 1919, and proved false in 1958 by C. Brian Haselgrove. ... | Wikipedia/Pólya_conjecture |
In number theory, Artin's conjecture on primitive roots states that a given integer a that is neither a square number nor −1 is a primitive root modulo infinitely many primes p. The conjecture also ascribes an asymptotic density to these primes. This conjectural density equals Artin's constant or a rational multiple th... | Wikipedia/Artin's_conjecture_on_primitive_roots |
In number theory, the Bateman–Horn conjecture is a statement concerning the frequency of prime numbers among the values of a system of polynomials, named after mathematicians Paul T. Bateman and Roger A. Horn who proposed it in 1962. It provides a vast generalization of such conjectures as the Hardy and Littlewood conj... | Wikipedia/Bateman–Horn_conjecture |
In number theory, Lemoine's conjecture, named after Émile Lemoine, also known as Levy's conjecture, after Hyman Levy, states that all odd integers greater than 5 can be represented as the sum of an odd prime number and an even semiprime.
== History ==
The conjecture was posed by Émile Lemoine in 1895, but was errone... | Wikipedia/Lemoine's_conjecture |
In number theory, Polignac's conjecture was made by Alphonse de Polignac in 1849 and states:
For any positive even number n, there are infinitely many prime gaps of size n. In other words: There are infinitely many cases of two consecutive prime numbers with difference n.
Although the conjecture has not yet been prove... | Wikipedia/Polignac's_conjecture |
In number theory, Grimm's conjecture (named after Carl Albert Grimm, 1 April 1926 – 2 January 2018) states that to each element of a set of consecutive composite numbers one can assign a distinct prime that divides it. It was first published in American Mathematical Monthly, 76(1969) 1126-1128.
== Formal statement ==... | Wikipedia/Grimm's_conjecture |
In number theory, the second Hardy–Littlewood conjecture concerns the number of primes in intervals. Along with the first Hardy–Littlewood conjecture, the second Hardy–Littlewood conjecture was proposed by G. H. Hardy and John Edensor Littlewood in 1923.
== Statement ==
The conjecture states that
... | Wikipedia/Second_Hardy–Littlewood_conjecture |
In number theory, Cramér's conjecture, formulated by the Swedish mathematician Harald Cramér in 1936, is an estimate for the size of gaps between consecutive prime numbers: intuitively, that gaps between consecutive primes are always small, and the conjecture quantifies asymptotically just how small they must be. It s... | Wikipedia/Cramér's_conjecture |
In number theory, a branch of mathematics, Dickson's conjecture is the conjecture stated by Dickson (1904) that for a finite set of linear forms a1 + b1n, a2 + b2n, ..., ak + bkn with bi ≥ 1, there are infinitely many positive integers n for which they are all prime, unless there is a congruence condition preventing th... | Wikipedia/Dickson's_conjecture |
Uncle Petros and Goldbach's Conjecture is a 1992 novel by Greek author Apostolos Doxiadis. It concerns a young man's interaction with his reclusive uncle, who sought to prove a famous unsolved mathematics problem, called Goldbach's conjecture, that every even number greater than two is the sum of two primes. The novel ... | Wikipedia/Uncle_Petros_and_Goldbach's_Conjecture |
In number theory the Agoh–Giuga conjecture on the Bernoulli numbers Bk postulates that p is a prime number if and only if
p
B
p
−
1
≡
−
1
(
mod
... | Wikipedia/Agoh–Giuga_conjecture |
In number theory, Firoozbakht's conjecture (or the Firoozbakht conjecture) is a conjecture about the distribution of prime numbers. It is named after the Iranian mathematician Farideh Firoozbakht who stated it in 1982.
The conjecture states that
p
n
... | Wikipedia/Firoozbakht's_conjecture |
In number theory, Goldbach's weak conjecture, also known as the odd Goldbach conjecture, the ternary Goldbach problem, or the 3-primes problem, states that
Every odd number greater than 5 can be expressed as the sum of three primes. (A prime may be used more than once in the same sum.)
This conjecture is called "weak"... | Wikipedia/Goldbach's_weak_conjecture |
In number theory, Goldbach's weak conjecture, also known as the odd Goldbach conjecture, the ternary Goldbach problem, or the 3-primes problem, states that
Every odd number greater than 5 can be expressed as the sum of three primes. (A prime may be used more than once in the same sum.)
This conjecture is called "weak"... | Wikipedia/Weak_Goldbach_conjecture |
Andrica's conjecture (named after Romanian mathematician Dorin Andrica (es)) is a conjecture regarding the gaps between prime numbers.
The conjecture states that the inequality
p
n
+
1
... | Wikipedia/Andrica's_conjecture |
In computer graphics, the midpoint circle algorithm is an algorithm used to determine the points needed for rasterizing a circle. It is a generalization of Bresenham's line algorithm. The algorithm can be further generalized to conic sections.
== Summary ==
This algorithm draws all eight octants simultaneously, start... | Wikipedia/Midpoint_circle_algorithm |
In mathematics and its applications, the signed distance function or signed distance field (SDF) is the orthogonal distance of a given point x to the boundary of a set Ω in a metric space (such as the surface of a geometric shape), with the sign determined by whether or not x is in the interior of Ω. The function has p... | Wikipedia/Signed_distance_function |
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. The name comes from the Monte Carlo Casino in Monaco, ... | Wikipedia/Monte_Carlo_methods |
In numerical linear algebra, the Gauss–Seidel method, also known as the Liebmann method or the method of successive displacement, is an iterative method used to solve a system of linear equations. It is named after the German mathematicians Carl Friedrich Gauss and Philipp Ludwig von Seidel. Though it can be applied t... | Wikipedia/Gauss–Seidel_method |
In computer graphics, a digital differential analyzer (DDA) is hardware or software used for interpolation of variables over an interval between start and end point. DDAs are used for rasterization of lines, triangles and polygons. They can be extended to non linear functions, such as perspective correct texture mappin... | Wikipedia/Digital_differential_analyzer_(graphics_algorithm) |
The Warnock algorithm is a hidden surface algorithm invented by John Warnock that is typically used in the field of computer graphics.
It solves the problem of rendering a complicated image by recursive subdivision of a scene until areas are obtained that are trivial to compute. In other words, if the scene is simple ... | Wikipedia/Warnock_algorithm |
In physics, the cross section is a measure of the probability that a specific process will take place in a collision of two particles. For example, the Rutherford cross-section is a measure of probability that an alpha particle will be deflected by a given angle during an interaction with an atomic nucleus. Cross sect... | Wikipedia/Cross_section_(physics) |
The painter's algorithm (also depth-sort algorithm and priority fill) is an algorithm for visible surface determination in 3D computer graphics that works on a polygon-by-polygon basis rather than a pixel-by-pixel, row by row, or area by area basis of other Hidden-Surface Removal algorithms. The painter's algorithm cre... | Wikipedia/Painter's_algorithm |
Xiaolin Wu's line algorithm is an algorithm for line antialiasing.
== Antialiasing technique ==
Xiaolin Wu's line algorithm was presented in the article "An Efficient Antialiasing Technique" in the July 1991 issue of Computer Graphics, as well as in the article "Fast Antialiasing" in the June 1992 issue of Dr. Dobb's... | Wikipedia/Xiaolin_Wu's_line_algorithm |
The Oren–Nayar reflectance model, developed by Michael Oren and Shree K. Nayar, is a reflectivity model for diffuse reflection from rough surfaces. It has been shown to accurately predict the appearance of a wide range of natural surfaces, such as concrete, plaster, sand, etc.
== Introduction ==
Reflectance is a phy... | Wikipedia/Oren–Nayar_reflectance_model |
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