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Boolean Differential Calculus
Boolean differential calculus (BDC) (German: (BDK)) is a subject field of Boolean algebra discussing changes of Boolean variables and Boolean functions. Boolean differential calculus concepts are analogous to those of classical differential calculus, notably studying the changes in functions and variables with respect to another/others.H. WehlanBoolean Algebra in ''Encyclopedia of Mathematics''/ref> The Boolean differential calculus allows various aspects of dynamical systems theory such as * automata theory on finite automata * Petri net theory * supervisory control theory (SCT) to be discussed in a united and closed form, with their individual advantages combined. History and applications Originally inspired by the design and testing of switching circuits and the utilization of error-correcting codes in electrical engineering, the roots for the development of what later would evolve into the Boolean differential calculus were initiated by works of Irving S. Reed, Dav ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boolean Algebra
In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth values ''true'' and ''false'', usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers. Second, Boolean algebra uses logical operators such as conjunction (''and'') denoted as ∧, disjunction (''or'') denoted as ∨, and the negation (''not'') denoted as ¬. Elementary algebra, on the other hand, uses arithmetic operators such as addition, multiplication, subtraction and division. So Boolean algebra is a formal way of describing logical operations, in the same way that elementary algebra describes numerical operations. Boolean algebra was introduced by George Boole in his first book ''The Mathematical Analysis of Logic'' (1847), and set forth more fully in his '' An Investigation of the Laws of Thought'' (1854). According to Huntington, the term "Boolean algebr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential (mathematics)
In mathematics, differential refers to several related notions derived from the early days of calculus, put on a rigorous footing, such as infinitesimal differences and the derivatives of functions. The term is used in various branches of mathematics such as calculus, differential geometry, algebraic geometry and algebraic topology. Introduction The term differential is used nonrigorously in calculus to refer to an infinitesimal ("infinitely small") change in some varying quantity. For example, if ''x'' is a variable, then a change in the value of ''x'' is often denoted Δ''x'' (pronounced '' delta x''). The differential ''dx'' represents an infinitely small change in the variable ''x''. The idea of an infinitely small or infinitely slow change is, intuitively, extremely useful, and there are a number of ways to make the notion mathematically precise. Using calculus, it is possible to relate the infinitely small changes of various variables to each other mathematically ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Operator
In mathematics, a differential operator is an operator defined as a function of the differentiation operator. It is helpful, as a matter of notation first, to consider differentiation as an abstract operation that accepts a function and returns another function (in the style of a higher-order function in computer science). This article considers mainly linear differential operators, which are the most common type. However, non-linear differential operators also exist, such as the Schwarzian derivative. Definition An order-m linear differential operator is a map A from a function space \mathcal_1 to another function space \mathcal_2 that can be written as: A = \sum_a_\alpha(x) D^\alpha\ , where \alpha = (\alpha_1,\alpha_2,\cdots,\alpha_n) is a multi-index of non-negative integers, , \alpha, = \alpha_1 + \alpha_2 + \cdots + \alpha_n, and for each \alpha, a_\alpha(x) is a function on some open domain in ''n''-dimensional space. The operator D^\alpha is interpreted as D^\ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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Lattice (module)
Lattice may refer to: Arts and design * Latticework, an ornamental criss-crossed framework, an arrangement of crossing laths or other thin strips of material * Lattice (music), an organized grid model of pitch ratios * Lattice (pastry), an ornamental pattern of crossing strips of pastry Companies * Lattice Engines, a technology company specializing in business applications for marketing and sales * Lattice Group, a former British gas transmission business * Lattice Semiconductor, a US-based integrated circuit manufacturer Science, technology, and mathematics Mathematics * Lattice (group), a repeating arrangement of points ** Lattice (discrete subgroup), a discrete subgroup of a topological group whose quotient carries an invariant finite Borel measure ** Lattice (module), a module over a ring which is embedded in a vector space over a field ** Lattice graph, a graph that can be drawn within a repeating arrangement of points ** Lattice-based cryptography, encryption systems b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] " target=_blank style="text-decoration:none;"> [Bing] --> " target=_blank style="text-decoration:none;"> [Yahoo] --> " target=_blank style="text-decoration:none;"> [DuckDuckGo] --> [Baidu] |
Multi-valued Function
In mathematics, a multivalued function, also called multifunction, many-valued function, set-valued function, is similar to a function, but may associate several values to each input. More precisely, a multivalued function from a domain to a codomain associates each in to one or more values in ; it is thus a serial binary relation. Some authors allow a multivalued function to have no value for some inputs (in this case a multivalued function is simply a binary relation). However, in some contexts such as in complex analysis (''X'' = ''Y'' = C), authors prefer to mimic function theory as they extend concepts of the ordinary (single-valued) functions. In this context, an ordinary function is often called a single-valued function to avoid confusion. The term ''multivalued function'' originated in complex analysis, from analytic continuation. It often occurs that one knows the value of a complex analytic function f(z) in some neighbourhood of a point z=a. This is the cas ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Communication Protocol
A communication protocol is a system of rules that allows two or more entities of a communications system to transmit information via any kind of variation of a physical quantity. The protocol defines the rules, syntax, semantics and synchronization of communication and possible error recovery methods. Protocols may be implemented by hardware, software, or a combination of both. Communicating systems use well-defined formats for exchanging various messages. Each message has an exact meaning intended to elicit a response from a range of possible responses pre-determined for that particular situation. The specified behavior is typically independent of how it is to be implemented. Communication protocols have to be agreed upon by the parties involved. To reach an agreement, a protocol may be developed into a technical standard. A programming language describes the same for computations, so there is a close analogy between protocols and programming languages: ''protocols are to co ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Digital Network
A computer network is a set of computers sharing resources located on or provided by network nodes. The computers use common communication protocols over digital interconnections to communicate with each other. These interconnections are made up of telecommunication network technologies, based on physically wired, optical, and wireless radio-frequency methods that may be arranged in a variety of network topologies. The nodes of a computer network can include personal computers, servers, networking hardware, or other specialised or general-purpose hosts. They are identified by network addresses, and may have hostnames. Hostnames serve as memorable labels for the nodes, rarely changed after initial assignment. Network addresses serve for locating and identifying the nodes by communication protocols such as the Internet Protocol. Computer networks may be classified by many criteria, including the transmission medium used to carry signals, bandwidth, communications protocol ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Discrete Event Dynamic System
In control engineering, a discrete-event dynamic system (DEDS) is a discrete-state, event-driven system of which the state evolution depends entirely on the occurrence of asynchronous discrete events over time. Although similar to continuous-variable dynamic systems (CVDS), DEDS consists solely of discrete state spaces and event-driven state transition mechanisms. Topics in DEDS include: * Automata theory * Supervisory control theory * Petri net theory * Discrete event system specification * Boolean differential calculus * Markov chain * Queueing theory * Discrete-event simulation * Concurrent estimation References * * * {{cite book , author-last1=Kumar , author-first1=Ratnesh , author-last2=Garg , author-first2=Vijay K. , date=1995 , title=Modeling and Control of Logical Discrete Event Systems , publisher=Springer Springer or springers may refer to: Publishers * Springer Science+Business Media, aka Springer International Publishing, a worldwide publishing group founded i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Christian Posthoff
Christians () are people who follow or adhere to Christianity, a monotheistic Abrahamic religion based on the life and teachings of Jesus Christ. The words ''Christ'' and ''Christian'' derive from the Koine Greek title ''Christós'' (Χριστός), a translation of the Biblical Hebrew term ''mashiach'' (מָשִׁיחַ) (usually rendered as ''messiah'' in English). While there are diverse interpretations of Christianity which sometimes conflict, they are united in believing that Jesus has a unique significance. The term ''Christian'' used as an adjective is descriptive of anything associated with Christianity or Christian churches, or in a proverbial sense "all that is noble, and good, and Christ-like." It does not have a meaning of 'of Christ' or 'related or pertaining to Christ'. According to a 2011 Pew Research Center survey, there were 2.2 billion Christians around the world in 2010, up from about 600 million in 1910. Today, about 37% of all Christians live in the A ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Jean-Pierre Deschamps
Jean-Pierre or Jean Pierre may refer to: People * Karine Jean-Pierre b.1977, White House Deputy Press Secretary for President Joe Biden 2021- * Jean-Pierre, Count of Montalivet (1766–1823), French statesman and Peer of France * Eugenia Pierre (better known as Jean Pierre, 1944–2002), Trinidadian netballer and parliamentarian Places * Jean-Pierre Bay, on the Gouin Reservoir in Quebec, Canada Arts and entertainment *"Jean Pierre", song by Miles Davis from ''Miles! Miles! Miles!'' * Jean-Pierre, chef on television series ''Metalocalypse'' * Jean-Pierre Delmas, in French animated television series ''Code Lyoko'' * Jean Pierre, a character in ''Fighter's History is a series of fighting games that were produced by Data East during the 1990s. The original ''Fighter's History'' was first released for the arcades in 1993 and ported to the Super Nintendo Entertainment System in 1994. Two different seque ...'' * Jean Pierre Polnareff, a character from ''JoJo's Bizarre Ad ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marc Davio
Marc or MARC may refer to: People * Marc (given name), people with the first name * Marc (surname), people with the family name Acronyms * MARC standards, a data format used for library cataloging, * MARC Train, a regional commuter rail system of the State of Maryland, serving Maryland, Washington, D.C., and eastern West Virginia * MARC (archive), a computer-related mailing list archive * M/A/R/C Research, a marketing research and consulting firm * Massachusetts Animal Rights Coalition, a non-profit, volunteer organization * Matador Automatic Radar Control, a guidance system for the Martin MGM-1 Matador cruise missile * Mid-America Regional Council, the Council of Governments and the Metropolitan Planning Organization for the bistate Kansas City region * Midwest Association for Race Cars, a former American stock car racing organization * Revolutionary Agrarian Movement of the Bolivian Peasantry (''Movimiento Agrario Revolucionario del Campesinado Boliviano''), a defunct right- ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
