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...$T$ is a finite set of symbols called ''transitions'', $P$ is a finite set of symbols called ''places'', $P \cap T = \emptyset$, $F$ is an incidence func ...aking, a Petri net is a labelled oriented [[bipartite graph]] having a set of vertices $T \cup P$ (see Figure, in which $P = \{p_1,p_2,p_3\}$, $T = \{a,b

$#C+1 = 37 : ~/encyclopedia/old_files/data/M062/M.0602040 Machine ''(in mathematics)''

$#C+1 = 2 : ~/encyclopedia/old_files/data/F040/F.0400950 Fortran One of the original programming languages for problems of computational mathematics, developed in 1954–1956 for the IBM 704 machine, and in the version Fortr

$#C+1 = 10 : ~/encyclopedia/old_files/data/F042/F.0402110 Functional system ...f propositions with logical operations on them; and from the point of view of algebra, as universal algebras.

...ed in mathematics is continuously expanding; so this general definition of mathematics becomes ever richer in content. ...he first problems of mechanics and physics were already in this collection of fundamental mathematical ideas.

$#C+1 = 189 : ~/encyclopedia/old_files/data/C022/C.0202890 Coding and decoding ...on of it. In the mathematical literature an encoding (coding) is a mapping of an arbitrary set $ A $

...ighted by the author(s), the article has been donated to ''Encyclopedia of Mathematics'', and its further issues are under ''Creative Commons Attribution Share-Al of characteristic functions; concepts such as 'closeness' and 'asymptotic

$#C+1 = 48 : ~/encyclopedia/old_files/data/I052/I.0502130 Intuitionism ...proach to the definition of mathematical concepts, as well as certain ways of reasoning customary in classical logic.

...ighted by the author(s), the article has been donated to ''Encyclopedia of Mathematics'', and its further issues are under ''Creative Commons Attribution Share-Al '''Summary.''' Founding Director of the Central Bureau of Statistics in

$#C+1 = 33 : ~/encyclopedia/old_files/data/A011/A.0101910 Algorithms, theory of ...he concept of an algorithm more precise by the introduction of the concept of a [[Normal algorithm|normal algorithm]] [[#References|[10]]]. A.N. Kolmogor

$#C+1 = 207 : ~/encyclopedia/old_files/data/E036/E.0306230 Error\AAhcorrecting code, ...or other. For example, the sequence of symbols may be divided into blocks of a fixed length $ k $,

...ighted by the author(s), the article has been donated to ''Encyclopedia of Mathematics'', and its further issues are under ''Creative Commons Attribution Share-Al Biostatistics Unit, Department of Public Heath

...ighted by the author(s), the article has been donated to ''Encyclopedia of Mathematics'', and its further issues are under ''Creative Commons Attribution Share-Al Department of Economics, European University Institute, Via della

$#C+1 = 169 : ~/encyclopedia/old_files/data/A012/A.0102980 Approximation of functions, linear methods by means of functions in $ \mathfrak N $.

"a history of Hilbert’s program for the foundations of mathematics, initiated by his Problems Address given in Paris, 1900" -- see [[Hilbert p ...ed to” (proved indirectly as a result of proving directly) the consistency of analysis:<ref>Hilbert (1902) §2</ref>

$#C+1 = 54 : ~/encyclopedia/old_files/data/W097/W.0907750 White noise ...[Spectral density|spectral density]]. The generalized correlation function of white noise has the form $ B( t) = \sigma ^ {2} \delta ( t) $,

$#C+1 = 123 : ~/encyclopedia/old_files/data/C027/C.0207480 Cybernetics ...used as a research technique in other sciences. Furthermore, the spectrum of problems amenable to investigation by cybernetic methods is, by comparison

$#C+1 = 163 : ~/encyclopedia/old_files/data/I110/I.1100020 Idempotent analysis, ...mpotent calculus) is well established in the literature since the activity of V.P. Maslov and his collaborators (see e.g. [[#References|[a1]]], [[#Refere

...lopedia/old_files/data/O068/O.0608430 Optimal control, mathematical theory of ...y be chosen according to certain constraints prescribed by the formulation of the problem.

$#C+1 = 92 : ~/encyclopedia/old_files/data/R082/R.0802480 Rings and algebras has no divisors of zero, that is, if $ x y \neq 0 $

...ighted by the author(s), the article has been donated to ''Encyclopedia of Mathematics'', and its further issues are under ''Creative Commons Attribution Share-Al <center>''University of Saint-Petersburg''</center>

$#C+1 = 198 : ~/encyclopedia/old_files/data/A012/A.0102950 Approximation of functions The replacement, according to a definite rule, of a function by a function $ \phi $

...ighted by the author(s), the article has been donated to ''Encyclopedia of Mathematics'', and its further issues are under ''Creative Commons Attribution Share-Al Mixture distributions are convex combinations of ''component''

$#C+1 = 231 : ~/encyclopedia/old_files/data/O070/O.0700310 Orthogonal Latin squares A pair of Latin squares (cf. [[Latin square|Latin square]]) $ A = \| a _ {ij} \| $,

$#C+1 = 58 : ~/encyclopedia/old_files/data/M062/M.0602710 Mathematical statistics ...al conclusions. Here, by statistical data is meant information on a number of objects in some, more or less extensive, collection, which have some specif

...ighted by the author(s), the article has been donated to ''Encyclopedia of Mathematics'', and its further issues are under ''Creative Commons Attribution Share-Al intend to share with others. Wide dissemination of data facilitates advances in science

$#C+1 = 87 : ~/encyclopedia/old_files/data/N067/N.0607900 Number ...f mathematics on the other, have determined the development of the concept of a number.

...ighted by the author(s), the article has been donated to ''Encyclopedia of Mathematics'', and its further issues are under ''Creative Commons Attribution Share-Al scoundrel, was the most important developer of statistical graphics.

...ighted by the author(s), the article has been donated to ''Encyclopedia of Mathematics'', and its further issues are under ''Creative Commons Attribution Share-Al '''Summary''' Pascal introduced the concept of mathematical expectation and

$#C+1 = 196 : ~/encyclopedia/old_files/data/C027/C.0207180 Cryptology ...lar [[#References|[a13]]], for a detailed historical perspective. For more information and additional references on the topics treated here, see [[#References|[a3

...ighted by the author(s), the article has been donated to ''Encyclopedia of Mathematics'', and its further issues are under ''Creative Commons Attribution Share-Al '''Summary.''' From a strictly statistical point of view, Gini's

...ighted by the author(s), the article has been donated to ''Encyclopedia of Mathematics'', and its further issues are under ''Creative Commons Attribution Share-Al prominent exponent of 19th

$#C+1 = 85 : ~/encyclopedia/old_files/data/T092/T.0902980 Tomography ...iqueness and stability of inversion procedures, as well as the development of efficient numerical algorithms. In tomography a fundamental role is played

...ighted by the author(s), the article has been donated to ''Encyclopedia of Mathematics'', and its further issues are under ''Creative Commons Attribution Share-Al ...e carefully designed and implemented. This entry focuses on the estimation of such finite population parameters using what is known as the randomization

$#C+1 = 164 : ~/encyclopedia/old_files/data/C024/C.0204230 Complexity theory ...s, such as systems for deciding the equivalence of programs or the halting of a program.

$#C+1 = 254 : ~/encyclopedia/old_files/data/K055/K.0505600 Knot theory The study of the imbedding of a $ 1 $-

...ighted by the author(s), the article has been donated to ''Encyclopedia of Mathematics'', and its further issues are under ''Creative Commons Attribution Share-Al the statistics of his day from a modest collection of useful ad hoc

...ighted by the author(s), the article has been donated to ''Encyclopedia of Mathematics'', and its further issues are under ''Creative Commons Attribution Share-Al population or a part of it, such as the residents of a country or the

$#C+1 = 81 : ~/encyclopedia/old_files/data/A014/A.0104120 Automaton ...modifications which reflect various features of real systems. In the case of a finite automaton $ (A, S, B, \phi , \psi ) $

$#C+1 = 144 : ~/encyclopedia/old_files/data/S091/S.0901910 Synthesis problems ...the elements, a rule for combining them and a means of using the structure of the control system to define the function which it realizes are given.

$#C+1 = 88 : ~/encyclopedia/old_files/data/M062/M.0602210 Manifold ...t which locally has the structure (topological, smooth, homological, etc.) of $ \mathbf R ^ {n} $

$#C+1 = 249 : ~/encyclopedia/old_files/data/M062/M.0602620 Mathematical economics ...Of particular significance is the connection with the science and practice of economics.

$#C+1 = 499 : ~/encyclopedia/old_files/data/D032/D.0302450 Dimension ''of a topological space $ X $''

...'the discretization program'".</ref>These efforts took place over a period of about 50 years, with the following results: # the establishment of fundamental concepts related to limits

...ighted by the author(s), the article has been donated to ''Encyclopedia of Mathematics'', and its further issues are under ''Creative Commons Attribution Share-Al Department of Statistics

$#C+1 = 498 : ~/encyclopedia/old_files/data/N067/N.0607520 Normal form The normal form of a matrix $ A $

...tatement of his 2nd problem, initiating his program for the foundations of mathematics'' -- see [[Hilbert problems]] By about 1820, mathematicians had developed deductively a large part of analysis using the real numbers and their properties as a starting point.