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De Bruijn
De Bruijn is a Dutch surname meaning "the brown". Notable people with the surname include: * (1887–1968), Dutch politician * Brian de Bruijn (b. 1954), Dutch-Canadian ice hockey player * Chantal de Bruijn (b. 1976), Dutch field hockey defender * Cornelis de Bruijn (1652–1726/7), Dutch artist and traveler * Daniëlle de Bruijn (b. 1978), Dutch water polo player * Frans de Bruijn Kops (1886–1979), Dutch footballer * Hans de Bruijn (b. 1962), Dutch political scientist * Inge de Bruijn (b. 1973), Dutch swimmer * (born 1965), Dutch billiards player * Jean Victor de Bruijn (1913–1979), Dutch district officer and ethnologist in the Dutch East Indies * Maarten de Bruijn (b. 1965), Dutch engineer * Maria Brigitta Catherina de Bruijn (1938–2006), Dutch GreenLeft politician * Matthijs de Bruijn (b. 1977), Dutch waterpolo player * Meike de Bruijn (born 1970), Dutch racing cyclist * Nick de Bruijn (b. 1987), Dutch racing driver * Nicolaas Govert de Bruijn (1918–2012), Dutch mathemat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
De Bruijn Sequence
In combinatorial mathematics, a de Bruijn sequence of order ''n'' on a size-''k'' alphabet ''A'' is a cyclic sequence in which every possible length-''n'' string on ''A'' occurs exactly once as a substring (i.e., as a ''contiguous'' subsequence). Such a sequence is denoted by and has length , which is also the number of distinct strings of length ''n'' on ''A''. Each of these distinct strings, when taken as a substring of , must start at a different position, because substrings starting at the same position are not distinct. Therefore, must have ''at least'' symbols. And since has ''exactly'' symbols, De Bruijn sequences are optimally short with respect to the property of containing every string of length ''n'' at least once. The number of distinct de Bruijn sequences is :\dfrac. The sequences are named after the Dutch mathematician Nicolaas Govert de Bruijn, who wrote about them in 1946. As he later wrote, the existence of de Bruijn sequences for each order together ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Nicolaas Govert De Bruijn
Nicolaas Govert (Dick) de Bruijn (; 9 July 1918 – 17 February 2012) was a Dutch mathematician, noted for his many contributions in the fields of analysis, number theory, combinatorics and logic.Nicolaas Govert de Bruijn's obituary 2012 Biography De Bruijn was born in where he attended elementary school between 1924 and 1930 and secondary school until 1934. He started studies in mathematics at in 1936 but his studies were interrupted by the outbreak of |
Brian De Bruijn
Brian Austin de Bruijn (born September 4, 1954) is a former Dutch-Canadian ice hockey player. He played for the Netherlands men's national ice hockey team at the 1980 Winter Olympics The 1980 Winter Olympics, officially the XIII Olympic Winter Games and also known as Lake Placid 1980, were an international multi-sport event held from February 13 to 24, 1980, in Lake Placid, New York, United States. Lake Placid was elected ... in Lake Placid. References External links * 1954 births Living people Ice hockey players at the 1980 Winter Olympics Olympic ice hockey players for the Netherlands Dutch ice hockey forwards De Bruijn, Brian De Bruijn, Brian Heerenveen Flyers players Nijmegen Tigers players Tilburg Trappers players Canadian people of Dutch descent {{Netherlands-icehockey-bio-stub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
De Bruin
De Bruin is a Dutch surname meaning "the brown" or "the brown one". It is common in the Netherlands (17,650 people in 2007). at the Meertens Institute database of surnames in the Netherlands. People named "de Bruin" include: * (b. 1993), South African rugby player * (b. 1989), Canadian bobsledder. * (b. 1976), Dutch discus thr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
De Bruyn
De Bruyn is a Dutch and Afrikaans surname. "Bruyn" or "bruijn" is an archaic spelling of "bruin", meaning "brown". People with the name include: * Aad de Bruyn (1910–1991), Dutch 35-fold national champion in discus, shot put and hammer throw *Abraham de Bruyn (c.1539–1587), Flemish engraver * Anna Maria de Bruyn (1708–1744), Dutch stage actress and ballet dancer *Brian de Bruyn (b. 1954), Canadian-born Dutch ice hockey player *Erik de Bruyn (b. 1962), Dutch film director and actor *Ettiene de Bruyn (b. 1977), South African cricketer *Frans De Bruyn (1924–2014), Flemish writer *Günter de Bruyn (1926–2020), German author *Joe de Bruyn (b. 1949), Australian trade union official *John de Bruyn (b. 1956), Dutch-Canadian ice hockey goaltender * (1838–1908), Belgian politician *Michelle De Bruyn (b. 1965), New Zealand professional football player *Nicolaes de Bruyn (1571–1656), Flemish engraver * Paul de Bruyn (1907–1997), German-American marathon runner *Pierre de Bruyn (b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
De Bruijn's Theorem
In a 1969 paper, Dutch mathematician Nicolaas Govert de Bruijn proved several results about packing congruent rectangular bricks (of any dimension) into larger rectangular boxes, in such a way that no space is left over. One of these results is now known as de Bruijn's theorem. According to this theorem, a "harmonic brick" (one in which each side length is a multiple of the next smaller side length) can only be packed into a box whose dimensions are multiples of the brick's dimensions.. Example De Bruijn was led to prove this result after his then-seven-year-old son, F. W. de Bruijn, was unable to pack bricks of dimension 1\cdot 2\cdot 4 into a 6\cdot 6\cdot 6 cube. The cube has a volume equal to that of 27 bricks, but only 26 bricks may be packed into it. One way to see this is to partition the cube into 27 smaller cubes of size 2\cdot 2\cdot 2 colored alternately black and white. This coloring has more unit cells of one color than of the other, but with this coloring any placemen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
De Bruijn Notation
In mathematical logic, the De Bruijn notation is a syntax for terms in the λ calculus invented by the Dutch mathematician Nicolaas Govert de Bruijn. It can be seen as a reversal of the usual syntax for the λ calculus where the argument in an application is placed next to its corresponding binder in the function instead of after the latter's body. Formal definition Terms (M, N, \ldots) in the De Bruijn notation are either variables (v), or have one of two ''wagon'' prefixes. The ''abstractor wagon'', written /math>, corresponds to the usual λ-binder of the λ calculus, and the ''applicator wagon'', written (M), corresponds to the argument in an application in the λ calculus. :M,N,... ::=\ v\ , \ ;M\ , \ (M)\;N Terms in the traditional syntax can be converted to the De Bruijn notation by defining an inductive function \mathcal for which: \begin \mathcal(v) &= v \\ \mathcal(\lambda v.\ M) &= ;\mathcal(M) \\ \mathcal(M\;N) &= (\mathcal(N))\mathcal(M). \end All opera ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
De Bruijn–Newman Constant
The de Bruijn–Newman constant, denoted by Λ and named after Nicolaas Govert de Bruijn and Charles M. Newman, is a mathematical constant defined via the zero of a function, zeros of a certain function (mathematics), function ''H''(''λ'', ''z''), where ''λ'' is a real number, real parameter and ''z'' is a complex number, complex variable. More precisely, :H(\lambda, z):=\int_^ e^ \Phi(u) \cos (z u) d u, where \Phi is the super-exponential function, super-exponentially decaying function :\Phi(u) = \sum_^ (2\pi^2n^4e^ - 3 \pi n^2 e^ ) e^ and Λ is the unique real number with the property that ''H'' has only real zeros if and only if ''λ'' ≥ Λ. The constant is closely connected with Riemann hypothesis, Riemann's hypothesis concerning the zeros of the Riemann zeta function, Riemann zeta-function: since the Riemann hypothesis is equivalent to the claim that all the zeroes of ''H''(0, ''z'') are real, the Riemann hypothesis is equivalent to the conjecture tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
De Bruijn Index
In mathematical logic, the De Bruijn index is a tool invented by the Dutch mathematician Nicolaas Govert de Bruijn for representing terms of lambda calculus without naming the bound variables. Terms written using these indices are invariant with respect to α-conversion, so the check for α-equivalence is the same as that for syntactic equality. Each De Bruijn index is a natural number that represents an occurrence of a variable in a λ-term, and denotes the number of binders that are in scope between that occurrence and its corresponding binder. The following are some examples: * The term λ''x''. λ''y''. ''x'', sometimes called the K combinator, is written as λ λ 2 with De Bruijn indices. The binder for the occurrence ''x'' is the second λ in scope. * The term λ''x''. λ''y''. λ''z''. ''x'' ''z'' (''y'' ''z'') (the S combinator), with De Bruijn indices, is λ λ λ 3 1 (2 1). * The term λ''z''. (λ''y''. ''y'' (λ''x''. ''x'')) (λ''x''. ''z'' ''x'') is λ (λ 1 (λ 1) ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
De Bruijn–Erdős Theorem (incidence Geometry)
In incidence geometry, the De Bruijn–Erdős theorem, originally published by , states a lower bound on the number of lines determined by ''n'' points in a projective plane. By Duality (projective geometry), duality, this is also a bound on the number of intersection points determined by a configuration of lines. Although the proof given by De Bruijn and Erdős is Combinatorial proof, combinatorial, De Bruijn and Erdős noted in their paper that the analogous (Euclidean geometry, Euclidean) result is a consequence of the Sylvester–Gallai theorem, by an Mathematical induction, induction on the number of points. Statement of the theorem Let ''P'' be a configuration of ''n'' points in a projective plane, not all on a line. Let ''t'' be the number of lines determined by ''P''. Then, * ''t'' ≥ ''n'', and * if ''t'' = ''n'', any two lines have exactly one point of ''P'' in common. In this case, ''P'' is either a projective plane or ''P'' is a ''near pencil'', meaning that e ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
De Bruijn–Erdős Theorem (graph Theory)
In graph theory, the De Bruijn–Erdős theorem relates graph coloring of an infinite graph to the same problem on its finite subgraphs. It states that, when all finite subgraphs can be colored with c colors, the same is true for the whole graph. The theorem was proved by Nicolaas Govert de Bruijn and Paul Erdős (1951), after whom it is named. The De Bruijn–Erdős theorem has several different proofs, all depending in some way on the axiom of choice. Its applications include extending the four-color theorem and Dilworth's theorem from finite graphs and partially ordered sets to infinite ones, and reducing the Hadwiger–Nelson problem on the chromatic number of the plane to a problem about finite graphs. It may be generalized from finite numbers of colors to sets of colors whose cardinality is a strongly compact cardinal. Definitions and statement An undirected graph is a mathematical object consisting of a set of vertices and a set of edges that link pairs of vertices. Th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
