Search results for "Number"
showing 10 items of 3939 documents
Thin bases of order h
2003
Abstract A subset A⊆ N 0 is called a basis of order h if every positive integer can be represented as a sum of h members of A . Thin bases of order h will be constructed in this paper, for each h ⩾2, where the value of lim sup A(n)/ n h is smaller than that of thin bases known so far. In the most important case h =2 it is shown that for the considered class of bases (which generalizes an ansatz of Stohr) the result is best possible up to an e >0.
Mixed intersections of non quasi-analytic classes
2008
Given two semi-regular matrices M and M' and two open subsets O and O' [resp. two compact subsets K and K'] of Rr and Rs respectively, we introduce the spaces E(M×M')(O × O') and D(M×M')(O × O') [resp. D(M×M')(K × K')]. In this paper we study their locally convex properties and the structure of their elements. This leads in [10] to tensor product representations of these spaces and to some kernel theorems.
Über die Schnittzahlen mehrfach balancierter blockpläne
1991
Abstract For a finite incidence structure D with a set X of blocks let [ X ] be the number of points common with all blocks contained in X . We define the functions M(t)(B1,…; B1)=ΣB [B1, B]…[B1,B], and, for every partition ϖ = ϖ1,…,ϖ1) of t, the function Mϖ(B1,…,B1) = Σ Πm [Bi | i ϵ Rm], sum over all decompositions {l, …, t} = R1, ⊃ … ⊃ Rl, |Rm| = ϖm. We show: If D is t-fold balanced, then M(t) = Σϖ cϖMϖ, where the, coefficients cϖ are linear combinations of the parameters b1,…,bt, the constant numbers of blocks through any l,…, t distinct points. Conversely, if the rank of the b × b-matrix ([B, B∗])B,B∗ is equal to the number ν of points and M(t) is a rational linear combination of the fu…
Kolmogorov numberings and minimal identification
1997
Abstract Identification of programs for computable functions from their graphs by algorithmic devices is a well studied problem in learning theory. Freivalds and Chen consider identification of ‘minimal’ and ‘nearly minimal’ programs for functions from their graphs. To address certain problems in minimal identification for Godel numberings, Freivalds later considered minimal identification in Kolmogorov numberings. Kolmogorov numberings are in some sense optimal numberings and have some nice properties. We prove certain separation results for minimal identification in every Kolmogorov numbering. In addition we also compare minimal identification in Godel numberings versus minimal identifica…
On lazy representations and Sturmian graphs
2011
In this paper we establish a strong relationship between the set of lazy representations and the set of paths in a Sturmian graph associated with a real number α. We prove that for any non-negative integer i the unique path weighted i in the Sturmian graph associated with α represents the lazy representation of i in the Ostrowski numeration system associated with α. Moreover, we provide several properties of the representations of the natural integers in this numeration system.
Subvarieties of the Varieties Generated by the SuperalgebraM1, 1(E) orM2(𝒦)
2003
Abstract Let 𝒦 be a field of characteristic zero, and let us consider the matrix algebra M 2(𝒦) endowed with the ℤ2-grading (𝒦e 11 ⊕ 𝒦e 22) ⊕ (𝒦e 12 ⊕ 𝒦e 21). We define two superalgebras, ℛ p and 𝒮 q , where p and q are positive integers. We show that if 𝒰 is a proper subvariety of the variety generated by the superalgebra M 2(𝒦), then the even-proper part of the T 2-ideal of graded polynomial identities of 𝒰 asymptotically coincides with the even-proper part of the graded polynomial identities of the variety generated by the superalgebra ℛ p ⊕ 𝒮 q . This description also affords an even-asymptotic desc…
Graphes connexes représentation des entiers et équirépartition
1983
Abstract Let q be an integer ≥2 and Ω a suitable subset of {0,…,q − 1}2; C (q; Ω) denotes the set of natural integers, the pairs of successive q-adic digits of which are in Ω. If P is an irrational polynomial, the sequence (P(n): n ∈ C (q; Ω)) is uniformly distributed modulo one.
On the Distribution ofB3-Sequences
1996
Abstract An infinite set of natural numbers is called aB3-sequence if all sumsa1+a2+a3withaj∈Aanda1⩽a2⩽a3are distinct. LetA(n) be the number of positive elements ⩽ninA. P. Erdos conjectures that everyB3-sequenceAsatisfies lim infn→∞ A(n) n−1/3=0. In this paper we prove that no sequence satisfyingA(n)∼αn1/3can be aB3-sequence. We also give other necessary conditions for aB3-sequence.
Codimension growth of two-dimensional non-associative algebras
2007
Let F be a field of characteristic zero and let A be a two-dimensional non-associative algebra over F. We prove that the sequence c n (A), n =1,2,..., of codimensions of A is either bounded by n + 1 or grows exponentially as 2 n . We also construct a family of two-dimensional algebras indexed by rational numbers with distinct T-ideals of polynomial identities and whose codimension sequence is n + 1, n > 2.
On the family ofr-regular graphs with Grundy numberr+1
2014
Abstract The Grundy number of a graph G , denoted by Γ ( G ) , is the largest k such that there exists a partition of V ( G ) , into k independent sets V 1 , … , V k and every vertex of V i is adjacent to at least one vertex in V j , for every j i . The objects which are studied in this article are families of r -regular graphs such that Γ ( G ) = r + 1 . Using the notion of independent module, a characterization of this family is given for r = 3 . Moreover, we determine classes of graphs in this family, in particular, the class of r -regular graphs without induced C 4 , for r ≤ 4 . Furthermore, our propositions imply results on the partial Grundy number.