共查询到20条相似文献,搜索用时 31 毫秒
1.
Mourad E.H Ismail Thanaa M.T Rashed 《Journal of Mathematical Analysis and Applications》1977,57(3):724-731
We study expansions in polynomials {Pn(x)}∞o generated by ∑∞n = oPn(x)tn = A(t) φ(xtkθ(t)), θ(0) ≠ 0, and ∑∞n = 0Pn(x)tn = ∑kj = 1Aj(t) φ(xt?j), ?1,…,?k being the k roots of unity. The case k = 1 is contained in a recent work by Fields and Ismail. We also prove a new generalization of Vandermond's inverse relations. 相似文献
2.
Steven M Serbin 《Journal of Mathematical Analysis and Applications》1977,57(1):27-35
We consider the problem of the identification of the time-varying matrix A(t) of a linear m-dimensional differential system y′ = A(t)y. We develop an approximation An,k = ∑nj ? 1cj{Y(tk + τj) Y?1(tk) ? I} to A(tk) for grid points tk = a + kh, k = 0,…, N using specified τj = θjh, 0 < θj < 1, j = 1, …, n, and show that for each tk, the L1 norm of the error matrix is (hn). We demonstrate an efficient scheme for the evaluation of An,k and treat sample problems. 相似文献
3.
In this paper we discuss a combinatorial problem involving graphs and matrices. Our problem is a matrix analogue of the classical problem of finding a system of distinct representatives (transversal) of a family of sets and relates closely to an extremal problem involving 1-factors and a long standing conjecture in the dimension theory of partially ordered sets. For an integer n ?1, let n denote the n element set {1,2,3,…, n}. Then let A be a k×t matrix. We say that A satisfies property P(n, k) when the following condition is satisfied: For every k-taple (x1,x2,…,xk?nk there exist k distinct integers j1,j2,…,jk so that xi= aii for i= 1,2,…,k. The minimum value of t for which there exists a k × t matrix A satisfying property P(n,k) is denoted by f(n,k). For each k?1 and n sufficiently large, we give an explicit formula for f(n, k): for each n?1 and k sufficiently large, we use probabilistic methods to provide inequalities for f(n,k). 相似文献
4.
S. A. Pichugov 《Mathematical Notes》2014,96(1-2):261-267
It is proved that, in the space L ∞[0, 2π], the following equalities hold for all k = 0, 1, 2, …, n ∈ ?, r = 1, 3, 5, …, µ≥ r: where E n?1(f) and E n,µ (f) are the best approximations of f by, respectively, trigonometric polynomials of degree n ? 1 and 2π-periodic splines of minimal deficiency of order µ with 2n equidistant nodes, ω(f (r), h) is the modulus of continuity of f (r), Ψ r,2k+1 is the rth periodic integral of the special function Ψ 0,2k+1, which is odd and piecewise constant on the partition jπ/(2k + 1), j ∈ ?. For k = 0, this result was obtained earlier by Ligun. 相似文献
5.
HE Dan LIN Wen-song 《高校应用数学学报(英文版)》2014,29(2):230-240
For a graph G and two positive integers j and k, an m-L(j, k)-edge-labeling of G is an assignment on the edges to the set {0, 1, 2,..., m}, such that adjacent edges which receive labels differ at least by j, and edges which are distance two apart receive labels differ at least by kThe λ j,k-number of G is the minimum m such that an m-L(j, k)-edge-labeling is admitted by GIn this article, the L(1, 2)-edge-labeling for the hexagonal lattice, the square lattice and the triangular lattice are studied, and the bounds for λ j,k-numbers of these graphs are obtained. 相似文献
6.
F. De Vylder 《Insurance: Mathematics and Economics》1983,2(3):139-145
Let Lj (j = 1, …, n + 1) be real linear functions on the convex set of probability distributions. We consider the problem of maximization of Ln+1(F) under the constraint F ? and the equality constraints L1(F) = z1 (i = 1, …, n). Incorporating some of the equality constraints into the basic set , the problem is equivalent to a problem with less equality constraints. We also show how the dual problems can be eliminated from the statement of the main theorems and we give a new illuminating proof of the existence of particular solutions.The linearity of the functions Lj(j = 1, …, n + 1) can be dropped in several results. 相似文献
7.
Richard P Stanley 《Journal of Combinatorial Theory, Series A》1973,14(2):209-214
Let (r1, r2, …) be a sequence of non-negative integers summing to n. We determine under what conditions there exists a finite distributive lattice L of rank n with ri join-irreducibles of rank i, for all i = 1, 2, …. When L exists, we give explicit expressions for the greatest number of elements L can have of any given rank, and for the greatest total number of elements L can have. The problem is also formulated in terms of finite topological spaces. 相似文献
8.
R.S. Singh 《Journal of multivariate analysis》1976,6(2):338-342
Let Xj = (X1j ,…, Xpj), j = 1,…, n be n independent random vectors. For x = (x1 ,…, xp) in Rp and for α in [0, 1], let Fj(x) = αI(X1j < x1 ,…, Xpj < xp) + (1 ? α) I(X1j ≤ x1 ,…, Xpj ≤ xp), where I(A) is the indicator random variable of the event A. Let Fj(x) = E(Fj(x)) and Dn = supx, α max1 ≤ N ≤ n |Σ0n(Fj(x) ? Fj(x))|. It is shown that P[Dn ≥ L] < 4pL exp{?2(L2n?1 ? 1)} for each positive integer n and for all L2 ≥ n; and, as n → ∞, with probability one. 相似文献
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Using old results on the explicit calculation of determinants, formulae are given for the coefficients of P0(z) and P0(z)fi(z) ? Pi(z), where Pi(z) are polynomials of degree σ ? ρi (i=0,1,…,n), P0(z)fi(z) ? Pi(z) are power series in which the terms with zk, 0?k?σ, vanish (i=1,2,…,n), (ρ0,ρ1,…,ρn) is an (n+1)-tuple of nonnegative integers, σ=ρ0+ρ1+?+ρn, and {fi}ni=1 is the set of hypergeometric functions {1F1(1;ci;z)}ni=1 or {2F0(ai,1;z)}ni=1 under the condition ρ0?ρi ? 1 (i=1,2,…,n). 相似文献
12.
Zoltán Finta 《Central European Journal of Mathematics》2013,11(12):2257-2261
For certain generalized Bernstein operators {L n } we show that there exist no i, j ∈ {1, 2, 3,…}, i < j, such that the functions e i (x) = x i and e j (x) = x j are preserved by L n for each n = 1, 2,… But there exist infinitely many e i such that e 0(x) = 1 and e j (x) = x j are its fixed points. 相似文献
13.
Allan M Krall 《Journal of Mathematical Analysis and Applications》1979,70(1):267-279
When ?j ? 1 < α < ?j, where j is a positive integer, the Laguerre polynomials {Ln(α)}n = 0∞ form a complete orthogonal set in a nondegenerate inner product space H which is defined by employing an appropriate regularized linear functional on H(j)[[0, ∞); xα + je?x]. Expansions in terms of these Laguerre polynomials are exhibited. The Laguerre differential operator is shown to be self-adjoint with real, discrete, integer eigenvalues. Its spectral resolution and resolvent are exhibited and discussed. 相似文献
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Michael L Fredman 《Journal of Combinatorial Theory, Series A》1975,18(2):199-202
Let S(n, k, v) denote the number of vectors (a0,…, an?1) with nonnegative integer components that satisfy a0 + … + an ? 1 = k and Σi=0n?1iai ≡ v (mod n). Two proofs are given for the relation S(n, k, v) = S(k, n, v). The first proof is by algebraic enumeration while the second is by combinatorial construction. 相似文献
16.
Jarmila Chvátalová 《Discrete Mathematics》1975,11(3):249-253
If G is a graph with p vertices and at least one edge, we set φ (G) = m n max |f(u) ? f(v)|, where the maximum is taken over all edges uv and the minimum over all one-to-one mappings f : V(G) → {1, 2, …, p}: V(G) denotes the set of vertices of G.Pn will denote a path of length n whose vertices are integers 1, 2, …, n with i adjacent to j if and only if |i ? j| = 1. Pm × Pn will denote a graph whose vertices are elements of {1, 2, …, m} × {1, 2, …, n} and in which (i, j), (r, s) are adjacent whenever either i = r and |j ? s| = 1 or j = s and |i ? r| = 1.Theorem.If max(m, n) ? 2, thenφ(Pm × Pn) = min(m, n). 相似文献
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Real constant coefficient nth order elliptic operators, Q, which generate strongly continuous semigroups on L2(k) are analyzed in terms of the elementary generator, , for n even. Integral operators are defined using the fundamental solutions pn(x, t) to ut = Au and using real polynomials ql,…, qk on m by the formula, for q = (ql,…, qk), m. It is determined when, strongly on L2(k), . If n = 2 or k = 1, this can always be done. Otherwise the symbol of Q must have a special form. 相似文献
19.
G.F Clements 《Journal of Combinatorial Theory, Series A》1984,37(1):91-97
Let kn ? kn?1 ? … ? k1 be positive integers and let () denote the coefficient of xi in . For given integers l, m, where 1 ? l ? kn + kn?1 + … + k1 and , it is shown that there exist unique integers m(l), m(l ? 1),…, m(t), satisfying certain conditions, for which . Moreover, any m l-subsets of a multiset with ki elements of type i, i = 1, 2,…, n, will contain at least different (l ? 1)-subsets. This result has been anticipated by Greene and Kleitman, but the formulation there is not completely correct. If k1 = 1, the numbers () are binomial coefficients and the result is the Kruskal-Katona theorem. 相似文献
20.
O. N. Kosukhin 《Mathematical Notes》2012,92(5-6):779-789
For any natural number n and any C > 0, we obtain an integral formula for calculating the lengths |L(P n , C)| of the lemniscates $$L\left( {P_n ,C} \right): = \left\{ {z:\left| {P_n \left( z \right)} \right| = C} \right\}$$ of algebraic polynomials P n (z):= z n + c n?1 z n?1 + ... + c 0 in the complex variable z with complex coefficients c j , j = 0, ..., n ? 1, and establish the upper bound for the quantities $$\lambda _n : = \sup \left\{ {\left| {L\left( {P_n ,1} \right)} \right|:P_n (z)} \right\},$$ which is currently best for 3 ≤ n ≤ 1014. We also study the properties of the derivative S′(C) of the area function S(C) of the set {z: |P n (z)| ≤ C}. 相似文献