共查询到20条相似文献,搜索用时 31 毫秒
1.
Mourad E.H Ismail 《Journal of Mathematical Analysis and Applications》1985,108(2):575-594
A single serving queueing model is studied where potential customers are discouraged at the rate λn = λqn, 0 < q < 1, n is the queue length. The serving rate is μn = μ(1 ? qn), n = 0, 1,…. The spectral function is computed and the corresponding set of orthogonal polynomials is studied in detail. The slightly more general model with and the analogous orthogonal polynomials are also investigated. In both cases a method developed by Pollaczek is used which has been used very successfully to study new sets of orthogonal polynomials by Askey and Ismail. 相似文献
2.
Z Füredi 《Journal of Combinatorial Theory, Series B》1983,34(2):187-190
Let f(n) denote the maximum number of edges of a graph on n vertices not containing a circuit of length 4. It is well known that . The old conjecture is proved for infinitely many q (whenever q = 2k). 相似文献
3.
4.
Peter Wolfe 《Journal of Functional Analysis》1980,36(1):105-113
Let Lu be the integral operator defined by where S is the interior of a smooth, closed Jordan curve in the plane, k is a complex number with Re k ? 0, Im k ? 0, and ?2 = (x ?x′)2 + (y ? y′)2. We define , where in the definition of W21(q, S) the derivatives are taken in the sense of distributions. We prove that Lk is a continuous 1-l mapping of L2(q, S) onto W21(q, S). 相似文献
5.
On , n?1 and n≠2, we prove the existence of a sharp constant for Sobolev inequalities with higher fractional derivatives. Let s be a positive real number. For n>2s and any function satisfies where the operator (?Δ)s in Fourier spaces is defined by . To cite this article: A. Cotsiolis, N.C. Tavoularis, C. R. Acad. Sci. Paris, Ser. I 335 (2002) 801–804. 相似文献
6.
A.M Fink 《Journal of Mathematical Analysis and Applications》1977,61(2):404-408
We show how inequalities of the type when F(0) = 0 can be used to find lower bounds of the first eigenvalue of the integral equation F(z) = λ ∝0ak(s, z)F(s) ds. 相似文献
7.
Edward Spence 《Journal of Combinatorial Theory, Series A》1977,22(1):103-106
A construction is given for difference sets with parameters , in certain noncyclic groups of order v. For s = 1 it is shown that the construction yields all possible difference sets with parameters (36, 15, 6, 9) in an abelian group of order 36. 相似文献
8.
M.M Dodson 《Journal of Number Theory》1973,5(4):287-292
Let θ(k, pn) be the least s such that the congruence (mod pn) has a nontrivial solution. It is shown that if k is sufficiently large and divisible by p but not by p ? 1, then . We also obtain the average order of θ(k), the least s such that the above congruence has a nontrivial solution for every prime p and every positive integer n. 相似文献
9.
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
10.
In two party elections with popular vote ratio , a theoretical model suggests replacing the so-called MacMahon cube law approximation , for the ratio of candidates elected, by the ratio of the two half sums in the binomial expansion of (p+q)2k+1 for some k. This ratio is nearly when k = 6. The success probability for the power law is shown to so closely approximate , if we choose , that for . Computationally, we avoid large binomial coefficients in computing for k>22 by expressing as the sum , whose terms decrease by the factors . Setting K = 4k+3, we compute ak for the large k using a continued fraction derived from the ratio of π to the finite Wallis product approximation. 相似文献
11.
Z Füredi 《Journal of Combinatorial Theory, Series A》1982,32(1):66-72
Suppose that is a finite set-system of N elements with the property |A ∩ A′| = 0, 1 or k for any two different A, A′ ?A. We show that for N > k14 where equality holds if and only if k = q + 1 (q is a prime power) and is the set of subspaces of dimension at most two of the t-dimensional finite projective space of order q. 相似文献
12.
J.-C. Panayiotopoulos 《European Journal of Operational Research》1982,9(1):77-82
This paper deals with probabilistic analysis of optimal solutions of the asymmetric traveling salesman problem. The exact distribution for the number of required next-best solutions of the assignment problem with random data in order to find an optimal tour is given. For every n-city asymmetric problem, there exists an algorithm such that (i) with probability 1 ? s, s?(0,1) the algorithm produces an optimal tour, (ii) it runs in time , and (iii) it requires less than w((w + n ? 1) computational steps, where w = log(s)/log(1 ? En); En ?(0,1) is given by a simple mathematical formula. Additionally, the polynomial of (iii) gives the exact (deterministic) execution time to find w =1 ,2…. next-best solutions of the assignment problem. 相似文献
13.
14.
D Zwick 《Journal of Mathematical Analysis and Applications》1984,104(2):435-436
For a(1) ? a(2) ? ··· ? a(n) ? 0, b(1) ? b(2) ? ··· ? b(n) ? 0, the ordered values of ai, bi, i = 1, 2,…, n, m fixed, m ? n, and p ? 1 it is shown that where is the integer such that and . The inequality is shown to be sharp. When p < 1 and a(i)'s are in increasing order then the inequality is reversed. 相似文献
15.
Chungming An 《Journal of Number Theory》1974,6(1):1-6
A Dirichlet series associated with a positive definite form of degree δ in n variables is defined by where ? ∈ , α ∈ n, 〈x, y〉 = x1y1 + ? + xnyn, e(a) = exp (2πia) for a ∈ , and s = σ + ti is a complex number. The author proves that: (1) DF(s, ?, α) has analytic continuation into the whole s-plane, (2) DF(s, ?, α), ? ≠ 0, is a meromorphic function with at most a simple pole at . The residue at is given explicitly. (3) ? = 0, α ? n, DF(s, 0, α) is analytic for . 相似文献
16.
A mean M(u, v) is defined to be a homogeneous symmetric function of two positive real variables satisfying min(u, v) ? M(u, v) ? max(u, v) for all u and v. Setting M(u, v) = uM(1, vu?1) = uM(1, 1 ? t), 0 ? t < 1, we determine power series expansions in t of various generalized means, including (Stolarsky's mean), (Lehmer's mean), (Leach and Sholander's mean), and (Gini's mean). The explicit power series coefficients and recurrence relations for these coefficients are found. Finally, applications are shown by proving a theorem that generalizes one due to Lehmer. 相似文献
17.
Hermann König 《Journal of Functional Analysis》1977,24(1):32-51
For an open set Ω ? N, 1 ? p ? ∞ and λ ∈ +, let denote the Sobolev-Slobodetzkij space obtained by completing in the usual Sobolev-Slobodetzkij norm (cf. A. Pietsch, “r-nukleare Sobol. Einbett. Oper., Ellipt. Dgln. II,” Akademie-Verlag, Berlin, 1971, pp. 203–215). Choose a Banach ideal of operators , 1 ? p, q ? ∞ and a quasibounded domain Ω ? N. Theorem 1 of the note gives sufficient conditions on λ such that the Sobolev-imbedding map exists and belongs to the given Banach ideal : Assume the quasibounded domain fulfills condition Ckl for some l > 0 and 1 ? k ? N. Roughly this means that the distance of any to the boundary ?Ω tends to zero as for , and that the boundary consists of sufficiently smooth ?(N ? k)-dimensional manifolds. Take, furthermore, 1 ? p, q ? ∞, p > k. Then, if μ, ν are real positive numbers with λ = μ + v ∈ , μ > λ S(; p,q:N) and v > N/l · λD(;p,q), one has that belongs to the Banach ideal . Here λD(;p,q;N)∈+ and λS(;p,q;N)∈+ are the D-limit order and S-limit order of the ideal , introduced by Pietsch in the above mentioned paper. These limit orders may be computed by estimating the ideal norms of the identity mappings lpn → lqn for n → ∞. Theorem 1 in this way generalizes results of R. A. Adams and C. Clark for the ideals of compact resp. Hilbert-Schmidt operators (p = q = 2) as well as results on imbeddings over bounded domains.Similar results over general unbounded domains are indicated for weighted Sobolev spaces.As an application, in Theorem 2 an estimate is given for the rate of growth of the eigenvalues of formally selfadjoint, uniformly strongly elliptic differential operators with Dirichlet boundary conditions in , where Ω fulfills condition C1l.For an open set Ω in N, let denote the Sobolev-Slobodetzkij space obtained by completing in the usual Sobolev-Slobodetzkij norm, see below. Taking a fixed Banach ideal of operators and 1 ? p, q ? ∞, we consider quasibounded domains Ω in N and give sufficient conditions on λ such that the Sobolev imbedding operator exists and belongs to the Banach ideal. This generalizes results of C. Clark and R. A. Adams for compact, respectively, Hilbert-Schmidt operators (p = q = 2) to general Banach ideals of operators, as well as results on imbeddings over bounded domains. Similar results over general unbounded domains may be proved for weighted Sobolev spaces. As an application, we give an estimate for the rate of growth of the eigenvalues of formally selfadjoint, uniformly strongly elliptic differential operators with Dirichlet boundary conditions in , where Ω is a quasibounded open set in N. 相似文献
18.
Let θ(n) denote the maximum likelihood estimator of a vector parameter, based on an i.i.d. sample of size n. The class of estimators θ(n) + n?1q(θ(n)), with q running through a class of sufficiently smooth functions, is essentially complete in the following sense: For any estimator T(n) there exists q such that the risk of θ(n) + n?1q(θ(n)) exceeds the risk of T(n) by an amount of order o(n?1) at most, simultaneously for all loss functions which are bounded, symmetric, and neg-unimodal. If is chosen such that is unbiased up to , then this estimator minimizes the risk up to an amount of order o(n?1) in the class of all estimators which are unbiased up to .The results are obtained under the assumption that T(n) admits a stochastic expansion, and that either the distributions have—roughly speaking—densities with respect to the lebesgue measure, or the loss functions are sufficiently smooth. 相似文献
19.
Let x?Sn, the symmetric group on n symbols. Let θ? Aut(Sn) and let the automorphim order of x with respect to θ be defined by where xθ is the image of x under θ. Let αg? Aut(Sn) denote conjugation by the element g?Sn. Let where s and k are positive integers and denotes a divides b. Further h(s, k : n) ≡ b(1; s, k : n), where 1 denotes the identity automorphim. If g?Sn let c = f(g, s) denote the number of symbols in g which are in cycles of length not dividing the integer s, and let gs denote the product of all cycles in g whose lengths do not divide s. Then gs moves c symbols. The main results proved are: (1) recursion: if n ? c + 1 and t = n ? c ? 1 then (2) reduction: b(g; s, 1 : c)h(s, 1 : i) = b(g; s, 1 : i + c); (3) distribution: let D(θ, n) ≡ {(k, b) : k?Z+ and b = b(θ; 1, k : n) ≠ 0}; then D(θ, m) = D(φ, m) ∨ m ? N = N(θ, φ) iff θ is conjugate to φ; (4) evaluation: the number of cycles in gss of any given length is smaller than the smallest prime dividing s iff b(gs; s, 1 : c) = 1. If g = (12 … pm)t and then . 相似文献
20.
B.A Anderson P.J Schellenberg D.R Stinson 《Journal of Combinatorial Theory, Series A》1984,36(1):23-55
A Howell design of side s and order 2n, or more briefly, an H(s, 2n), is an s × s array in which each cell either is empty or contains an unordered pair of elements from some 2n-set, say X, such that (i) each row and column is Latin (that is, every element of X is in precisely one cell of each row and column) and (ii) any unordered pair of elements of X is in at most one cell of the array. A necessary condition for the existence of an H(s, 2n) is that n = 0 or n ? s ? 2n ?1. An is an H(s, 2n) in which there is a subset of X, say Y, of cardinality 2n ? s such that no pair of elements from Y is in any cell of the array. In this paper it is shown that if s is an even positive integer, if s and n satisfy the necessary condition and if (s, 2n) ≠ (2, 4) or (6, 12), then there is an ; furthermore, there is no H(2, 4) nor any though there is an H(6, 12). 相似文献