共查询到20条相似文献,搜索用时 93 毫秒
1.
Joseph F. McGrath 《Applied mathematics and computation》1976,2(2):113-160
The objective of this paper is the rigorous derivation of an invariant imbedding algorithm for the solution of the integral equation for , under suitable restrictions on g, K, and γ. First a set of conditions is determined under which Eq. (1) has a unique solution. The function ø(z) is shown to be approximated almost uniformly for Y=0 and as x→∞ by the solution of 相似文献
2.
A.M Fink 《Journal of Mathematical Analysis and Applications》1982,90(1):251-258
Presented in this report are two further applications of very elementary formulae of approximate differentiation. The first is a new derivation in a somewhat sharper form of the following theorem of V. M. Olovyani?nikov: LetNn (n ? 2) be the class of functionsg(x) such thatg(x), g′(x),…, g(n)(x) are ? 0, bounded, and nondecreasing on the half-line ?∞ < x ? 0. A special element ofNnis. Ifg(x) ∈ Nnis such that, thenfor
1
. Moreover, if we have equality in (1) for some value of v, then we have there equality for all v, and this happens only if in (?∞, 0].The second application gives sufficient conditions for the differentiability of asymptotic expansions (Theorem 4). 相似文献
3.
If f is a positive function on (0, ∞) which is monotone of order n for every n in the sense of Löwner and if Φ1 and Φ2 are concave maps among positive definite matrices, then the following map involving tensor products: is proved to be concave. If Φ1 is affine, it is proved without use of positivity that the map is convex. These yield the concavity of the map (0<p?1) (Lieb's theorem) and the convexity of the map (0<p?1), as well as the convexity of the map .These concavity and convexity theorems are then applied to obtain unusual estimates, from above and below, for Hadamard products of positive definite matrices. 相似文献
4.
Let Ms, be the number of solutions of the equation in the finite field GF(p). For a prime p ≡ 1(mod 3), , , and . Here d is uniquely determined by . 相似文献
5.
Ludwig Arnold 《Linear algebra and its applications》1976,13(3):185-199
It is proved that Wigner's semicircle law for the distribution of eigenvalues of random matrices, which is important in the statistical theory of energy levels of heavy nuclei, possesses the following completely deterministic version. Let An=(aij), 1?i, ?n, be the nth section of an infinite Hermitian matrix, {λ(n)}1?k?n its eigenvalues, and {uk(n)}1?k?n the corresponding (orthonormalized column) eigenvectors. Let , put (bookeeping function for the length of the projections of the new row v1n of An onto the eigenvectors of the preceding matrix An?1), and let finally (empirical distribution function of the eigenvalues of . Suppose (i) , (ii) limnXn(t)=Ct(0<C<∞,0?t?1). Then ,where W is absolutely continuous with (semicircle) density 相似文献
6.
It is shown that if satisfies , where σk(A) denotes the sum of all kth order subpermanent of A, then Per[λJn+(1?λ)A] is strictly decreasing in the interval 0<λ<1. 相似文献
7.
Moshe Roitman 《Advances in Mathematics》1981,41(3):301-311
For a finite group G and a set I ? {1, 2,…, n} let ,where We prove, among other results, that the positive integers for 1 ? j ? r, Ij1 ∩ Ij2 ∩ Ij3 ∩ Ij4 = Ø for any 1 ? j1 <j2 <j3 <j4 ? r, determine G up to isomorphism. We also show that under certain assumptions finite groups are determined up to isomorphism by the number of their subgroups. 相似文献
8.
In the third paper of this series on cardinal spline interpolation [4] Lipow and Schoenberg study the problem of Hermite interpolation . The B-splines are there conspicuous by their absence, although they were found very useful for the case γ = 1 of ordinary (or Lagrange) interpolation (see [5–10]). The purpose of the present paper is to investigate the B-splines for the case of Hermite interpolation (γ > 1). In this sense the present paper is a supplement to [4] and is based on its results. This is done in Part I. Part II is devoted to the special case when we want to solve the problem by quintic spline functions of the class C?(– ∞, ∞). This is the simplest nontrivial example for the general theory. In Part II we derive an explicit solution for the problem (1), where v = 0, 1,…, n. 相似文献
9.
An n-tournament is a complete labelled digraph on n vertices without loops or multiple arcs. A tournament's score sequence is the sequence of the out-degrees of its vertices arranged in nondecreasing order. The number Sn of distinct score sequences arising from all possible n-tournaments, as well as certain generalizations are investigated. A lower bound of the form (C1 a constant) and an upper bound of the form are proved. A q-extension of the Catalan numbers is defined. It is conjectured that all coefficients in the polynomial Cn(q) are at most . It is shown that if this conjecture is true, then 相似文献
10.
Thomas G. Kurtz 《Stochastic Processes and their Applications》1978,6(3):223-240
A variety of continuous parameter Markov chains arising in applied probability (e.g. epidemic and chemical reaction models) can be obtained as solutions of equations of the form where , the Y1 are independent Poisson processes, and N is a parameter with a natural interpretation (e.g. total population size or volume of a reacting solution).The corresponding deterministic model, satisfies Under very general conditions limN→∞XN(t)=X(t) a.s. The process XN(t) is compared to the diffusion processes given by and Under conditions satisfied by most of the applied probability models, it is shown that XN,ZN and V can be constructed on the same sample space in such a way that and 相似文献
11.
Robert Donaghey 《Journal of Combinatorial Theory, Series A》1976,21(2):155-163
This paper treats the class of sequences {an} that satisfy the recurrence relation between the odd and even terms of {an} that involves the coefficients of tan(t), namely A combinatorial setting is then provided to elucidate the appearance of the tangent coefficients in this equation. 相似文献
12.
R.J Cook 《Journal of Number Theory》1983,17(1):80-92
Let k be an odd positive integer. Davenport and Lewis have shown that the equations with integer coefficients, have a nontrivial solution in integers x1,…, xN provided that Here it is shown that for any ? > 0 and k > k0(?) the equations have a nontrivial solution provided that 相似文献
13.
14.
Let and be polynomials with real zeros satisfying An?1 = Bn?1 = 0, and let Using the recently proved validity of the van der Waerden conjecture on permanents, some results on the real zeros of H(x) are obtained. These results are related to classical results on composite polynomials. 相似文献
15.
Stanisław Lewanowicz 《Journal of Computational and Applied Mathematics》1979,5(3):193-206
In this paper we are constructing a recurrence relation of the form for integrals (called modified moments) in which Ck(λ) is the k-th Gegenbauer polynomial of order , and f is a function satisfying the differential equation of order n, where p0, p1, …, pn ? 0 are polynomials, and mk〈λ〉[p] is known for every k. We give three methods of construction of such a recurrence relation. The first of them (called Method I) is optimum in a certain sense. 相似文献
16.
Aboubakary Diakhaby 《Comptes Rendus Mathematique》2002,334(7):597-602
Our aim is to generalize some results obtained for a Poisson point process in [7], to a general point process. Those results are in field of complete convergence of two like Parzen–Rosenblatt estimates of density of mean measure function and regression curves. Those estimates are defined from the superposition of n i.i.d. point processes as: where m is the number of seem generics points of the superposition. We give some sufficient conditions for the convergence of those kernel-like estimators. To cite this article: A. Diakhaby, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 597–602. 相似文献
17.
We calculate some size Ramsey numbers involving stars. For example we prove that for t ? k ? 2 and n sufficiently large the size Ramsey number. 相似文献
18.
In this Note we consider nonnegative solutions for the nonlinear equation in , where is the so called Pucci operator and the ei are the eigenvalues of M et Λ?λ>0. We prove that if u satisfies the decreasing estimate for some β satisfying (β?1)(p?1)>2+α then u is radial. In a second time we prove that if and u is a nonnegative radial solution of (1), u(x)=g(r), such that g″ changes sign at most once, then u is zero. To cite this article: I. Birindelli, F. Demengel, C. R. Acad. Sci. Paris, Ser. I 336 (2003). 相似文献
19.
L.B Richmond 《Journal of Number Theory》1976,8(4):390-396
Asymptotic results are obtained for pA(k)(n), the kth difference of the function pA(n) which is the number of partitions of n into integers from A. Under certain restrictions on A it is shown that thereby verifying for these A a conjecture of Bateman and Erdös. 相似文献
20.
Homogenization in open sets with holes 总被引:1,自引:0,他引:1
Doina Cioranescu Jeannine Saint Jean Paulin 《Journal of Mathematical Analysis and Applications》1979,71(2):590-607
Let Qr be a cylindrical bar with r cylindrical cavities having generators parallel to those of Qr. Let Ω be the cross-section of the bar, Ω1 the cross-section of the domain occupied by the material and the cross- sections of the cavities: . The study of the elastic torsion of this bar leads to the following problem [see 2., 3., 267–320)]: (1) where μ is the shear modulus of the material, α is the angle of twist and represents the stress function. In this paper the problem (1) with an increasing number of holes which are distributed periodically is considered. One would like to know if has a limit , and if so, the equation satisfied by this limit. This is an “homogenization” problem — the heterogeneous bar Qr is replaced by a homogeneous one, the response of which under torsion approximates as closely as possible that of Qr. A more general problem will be studied and the case of elastic torsion will be obtained as an application. The proof uses the energy method [see Lions (Collège de France, 1975–1977), Tartar (Collège de France, 1977)] and extension theorems. A related problem is the homogenization of a perforated plate [cf. Duvaut (to appear)]. 相似文献