共查询到20条相似文献,搜索用时 234 毫秒
1.
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
2.
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
3.
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
4.
A technique for the numerical approximation of matrix-valued Riemann product integrals is developed. For a ? x < y ? b, Im(x, y) denotes , and Am(x, y) denotes an approximation of Im(x, y) of the form , where ak and yik are fixed numbers for i = 1, 2,…, m and k = 1, 2,…, N and xik = x + (y ? x)yik. The following result is established. If p is a positive integer, F is a function from the real numbers to the set of w × w matrices with real elements and F(1) exists and is continuous on [a, b], then there exists a bounded interval function H such that, if n, r, and s are positive integers, , then Further, if F(j) exists and is continuous on [a, b] for j = 1, 2,…, p + 1 and A is exact for polynomials of degree less than p + 1 ? j for j = 1, 2,…, p, then the preceding result remains valid when Aj is substituted for Ij. 相似文献
5.
6.
Let A be an n-square normal matrix over , and Qm, n be the set of strictly increasing integer sequences of length m chosen from 1,…, n. For α,β∈Qm, n denote by A[α|β] the submatrix obtained from A by using rows numbered α and columns numbered β. For k∈{0,1,…,m} write z.sfnc;α∩β|=k if there exists a rearrangement of 1,…,m, say i1,…,ik, ik+1,…,im, such that α(ij)=β(ij), j=1,…,k, and {α(ik+1),…,α(im)};∩{β(ik+1),…,β(im)}=ø. Let be the group of n-square unitary matrices. Define the nonnegative number , where |α∩β|=k. Theorem 1 establishes a bound for ?k(A), 0?k<m?1, in terms of a classical variational inequality due to Fermat. Let A be positive semidefinite Hermitian, n?2m. Theorem 2 leads to an interlacing inequality which, in the case n=4, m=2, resolves in the affirmative the conjecture that . 相似文献
7.
Patrick J Browne 《Journal of Differential Equations》1977,23(2):285-292
In this paper we study the linked nonlinear multiparameter system , where xr? [ar, br], yr is subject to Sturm-Liouville boundary conditions, and the continuous functions ars satisfy ¦ . Conditions on the polynomial operators Mr, Prs are produced which guarantee a sequence of eigenfunctions for this problem yn(x) = Πr=1kyrn(xr), n ? 1, which form a basis in . Here [a, b] = [a1, b1 × … × [ak, bk]. 相似文献
8.
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
9.
J.E Nymann 《Journal of Number Theory》1975,7(4):406-412
Given a set S of positive integers let denote the number of k-tuples 〈m1, …, mk〉 for which and (m1, …, mk) = 1. Also let denote the probability that k integers, chosen at random from , are relatively prime. It is shown that if P = {p1, …, pr} is a finite set of primes and S = {m : (m, p1 … pr) = 1}, then if k ≥ 3 and where d(S) denotes the natural density of S. From this result it follows immediately that as n → ∞. This result generalizes an earlier result of the author's where and S is then the whole set of positive integers. It is also shown that if S = {p1x1 … prxr : xi = 0, 1, 2,…}, then as n → ∞. 相似文献
10.
Emma Lehmer 《Journal of Number Theory》1983,17(1):37-46
This paper examines the question of whether a given pattern of kth power residues of length m can be postponed indefinitely. This is the case when there exists a prime q, called a delay prime, which does not contain this pattern even if q itself is considered as a kth power residue. It is conjectured that if there exists no delay prime then there exists a finite limit for which the corresponding pattern will occur before Λ in every sufficiently large prime of the form kn + 1. 相似文献
11.
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
12.
we prove that if R is a nonscalar Toeplitz matrix Ri, j=r?i?j? which commutes with a tridiagonal matrix with simple spectrum, then , k=4, 5,…, with Uk the Chebychev polynomial of the second kind, where p is determined from . 相似文献
13.
14.
R.N. Buttsworth 《Journal of Number Theory》1980,12(4):487-498
The polynomial functions f1, f2,…, fm are found to have highest common factor h for a set of values of the variables x1, x2,…,xm whose asymptotic density is For the special case f1(x) = f2(x) = … = fm(x) = x and h = 1 the above formula reduces to , the density if m-tuples with highest common factor 1. Necessary and sufficient conditions on the polynomials f1, f2,…, fm for the asymptotic density to be zero are found. In particular it is shown that either the polynomials may never have highest common factor h or else h is the highest common factor infinitely often and in fact with positive density. 相似文献
15.
A study is made of the number of cycles of length k which can be produced by a general n-stage feedback shift register. This problem is equivalent to finding the number of cycles of length k on the so-called de Bruijn-Good graph (Proc. K. Ned. Akad. Wet.49 (1946), 758–764; J. London Math. Soc.21 (3) (1946), 169–172). The number of cycles of length k in such a graph is denoted by β(n, k). From the-de Bruijn-Good graph, it can be shown that β(n, k) is also the number of cyclically distinct binary sequences of length k which have all k successive sets of n adjacent digits (called “n windows”) distinct (the sequence to be considered cyclically). After listing some known results for β(n, k), we show that , where the number of integers l ? k such that (k, l) ? r, and (k, l) denotes the greatest common divisor of k and l. From the results of several computer programs, it is conjectured that , 相似文献
16.
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
17.
Let n1+n2+?+nm=n where the ni's are integers (possibly negative or greater than n). Let p=(k1,…,km), where k1+k2+?+km=k, be a partition of the nonnegative integer k into m nonnegative integers and let P denote the set of all such partitions. For m?2, we prove the combinatorial identity which implies the surprising result that the left side of the above equation depends on n but not on the ni's. 相似文献
18.
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.
Ian Knowles 《Journal of Mathematical Analysis and Applications》1978,66(3):574-585
A sufficient condition is given for the operator T0: C∞0(Rm) → L2(Rm) given by to be essentially self-adjoint. This condition is sufficiently general to admit certain potentials q having unbounded oscillations in a neighborhood of ∞. 相似文献
20.
A configuration with parameters (v, b, r, k) is an incidence structure (, , ), where is a set of v “points”, is a set of b “blocks” and is an “incidence relation” between points and blocks such that each point is incident with r blocks, and each blok is incident with k points. A block may be regarded as the subset of those points of with which it is incident.A regular two component pairwise balanced design with parameters is an incidence structure = (, 1 ∪ 2, ), where i = (, i,) is a configuration with parameters (v, bi, ri, ki), i = 1,2, bi = vri/ki, and such that any two distinct points of are contained in exactly one block of 1 ∪ 2. The configuration i is called the ith component of , i = 1,2.Hence by deleting the points of an oval S from a projective plane П of even order q, we obtain a regular two component pairwise balanced design for which In this paper, we investigate the converse question and prove: Given a regular two component pairwise balanced design with the above parameters, then if q ≠ 6, the design can be embedded in a projective plane of order q. 相似文献