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1.
A finite group G is called an ah-group if any two distinct conjugacy classes of G have distinct cardinality. We show that if G is an ah-group, then the non-abelian socle of G is isomorphic to one of the following:
- 1. , for 1a5, a≠2.
- 2. A8.
- 3. PSL(3,4)e, for 1e10.
- 4. A5×PSL(3,4)e, for 1e10.
- 1. , for 3a5.
- 2. PSL(3,4)e, for 1e10.
2.
In this paper we present some new results about unlike powers in arithmetic progression. We prove among other things that for given k 4 and L 3 there are only finitely many arithmetic progressions of the form with xi , gcd(x0, xl) = 1 and 2 li L for i = 0, 1, …, k − 1. Furthermore, we show that, for L = 3, the progression (1, 1,…, 1) is the only such progression up to sign. Our proofs involve some well-known theorems of Faltings [9], Darmon and Granville [6] as well as Chabauty's method applied to superelliptic curves. 相似文献
3.
Suppose that G is a graph with n vertices and m edges, and let μ be the spectral radius of its adjacency matrix.Recently we showed that if G has no 4-cycle, then μ2-μn-1, with equality if and only if G is the friendship graph.Here we prove that if m9 and G has no 4-cycle, then μ2m, with equality if G is a star. For 4m8 this assertion fails. 相似文献
4.
5.
Let k1 be an integer and G be a graph of order n3k satisfying the condition that σ2(G)n+k-1. Let v1,…,vk be k independent vertices of G, and suppose that G has k vertex-disjoint triangles C1,…,Ck with viV(Ci) for all 1ik.Then G has k vertex-disjoint cycles such that
- (i) for all 1ik.
- (ii) , and
- (iii) At least k-1 of the k cycles are triangles.
Keywords: Degree sum condition; Independent vertices; Vertex-disjoint cycles 相似文献
6.
Let μ be a real measure on the line such that its Poisson integral M(z) converges and satisfies|M(x+iy)|Ae−cyα, y→+∞,for some constants A,c>0 and 0<α1. We show that for 1/2<α1 the measure μ must have many sign changes on both positive and negative rays. For 0<α1/2 this is true for at least one of the rays, and not always true for both rays. Asymptotical bounds for the number of sign changes are given which are sharp in some sense. 相似文献
7.
We compute the best constants of approximation by entire functions of spherical type and by trigonometric polynomials of spherical degree on classes of functions f satisfying the condition ΔkfLp1, where p=1 or 2 and Δ is the Laplace operator. 相似文献
8.
C. Iliopoulos K. Perdikuri E. Theodoridis A. Tsakalidis K. Tsichlas 《Journal of Discrete Algorithms》2007,5(2):229-242
In this paper we present three algorithms for the Motif Identification Problem in Biological Weighted Sequences. The first algorithm extracts repeated motifs from a biological weighted sequence. The motifs correspond to repetitive words which are approximately equal, under a Hamming distance, with probability of occurrence 1/k, where k is a small constant. The second algorithm extracts common motifs from a set of N2 weighted sequences. In this case, the motifs consists of words that must occur with probability 1/k, in 1qN distinct sequences of the set. The third algorithm extracts maximal pairs from a biological weighted sequence. A pair in a sequence is the occurrence of the same word twice. In addition, the algorithms presented in this paper improve previous work on these problems. 相似文献
9.
Boris Rubin 《Advances in Mathematics》2002,170(2):206-223
New pointwise inversion formulae are obtained for the d-dimensional totally geodesic Radon transform on the n-dimensional real hyperbolic space, 1dn−1, in terms of polynomials of the Laplace–Beltrami operator and intertwining fractional integrals. Similar results are established for hyperbolic cosine and sine transforms. 相似文献
10.
Alexandre Junod 《Expositiones Mathematicae》2003,21(1):63
We develop a general context for the computation of the determinant of a Hankel matrix Hn = (αi+j)0i,jn, assuming some suitable conditions for the exponential (or ordinary) generating function of the sequence (αn)n0. Several well-known particular cases are thus derived in a unified way. 相似文献
11.
12.
Let Lq (1q<∞) be the space of functions f measurable on I=[−1,1] and integrable to the power q, with normL∞ is the space of functions measurable on I with normWe denote by AC the set of all functions absolutely continuous on I. For nN, q[1,∞] we setWn,q={f:f(n−1)AC, f(n)Lq}.In this paper, we consider the problem of accuracy of constants A, B in the inequalities (1) || f(m)||qA|| f||p+B|| f(m+k+1)||r, mN, kW; p,q,r[1,∞], fWm+k+1,r. 相似文献
13.
In this paper we investigate the existence of holey self-orthogonal Latin squares with a symmetric orthogonal mate of type 2nu1 (HSOLSSOM(2nu1)). For u2, necessary conditions for existence of such an HSOLSSOM are that u must be even and n3u/2+1. Xu Yunqing and Hu Yuwang have shown that these HSOLSSOMs exist whenever either (1) n9 and n3u/2+1 or (2) n263 and n2(u-2). In this paper we show that in (1) the condition n9 can be extended to n30 and that in (2), the condition n263 can be improved to n4, except possibly for 19 pairs (n,u), the largest of which is (53,28). 相似文献
14.
Leonid Golinskii 《Journal of Approximation Theory》2002,118(2):257-274
Orthogonal polynomials on the unit circle are completely determined by their reflection coefficients through the Szeg
recurrences. We assume that the reflection coefficients tend to some complex number a with 0<a<1. The orthogonality measure μ then lives essentially on the arc {eit :αt2π−α} where sin
with α(0,π). Under the certain rate of convergence it was proved in (Golinskii et al. (J. Approx. Theory96 (1999), 1–32)) that μ has no mass points inside this arc. We show that this result is sharp in a sense. We also examine the case of the whole unit circle and some examples of singular continuous measures given by their reflection coefficients. 相似文献
15.
Given a set TGF(q), |T|=t, wT is defined as the smallest positive integer k for which ∑yTyk≠0. It can be shown that wTt always and wTt−1 if the characteristic p divides t. T is called a Vandermonde set if wTt−1 and a super-Vandermonde set if wT=t. This (extremal) algebraic property is interesting for its own right, but the original motivation comes from finite geometries. In this paper we classify small and large super-Vandermonde sets. 相似文献
16.
Let m and n be positive integers with n2 and 1mn−1. We study rearrangement-invariant quasinorms R and D on functions f: (0, 1)→
such that to each bounded domain Ω in
n, with Lebesgue measure |Ω|, there corresponds C=C(|Ω|)>0 for which one has the Sobolev imbedding inequality R(u*(|Ω| t))CD(|mu|* (|Ω| t)), uCm0(Ω), involving the nonincreasing rearrangements of u and a certain mth order gradient of u. When m=1 we deal, in fact, with a closely related imbedding inequality of Talenti, in which D need not be rearrangement-invariant, R(u*(|Ω| t))CD((d/dt) ∫{x
n : |u(x)|>u*(|Ω| t)} |(u)(x)| dx), uC10(Ω). In both cases we are especially interested in when the quasinorms are optimal, in the sense that R cannot be replaced by an essentially larger quasinorm and D cannot be replaced by an essentially smaller one. Our results yield best possible refinements of such (limiting) Sobolev inequalities as those of Trudinger, Strichartz, Hansson, Brézis, and Wainger. 相似文献
17.
The continuity conditions at the endpoints of interpolation theorems, TaBjMj aAj for j=0, 1, can be written with the help of the approximation functional: E(t, Ta; B1, B0)L∞M0 aA0 and E(t, Ta; B0, B1)L∞M1 aA1. As a special case of the results we present here we show that in the hypotheses of the interpolation theorem the L∞ norms can be replaced by BMO(
+) norms. This leads to a strong version of the Stein-Weiss theorem on interpolation with change of measure. Another application of our results is that the condition fL0, i.e., f*L∞, where f*(γ)=μ{|f|>γ} is the distribution function of f, can be replaced in interpolation with L(p, q) spaces by the weaker f*BMO(
+). 相似文献
18.
S. Bandyopadhyay B. Dacorogna 《Annales de l'Institut Henri Poincaré (C) Analyse Non Linéaire》2009,26(5):1717-1741
We discuss the existence of a diffeomorphism such that
φ*(g)=f