共查询到20条相似文献,搜索用时 15 毫秒
1.
Dragomir Ž. Ðoković 《Linear algebra and its applications》2012,437(10):2680-2682
Mirsky proved that, for the existence of a complex matrix with given eigenvalues and diagonal entries, the obvious necessary condition is also sufficient. We generalize this theorem to matrices over any field and provide a short proof. Moreover, we show that there is a unique companion-matrix-type solution for this problem. 相似文献
2.
In this note, two classes of quasi-difference matrices, -QDM and -QDM, are constructed. Combining the known results of quasi-difference matrices and difference matrices, a new short disproof of Euler’s conjecture on mutually orthogonal Latin squares is given. 相似文献
3.
A. J. Hoffman 《Israel Journal of Mathematics》1974,17(1):69-75
To every symmetric matrixA with entries ±1, we associate a graph G(A), and ask (for two different definitions of distance) for the distance ofG(A) to the nearest complete bipartite graph (cbg). Letλ
1(A),λ
1 (A) be respectively the algebraically largest and least eigenvalues ofA. The Frobenius distance (see Section 4) to the nearest cbg is bounded above and below by functions ofn −λ
1 (A), wheren=ord A. The ordinary distance (see Section 1) to the nearest cbg is shown to be bounded above and below by functions ofλ
1 (A). A curious corollary is: there exists a functionf (independent ofn, and given by (1.1)), such that |λ
i
(A) | ≦f(λ
1(A), whereλ
i
(A) is any eigenvalue ofA other thanλ
i
(A).
This work was supported (in part) by the U.S. Army under contract #DAHC04-C-0023. 相似文献
4.
L. Yu. Kolotilina 《Journal of Mathematical Sciences》2005,127(3):1969-1975
The lower bound
l1 (A) - ln (A) \geqslant 2||A12 ||\lambda _1 (A) - \lambda _n (A) \geqslant 2\parallel A_{12} \parallel 相似文献
5.
Samuel Krushkal 《Central European Journal of Mathematics》2007,5(3):551-580
The Grunsky and Teichmüller norms ϰ(f) and k(f) of a holomorphic univalent function f in a finitely connected domain D ∋ ∞ with quasiconformal extension to
are related by ϰ(f) ≤ k(f). In 1985, Jürgen Moser conjectured that any univalent function in the disk Δ* = {z: |z| > 1} can be approximated locally uniformly by functions with ϰ(f) < k(f). This conjecture has been recently proved by R. Kühnau and the author. In this paper, we prove that approximation is possible
in a stronger sense, namely, in the norm on the space of Schwarzian derivatives. Applications of this result to Fredholm eigenvalues
are given. We also solve the old Kühnau problem on an exact lower bound in the inverse inequality estimating k(f) by ϰ(f), and in the related Ahlfors inequality.
To Reiner Kühnau on his 70th birthday 相似文献
6.
7.
On Hua-Tuan’s conjecture 总被引:2,自引:0,他引:2
Let G be a finite group and |G| = pn, p be a prime. For 0 m n, sm(G) denotes the number of subgroups of of order pm of G. Loo-Keng Hua and Hsio-Fu Tuan have ever conjectured: for an arbitrary finite p-group G, if p > 2, then sm(G) ≡ 1, 1 + p, 1 + p + p2 or 1 + p + 2p2 (mod p3). In this paper, we investigate the conjecture, and give some p-groups in which the conjecture holds and some examples in which the conjecture does not hold. 相似文献
8.
9.
In this paper, we proposed an implementation of stochastic perturbation of reduced gradient and bisection (SPRGB) method for optimizing a non-convex differentiable function subject to linear equality constraints and non-negativity bounds on the variables. In particular, at each iteration, we compute a search direction by reduced gradient, and optimal line search by bisection algorithm along this direction yields a decrease in the objective value. SPRGB method is desired to establish the global convergence of the algorithm. An implementation and tests of SPRGB algorithm are given, and some numerical results of large-scale problems are presented, which show the efficient of this approach. 相似文献
10.
D. Gaitsgory 《Israel Journal of Mathematics》2007,157(1):155-191
Let X be a smooth projective curve over a finite field F
q
. Let ρ be a continuous representation π(X) → GL
n
(F), where F = F
l
((t)) with F
l
being another finite field of order prime to q.
Assume that
is irreducible. De Jong’s conjecture says that in this case
is finite. As was shown in the original paper of de Jong, this conjecture follows from an existence of an F-valued automorphic form corresponding to ρ is the sense of Langlands. The latter follows, in turn, from a version of the Geometric Langlands conjecture.
In this paper we sketch a proof of the required version of the geometric conjecture, assuming that char(F) ≠ 2, thereby proving de Jong’s conjecture in this case. 相似文献
11.
Let G be a group of order pn, p a prime. For 0 m n, sm(G) denotes the number of subgroups of order pm of G. Loo-Keng Hua and Hsio-Fu Tuan had ever conjectured: for an arbitrary finite p-group G, if p > 2, then sm(G) ≡ 1, 1+p, 1+p+p2 or 1+p+2p2(mod p3). The conjecture has a negative answer. In this paper, we further investigate the conjecture and propose two new conjectures. 相似文献
12.
We show that if X is a smooth complex projective variety with Kodaira dimension 0 then the Kodaira dimension of a general fiber of its Albanese
map is at most .
J. A. Chen was partially supported by NCTS, TIMS, and NSC of Taiwan. C. D. Hacon was partially supported by NSF research grant
no: 0456363 and an AMS Centennial Scholarship. We would like to thank J. Kollár, R. Lazarsfeld, C.-H. Liu, M. Popa, P. Roberts,
and A. Singh for many useful comments on the contents of this paper. 相似文献
13.
Michael Gil’ 《Quaestiones Mathematicae》2016,39(2):145-152
Let SNr (r ≥ 1) denote the Schatten-von Neumann ideal of compact operators in a separable Hilbert space. For the block matrixthe inequality(p = 2; 3;?…?) is proved, where λk(A) (k = 1; 2;?…?) are the eigenvalues of A and Nr(.) is the norm in SNr. Moreover, let P(z) = z2I + Bz + C (z ∈ ?) with B ∈ SN2p, C ∈ SNp. By zk(P) (k = 1; 2;?…?) the characteristic values of the pencil P are denoted. It is shown thatIn the case p = 1, sharper results are established. In addition, it is derived that 相似文献
14.
Gabriele Di Cerbo 《Mathematische Annalen》2016,366(1-2):447-457
15.
The set of homotopy classes of self maps of a compact, connected Lie group G is a group by the pointwise multiplication which we denote by H(G), and it is known to be nilpotent. ōshima [H. ōshima, Self homotopy group of the exceptional Lie group G2, J. Math. Kyoto Univ. 40 (1) (2000) 177-184] conjectured: if G is simple, then H(G) is nilpotent of class ?rankG. We show this is true for PU(p) which is the first high rank example. 相似文献
16.
17.
Using a criterion due to Bourgain [10] and the generalization of the self-dual induction defined in [19], for each primitive permutation we build a large family of k-interval exchanges satisfying Sarnak’s conjecture, and, for at least one permutation in each Rauzy class, smaller families for which we have weak mixing, which implies a prime number theorem, and simplicity in the sense of Veech. 相似文献
18.
I. B. Gorshkov 《Proceedings of the Steklov Institute of Mathematics》2016,293(1):58-65
Let G be a finite group G, and let N(G) be the set of sizes of its conjugacy classes. It is shown that, if N(G) equals N(Alt n ) or N(Sym n ), where n > 1361, then G has a composition factor isomorphic to an alternating group Altm with m ≤ n and the interval (m, n] contains no primes. 相似文献
19.
20.
In 1979,De Giorgi conjectured that the only bounded monotone solutions to the Allen-Cahn equation △u+u-u~3=0 in R~N,are one-dimensional.This conjecture and its connection with minimal surfaces and Toda systems are the subject of this survey article. 相似文献
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