共查询到20条相似文献,搜索用时 15 毫秒
1.
L. Yu. Kolotilina 《Journal of Mathematical Sciences》2009,157(5):701-714
The paper presents a general approach to deriving inclusion sets for the singular values of a matrix A = (aij) ∈ ℂ
n×n. The key to the approach is the following result: If σ is a singular value of A, then a certain matrix C(σ, A) of order 2n,
whose diagonal entries are σ2 − | aii|2, i = 1, …, n, is singular. Based on this result, we use known diagonal-dominance type nonsingularity conditions to obtain
inclusion sets for the singular values of A. Scaled versions of the inclusion sets, allowing one, in particular, to obtain
Ky Fan type results for the singular values, are derived by passing to the conjugated matrix D−1C(σ, A)D, where D is a positive-definite diagonal matrix. Bibliography: 16 titles.
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 359, 2008, pp. 52–77. 相似文献
2.
3.
Shui Cao ZHENG Huo Nan LIN Di He HU 《数学学报(英文版)》2005,21(5):1137-1148
In this paper, we investigate the Hausdorff measure for level sets of N-parameter Rd-valued stable processes, and develop a means of seeking the exact Hausdorff measure function for level sets of N-parameter Rd-valued stable processes. We show that the exact Hausdorff measure function of level sets of N-parameter Rd-valued symmetric stable processes of index α is Ф(r) = r^N-d/α (log log l/r)d/α when Nα 〉 d. In addition, we obtain a sharp lower bound for the Hausdorff measure of level sets of general (N, d, α) strictly stable processes. 相似文献
4.
Kurt FALK Bernd O. STRATMANN 《数学学报(英文版)》2006,22(2):431-446
In this paper, we study exhaustions, referred to as p-restrictions, of arbitrary nonelementary Kleinian groups with at most finitely many bounded parabolic elements. Special emphasis is put on the geometrically infinite case, where we obtain that the limit set of each of these Kleinian groups contains an infinite family of closed subsets, referred to as p-restricted limit sets, such that there is a Poincaré series and hence an exponent of convergence δp, canonically associated with every element in this family. Generalizing concepts which are well known in the geometrically finite case, we then introduce the notion of p-restricted Patterson measure, and show that these measures are non-atomic, δp-harmonic, δp-subconformal on special sets and δp-conformal on very special sets. Furthermore, we obtain the results that each p-restriction of our Kleinian group is of δp-divergence type and that the Hausdorff dimension of the p-restricted limit set is equal to δp. 相似文献
5.
L. Yu. Kolotilina 《Journal of Mathematical Sciences》2006,137(3):4815-4834
The paper presents new pseudoblock diagonal-dominance conditions for matrices with fixed block partitioning, which generalize
the pointwise kth-order diagonal-dominance conditions and pointwise circuit diagonal-dominance conditions. For matrices satisfying
pseudoblock conditions, the singularity/nonsingularity problem is considered. In particular, for block 2 × 2 matrices, certain
known results are improved and generalized. Some eigenvalue inclusion regions corresponding to pseudoblock nonsingularity
conditions are presented. Bibliography: 11 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 323, 2005, pp. 94–131. 相似文献
6.
7.
8.
In this paper we prove the independence of a system of five axioms (S1)–(S5), which was proposed in the book of Pallaschke
and Urbański (Pairs of Compact Convex Sets, vol. 548, Kluwer Academic Publishers, Dordrecht, 2002) for partially ordered commutative semigroups. These five axioms (S1)–(S5) are stated in the introduction below. A partially
ordered commutative semigroup satisfying these axioms is called a F-semigroup. By the use of a further axiom (S6) we define an abstract difference for the elements of a F-semigroup and prove some basic properties. The most interesting example of a F-semigroup are the nonempty compact convex sets of a topological vector space endowed with the Minkowski sum as operation
and the inclusion as partial order. In Section 4 we apply the abstract difference to the problem of minimality of convex fractions.
Dedicated to Boris Mordukhovich in honour of his 60th birthday. 相似文献
9.
Sriram Balasubramanian 《Integral Equations and Operator Theory》2010,68(4):529-550
We prove a Carathéodory–Fejér type interpolation theorem for certain matrix convex sets in
\mathbbCd{\mathbb{C}^d} using the Blecher–Ruan–Sinclair characterization of abstract operator algebras. Our results generalize the work of Dmitry
S. Kalyuzhnyĭ-Verbovetzkiĭ for the d-dimensional non-commutative polydisc. 相似文献
10.
We prove that every Ariki–Koike algebra is Morita equivalent to a direct sum of tensor products of smaller Ariki–Koike algebras
which have q–connected parameter sets. A similar result is proved for the cyclotomic q–Schur algebras. Combining our results with work of Ariki and Uglov, the decomposition numbers for the Ariki–Koike algebras
defined over fields of characteristic zero are now known in principle.
Received: 22 March 2000; in final form: 19 September 2001 / Published online: 29 April 2002 相似文献
11.
L. Yu. Kolotilina 《Journal of Mathematical Sciences》2009,157(5):723-729
The paper generalizes certain inclusion sets for the singular values of a square matrix to the case of an m × n matrix. In
particular, it is shown that under a nonrestrictive assumption on the ordering of the matrix columns (if m < n) or the matrix
rows (if m > n), a natural counterpart of the Gerschgorin theorem on the eigenvalue location is valid. Bibliography: 14 titles.
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 359, 2008, pp. 94–105. 相似文献
12.
I. A. Lavrov 《Algebra and Logic》1996,35(3):164-171
A new approach to the study of creative sets using the notion of a table is offered. Making use of tables conforming to recursively
enumerable sets, novel properties of creative sets are established. Harrington's theorem on the definability of creative sets
in the lattice of recursively enumerable sets is proved, and we reprove Lachlan's theorem which states that one of the factors
in a direct product of creative sets is again creative.
Supported by RFFR grant No. 93-01-16014.
Translated fromAlgebra i Logika, Vol. 35, No. 3, pp. 294–307, May–June, 1996. 相似文献
13.
New concepts of fuzzy semi δ-V and fuzzy semi δ-Λ sets were introduced in our work “On fuzzy semi δ-Λ sets and fuzzy semi δ-V sets V-6,” J. Trip. Math. Soc., 6, 81–88 (2004). It was shown that the family of all fuzzy semi δ-V sets forms a fuzzy supra topological space on X denoted by (X, FS
δV
). The aim of this paper is to introduce the concept of fuzzy semi δ-V continuity in a fuzzy δ-V topological space. Finally, some properties, preservation theorems, etc., are studied.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 5, pp. 712–717, May, 2008. 相似文献
14.
V. L. Mel’nik 《Ukrainian Mathematical Journal》1998,50(9):1416-1423
We investigate the properties of (n−1)-convex sets associated with the properties of conjugate sets. We give a complete topological classification of (n−1)-convex sets.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 9, pp. 1236–1243, September, 1998. 相似文献
15.
Karoline Johansson Stevan Pilipovi? Nenad Teofanov Joachim Toft 《Monatshefte für Mathematik》2012,17(3):181-199
We introduce admissible lattices and Gabor pairs to define discrete versions of wave-front sets with respect to Fourier–Lebesgue
and modulation spaces. We prove that these wave-front sets agree with each other and with corresponding wave-front sets of
“continuous type”. This implies that the coefficients of a Gabor frame expansion of f are parameter dependent, and describe the wave-front set of f. 相似文献
16.
We introduce a new probabilistic technique for finding ‘almost-periods’ of convolutions of subsets of groups. This gives results
similar to the Bogolyubovtype estimates established by Fourier analysis on abelian groups but without the need for a nice
Fourier transform to exist. We also present applications, some of which are new even in the abelian setting. These include
a probabilistic proof of Roth’s theorem on three-term arithmetic progressions and a proof of a variant of the Bourgain–Green
theorem on the existence of long arithmetic progressions in sumsets A+B that works with sparser subsets of {1, . . . , N} than previously possible. In the non-abelian setting we exhibit analogues of the Bogolyubov–Freiman–Halberstam–Ruzsa-type
results of additive combinatorics, showing that product sets A
1 · A
2 · A
3 and A
2 · A
−2 are rather structured, in the sense that they contain very large iterated product sets. This is particularly so when the
sets in question satisfy small-doubling conditions or high multiplicative energy conditions. We also present results on structures
in A · B. 相似文献
17.
Jennie Danielsson 《Journal of Geometry》2008,88(1-2):15-18
A general construction of minimal blocking sets of size 2p – 3, where p is a prime and p ≡ 1 (mod 4), p > 5, and of size 2p – 2, where p is a prime and p ≡ 3 (mod 4), p > 5 in PG(2, p) is presented. These blocking sets are all of Rédei type.
相似文献
18.
Christof Külske 《Probability Theory and Related Fields》2003,126(1):29-50
We consider diffraction at random point scatterers on general discrete point sets in ℝν, restricted to a finite volume. We allow for random amplitudes and random dislocations of the scatterers. We investigate
the speed of convergence of the random scattering measures applied to an observable towards its mean, when the finite volume
tends to infinity. We give an explicit universal large deviation upper bound that is exponential in the number of scatterers.
The rate is given in terms of a universal function that depends on the point set only through the minimal distance between
points, and on the observable only through a suitable Sobolev-norm. Our proof uses a cluster expansion and also provides a
central limit theorem.
Received: 10 October 2001 / Revised version: 26 January 2003 /
Published online: 15 April 2003
Work supported by the DFG
Mathematics Subject Classification (2000): 78A45, 82B44, 60F10, 82B20
Key words or phrases: Diffraction theory – Random scatterers – Random point sets – Quasicrystals – Large deviations – Cluster expansions 相似文献
19.
The Bartle–Dunford–Schwartz integral for scalar functions with respect to vector measures is characterized by means of Riemann-type
sums based on partitions of the domain into countably many measurable sets. In this setting, two natural notions of integrability
(Birkhoff integrability and Kolmogoroff integrability) turn out to be equivalent to Bartle–Dunford–Schwartz integrability.
A. Fernández, F. Mayoral and F. Naranjo were supported by MEC and FEDER (project MTM2006–11690–C02–02) and La Junta de Andalucía. J. Rodríguez was supported by MEC and FEDER (project MTM2005-08379), Fundación Séneca (project 00690/PI/04) and the Juan de la Cierva Programme (MEC and FSE). 相似文献
20.
Ikuo Yoneda 《Archive for Mathematical Logic》2003,42(5):423-433
We show that any relational generic structure whose theory has finite closure and amalgamation over closed sets is stable
CM-trivial with weak elimination of imaginaries.
Received: 21 December 2001 /
Published online: 5 November 2002
Mathematics Subject Classification (2000): 03C45
Key words or phrases: CM-triviality – Generic structures – Stability 相似文献