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1.
Kazem Ghanbari 《Positivity》2006,10(4):721-729
We denote the spectrum of an square matrix A by σ(A), and that of the matrix obtained by deleting the first i rows and columns of A by σi(A). It is known that a symmetric pentadiagonal oscillatory (SPO) matrix may be constructed from σ, σ1 and σ2. The pairs σ, σ1 and σ1, σ2 must interlace; the construction is not unique; and the conditions on the data which ensure that A is oscillatory are extremely complicated. Given one SPO matrix A, the paper shows that operations may be applied to A to construct a family of such matrices with σ and σ1 in common. Moreover, given one totally positive (TP) matrix A, we construct a family of TP matrices with σ, σ1 and σ2 in common. 相似文献
2.
TanBo WenZhixiong ZhangYiping 《分析论及其应用》2003,19(4):365-382
We study the structure of invertible substitutions on three-letter alphabet. We show that there exists a fi-nite set S of invertible substitutions such that any invertible substitution can be written as Iw^oQ1^oQ2^o……^oQk,,where Iw is the inner automorphism associated with w, and ajЕS for l≤j≤k. As a consequence, M is thematrix of an invertible substitution if and only if it is a finite product of non-negative elementary matrices. 相似文献
3.
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
4.
In this article we study the common dynamics of two different Pisot substitutions σ
1 and σ
2 having the same incidence matrix. This common dynamics arises in the study of the adic systems associated with the substitutions
σ
1 and σ
2. Since the adic systems considered here have geometric realizations given by solutions to graph-directed iterated function
systems, we actually study topological and measure-theoretic properties of the solution of those iterated function systems
which describe the common dynamics. We also consider generalizations of these results to the nonunimodular case, the case
of more than two substitutions and the case of two substitutions with different incidence matrices. 相似文献
5.
6.
Let (ℋ, ℳ) be a linear matrix problem induced from a finite dimensional algebra ∧. Then anṉ ×ṉ matrix M in R(ℋ, ℳ) is indecomposable if and only if the number of links in the canonical formM
(∞) of M is equal to. ℳ-dimṉ − 1. On the other hand, the dimension of the endomorphism ring of M is equal to ℋ-dimṉ − σ(M). 相似文献
7.
8.
We characterize the surjective additive maps compressing the spectral function Δ(·) between standard operator algebras acting on complex Banach spaces, where Δ(·) stands for any one of nine spectral functions σ(·), σl(·), σr(·),σl(·) ∩ σr(·), δσ(·), ησ(·), σap(·), σs(·), and σap(·) ∩ σs(·). 相似文献
9.
Zhi-jian QIU Department of Economic Mathematics Southwestern University of Finance Economics Chengdu China 《中国科学A辑(英文版)》2007,50(3):305-312
For a compact subset K in the complex plane, let Rat(K) denote the set of the rational functions with poles off K. Given a finite positive measure with support contained in K, let R2(K,v) denote the closure of Rat(K) in L2(v) and let Sv denote the operator of multiplication by the independent variable z on R2(K, v), that is, Svf = zf for every f∈R2(K, v). SupposeΩis a bounded open subset in the complex plane whose complement has finitely many components and suppose Rat(Ω) is dense in the Hardy space H2(Ω). Letσdenote a harmonic measure forΩ. In this work, we characterize all subnormal operators quasi-similar to Sσ, the operators of the multiplication by z on R2(Ω,σ). We show that for a given v supported onΩ, Sv is quasi-similar to Sσif and only if v/■Ω■σ and log(dv/dσ)∈L1(σ). Our result extends a well-known result of Clary on the unit disk. 相似文献
10.
G. P. Galdi K. Pileckas A. L. Silvestre 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2007,8(4):994-1007
We show that in an unsteady Poiseuille flow of a Navier–Stokes fluid in an infinite straight pipe of constant cross-section,
σ, the flow rate, F(t), and the axial pressure drop, q(t), are related, at each time t, by a linear Volterra integral equation of the second type, where the kernel depends only upon t and σ. One significant consequence of this result is that it allows us to prove that the inverse parabolic problem of finding a
Poiseuille flow corresponding to a given F(t) is equivalent to the resolution of the classical initial-boundary value problem for the heat equation. 相似文献
11.
E. A. Barabanov 《Differential Equations》2010,46(5):613-627
We consider families of linear differential systems continuously depending on a real parameter. The stability (respectively,
asymptotic stability) set of such a family is defined as the set of all values of the parameter for which the corresponding
systems in the family are stable (respectively, asymptotically stable). We show that a set on the real axis is the stability
(respectively, asymptotic stability) set of some family of this kind if and only if it is an F
σ
-set (respectively, an F
σδ
-set). For families in which the parameter occurs only as a factor multiplying the matrix of the system, their stability sets
are exactly F
σ
-sets containing zero on the real line. The asymptotic stability sets of such families will be described in the second part
of the present paper. 相似文献
12.
13.
Tight Distance-Regular Graphs and the Q-Polynomial Property 总被引:1,自引:0,他引:1
Arlene A. Pascasio 《Graphs and Combinatorics》2001,17(1):149-169
Let Γ denote a distance-regular graph with diameter d≥3, and assume Γ is tight (in the sense of Jurišić, Koolen and Terwilliger). Let θ denote the second largest or smallest eigenvalue
of Γ, and let σ0,σ1,…,σ
d
denote the associated cosine sequence. We obtain an inequality involving σ0,σ1,…,σ
d
for each integer i (1≤i≤d−1), and we show equality for all i is closely related to Γ being Q-polynomial with respect to θ. We use this idea to investigate the Q-polynomial structures in tight distance-regular graphs.
Received: January 30, 1998 Final version received: August 14, 1998 相似文献
14.
We investigate the semigroups of full and partial transformations of a set X which preserve a binary relation σ defined on X. We consider in detail the case where σ is an order or a quasi-order relation. There are conditions of regularity of such semigroups. We introduce two definitions
of preservation of σ for the semigroup of binary relations. It is proved that subsets of B(X) preserving σ are semigroups in each case. We give the condition of regularity of B
σ
(X) in the case where σ(X) is a quasi-order. 相似文献
15.
NS Condition of Admissibility for the Linear Estimator of Normal Mean with Unknown Variance 总被引:1,自引:0,他引:1
Xing Zhong XU Qi Guang WU 《数学学报(英文版)》2005,21(5):1083-1086
Suppose Y - N(β, σ^2 In), where β ∈ R^n and σ^2 〉 0 are unknown. We study the admissibility of linear estimators of mean vector under a quadratic loss function. A necessary and sufficient condition of the admissible linear estimator is given. 相似文献
16.
Jorge García-Melián José C. Sabina De Lis Julio D. Rossi 《NoDEA : Nonlinear Differential Equations and Applications》2007,14(5-6):499-525
We deal with positive solutions of Δu = a(x)u
p
in a bounded smooth domain subject to the boundary condition ∂u/∂v = λu, λ a parameter, p > 1. We prove that this problem has a unique positive solution if and only if 0 < λ < σ1 where, roughly speaking, σ1 is finite if and only if |∂Ω ∩ {a = 0}| > 0 and coincides with the first eigenvalue of an associated eigenvalue problem. Moreover, we find the limit profile
of the solution as λ → σ1.
Supported by DGES and FEDER under grant BFM2001-3894 (J. García-Melián and J. Sabina) and ANPCyT PICT No. 03-05009 (J. D.
Rossi). J.D. Rossi is a member of CONICET. 相似文献
17.
18.
σ
k
-Yamabe equations are conformally invariant equations generalizing the classical Yamabe equation. In (J. Funct. Anal. 233:
380–425, 2006) YanYan Li proved that an admissible solution with an isolated singularity at 0∈ℝ
n
to the σ
k
-Yamabe equation is asymptotically radially symmetric. In this work we prove that such a solution is asymptotic to a radial
solution to the same equation on ℝ
n
∖{0}. These results generalize earlier pioneering work in this direction on the classical Yamabe equation by Caffarelli, Gidas,
and Spruck. In extending the work of Caffarelli et al., we formulate and prove a general asymptotic approximation result for
solutions to certain ODEs which include the case for scalar curvature and σ
k
curvature cases. An alternative proof is also provided using analysis of the linearized operators at the radial solutions,
along the lines of approach in a work by Korevaar, Mazzeo, Pacard, and Schoen. 相似文献
19.
Given a locally compact group G acting on a locally compact space X and a probability measure σ on G, a real Borel function f on X is called σ-harmonic if it satisfies the convolution equation . We give conditions for the absence of nonconstant bounded harmonic functions. We show that, if G is a union of σ-admissible neighbourhoods of the identity, relative to X, then every bounded σ-harmonic function on X is constant. Consequently, for spread out σ, the bounded σ-harmonic functions are constant on each connected component of
a [SIN]-group and, if G acts strictly transitively on a splittable metric space X, then the bounded σ-harmonic functions on X are constant which extends Furstenberg’s result for connected semisimple Lie groups.
(Received 13 June 1998; in revised form 31 March 1999) 相似文献
20.
Summary. We study the F?ppl—von Kármán theory for isotropically compressed thin plates in a geometrically linear setting, which is
commonly used to model weak buckling of thin films. We consider generic smooth domains with clamped boundary conditions, and
obtain rigorous upper and lower bounds on the minimum energy linear in the plate thickness σ . This energy is much lower than previous estimates based on certain dimensional reductions of the problem, which had lead
to energies of order 1+σ (scalar approximation) or σ
2/3
(two-component approximation).
Received August 7, 2000; accepted September 8, 2000 %%%Online publication November 15, 2000 Communicated by Robert V. Kohn 相似文献