共查询到20条相似文献,搜索用时 46 毫秒
1.
Viktor S. Rykhlov 《Results in Mathematics》1999,36(3-4):342-353
In this paper a system of differential equations y′ ? A(·,λ)y = 0 is considered on the finite interval [a,b] where λ ∈ C, A(·, λ):= λ A1+ A 0 +λ ?1A?1(·,λ) and A 1,A 0, A ? 1 are n × n matrix-functions. The main assumptions: A 1 is absolutely continuous on the interval [a, b], A 0 and A - 1(·,λ) are summable on the same interval when ¦λ¦ is sufficiently large; the roots φ1(x),…,φn (x) of the characteristic equation det (φ E — A 1) = 0 are different for all x ∈ [a,b] and do not vanish; there exists some unlimited set Ω ? C on which the inequalities Re(λφ1(x)) ≤ … ≤ Re (λφn(x)) are fulfilled for all x ∈ [a,b] and for some numeration of the functions φj(x). The asymptotic formula of the exponential type for a fundamental matrix of solutions of the system is obtained for sufficiently large ¦λ¦. The remainder term of this formula has a new type dependence on properties of the coefficients A 1 (x), A o (x) and A - 1 (x). 相似文献
2.
Boris Bukh 《Israel Journal of Mathematics》2017,218(1):165-173
It is consistent that P(ω 1) is the union of less than \({2^{{\aleph _1}}}\) parts such that if A 0,..., A n?1, B 0,..., B m?1 are distinct elements of the same part, then |A 0 ∩ · · · ∩ A n?1 ∩ (ω 1 ? B 0) ∩ · · ·∩ (ω 1 ? B m?1)| = N1. 相似文献
3.
Let qυ=υ(υ–1)(υ–2)/24 and let Iυ={0, 1, 2, …, qυ–14}∪{qυ–12, qυ–8, qυ}, for υ?8 Further, let J[υ] denote the set of all k such that there exists a pair of Steiner quadruple systems of order υ having exactly k blocks in common. We determine J[υ] for all υ=2n, n?2, with the possible exception of 7 cases for υ=16 and of 5 cases for each υ?32. In particular we show: J[υ]?Iυ for all υ≡2 or 4 (mod 6) and υ?8, J[4]={1}, J[8]=I8={0, 2, 6, 14}, I16?{103, 111, 115, 119, 121, 122, 123}?J[16], and Iυ? {qυ–h:h=17, 18, 19, 21, 25}?J[υ] for all υ=2n, n?5. 相似文献
4.
Roy Mathias 《Linear and Multilinear Algebra》2013,61(1-4):57-70
Let σ1(X)≤ · ≤ σN(X)≤0 denote the ordered singular values ofan n × n matrix X and let α1 (X) ≤ α2(X)≤ · ≤ αn(X) denote its ordered main diagonal entries (assuming that they are real). Let B be any complex n × n skew-symmetric matrix and ||.|| any unitarily invariant norm. It is shown that for any rea positive semidefinite n × n matrix A. 相似文献
5.
Let ‖·‖ be a norm on the algebra ?n of all n × n matrices over ?. An interesting problem in matrix theory is that “Are there two norms ‖·‖1 and ‖·‖2 on ?n such that ‖A‖ = max|‖Ax‖2: ‖x‖1 = 1} for all A ∈ ?n?” We will investigate this problem and its various aspects and will discuss some conditions under which ‖·‖1 = ‖·‖2. 相似文献
6.
7.
Thomas H. Pate 《Linear algebra and its applications》1976,14(3):285-292
Suppose each of m, n, and k is a positive integer, k ? n, A is a (real-valued) symmetric n-linear function on Em, and B is a k-linear symmetric function on Em. The tensor and symmetric products of A and B are denoted, respectively, by A ?B and A?B. The identity is proven by Neuberger in [1]. An immediate consequence of this identity is the inequality In this paper a necessary and sufficient condition for is given. It is also shown that under certain conditions the inequality can be considerably improved. This improvement results from an analysis of the terms 6A?qB6, 1?q?n, appearing in the identity. 相似文献
8.
From the equationp n?k sinnθ?ρ n sin(n?k)θ=sinkθ we will show that the function σ=σ(θ) is increasing for the arcsA m , obtained when one putsn=m, k=m?1 andm=3,4,5,… Next, we will study the arcsB m obtained whenn=m, k=m?2 andm an odd integer larger than 3. In this case, σ(θ) will be shown to be a decreasing function. Finally, the Farey arcsF(p,q;r,s) are obtained whenn=s, k=q, s andq relatively prime. It will be proved that the function σ(θ) is strictly quasi-convex. 相似文献
9.
The singular pairs of n × n matrices [those satisfying det(A? λB) 0] form a closed set of codimension n + 1 inside the space of all matrix pairs. The same holds for singular symmetric pairs. For Hermitian pairs, the singular ones form a closed set of codimension n+ 1 orn + 2 according as n is odd or even. The irreducible components of these closed sets are determined by various basic singular summands. 相似文献
10.
In this paper, we prove that, if the product A=A1?An is a Fredholm operator where the ascent and descent of A are finite, then Aj is a Fredholm operator of index zero for all j, 1?j?n, where A1,…,An be a symmetric family of bounded operators. Next, we investigate a useful stability result for the Rako?evi?/Schmoeger essential spectra. Moreover, we show that some components of the Fredholm domains of bounded linear operators on a Banach space remain invariant under additive perturbations belonging to broad classes of operators A such as γ(Am)<1 where γ(⋅) is a measure of noncompactness. We also discuss the impact of these results on the behavior of the Rako?evi?/Schmoeger essential spectra. Further, we apply these latter results to investigate the Rako?evi?/Schmoeger essential spectra for singular neutron transport equations in bounded geometries. 相似文献
11.
Let ∥·∥ be an operator norm and ∥·∥D its dual. Then it is shown that ∥A∥D? ∑|λi(A)|, where λi(A) are the eigenvalues of A, holds for all matrices A if and only if ∥·∥ is the operator norm subordinate to a Euclidian vector norm. 相似文献
12.
Gaywalee Yamskulna 《代数通讯》2013,41(12):4137-4162
We study relationships between vertex Poisson algebras and Courant algebroids. For any ?-graded vertex Poisson algebra A = ? n∈? A (n), we show that A (1) is a Courant A (0)-algebroid. On the other hand, for any Courant 𝒜-algebroid ?, we construct an ?-graded vertex Poisson algebra A = ? n∈? A (n) such that A (0) is 𝒜 and the Courant 𝒜-algebroid A (1) is isomorphic to ? as a Courant 𝒜-algebroid. 相似文献
13.
V. V. Kozlov 《Functional Analysis and Its Applications》2017,51(4):306-309
Systems of equations f 1 = ··· = f n?1 = 0 in ? n = {x} having the solution x = 0 are considered under the assumption that the quasi-homogeneous truncations of the smooth functions f 1,..., f n?1 are independent at x ≠ 0. It is shown that, for n ≠ 2 and n ≠ 4, such a system has a smooth solution which passes through x = 0 and has nonzero Maclaurin series. 相似文献
14.
This paper is devoted to investigating the asymptotic properties of the renormalized solution to the viscosity equation tfε + v ·▽xfε = Q (fε,fε ) + εΔvfε as ε→ 0+ . We deduce that the renormalized solution of the viscosity equation approaches to the one of the Boltzmann equation in L1 ((0 , T ) × RN × RN ). The proof is based on compactness analysis and velocity averaging theory. 相似文献
15.
Let pk(A), k=2,…,n, denote the sum of the permanents of all k×k submatrices of the n×n matrix A. A conjecture of Ðokovi?, which is stronger than the famed van der Waerden permanent conjecture, asserts that the functions pk((1?θ)Jn+;θA), k=2,…, n, are strictly increasing in the interval 0?θ?1 for every doubly stochastic matrix A. Here Jn is the n×n matrix all whose entries are equal . In the present paper it is proved that the conjecture holds true for the circulant matrices A=αIn+ βPn, α, β?0, α+;β=1, and , where In and Pn are respectively the n×n identify matrix and the n×n permutation matrix with 1's in positions (1,2), (2,3),…, (n?1, n), (n, 1). 相似文献
16.
Let A be an mth order n-dimensional tensor, where m, n are some positive integers and N:= m(n?1). Then A is called a Hankel tensor associated with a vector v ∈ ?N+1 if Aσ = v k for each k = 0, 1,...,N whenever σ = (i1,..., im) satisfies i1 +· · ·+im = m+k. We introduce the elementary Hankel tensors which are some special Hankel tensors, and present all the eigenvalues of the elementary Hankel tensors for k = 0, 1, 2. We also show that a convolution can be expressed as the product of some third-order elementary Hankel tensors, and a Hankel tensor can be decomposed as a convolution of two Vandermonde matrices following the definition of the convolution of tensors. Finally, we use the properties of the convolution to characterize Hankel tensors and (0,1) Hankel tensors. 相似文献
17.
Richard Sinkhorn 《Linear algebra and its applications》1977,16(1):79-82
Let A be an n×n doubly stochastic matrix and suppose that 1?m?n?1. Let τ1,…,τm be m mutually disjoint zero diagonals in A, and suppose that every diagonal of A disjoint from τ1,…,τm has a constant sum. Then aall entries of A off the m zero diagonals have the value (n?m)?1. This verifies a conjecture of E.T. Wang. 相似文献
18.
An anti-Hadamard matrix may be loosely defined as a real (0, 1) matrix which is invertible, but only just. Let A be an invertible (0, 1) matrix with eigenvalues λi, singular values σi, and inverse B = (bij). We are interested in the four closely related problems of finding λ(n) = minA, i|λi|, σ(n) = minA, iσi, χ(n) = maxA, i, j |bij|, and μ(n) = maxAΣijb2ij. Then A is an anti-Hadamard matrix if it attains μ(n). We show that λ(n), σ(n) are between and c√n (2.274)?n, where c is a constant, , and . We also consider these problems when A is restricted to be a Toeplitz, triangular, circulant, or (+1, ?1) matrix. Besides the obvious application—to finding the most ill-conditioned (0, 1) matrices—there are connections with weighing designs, number theory, and geometry. 相似文献
19.
R.A. Willoughby 《Linear algebra and its applications》1977,18(1):75-94
One aspect of the inverse M-matrix problem can be posed as follows. Given a positive n × n matrix A=(aij) which has been scaled to have unit diagonal elements and off-diagonal elements which satisfy 0 < y ? aij ? x < 1, what additional element conditions will guarantee that the inverse of A exists and is an M-matrix? That is, if A?1=B=(bij), then bii> 0 and bij ? 0 for i≠j. If n=2 or x=y no further conditions are needed, but if n ? 3 and y < x, then the following is a tight sufficient condition. Define an interpolation parameter s via x2=sy+(1?s)y2; then B is an M-matrix if s?1 ? n?2. Moreover, if all off-diagonal elements of A have the value y except for aij=ajj=x when i=n?1, n and 1 ? j ? n?2, then the condition on both necessary and sufficient for B to be an M-matrix. 相似文献
20.
Bhagwati P. Duggal Slavisa V. Djordjević Carlos S. Kubrusly 《Rendiconti del Circolo Matematico di Palermo》2010,59(3):473-481
Given Banach space operators A ∈ B( ) and B ∈ B( ), let A?B ∈ B( ? ) denote the tensor product of A and B. Let σ a , σ aw and σ ab denote the approximate point spectrum, the Weyl approximate point spectrum and the Browder approximate point spectrum, respectively. Then σ aw (A?B) ? σ a (A)σ aw (B) ? σ aw (A)σ a (B) ? σ a (A)σ ab (B) ? σ ab (A)σ a (B) = σ ab (A?B), and a sufficient condition for the (a-Weyl spectrum) identity σ aw (A?B) = σ a (A)σ aw (B) ? σ aw (A)σ a (B) to hold is that σ aw (A?B) = σ ab (A?B). Equivalent conditions are proved in Theorem 1, and the problem of the transference of a-Weyl’s theorem for a-isoloid operators A and B to their tensor product A?B is considered in Theorem 2. Necessary and sufficient conditions for the (plain) Weyl spectrum identity are revisited in Theorem 3. 相似文献