共查询到20条相似文献,搜索用时 390 毫秒
1.
It is shown that if A and B are n × n complex matrices with , then there exist n × n matrices A′ and B′ with . 相似文献
2.
Results on partition of energy and on energy decay are derived for solutions of the Cauchy problem . Here the Aj's are constant, k × k Hermitian matrices, x = (x1,…, xn), t represents time, and u = u(t, x) is a k-vector. It is shown that the energy of Mu approaches a limit , where M is an arbitrary matrix; that there exists a sufficiently large subspace of data ?, which is invariant under the solution group U0(t) and such that depending on ? and that the local energy of nonstatic solutions decays as . More refined results on energy decay are also given and the existence of wave operators is established, considering a perturbed equation at infinity. 相似文献
3.
Motivated by models from stochastic population biology and statistical mechanics, we proved new inequalities of the form , where A and B are n × n complex matrices, 1<n<∞, and ? is a real-valued continuous function of the eigenvalues of its matrix argument. For example, if A is essentially nonnegative, B is diagonal real, and ? is the spectral radius, then (1) holds; if in addition A is irreducible and B has at least two different diagonal elements, then the inequality (1) is strict. The proof uses Kingman's theorem on the log-convexity of the spectral radius, Lie's product formula, and perturbation theory. We conclude with conjectures. 相似文献
4.
Pascal Cherrier 《Journal of Functional Analysis》1984,57(2):154-206
Nonlinear Neumann problems on riemannian manifolds. Let () be a C∞ compact riemannian manifold of dimension n ? 2 whose boundary B is an (n ? 1)-dimensional submanifold and let be the interior of . Study of Neumann problems of the form: , where, for every are bounded by . Application to the determination of a conformal metric for which the scalar curvature of M and the mean curvature of B take prescribed values. 相似文献
5.
Rudolf Wegmann 《Journal of Mathematical Analysis and Applications》1976,56(1):113-132
For an n × n Hermitean matrix A with eigenvalues λ1, …, λn the eigenvalue-distribution is defined by · number {λi: λi ? x} for all real x. Let An for n = 1, 2, … be an n × n matrix, whose entries aik are for i, k = 1, …, n independent complex random variables on a probability space (Ω, , p) with the same distribution Fa. Suppose that all moments | a | k, k = 1, 2, … are finite, a=0 and | a | 2. Let with complex numbers θσ and finite products Pσ of factors A and (= Hermitean conjugate) be a function which assigns to each matrix A an Hermitean matrix M(A). The following limit theorem is proved: There exists a distribution function G0(x) = G1x) + G2(x), where G1 is a step function and G2 is absolutely continuous, such that with probability converges to G0(x) as n → ∞ for all continuity points x of G0. The density g of G2 vanishes outside a finite interval. There are only finitely many jumps of G1. Both, G1 and G2, can explicitly be expressed by means of a certain algebraic function f, which is determined by equations, which can easily be derived from the special form of M(A). This result is analogous to Wigner's semicircle theorem for symmetric random matrices (E. P. Wigner, Random matrices in physics, SIAM Review9 (1967), 1–23). The examples , , , r = 1, 2, …, are discussed in more detail. Some inequalities for random matrices are derived. It turns out that with probability 1 the sharpened form of Schur's inequality for the eigenvalues λi(n) of An holds. Consequently random matrices do not tend to be normal matrices for large n. 相似文献
6.
Wolfgang Wasow 《Linear algebra and its applications》1977,18(2):163-170
Let A(x,ε) be an n×n matrix function holomorphic for |x|?x0, 0<ε?ε0, and possessing, uniformly in x, an asymptotic expansion , as ε→0+. An invertible, holomorphic matrix function P(x,ε) with an asymptotic expansion , as ε→0+, is constructed, such that the transformation y = P(x,ε)z takes the differential equation a positive integer, into , where B(x,ε) is asymptotically equal, to all orders, to a matrix in a canonical form for holomorphic matrices due to V.I. Arnold. 相似文献
7.
Tomas Schonbek 《Journal of Differential Equations》1985,56(2):290-296
New and more elementary proofs are given of two results due to W. Littman: (1) Let . The estimate cannot hold for all u?C0∞(Q), Q a cube in , some constant C. (2) Let n ? 2, p ≠ 2. The estimate cannot hold for all C∞ solutions of the wave equation □u = 0 in ; all t ?; some function C: → . 相似文献
8.
Oscar H Ibarra Shlomo Moran Roger Hui 《Journal of Algorithms in Cognition, Informatics and Logic》1982,3(1):45-56
We show that any m × n matrix A, over any field, can be written as a product, LSP, of three matrices, where L is a lower triangular matrix with l's on the main diagonal, S is an m × n matrix which reduces to an upper triangular matrix with nonzero diagonal elements when the zero rows are deleted, and P is an n × n permutation matrix. Moreover, L, S, and P can be found in O(mα?1n) time, where the complexity of matrix multiplication is O(mα). We use the LSP decomposition to construct fast algorithms for some important matrix problems. In particular, we develop O(mα?1n) algorithms for the following problems, where A is any m × n matrix: (1) Determine if the system of equations (where is a column vector) has a solution, and if so, find one such solution. (2) Find a generalized inverse, , of A (i.e., ). (3) Find simultaneously a maximal independent set of rows and a maximal independent set of columns of A. 相似文献
9.
J.W Layman 《Journal of Combinatorial Theory, Series A》1985,40(1):161-168
For any prime p, the sequence of Bell exponential numbers Bn is shown to have p ? 1 consecutive values congruent to zero (mod p), beginning with Bm, where (). This is an improvement over previous results on the maximal strings of zero residues of the Bell numbers. Similar results are obtained for the sequence of generalized Bell numbers An generated by . 相似文献
10.
Let be a real or complex n × n interval matrix. Then it is shown that the Neumann series is convergent iff the sequence {k} converges to the null matrix , i.e., iff the spectral radius of the real comparison matrix constructed in [2] is less than one. 相似文献
11.
12.
David L Johnson 《Journal of Mathematical Analysis and Applications》1982,89(2):359-369
It is shown that the set m × n of complex m × n matrices forms a lower semilattice under the partial ordering A ? B defined by denotes the conjugate transpose of A. As a special case of a result for division rings, it is further shown that, over any field F, form = n = 2 and any proper involution 1 of F2 × 2, the corresponding intersections A ∩ B all exist. 相似文献
13.
Zeev Schuss 《Journal of Mathematical Analysis and Applications》1977,59(2):227-241
Let A and B be uniformly elliptic operators of orders 2m and 2n, respectively, m > n. We consider the Dirichlet problems for the equations (?2(m ? n)A + B + λ2nI)u? = f and (B + λ2nI)u = f in a bounded domain Ω in Rk with a smooth boundary ?Ω. The estimate is derived. This result extends the results of [7, 9, 10, 12, 14, 15, 18]by giving estimates up to the boundary, improving the rate of convergence in ?, using lower norms, and considering operators of higher order with variable coefficients. An application to a parabolic boundary value problem is given. 相似文献
14.
The initial and boundary value problem for the degenerate parabolic equation vt = Δ(?(v)) + F(v) in the cylinder bounded, for a certain class of point functions ? satisfying ?′(v) ? 0 (e.g., ) is considered. In the case that F(v) sign , the equation has a global time solution. The same is true for α = 1 provided the measure of Ω is sufficiently small. In the case that is nondecreasing a condition is given on the initial state v(x, 0) which implies that the solution must blow up in finite time. The existence of such initial states is discussed. 相似文献
15.
David Gurarie 《Journal of Mathematical Analysis and Applications》1985,108(1):223-229
For elliptic operators on Rn and certain of their singular perturbations relative compactness of B with respect to A is established. This result applies to the study of Lp-spectra of elliptic operators for different p. 相似文献
16.
Some techniques for the study of the algebraic curve C(A) which generates the numerical range W(A) of an n×n matrix A as its convex hull are developed. These enable one to give an explicit point equation of C(A) and a formula for the curvature of C(A) at a boundary point of W(A). Applied to the case of a nonnegative matrix A, a simple relation is found between the curvature of the function Φ(A)=p((1?α)A+ αAT) (pbeingthePerronroot) at and the curvature of W(A) at the Perron root of . A connection with 2-dimensional pencils of Hermitian matrices is mentioned and a conjecture formulated. 相似文献
17.
It is well known that every weak solution (with boundary values 0) of a semilinear equation is a regular solution if ? fulfils the growth condition . Here 2m is the order of A. In this paper we weaken this condition to . This requires a technique completely different from that which may be applied in case (1). 相似文献
18.
Juan C. Peral 《Journal of Functional Analysis》1980,36(1):114-145
Let u(x, t) be the solution of utt ? Δxu = 0 with initial conditions . Consider the linear operator . (Here g = 0.) We prove for t fixed the following result. Theorem 1: T is bounded in Lp if and only if . Theorem 2: If the coefficients are variables in C and constant outside of some compact set we get: (a) If n = 2k the result holds for . (b) If n = 2k ? 1, the result is valid for . This result are sharp in the sense that for p such that we prove the existence of in such a way that . Several applications are given, one of them is to the study of the Klein-Gordon equation, the other to the completion of the study of the family of multipliers and finally we get that the convolution against the kernel is bounded in H1. 相似文献
19.
Let A be a real symmetric n × n matrix of rank k, and suppose that A = BB′ for some real n × m matrix B with nonnegative entries (for some m). (Such an A is called completely positive.) It is shown that such a B exists with , where 2N is the maximal number of (off-diagonal) entries which equal zero in a nonsingular principal submatrix of A. An example is given where the least m which works is (k odd), (k even). 相似文献
20.
Let Fn denote the ring of n×n matrices over the finite field F=GF(q) and let A(x)=ANxN+ ?+ A1x+A0?Fn[x]. A function is called a right polynomial function iff there exists an A(x)?Fn[x] such that for every B?Fn. This paper obtains unique representations for and determines the number of right polynomial functions. 相似文献