共查询到20条相似文献,搜索用时 31 毫秒
1.
We are interested in the parallel computation of a linear mapping of n real variables by a network of computers with restricted means of communication between them and without any common memory. Let denote the algebra of n×n real matrices, and let G be the graph associated with a binary, reflexive and symmetric relation R over {1,2, …,n}. We define A matrix is said to be realizable on G if it can be expressed as a product of elements of AR. Therefore, every matrix of is realizable on G if and only if AR generates . We show that AR generates if and only if G is connected. 相似文献
2.
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
3.
Raul Cordovil 《Journal of Combinatorial Theory, Series B》1983,34(2):209-223
A natural sufficient condition for a finite family of single element extensions of a matroid to be compatible is given. Characterizations of all the finite extensions N of a matroid M(E) are given for which the rank function satisfies or equivalently the closure operator satisfies . The single element extensions and the principal extensions are examples of such matroids. The notion of a sheaf of flats of M. Las Vergnas is used in the proof of a new necessary and sufficient condition for two single element extensions of a matroid to be compatible. An initial announcement of part of these results appeared in R. Cordovil (C. R. Acad. Sci. Paris. A284 (1977), 1249–1252). 相似文献
4.
M. Neumann 《Linear algebra and its applications》1976,14(1):41-51
In this paper iterative schemes for approximating a solution to a rectangular but consistent linear system Ax = b are studied. Let A?Cm × nr. The splitting A = M ? N is called subproper if R(A) ? R(M) and . Consider the iteration . We characterize the convergence of this scheme to a solution of the linear system. When A?Rm×nr, monotonicity and the concept of subproper regular splitting are used to determine a necessary and a sufficient condition for the scheme to converge to a solution. 相似文献
5.
Kenny Koffi Siggini 《Comptes Rendus Mathematique》2002,334(11):949-952
Let be the space of positive -regular set-valued measures defined on a σ-algebra with values in the space of all compact non empty convex subsets of a Banach space E. We characterize the compact subsets of endowed with the weakest topology for which all mappings M→M(A), are continuous. The case of real nonnegative measures has been investigated by Topsøe [6], Grothendieck [3] and others. To cite this article: K.K. Siggini, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 949–952. 相似文献
6.
Let B(H) be the bounded operators on a Hilbert space H. A linear subspace R ? B(H) is said to be an operator system if 1 ?R and R is self-adjoint. Consider the category of operator systems and completely positive linear maps. R ∈ is said to be injective if given A ? B, A, B ∈ , each map A → R extends to B. Then each injective operator system is isomorphic to a conditionally complete C1-algebra. Injective von Neumann algebras R are characterized by any one of the following: (1) a relative interpolation property, (2) a finite “projectivity” property, (3) letting Mm = B(Cm), each map R → N ? Mm has approximate factorizations R → Mn → N, (4) letting K be the orthogonal complement of an operator system N ? Mm, each map has approximate factorizations . Analogous characterizations are found for certain classes of C1-algebras. 相似文献
7.
It is shown that if satisfies , where σk(A) denotes the sum of all kth order subpermanent of A, then Per[λJn+(1?λ)A] is strictly decreasing in the interval 0<λ<1. 相似文献
8.
《Journal of Functional Analysis》1987,73(1):122-134
Let Ω denote a connected and open subset of n. The existence of n commuting self-adjoint operators H1,…, Hn on such that each Hj is an extension of (acting on is shown to be equivalent to the existence of a measure μ on n such that f → tf (the Fourier transform of f) is unitary from onto Ω. It is shown that the support of μ can be chosen as a subgroup of n iff H1,…, Hn can be chosen such that the unitary groups generated by H1,…, Hn act multiplicatively on . This happens iff Ω (after correction by a null set) forms a system of representatives for the quotient of n by some subgroup, i.e., iff Ω is essentially a fundamental domain. 相似文献
9.
Let be the n-dimensional ice cream cone, and let Γ(Kn) be the cone of all matrices in nn mapping Kn into itself. We determine the structure of Γ(Kn), and in particular characterize the extreme matrices in Γ(Kn). 相似文献
10.
Let {Xn} be a stationary Gaussian sequence with E{X0} = 0, {X20} = 1 and E{X0Xn} = rnn Let cn = (2ln n), bn = cn? c-1n ln(4π ln n), and set Mn = max0 ?k?nXk. A classical result for independent normal random variables is that Berman has shown that (1) applies as well to dependent sequences provided rnlnn = o(1). Suppose now that {rn} is a convex correlation sequence satisfying rn = o(1), (rnlnn)-1 is monotone for large n and o(1). Then for all x, where Ф is the normal distribution function. While the normal can thus be viewed as a second natural limit distribution for {Mn}, there are others. In particular, the limit distribution is given below when rn is (sufficiently close to) γ/ln n. We further exhibit a collection of limit distributions which can arise when rn decays to zero in a nonsmooth manner. Continuous parameter Gaussian processes are also considered. A modified version of (1) has been given by Pickands for some continuous processes which possess sufficient asymptotic independence properties. Under a weaker form of asymptotic independence, we obtain a version of (2). 相似文献
11.
David A Senechalle 《Journal of Functional Analysis》1978,27(2):203-214
Let L be a finite-dimensional normed linear space and let M be a compact subset of L lying on one side of a hyperplane through 0. A measure of flatness for M is the number , where the infimum is over all f in which are positive on M. Thus D(M) = 1 if M is flat, but otherwise D(M) > 1. On the other hand, let E(M) be a second measure on M defined as follows: If M is linearly independent, E(M) = 1. If M is linearly dependent, then (1) let Z be a minimal, linearly dependent subset of M; (2) partition Z into mutually exclusive subsets U = {u1, …, up} and V = {v1, …, vq} such that there exist positive coefficients ai and bi for which Σi = 1paiui = Σi = 1qbivi; (3) let ; (4) let E(M) be the supremum of all ratios r which can be formed by steps (1), (2) and (3). The main result of this paper is that these two measures are the same: D(M) = E(M). This result is then used to obtain results concerning the Banach distance-coefficient between an arbitrary finite-dimensional normed linear space and Hilbert space. 相似文献
12.
Let be the Clifford algebra constructed over a quadratic n-dimensional real vector space with orthogonal basis {e1,…, en}, and e0 be the identity of . Furthermore, let Mk(Ω;) be the set of -valued functions defined in an open subset Ω of Rm+1 (1 ? m ? n) which satisfy Dkf = 0 in Ω, where D is the generalized Cauchy-Riemann operator and k? N. The aim of this paper is to characterize the dual and bidual of Mk(Ω;). It is proved that, if Mk(Ω;) is provided with the topology of uniform compact convergence, then its strong dual is topologically isomorphic to an inductive limit space of Fréchet modules, which in its turn admits Mk(Ω;) as its dual. In this way, classical results about the spaces of holomorphic functions and analytic functionals are generalized. 相似文献
13.
Detlef Müller 《Journal of Functional Analysis》1982,47(2):247-280
Let F1(Rn) denote the Fourier algebra on n, and (n) the space of test functions on n. A closed subset E of n is said to be of spectral synthesis if the only closed ideal J in F1(Rn) which has E as its hull is the ideal . We consider sufficiently regular compact subsets of smooth submanifolds of n with constant relative nullity. For such sets E we give an estimate of the degree of nilpotency of the algebra , where j(E) denotes the smallest closed ideal in F1(Rn) with hull E. Especially in the case of hypersurfaces this estimate turns out to be exact. Moreover for this case we prove that k(E)∩D(Rn) is dense in k(E). Together this solves the synthesis problem for such sets. 相似文献
14.
This paper considers canonical forms for the similarity action of Gl(n) on : , Those canonical forms are obtained as an application of a more general method to select canonical elements Mc in the orbits of a matrix group G acting on a set of matrices . We define a total order (?) on , different from the lexicographic order l? [0l?x ? x <0, but and consider normalized -elements with a minimal number of parameters: It is shown that the row and column echelon forms, the Jordan canonical form, and “nice” control canonical forms for reachable (A,B)-pairs have a homogeneous interpretation as such (?)-minimal orbit elements. Moreover new canonical forms for the general action (?) are determined via this method. 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.
We characterize the uniform algebras A on a compact Hausdorff space X which contain a sequence {uj}j = 0∞ of unimodular elements with and closed span in terms of the maximal ideal space of A. Roughly, the essential set of A looks like (at most) countably many copies of the boundary of the unit disk, and A looks like the disk algebra on each. 相似文献
17.
Elliptic operators , α a multi-index, with leading term positive and constant coefficient, and with lower order coefficients defined on or a quotient space are considered. It is shown that the Lp-spectrum of A is contained in a “parabolic region” Ω of the complex plane enclosing the positive real axis, uniformly in p. Outside Ω, the kernel of the resolvent of A is shown to be uniformly bounded by an L1 radial convolution kernel. Some consequences are: A can be closed in all Lp (1 ? p ? ∞), and is essentially self-adjoint in L2 if it is symmetric; A generates an analytic semigroup e?tA in the right half plane, strongly Lp and pointwise continuous at t = 0. A priori estimates relating the leading term and remainder are obtained, and summability , with φ analytic, is proved for , with convergence in Lp and on the Lebesgue set of ?. More comprehensive summability results are obtained when A has constant coefficients. 相似文献
18.
R.J. Williams 《Advances in Applied Mathematics》1985,6(1):1-3
Let {Xt, t ≥ 0} be Brownian motion in d (d ≥ 1). Let D be a bounded domain in d with C2 boundary, ?D, and let q be a continuous (if d = 1), Hölder continuous (if d ≥ 2) function in D?. If the Feynman-Kac “gauge” Ex{exp(∝0τDq(Xt)dt)1A(XτD)}, where τD is the first exit time from D, is finite for some non-empty open set A on ?D and some x?D, then for any ), is the unique solution in of the Schrödinger boundary value problem . 相似文献
19.
Let A be an n×n complex matrix. For a suitable subspace of Cn the Schur compression A and the (generalized) Schur complement A/ are defined. If A is written in the form according to the decomposition and if B is invertible, then and The commutativity rule for Schur complements is proved: This unifies Crabtree and Haynsworth's quotient formula for (classical) Schur complements and Anderson's commutativity rule for shorted operators. Further, the absorption rule for Schur compressions is proved: . 相似文献
20.
Let E be an algebraic (or holomorphic) vectorbundle over the Riemann sphere 1(). Then Grothendieck proved that E splits into a sum of line bundles E = ⊕Li and the isomorphism classes of the Li are (up to order) uniquely determined by E. The Li in turn are classified by an integer (their Chern numbers) so that m-dimensional vectorbundles over 1 are classified by an m-tuple of integers .In this short note we present a completely elementary proof of these facts which, as it turns out, works over any field k. 相似文献