共查询到20条相似文献,搜索用时 15 毫秒
1.
John Jones 《Mathematics and computers in simulation》1983,25(6):489-492
The main purpose of this work is to establish necessary conditions and sufficient conditions for the existence of a solution of matrix equations whose coefficient matrices have elements belonging to the ring of polynomials in n variables with complex coefficients and the ring of rational functions a(z1,z2,…zn)b(z1,z2,…,zn)?1 with real coefficients and b(z1,z2,…,zn)≠0 for all (z1,z2,…,zn) in Rn. Results obtained are useful in multidimensional systems theory and elsewhere. 相似文献
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W. Splettstösser 《Information Sciences》1982,28(2):115-130
A new method is used to construct coefficients akn such that any band-limited signal function with highest frequency ΠW can be reconstituted from its samples from the past via Although the existence of such predictor coefficients can be proved for each positive T < 1, so far they have been exhibited only for by J. L. Brown, Jr. [1]. Using the mathematical tool of power series expansions in the complex domain, T can be extended to at least , that is, the sampling rate has to exceed three-halves the Nyquist rate. Again the predictor coefficients akn do not depend on the structure of ? or on the bandwidth parameter W. 相似文献
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Osamu Watanabe 《Theoretical computer science》1983,24(1):105-117
A probabilistic Turing machine (PTM) is a Turing machine that flips an unbiased coin to decide its next movement and solves a problem with some error probability. It is expected that PTMs need more time if a smaller error probability is required. This is a sort of time-precision tradeoff and is shown to occur actually on on-line probabilistic Turing machine acceptors (ONPTMs). That is, we show the existence of a set such that it is recognized by an ONPTM with bounded error probability in O(n) time but for every , it requires more than O((n/log n)2) time to recognize this set with bounded error probability by ONPTMs. Moreover our result is also shown to be an example of difference between nondeterministic computations and probabilistic ones. 相似文献
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Keisuke Uchimura 《Theoretical computer science》1984,31(3):227-261
We consider an algebraic system over [x] of the form X = a0(x)Xk+ ak1(x)X+ak(x), where a0(x) and ak(x) are in x[x] and ak?1(x) is in x. Let A be the infinite incidence matrix associated with the algebraic system. Then we prove that the eigenvalues of northwest corner truncations of A are dense in some algebraic curves.Using this we get a result on positive algebraic series. We consider the case that the coefficients of a1(x)(i = 0,…,k?1, k) are positive. The algebraic series generated by the algebraic system may be viewed as a function in the complex variable x. Then by the above fact we prove that the radius of convergence of the function equals the least positive zero of the modified discriminant of the system.As an application to context free languages we show a procedure for calculating the entropy of some one counter languages. Other applications to Dyck languages and the Lukasiewicz language are also described. 相似文献
5.
Jacques Maurin 《Information Sciences》1976,11(2):141-185
First, on any sequence of real numbers (xλ), , the pseudo probability Pr(x, x′) of the event xλ?[x, x′[ is defined to be the limit when Λ → ∞ of the ratio of the number of xλ?[x, x′[ to the total number of xλ. The a.d.f. (asymptotic distribution function) of the sequence is then defined by F(x) = Pr(? ∞, x); it possesses the properties of a d.f. (distribution function). Consequently, what is said below applies equally to a sequence of r.v. (random variables) or to a sequence of p.r.v. (pseudorandom variables) consisting of a sequence (nxλ), of sequences nxλ, .A weyl's polynomial ?n(λ) is a polynomial such that one of its coefficieints other than ?(0) is irrational. Then any sequence, the fractional part of ?n(λ), , is asymptotically equidistributed on [0, 1].A property is given which permits the construction of a sequence (nxλ), of pseudostochastically independent sequences nxλ, .It is known that setting Yn = F(? 1)(Xn), it is possible to transform any sequence of r.v. Xn 相似文献
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The solution of the Dirichlet boundary value problem over a polyhedral domain Ω ? Rn, n ≥ 2, associated with a second-order elliptic operator, is approximated by the simplest finite element method, where the trial functions are piecewise linear. When the discrete problem satisfies a maximum principle, it is shown that the approximate solution uh converges uniformly to the exact solution u if u ? W1,p (Ω), with p > n, and that if u ? W2,p(Ω), with 2p > n. In the case of the model problem ?Δu+au = f in Ω, u = uo on δΩ, with a ? 0, a simple geometrical condition is given which insures the validity of the maximum principle for the discrete problem. 相似文献
8.
Clement H.C. Leung 《Information Processing Letters》1984,19(4):199-201
A new, intuitive derivation of the approximate average storage utilisation of B-trees is presented, which is generalised to the analysis of B1-trees whose average storage utilisation is found to be or 81%. The approximate average storage utilisation of trees with arbitrary minimum fullness factor f(0 <f<1) is also obtained and found to be . 相似文献
9.
M. Delfour 《Computer Methods in Applied Mechanics and Engineering》1985,50(3):231-261
Let Ω be a polygonal domain in , τh an associated triangulation and uh the finite element solution of a well-posed second-order elliptic problem on (Ω, τh). Let M = {Mi}p + qi = 1 be the set of nodes which defines the vertices of the triangulation τh: for each i, in Rn. The object of this paper is to provide a computational tool to approximate the best set of positions M? of the nodes and hence the best triangulation which minimizes the solution error in the natural norm associated with the problem.The main result of this paper are theorems which provide explicit expressions for the partial derivatives of the associated energy functional with respect to the coordinates xil, 1 ? l ? n, of each of the variable nodes Mi, i = 1,…, p. 相似文献
10.
Paavo Turakainen 《Information Sciences》1981,24(3):229-253
Using a simple method we find some nonstochastic and stochastic languages related to the Dyck sets and to the languages and . Using the theory of uniformly distributed sequences, we present a sufficient condition for a one-letter language to be nonstochastic. Among the applications is the result that {ap¦p is a prime} is nonstochastic. We also study the images of stochastic and rational stochastic languages under nonerasing and arbitrary homomorphisms as well as their relations to some well-known families. Finally, we introduce a large class of bounded languages and show that it is contained in /of∩ (DUP) = the smallest intersection-closed AFL containing , which is a subfamily of /oK(/oLQ = the image of the family of rational stochastic languages under nonerasing homomorphisms. 相似文献
11.
M. Becker W. Degenhardt J. Doenhardt S. Hertel G. Kaninke W. Keber K. Mehlhorn S. Näher H. Rohnert T. Winter 《Information Processing Letters》1982,15(3):135-136
A probabilistic algorithm is presented which computes the vertex connectivity of an undirected graph G = (V,E) in expected time with error probability at most e provided that |E|<frcase|1/2d|V|2 for some universal constant d<1. 相似文献
12.
Louis Monier 《Theoretical computer science》1980,12(1):97-108
We analyse two recent probabilistic primality testing algorithms; the first one is derived from Miller [6] in a formulation given by Rabin [7], and the second one is from Solovay and Strassen [9]. Both decide whether or not an odd number n is prime in time O(m, lognM(n)) with an error probability less than αm, for some . Our comparison shows that the first algorithm is always more efficient than the second, both in probabilistic and algorithmic terms. 相似文献
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L.P. Lefkovitch 《Information Sciences》1985,36(3):283-294
If the set covering constraints are Ax ? 1 and xj ∈ {0,1}, the prior probability that the jth subset participates in an optimal covering (independently of subset costs) is shown to be given by the principal row eigenvector of A1A, where . These probabilities lead to new and interesting objective functions, which are shown to be equivalent to cross entropy or weighted cross-entropy. The probabilities can also be used to obtain better bounds for heuristic solutions to optimal covering and set representation problems. 相似文献
15.
Frank M Callier 《Automatica》1975,11(1):85-91
This paper considers distributed n-inputn-output convolution feedback systems characterized by , and e = u ? z, where the forward path transfer function and the feedback path transfer function both contain a real single unstable pole at different locations. Theorem 1 gives necessary and sufficient conditions for both input-error and input-output stability. In addition to usual conditions that guarantee input-error stability a new condition is found which results in the fact that input-error stability will guarantee input-output stability. These conditions require to investigate only the open-loop characteristics. A basic device is the consideration of the residues of different transfer functions at the open-loop unstable poles. An example is given. 相似文献
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《Computers & Mathematics with Applications》2005,49(1):73-80
This paper is concerned with the nonlinear fractional differential equation L(D)u=f(x,u), u(0)=0, 0<x<1,where L(D) = Dsn − an−1Dsn−1 − … − a1Ds11 < s2 < … < sn < 1, and aj > 0, j = 1,2,…, n − 1. Some results are obtained for the existence, nonexistence, and multiplicity of positive solutions of the above equation by using Krasnoselskii's fixed-point theorem in a cone. In particular, it is proved that the above equation has N positive solutions under suitable conditions, where N is an arbitrary positive integer. 相似文献
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《Computers & Mathematics with Applications》2003,45(6-9):1461-1468
The authors consider the mth-order neutral difference equation Dm(y(n) + p(n)y(n − k) + q(n)f(y(σ(n))) = e(n), where m ≥ 1, {p(n)}, {q(n)}, {e(n)}, and {a1(n)}, {a2(n)}, …, {am−1(n)} are real sequences, ai(n) > 0 for i = 1,2,…, m−1, am(n) ≡ 1, D0z(n) = y(n)+p(n)y(n − k), Diz(n) = ai(n)ΔDi−1z(n) for i = 1,2, …, m, k is a positive integer, {σ(n)} → ∞ is a sequence of positive integers, and R → R is continuous with u f(u) > 0 for u ≠ 0. In the case where {q(n)} is allowed to oscillate, they obtain sufficient conditions for all bounded nonoscillatory solutions to converge to zero, and if {q(n)} is a nonnegative sequence, they establish sufficient conditions for all nonoscillatory solutions to converge to zero. Examples illustrating the results are included throughout the paper. 相似文献