共查询到20条相似文献,搜索用时 15 毫秒
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《Computers & Mathematics with Applications》2003,45(6-9):1059-1073
We extend Henry Poincaré's normal form theory for autonomous difference equations χk + 1 = f(χk) to nonautonomous difference equations χk + 1 = fk(χk). Poincaré's nonresonance condition for eigenvalues is generalized to the new nonresonance condition λj∪ for spectral intervals. 相似文献
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It is known that the similarity equations for the leeward line of symmetry of a cone have no solutions for , where k is the incidence parameter of Moore, and depend on the external Mach number and enthalpy ratio. In this paper we present evidence that a leeside integration for such k terminates at a finite distance from the vertex in a singularity of the type analyzed by Stewartson and Simpson for entry flow in a curved pipe, and compare the theory with a representative numerical solution at . A possible interpretation of this singularity is that the boundary layers growing from the windward line of symmetry have collided, and support for this view is given by windward to leeward integrations for a range of values of k. For k such that the similarity equations have solutions, these are interpreted as limits of more general solutions. 相似文献
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《Computers & Mathematics with Applications》2002,43(10-11):1239-1248
We give conditions on ƒ involving pairs of discrete lower and discrete upper solutions which lead to the existence of at least three solutions of the discrete two-point boundary value problem , where ƒ is continuous and vk = yk − yk−1, for k = 1,…,n. In the special case , we give growth conditions on ƒ and apply our general result to show the existence of three positive solutions. We give an example showing this latter result is sharp. Our results extend those of Avery and Peterson and are in the spirit of our results for the continuous analogue. 相似文献
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J.M.F. Chamayou 《Computer Physics Communications》1980,21(2):145-161
A method which consists in shifting different histograms of the same spectrum and then taking their average is presented in order to smooth the data and to increase the localization accuracy and separation of the peaks. The statistical properties of this method are investigated. The average of two histograms with shifted bin limits is studied. It is shown that for histograms with random bin limits, distributed according to ; where the standard deviation σ is very small compared to the difference of the means (μi+1 ? μi) for ll i the zero order approximation to the variance of this histogram is given by: , where and g is an unknown function fitted by the histogram. Formula (1) gives also the relation: , when H1 and H2 have stochastically independent bin limits.When the histogram H is considered as a spline function S of order one it is shown that for the minimization criterion with respect to the coefficient of the spline: , the following result holds: , where . If the number of shifted histograms tends to infinity, then , where , and h is a constant bin size. Then . Extensions to two-dimensional histograms and to higher order (empirical distributions) are presented. 相似文献
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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
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J.L. Brown 《Information Sciences》1977,12(2):93-103
A given deterministic signal x(.) is distorted by passing it through a linear time-invariant filter and also by subjecting it to the action of an instantaneous nonlinearity. The resulting time crosscorrelation of the two distorted versions of the original signal is expressed by the function , where x(.) is the given signal, k(.) is the nonnegative definite impulse response of the linear filter, and g(.) is the output-input characteristic of the zero-memory nonlinear device. The problem considered is that of determining conditions on the pair (x,g) such that R2(s) ? R2(0) for all s and any choice of nonnegative definite filter function k; the principal result is the formulation of a necessary and sufficient condition for R2 to have a global maximum at the origin. In particular, the peak value occurs at the origin if and only if is real and nonnegative for all ω ? 0, where Gx(.) and X(.) are the Fourier transforms of g[x(.)] and x(.), respectively. An equivalent condition is that the correlation function , previously studied by Richardson, be nonnegative definite.Several examples are given, and it is shown that, unlike the case for R1(.), monotonicity of g(.) is not a sufficient condition for R2(.) to have a global maximum at s = 0 independently of the choice of filter characteristic k. Certain extensions of these results are given for the case when x(.) is a Gaussian random input. 相似文献
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Donald J. Mintz 《Calphad》1979,3(4):259-273
By assuming a proportionality exists between a difference in Boltzmann factors and a difference in compositions, the following expression is developed for the mole fraction order parameter in symmetric binary liquid mixtures In the critical limit this expression reduces to the form for simple scaling fx253-fig 1 By treating the original components A and B as if they transfer between the phases in the form of aggregates with the empirical formulas AmB1?m and Bn, in which 0<m≤Landn>0, coexistence curves in diverse systems become symmetric and are fitted by the above expressions. Beta exponent values obtained from these fits range in value from 0.312±0.002 to 0.333±0.003. 相似文献
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Bezier's method is one of the most famous in computational geometry. In his book Numerical control Bezier gives excellent expositions of the mathematical foundations of this method. In this paper a new expression of the functions {fn,i(u)} is obtained.Using this formula, we have not only derived some properties of the functions {fn,i(u)} (for instance and functions {fn,i(u)} increase strictly at [0, 1] etc) but also simplified systematically all the mathematical discussions about Bezier's method.Finally we have proved the plotting theorem completely by matrix calculation. 相似文献
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William P. Wardlaw 《Computers & Education》1978,2(3):247-257
Two examples are given in which the computer was used to supplement intuition in abstract algebra. In the first example, the computer was used to search Cayley tables of 4 element groupoids to find those which are 5-associative but not 4-associative. (n-associative means that the product of any n elements is independent of the way the factors are grouped by parentheses.) The computer generated examples suggested the existence of n element groupoids which are (2n?2+1)-associative but not (2n-2)-associative, for each integer n≧4.In the second example, the computer counted the numbers g2(m) of invertible 2×2 matrices with entries chosen from the ring Zmof integers, for m = 2, 3, 4,…, 18. The insight gained from these results led to a proof that there are invertible n×n matrices over Zm.Some applications to graduate and undergraduate instruction are indicated. 相似文献
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L.L. Campbell 《Information Sciences》1985,35(3):199-210
?encov has shown that the Riemannian metric on the probability simplex ∑xi = 1 defined by has an invariance property under certain probabilistically natural mappings. No other Riemannian metric has the same property. The geometry associated with this metric is shown to lead almost automatically to measures of divergence between probability distributions which are associated with Kullback, Bhattacharyya, and Matusita. Certain vector fields are associated in a natural way with random variables. The integral curves of these vector fields yield the maximum entropy or minimum divergence estimates of probabilities. Some other consequences of this geometric view are also explored. 相似文献
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In this paper steady-state random-point results for single-server bulk-service system are related to imbedded Markov Chain results using the Erlangian technique. Steady-state results, including the expected number in queue at random and arrival epochs, and waiting time distribution are found in terms of the unique root of the characteristic equation. Examples of extensive numerical work are presented in tabular forms. 相似文献
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The high temperature phase relations in the FeMnC system have been analyzed in light of the recently developed thermodynamic method by the authors to obtain the Gibbs energies of formation of Mn23C6 and Mn,C. A new thermodyn/amic treatment is outlined and applied to obtain the stability of the ternary carbide M(Fe,Mn)3C without any a priori assumption of a solution model for the M3C phase. The recommended Gibbs energies of formation for the Mn carbides, Mn3C and Mn23C6 With γ-Mn (graphite) as the Standard states are: The present method can be extended to obtain a consistent set of thermodynamic data for binary and ternary carbides from various ternary metal-metal-carbon phase relations. 相似文献
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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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Mituhiko Araki 《Systems & Control Letters》1985,6(1):1-5
It is proved that, for a given stable transfer matrix G(s), there exists a constant diagonal matrix W which makes WG(s) positive-real if Re gii(jω) ≥ 0 and I?? is an M-matrix where ? = (?jk) is defined by ?ii = 0 and . 相似文献
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E.J. Davison 《Automatica》1974,10(3):309-316
The following problem is considered in this paper. Suppose a system S consists of a set of arbitrary interconnected subsystems Si, i = 1, 2, …, Ω; is it possible to stabilize and satisfactorily control the whole system S by using only local controllers about the individual subsystems without a knowledge of the manner of the actual interconnections of the whole system? Sufficient conditions are obtained for such a result to hold true; in particular it is shown that a system S consisting of a number of subsystems Si connected in an arbitrary way between themselves with finite gains: where Ai and bi have a particular structure, may be satisfactorily controlled by applying only local controllers Ci about the individual subsystems: Ci: ui = K′i(?)xi where Ki is a constant gain matrix with the scalar ? appearing as a parameter, provided ? is large enough. 相似文献