单频干涉仪瞬时相位计算的神经网络模型

用反三角函数表述的单频干涉仪瞬时相位的解析计算模型通常是分段或不连续的 ,不利于系统性能的综合分析。这里提出了基于神经网络的干涉仪瞬时相位的连续型计算模型 ,给出了网络学习方法。仿真研究结果表明 ,该模型对干涉仪瞬时相位的辨识精度优于 0 5° ,同时对干涉仪的光强波动有良好的鲁棒性 ;实验结果验证了这一点 ,为进一步提高单频干涉仪信号处理精度奠定了基础。此外 ,简要述及了该模型在其他测量领域 ,特别是速度 加速度测量领域的应用前景。     

图的剖分点-边冠运算下的规范拉普拉斯谱

A subdivision vertex-edge corona G_1~S?(∪ G_3~E) is a graph that consists of S(G_1),|V(G_1)| copies of G_2 and |I(G_1)| copies of G_3 by joining the i-th vertex in V(G_1) to each vertex in the i-th copy of G_2 and i-th vertex of I(G_1) to each vertex in the i-th copy of G_3.In this paper, we determine the normalized Laplacian spectrum of G_1~S?(G_2~V∪ G_3~E) in terms of the corresponding normalized Laplacian spectra of three connected regular graphs G_1, G_2 and G_3. As applications, we construct some non-regular normalized Laplacian cospectral graphs. In addition, we also give the multiplicative degree-Kirchhoff index, the Kemeny's constant and the number of the spanning trees of G_1~S?(G_2~V∪ G_3~E) on three regular graphs.     

On multivariate subdivision schemes with nonnegative finite masks

We study the convergence of multivariate subdivision schemes with nonnegative finite masks. Consequently, the convergence problem for the multivariate subdivision schemes with nonnegative finite masks supported on centered zonotopes is solved. Roughly speaking, the subdivision schemes defined by these masks are always convergent, which gives an answer to a question raised by Cavaretta, Dahmen and Micchelli in 1991.

     

A Metric of Constant Curvature on Polycycles

We prove the following main theorem of the theory of (r, q)-polycycles. Suppose a nonseparable plane graph satisfies the following two conditions:(1) each internal face is an r-gon, where r ≥ 3;(2) the degree of each internal vertex is q, where q ≥ 3, and the degree of each boundary vertex is at most q and at least 2.Then it also possesses the following third property:(3) the vertices, the edges, and the internal faces form a cell complex.Simple examples show that conditions (1) and (2) are independent even provided condition (3) is satisfied. These are the defining conditions for an (r, q)-polycycle.__________Translated from Matematicheskie Zametki, vol. 78, no. 2, 2005, pp. 223–233.Original Russian Text Copyright © 2005 by M. Deza, M. I. Shtogrin.     

Differentiability of multivariate refinable functions and factorization

The paper develops a necessary condition for the regularity of a multivariate refinable function in terms of a factorization property of the associated subdivision mask. The extension to arbitrary isotropic dilation matrices necessitates the introduction of the concepts of restricted and renormalized convergence of a subdivision scheme as well as the notion of subconvergence, i.e., the convergence of only a subsequence of the iterations of the subdivision scheme. Since, in addition, factorization methods pass even from scalar to matrix valued refinable functions, those results have to be formulated in terms of matrix refinable functions or vector subdivision schemes, respectively, in order to be suitable for iterated application. Moreover, it is shown for a particular case that the the condition is not only a necessary but also a sufficient one. Dedicated to Charles A. Micchelli, a unique person, friend, mathematician and collaborator, on the occasion of his sixtieth birthday Mathematics subject classifications (2000) 65T60, 65D99.     

Vector subdivision schemes in (Lp(Rs))r(1 ≤ p ≤∞) spaces

The purpose of this paper is to investigate the refinement equations of the form ψ(x) = ∑α∈Zs a(α)ψ(Mx - α), x ∈ Rs,where the vector of functions ψ=(ψ1,…,ψr)T is in (Lp(Rs))r, 1≤p≤∞,a(α),α∈Zs,is a finitely supported sequence of r × r matrices called the refinement mask, and M is an s × s integer matrix suchthat lim n→∞ M-n = 0. In order to solve the refinement equation mentioned above, we start with a vectorof compactly supported functions ψ0 ∈ (Lp(Rs))r and use the iteration schemes fn := Qnaψ0,n = 1,2,…,where Qa is the linear operator defined on (Lp(Rs))r given by Qaψ:= ∑α∈Zs a(α)ψ(M·- α),ψ∈ (Lp(Rs))r. This iteration scheme is called a subdivision scheme or cascade algorithm. In this paper, we characterize the Lp-convergence of subdivision schemes in terms of the p-norm joint spectral radius of a finite collection of somelinear operators determined by the sequence a and the set B restricted to a certain invariant subspace, wherethe set B is a complete set of representatives of the distinct cosets of the quotient group Zs/MZs containing 0.     

关于图的L(d,1)-标号问题

图G的L(2,1)-标号是一个从顶点集V(G)到非负整数集的函数f(x),使得若d(x,y)=1,则|f(x)-f(y)|≥2;若d(x,y)=2,则|f(x)-f(y)|≥1.图G的L(2,1)-标号数λ(G)是使得G有max{f(v)v∈V(G)}=k的L(2,1)-标号中的最小数k.Griggs和Yeh猜想对最大度为△的一般图G,有λ(G)≤△2.此文研究了作为L(2,1)-标号问题的推广的L(d,1)-标号问题,并得出了平面三角剖分图、立体四面体剖分图、平面近四边形剖分图的L(d,1)-标号的上界,作为推论证明了对上述几类图该猜想成立.     

A Doubly Adaptive Integration Algorithm Using Stratified Rules

A doubly adaptive integration algorithm chooses between a higher order rule applied on the current subinterval or the subdivision of the interval. We describe one such algorithm using a stratified sequence of integration rules. We present a criterion to select the suitable strategy, depending on the type of integrand, using available information.     

A piecewise polynomial approach to analyzing interpolatory subdivision

The four-point interpolatory subdivision scheme of Dubuc and its generalizations to irregularly spaced data studied by Warren and by Daubechies, Guskov, and Sweldens are based on fitting cubic polynomials locally. In this paper, we analyze the convergence of the scheme by viewing the limit function as the limit of piecewise cubic functions arising from the scheme. This allows us to recover the regularity results of Daubechies et al. in a simpler way and to obtain the approximation order of the scheme and its first derivative.