Spatiotemporal Pattern Extraction by Spectral Analysis of Vector-Valued Observables

Journal of Nonlinear Science - We present a data-driven framework for extracting complex spatiotemporal patterns generated by ergodic dynamical systems. Our approach, called vector-valued spectral...     

V-Limit Analysis of Vector-Valued Mappings

For an arbitrary net of mappings defined on subsets of the Hausdorff space (X, ) and acting into a vector topological space (Y, ) semiordered by a solid cone , we introduce the notion of V-limit. We investigate topological and sequential properties of V-limit mappings and establish sufficient conditions for their existence. The results presented can be used as a basis for the procedure of averaging of problems of vector optimization.     

Publisher Correction to: The Measurement and Analysis of Shapes

Annals of Global Analysis and Geometry -     

Spectral Analysis of Social Networks to Identify Periodicity

Two key problems in the study of longitudinal networks are determining when to chunk continuous time data into discrete time periods for network analysis and identifying periodicity in the data. In addition, statistical process control applied to longitudinal social network measures can be biased by the effects of relational dependence and periodicity in the data. Thus, the detection of change is often obscured by random noise. Fourier analysis is used to determine statistically significant periodic frequencies in longitudinal network data. Two approaches are then offered: using significant periods as a basis to chunk data for longitudinal network analysis or using the significant periods to filter the longitudinal data. E-mail communication collected at the United States Military Academy is examined.     

Correction to: Preface

Foundations of Computational Mathematics -     

离散超小波变换下双正交小波谱分析

在离散超小波交换下，双正交小波交换矩阵的谱是有界的，我们给出一个确定的界．任何一个双正交小波变换矩阵的谱不可能分布在1附近的某个开区间内，我们给出该区间估计，从而证明了任何一个双正交小波族变换矩阵的谱不可能无限接近于1（正交小波交换矩阵的谱）．     

Correction to: Principal component analysis constrained by layered simple structures

Advances in Data Analysis and Classification - A Correction to this paper has been published: 10.1007/s11634-022-00503-9     

Correction to: On the Approximation of Unbounded Convex Sets by Polyhedra

Journal of Optimization Theory and Applications - In this article, Algorithm 1 was duplicated instead of Algorithm 2.     

A Generalization of the Lagrange Mean Value Theorem to the Case of Vector-Valued Mappings

Siberian Mathematical Journal -     

Correction to: Sub-range Jacobi polynomials

Numerical Algorithms - The first equation in Eq. (2.9) should read     

Spectral computations: from operators to matrices

In this work we will address the problem of finding spectral values and bases for the corresponding spectral subspaces for a bounded operator on a Banach space. We will make a bridge between the spectral problem for the continuous operator and the computation of the eigenpairs of a matrix. This approximate problem results first from an approximation by a sequence of continuous operators with finite rank, followed by the reduction to a spectral problem for an operator whose domain as well as range are finite dimensional. Some discussion on defect correction procedures will be also presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Spectral Analysis of Model Couette Flows in Application to the Ocean

Computational Mathematics and Mathematical Physics - A method for analysis of the evolution equation of potential vorticity in the quasi-geostrophic approximation with allowance for vertical...     

Spectral Analysis of Higher-Order Differential Operators II: Fourth-Order Equations

We investigate the location and nature of the spectrum of thefourth-order self-adjoint equation (p₀ y')'+(p₁ y')'+qy=zwy subject to certain asymptotic assumptions on the coefficients.The main tools are the theory of asymptotic integration andthe Titchmarsh–Weyl M-matrix. Asymptotic integration yieldsasymptotic formulae for the solutions of the differential equationwhich are then used to derive properties of the M-matrix. Thecharacterisation of spectral properties in terms of the boundarybehaviour of M leads to the desired results.     

Vector-Valued Functions Generated by the Operator of Finite Order and Their Application to Solving Operator Equations in Locally Convex Spaces

This work is devoted to solving some classes of operator equations, based on the solution of auxiliary one-parameter family of equations, which is obtained fromthe original operator equation by formal replacement of the operator of the integrated parameter. Solutions are vector-valued functions represented by power series or integral. We investigate some properties of these solutions, namely, growth characteristics, the domain of analyticity. The investigation is realized by means of order and type of operator, operator order and operator type of the vector relative to the operator.     

Spectral Analysis of Randomly Sampled Signals

Various approaches to the problem of generating spectral estimatesfrom randomly sampled signals are discussed. A practically usefultechnique is developed and demonstrated by applying it to simulateddata. The variability of the alias-free spectral estimates soobtained is shown to conform to theoretical predictions.