On one representation of analytic functions by harmonic functions

Let u(x) be a function analytic in some neighborhood D about the origin, $ \mathcal{D} Let u(x) be a function analytic in some neighborhood D about the origin, ⊂ ℝ ⁿ . We study the representation of this function in the form of a series u(x) = u ₀(x) + |x|² u ₁(x) + |x|⁴ u ₂(x) + …, where u _k (x) are functions harmonic in . This representation is a generalization of the well-known Almansi formula. Original Russian Text ? V. V. Karachik, 2007, published in Matematicheskie Trudy, 2007, Vol. 10, No. 2, pp. 142–162.     

On sparse representation of analytic signal in Hardy space

This paper is concerned with the sparse representation of analytic signal in Hardy space , where is the open unit disk in the complex plane. In recent years, adaptive Fourier decomposition has attracted considerable attention in the area of signal analysis in . As a continuation of adaptive Fourier decomposition‐related studies, this paper proves rapid decay properties of singular values of the dictionary. The rapid decay properties lay a foundation for applications of compressed sensing based on this dictionary. Through Hardy space decomposition, this program contributes to sparse representations of signals in the most commonly used function spaces, namely, the spaces of square integrable functions in various contexts. Numerical examples are given in which both compressed sensing and ?₁‐minimization are used. Copyright © 2013 John Wiley & Sons, Ltd.     

Integral representation of an analytic function in a ring and its applications

An integral representation of an analytic function in a ring with corresponding limit values on the boundary is obtained. A new singular integral equation is suggested and solved in quadratures by using an integral representation and by complete investigation of the Cárleman problem for a ring (in the normal case).Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 3, pp. 322–329, March, 1995.     

The simplex dispersion ordering and its application to the evaluation of human corneal endothelia

A multivariate dispersion ordering based on random simplices is proposed in this paper. Given a R^d-valued random vector, we consider two random simplices determined by the convex hulls of two independent random samples of sizes d+1 of the vector. By means of the stochastic comparison of the Hausdorff distances between such simplices, a multivariate dispersion ordering is introduced. Main properties of the new ordering are studied. Relationships with other dispersion orderings are considered, placing emphasis on the univariate version. Some statistical tests for the new order are proposed. An application of such ordering to the clinical evaluation of human corneal endothelia is provided. Different analyses are included using an image database of human corneal endothelia.     

集对Fuzzy格及其在格表示论中的应用

用幂集格构造了集对 Ｆｕｚｚｙ 格（这与用整数对构造有理数集有相似之处）,并用它证明了完整的软代数表示定理,即定义了到自身的映射且有最大元和最小元的格为软代数的充要条件是它与某个集对 Ｆｕｚｚｙ 格的子格同构．这样,与分配格在幂集 Ｂｏｏｌｅ 格中表示相对应,软代数在集对 Ｆｕｚｚｙ 格中有表示,在理论上是很完美的     

Analytic center of spherical shells and its application to analytic center machine

The two-case pattern recognition problem aims to find the best way of linearly separate two different classes of data points with a good generalization performance. In the context of learning machines proposed to solve the pattern recognition problem, the analytic center machine (ACM) uses the analytic center cutting plane method restricted to spherical shells. In this work we prove existence and uniqueness of the analytic center of a spherical surface, which guarantees the well definedness of ACM problem. We also propose and analyze new primal, dual and primal-dual formulations based on interior point methods for the analytic center machine. Further, we provide a complexity bound on the number of iterations for the primal approach. F.M.P. Raupp was partially supported by CNPq Grant 475647/2006-8 and FAPERJ/CNPq through PRONEX-Computational Modeling. B.F. Svaiter was partially supported by CNPq Grants 300755/2005-8, 475647/2006-8 and by FAPERJ/CNPq through PRONEX-Optimization.     

Doubly coprime representation of linear systems and its application to simultaneous stabilization

This paper develops a new representation theory of multivariabletime-invariant linear systems based on the well-known coprimefactorizations of their transfer matrices. This representationfully uses the algebraic structure of coprime factorizations,and hence has a number of advantages for describing variousproperties of linear systems in simpler and/or more compactforms than the usual transfer matrix representation. In theframework of this new representation theory, various stabilityand stabilizability properties of linear systems are characterizedand finally a simultaneous stabilization problem for a givenset of linear systems is examined.     

On the convergence and application of Newton-like methods for analytic operators

We provide local and semilocal theorems for the convergence of Newton-like methods to a locally unique solution of an equation in a Banach space. The analytic property of the operator involved replaces the usual domain condition for Newton-like methods. In the case of the local results we show that the radius of convergence can be enlarged. A numerical example is given to justify our claim. This observation is important and finds applications in steplength selection in predictor-corrector continuation procedures.     

On the application of the flexible polyhedron method to solve mathematical programming problems

Translated fromIssledovaniya po Prikladnoi Matematike, No. 18, 1992, pp. 26–30.     

A representation theorem of harmonic functions and its application to BMO on manifolds

Abstract. In this paper a representation theorem of harmonic functions on manifolds is set up.As an application, a characterization of BMO in terms of Carleson measures is obtained.     

Functional-differential equations in a class of analytic functions and its application to elastic composites

According to Muskhelishvili’s approach, two-dimensional elastic problems for media with non-overlapping inclusions are reduced to boundary value problems for analytic functions in multiply connected domains. Using a method of functional equations developed by Mityushev, we reduce such a problem for a circular multiply connected domain to functional-differential equations. It is proved that the operator corresponding to the functional-differential equations is compact in the Hardy–Sobolev space. Moreover, these equations can be solved by the method of successive approximation under some natural conditions.     

Differential Galoisian approach to Jacobi integrability of general analytic dynamical systems and its application

The Morales-Ramis theory provides an effective and powerful non-integrability criterion for complex analytic Hamiltonian systems via the differential Galoisian obstruction. In this paper, we give a new Morales-Ramis type theorem on the meromorphic Jacobi non-integrability of general analytic dynamical systems. The key point is to show that the existence of Jacobian multipliers of a nonlinear system implies the existence of common Jacobian multipliers of Lie algebra associated with the identity c...     

Generalized representation theorem and its application to the construction of fuzzy sets: Existence and uniqueness

A new methodology for constructing a fuzzy subset of a universal set U from a family of subsets of U based on a pre-determined range S that is a subset of (0,1] is proposed in this paper. The uniqueness of this construction method is also investigated, which depends on the structure of subset S. Whether the supremum of S lies in S is an important issue. This concern will be thoroughly studied in this paper.     

An exact algorithm for the sequential ordering problem and its application to switching energy minimization in compilers

This article presents an exact algorithm for the precedence-constrained traveling salesman problem, which is also known as the sequential ordering problem. This NP-hard problem has applications in various domains, including operational research and compilers. In this article, the problem is presented and solved in the context of minimizing switching energy in compilers. Most previous work on minimizing switching energy in the compiler domain has been limited to simple heuristics that are not guaranteed to give an optimal solution. In this work, we present an exact algorithm for solving the switching energy minimization problem using a branch-and-bound approach. The proposed algorithm is simple and intuitive, yet powerful. It is the first exact algorithm for the switching energy problem that is shown to solve real instances of the problem within a few seconds per instance. Compared to previous work in the operational research domain, the proposed algorithm is believed to be the most powerful exact algorithm that does not require a linear programming formulation. The proposed algorithm is experimentally evaluated using instances taken from a production compiler. The results show that with a time limit of 10 ms per node, the proposed algorithm optimally solves 99.8 % of the instances. It optimally solves instances with up to 598 nodes within a few seconds. The resulting switching cost is 16 % less than that produced without energy awareness and 5 % less than that produced by a commonly used heuristic.     

On the application of alternating projection under the constraint of linear matrix inequalities

In this paper, alternating projection under the constraint oflinear matrix inequalities (LMIs) is investigated to solve thefollowing two problems: finding the intersection of severalconvex LMI sets and designing an output-feedback stabilizingcontroller. Each problem is formulated as a quadratic optimizationproblem under LMI constraints. A numerical algorithm based onthe concept of alternating projection is proposed. The algorithmis demonstrated using a vertical-strip pole-assignment example.