积分凸性及其应用

该文在Banach空间中通过向量值函数的Bochner积分引进集合与泛函的积分凸性以及集合的积分端点等概念. 文章主要证明有限维凸集、开凸集和闭凸集均是积分凸集，下半连续凸泛函与开凸集上的上半连续凸泛函均是积分凸的, 非空紧集具有积分端点, 对紧凸集来说其积分端点集与端点集一致, 最后给出积分凸性在最优化理论方面的两个应用.     

Estimates on level set integral operators in dimension two

Both oscillatory integral operators and level set operators appear naturally in the study of properties of degenerate Fourier integral operators (such as generalized Randon transforms). The properties of oscillatory integral operators have a longer history and are better understood. On the other hand, level set operators, while sharing many common characteristics with oscillatory integral operators, are easier to handle. We study L²-estimates on level set operators in dimension two and compare them with what is known about oscillatory integral operators. The cases include operators with non-degenerate phase functions and the level set version of Melrose-Taylor transform (as an example of a degenerate phase function). The estimates are formulated in terms of the Newton polyhedra and type conditions.     

Note on Integral Distances

A planar point set S is called an integral set if all the distances between the elements of S are integers. We prove that any integral set contains many collinear points or the minimum distance should be relatively large if |S| is large.     

Approximate construction of the set of trajectories of the control system described by a Volterra integral equation

In this paper the set of trajectories of the control system is investigated. It is assumed that the behavior of the control system is described by a Volterra integral equation which is nonlinear with respect to the state vector and is affine with respect to the control vector, and the control functions have an integral constraint. An approximation of the set of trajectories by the set which consists of a finite number of trajectories is given. The Hausdorff distance between the set of trajectories of the system and the set, consisting of a finite number of trajectories is evaluated.     

Über Picardmengen ganzer Funktionen

Following Lehto we call a set E in the complex plane a Picard set for integral functions, if every non-rational integral function omits at most one finite value in the complement (with respect to the plane) of E. The existence of non-trivial Picard sets was proved by Lehto [3]. The aim of this paper is to give a new criterion for denumberable point sets E to be Picard sets for integral functions. In some way the criterion given by theorem 1 is an extension of the result on Picard sets for integral functions given by Toppila [5] and improves the criterion given by the author in [6].     

Exponential dichotomy,integral separation and diagonalizability of linear systems of ordinary differential equations

This paper is concerned with linear systems of ordinary differential equations. A criterion for integral separation in terms of exponential dichotomy is given. As corollaries we obtain the roughness theorem for integral separation and the new result that an upper triangular system on a half-line is integrally separated if and only if the system corresponding to its diagonal is. We then show that a diagonal system on a half-line is integrally separated if and only if a certain perturbed system is diagonalizable. Using this result we are able to deduce that the interior of the set of diagonalizable systems on a half-line is the set of systems with integral separation and that the interior for the whole line is the set of systems which are integrally separated on both half-lines.     

The integral analog of a series with a two-point sum range

We consider an improper integral corresponding to the series with a two-point sum range which was constructed by Kornilov in the space of integrable functions. We verify that the sum range of the integral is equal to the set of all constant functions.     

A generalized Shimura correspondence for newforms

We associate a set of half integral weight forms to an integral weight newform of odd level. We prove an explicit identity relating the central values of the twist L-functions of the newform to the Fourier coefficients of the half integral weight forms.     

A weak existence theorem and weak permanence properties for strong liftings

On a locally compact space with a first-uncountable basis for its topology every positive Radon measure is majorized by an upper integral which admits a strong lifting. The set of B-continuous measures on any space that are majorized by an upper integral with strong lifting forms a band.Supported by NSF-Grant-20541     

On analogs of spectral decomposition of a quantum state

The set of quantum states in a Hilbert space is considered. The structure of the set of extreme points of the set of states is investigated and an arbitrary state is represented as the Pettis integral over a finitely additive measure on the set of vector states, which is a generalization of the spectral decomposition of a normal state.     

Represented value sets for integral binary quadratic forms and lattices

A characterization is given for the integral binary quadratic forms for which the set of represented values is closed under products. It is also proved that for an integral binary quadratic lattice over a Dedekind domain, the product of three values represented by the form is again a value represented by the form. This generalizes the trigroup property observed by V. Arnold in the case of integral binary quadratic forms.

     

Kites and residuated lattices

We investigate a construction of an integral residuated lattice starting from an integral residuated lattice and two sets with an injective mapping from one set into the second one. The resulting algebra has a shape of a Chinese cascade kite, therefore, we call this algebra simply a kite. We describe subdirectly irreducible kites and we classify them. We show that the variety of integral residuated lattices generated by kites is generated by all finite-dimensional kites. In particular, we describe some homomorphisms among kites.     

Electromagnetic scattering by a homogeneous chiral obstacle in a chiral environment

Time-harmonic electromagnetic waves are scattered by a homogeneouschiral obstacle embedded in a chiral environment. The correspondingtransmission problem is reduced, via Bohren's decomposition,to an integral equation over the interface between the obstacleand the surrounding medium. This integral equation is shownto be uniquely solvable except for a discrete set of electromagneticparameters of the obstacle.     

Bifurcation of common levels of first integrals of the kovalevskaya problem

The structure of integral manifolds in the Kovalevskaya problem of a heavy solid about a fixed point is considered. An analytic definition of a bifurcation set is obtained, and bifurcation diagrams are constructed. The number of two-dimensional toruses that appear in the composition of the integral manifold is indicated for each connected component, additional to the bifurcation set in the space of first integral constants.     

A differentiation formula for integrals overseas given by inclusion

Formulae for differentiation with respect to the parameter of an integral over the set given by an inclusion are proposed. The case with bounded and unbounded set is discussed. Such formulae can be used for differentiation of probability functions. An algorithm for solving chance constrainted optimization problems is considered.     

Asymmetric integral as a limit of generated Choquet integrals based on absolutely monotone real set functions

We introduce a generated Choquet integral with respect to absolutely monotone and sign stable set functions. Another type of integrals defined with respect to such a set function is obtained as a limit of an appropriate sequence of generated Choquet integrals.     

战斗对策:有约束极小极大途径(Ⅱ)

本文提出几个用集合,测度和积分工具来的极小极大判别准则,用来解有约束极小极大问题．     

On Stability of Integral Sets of Impulsive Differential Systems

We introduce the notion of stability of integral sets of impulsive differential systems of general form (with nonfixed times of impulse influence). We establish conditions sufficient for the stability of an integral set.     

Integral Newton-Type Polynomials with Continual Nodes

We construct an integral Newton-type interpolation polynomial with a continual set of nodes. This interpolant is unique and preserves an operator polynomial of the corresponding degree.     

Integration theory for Hammerstein operators

We develop in this article a strong nonlinear integral and obtain a Riesz-type theorem (utilizing this integral) for the class of (nonlinear) Hammerstein operators. The integral is extended to the class $\text{M}$_E($\text{B}$) of E-valued totally $\text{B}$-measurable functions and convergence theorems are studied. Then an exchange of information is carried out between the operators and the corresponding set functions; for example, the implication of the operator being compact or unconditionally summing is drawn. In the latter case it is shown that the representing set function is analogous to strongly bounded set functions. A vast body of literature exists for both of these concepts.