Archimedean ordered semigroups as ideal extensions

The main result of the paper is a structure theorem concerning the ideal extensions of archimedean ordered semigroups. We prove that an archimedean ordered semigroup which contains an idempotent is an ideal extension of a simple ordered semigroup containing an idempotent by a nil ordered semigroup. Conversely, if an ordered semigroup S is an ideal extension of a simple ordered semigroup by a nil ordered semigroup, then S is archimedean. As a consequence, an ordered semigroup is archimedean and contains an idempotent if and only if it is an ideal extension of a simple ordered semigroup containing an idempotent by a nil ordered semigroup.     

On the Existence of a Classical Optimal Solution and of an Almost Strongly Optimal Solution for an Infinite-Horizon Control Problem

We consider an infinite-horizon optimal control problem with the cost functional described either by an integral over an unbounded interval (a Lebesgue integral) or by a limit of integrals (an improper Lebesgue integral). We prove some theorems on the existence of solutions to such problems. The proofs are based on appropriate lower closure theorems and some extensions of Olech’s theorem on the lower semicontinuity of an integral functional; these extensions cover the cases of functionals described by an integral over an unbounded interval and by a limit of integrals.     

Problem of optimal endogenous growth with exhaustible resources and possibility of a technological jump

In 2013, S. Aseev, K. Besov, and S. Kaniovski (“The problem of optimal endogenous growth with exhaustible resources revisited,” Dyn. Model. Econometr. Econ. Finance 14, 3–30) considered the problem of optimal dynamic allocation of economic resources in an endogenous growth model in which both production and research sectors require an exhaustible resource as an input. The problem is formulated as an infinite-horizon optimal control problem with an integral constraint imposed on the control. A full mathematical study of the problem was carried out, and it was shown that the optimal growth is not sustainable under the most natural assumptions about the parameters of the model. In the present paper we extend the model by introducing an additional possibility of “random” transition (jump) to a qualitatively new technological trajectory (to an essentially unlimited backstop resource). As an objective functional to be maximized, we consider the expected value of the sum of the objective functional in the original problem on the time interval before the jump and an evaluation of the state of the model at the moment of the jump. The resulting problem also reduces to an infinite-horizon optimal control problem, and we prove an existence theorem for it and write down an appropriate version of the Pontryagin maximum principle. Then we characterize the optimal transitional dynamics and compare the results with those for the original problem (without a jump).     

保等价部分变换半群的变种半群上的正则元

在现有的保等价部分变换半群的基础上,引入了一个新的运算,得出保等价部分变换半群的变种半群的概念,利用格林关系及幂等元的正则性,讨论了这类半群中元素的正则性,给出了保等价部分变换半群的变种半群中一个元是正则元的充要条件     

格蕴涵代数中的扩张滤子

在格蕴涵代数中提出了扩张滤子的概念,讨论了扩张滤子与滤子,扩张滤子与素滤子,扩张滤子与滤子的根,扩张滤子与准素滤子,扩张滤子与最大滤子之间的关系.得到了扩张滤子的一些性质.最后,证明了在格H蕴涵代数中,扩张滤子与扩张滤子的根相等.     

Electromagnetic and thermal modelling of axisymmetric induction furnaces

A numerical method to describe the thermo-electric behavior of an induction heating furnace is introduced. It is obtained by using an enthalpy formulation concerning the thermal model and an integral representation of the electromagnetic potential in an unbounded domain. A BEM-FEM method is used and an iterative algorithm together with numerical results for an industrial heating system are presented. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

B-Construction and C-Construction

B-construction is a way of obtaining a graded algebra from the triple consisting of an additive category, an object, and an autoequivalence, while C-construction is a way of obtaining an algebra (without unity) from the pair consisting of an additive category and a set of objects. In this article, we study and compare three important classes of algebras in noncommutative algebraic geometry and representation theory of finite dimensional algebras, namely, quantum polynomial algebras, preprojetive algebras and trivial extensions, via these constructions.     

An Alternative Approach to Elliptical Motion

Elliptical rotation is the motion of a point on an ellipse through some angle about a vector. The purpose of this paper is to examine the generation of elliptical rotations and to interpret the motion of a point on an ellipsoid using elliptic inner product and elliptic vector product. To generate an elliptical rotation matrix, first we define an elliptical ortogonal matrix and an elliptical skew symmetric matrix using the associated inner product. Then we use elliptic versions of the famous Rodrigues, Cayley, and Householder methods to construct an elliptical rotation matrix. Finally, we define elliptic quaternions and generate an elliptical rotation matrix using those quaternions. Each method is proven and is provided with several numerical examples.     

pth Power Lagrangian Method for Integer Programming

When does there exist an optimal generating Lagrangian multiplier vector (that generates an optimal solution of an integer programming problem in a Lagrangian relaxation formulation), and in cases of nonexistence, can we produce the existence in some other equivalent representation space? Under what conditions does there exist an optimal primal-dual pair in integer programming? This paper considers both questions. A theoretical characterization of the perturbation function in integer programming yields a new insight on the existence of an optimal generating Lagrangian multiplier vector, the existence of an optimal primal-dual pair, and the duality gap. The proposed pth power Lagrangian method convexifies the perturbation function and guarantees the existence of an optimal generating Lagrangian multiplier vector. A condition for the existence of an optimal primal-dual pair is given for the Lagrangian relaxation method to be successful in identifying an optimal solution of the primal problem via the maximization of the Lagrangian dual. The existence of an optimal primal-dual pair is assured for cases with a single Lagrangian constraint, while adopting the pth power Lagrangian method. This paper then shows that an integer programming problem with multiple constraints can be always converted into an equivalent form with a single surrogate constraint. Therefore, success of a dual search is guaranteed for a general class of finite integer programming problems with a prominent feature of a one-dimensional dual search.     

Nonexistence of invariant semigroups in affine symmetric spaces

Let be an affine symmetric space with a simple Lie group, an involutive automorphism of and an open subgroup of the -fixed point group . It is proved here that the existence of a proper semigroup with and implies that is of Hermitian type, as conjectured by Hilgert and Neeb [4]. When exists, it turns out that it leaves invariant an open -orbit in a minimal flag manifold of . A byproduct of our approach is an alternate proof of the maximality of the compression semigroup of an open orbit (see Hilgert and Neeb [31]). Received: 10 September 1999 / Published online: 23 July 2001     

Almost contact Kähler manifolds of constant holomorphic sectional curvature

We introduce the notion of an almost contact Kähler structure. We also define the holomorphic sectional curvature of the distribution of an almost contact Kähler structure with respect to an interior metric connection and establish relations between the φ-sectional curvature of an almost contact Kähler manifold and the holomorphic sectional curvature of the distribution of an almost contact Kähler structure.     

Properties of Hamiltonian systems in the Pontryagin maximum principle for economic growth problems

We consider an optimal control problem with a functional defined by an improper integral. We study the concavity properties of the maximized Hamiltonian and analyze the Hamiltonian systems in the Pontryagin maximum principle. On the basis of this analysis, we propose an algorithm for constructing an optimal trajectory by gluing the dynamics of the Hamiltonian systems. The algorithm is illustrated by calculating an optimal economic growth trajectory for macroeconomic data.     

Algebraic geometry over algebraic structures. IV. Equational domains and codomains

We introduce and study equational domains and equational codomains. Informally, an equational domain is an algebra every finite union of algebraic sets over which is an algebraic set; an equational codomain is an algebra every proper finite union of algebraic sets over which is not an algebraic set.     

On evolution of an information dynamic system and its generating operator

States of a dynamical information system can be represented by points on a statistical manifold—a subset of a vector space endowed with an information topology. An evolution of such a system is considered here with respect to changes in information rather than changes in time, because differences between states are represented by an information distance. Here we consider an optimal system maximizing a utility of an abstract information resource, and then analyze properties of information such that an optimal system is described by an evolution operator or a semigroup. The latter is generated by an operator that can be interpreted as a utility, payoff or a fitness function. We discuss the advantages and applications of the proposed approach.     

带对称齐次核的级数算子的范数刻画及其应用

对带对称齐次核K(m,n)的级数算子T:T{an}=Σ_(n=1)~∞ K(m,n)an,{an}∈lω(n),l={{an)| an≥0,Σ_(n=1)~∞ω(n)an<+∞},本文研究了T的范数刻画,并讨论其应用.     

Excellent扩张和弱维数

在这篇文章里，我们证明了，当环Ｓ是Ｒ的ｅｘｃｅｌｌｅｎｔ扩张，Ｍ是Ｓ－模时，Ｍ做为Ｓ－模的弱维数与Ｍ做为Ｒ－模的弱维数相等。     

ON THE SPECTRAL PROPERTIES OF M-MATRICES AND ITS APPLICATIONS

1.IntroductionAndPreliminariesThespectralpropertiesofM-matricesplayanimportantroleinnonnegativemainstheory,andhavebeenappliedtostudythenumericalsolutionoflinearsystems.Recentlylmanyarticleshavediscussedwiththistopics(see[l--5]).ThepurposeofthispaperistoestablishthespectralinequalitiesofsingularM-matrices.ByapplyingthesepropertiesweanswerpartiallyanopenproblemandsolveanopenproblemposedbySchneiderin[4,5],somerecelltresultI2'4'6]onsplittingsofanM-matrixarealsoimproved.Allnotationsanddefinitio…     

Reversible and Bijectively Related Posets

Call a poset reversible if every of its order-preserving self-bijections is an automorphism. Call two posets bijectively related if from each of the two posets exists an order-preserving bijection to the other. We present two examples of pairs of non-isomorphic, bijectively related posets and an example of a non-reversible poset that is bijectively related only to itself. Also, three classes of reversible posets are described and a sufficient condition for an order-preserving bijection to be an isomorphism is presented.     

An internal language for autonomous categories

We present an internal language for symmetric monoidal closed (autonomous) categories analogous to the typed lambda calculus as an internal language for cartesian closed categories. The language we propose is the term assignment to the multiplicative fragment of Intuitionistic Linear Logic, which possesses exactly the right structure for an autonomous theory. We prove that this language is an internal language and show as an application the coherence theorem of Kelly and Mac Lane, which becomes straightforward to state and prove. Finally, we extend the language with the natural numbers and show that this corresponds to a weak Natural Numbers Object in an autonomous category.     

Some aspects of elliptic variational inequalities

In this paper we study an existence and the approximation of the solution of the elliptic variational inequality from an abstract axiomatic point of view. We discuss convergence results and give an error estimate for the difference of the two solutions in an appropriate norm. Also, we present some computational results by using fixed point method.