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.     

Artin HNN-extensions virtually embed in Artin groups

An Artin HNN-extension is an HNN-extension of an Artin groupin which the stable letter conjugates a pair of suitably chosensubsets of the standard generating set. We show that some finiteindex subgroup of an Artin HNN-extension embeds in an Artingroup. We also obtain an analogous result for Coxeter groups.     

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.     

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     

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.     

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)     

Enforced stability of an eigenvalue in the continuous spectrum of a waveguide with an obstacle

Perturbations of an eigenvalue in the continuous spectrum of the Neumann problem for the Laplacian in a strip waveguide with an obstacle symmetric about the midline are studied. Such an eigenvalue is known to be unstable, and an arbitrarily small perturbation can cause it to leave the spectrum to become a complex resonance point. Conditions on the perturbation of the obstacle boundary are found under which the eigenvalue persists in the continuous spectrum. The result is obtained via the asymptotic analysis of an auxiliary object, namely, an augmented scattering matrix.     

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.     

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).     

Estimation of the degree of differencing of an ARIMA process

Summary A method of estimating the degree of differencing of an ARIMA process is proposed. This is based on fitting an AR model to the original and to each differenced series and calculating the residual sum of squares. As an application, we suggest an identification method of an ARI (p, d) process combining our method of estimating the degree of differencing with Akaike's Information Criterion.     

A new kind of inequality for Bessel functions

We study a new type of inequality for Bessel functions. This is an analog of an inequality for Legendre polynomials, which plays an important role in studying the nonlinear Boltzmann equation. As an application of the Bessel case we treat the spherical functions associated with Minkowski space.     

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.     

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.     

One Property of the Renormalization Group Operator

We use an isotropic ferromagnet as an example to show that the renormalization group operator can be interpreted as an evolution operator for a system of spins evolving with an increase of the reduced temperature, i.e., as the order operator of the system.     

Regular expression transformations to extend regular languages (with application to a Datalog XML schema validator)

An XML schema is a set of rules for defining the allowed sub-elements of any element in an XML document. These rules use regular expressions to define the language of the element's children. Updates to an XML schema are updates to the regular expressions defined by the schema rules. We consider an interactive, data administration tool for XML databases. In this tool, changes on an XML schema are activated by updates that violate the validity of an XML document. Our schema validator is a Datalog program, resulting from the translation of a given XML schema. Changing the schema implies changing the validator.The main contribution of this paper is an algorithm allowing the evolution of XML schemas. This algorithm is based on the computation of new regular expressions to extend a given regular language in a conservative way, trying to foresee the needs of an application. A translation function from schema constraints to Datalog programs is introduced. The validation of an XML tree corresponds to the evaluation of the Datalog program over the tree. Our method allows the maintenance of the Datalog program in an incremental way, i.e., without redoing the entire translation.     

Optimal estimates for an average of Hurwitz class numbers

The Ramanujan Journal - In this paper, we give an optimal estimate of an average of Hurwitz class numbers. As an application, we give an equidistribution result of the family $$\Big...     

Étale endomorphisms of algebraic surfaces with $G_m$-actions

Let X be an algebraic surface defined over the complex field and endowed with an -fibration. As such a surface we have a Platonic -fiber space, a weighted hypersurface with its singular point deleted off and, more generally, an affine algebraic surface with an unmixed -action and its fixpoint deleted off. We consider an étale endomorphism and show that is an automorphism in most cases. Of particular interest is the case of a Platonic -fiber space, for which being an automorphism is closely related to the Jacobian Problem for the affine plane . We also investigate the automorphism group of such surfaces. Received January 7, 1999 / Published online October 30, 2000     

Optimality of Balanced Proper Orthogonal Decomposition for Data Reconstruction

Proper orthogonal decomposition (POD) finds an orthonormal basis yielding an optimal reconstruction of a given dataset. We consider an optimal data reconstruction problem for two general datasets related to balanced POD, which is an algorithm for balanced truncation model reduction for linear systems. We consider balanced POD outside of the linear systems framework, and prove that it solves the optimal data reconstruction problem. The theoretical result is illustrated with an example.     

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。