Self Extending Rings

A ring R is an IPQ (isomorphic proper quotient)-ring if R ? R/A for every proper ideal A ? R. If every ideal A ? R satisfies: either R ? A or R ? R/A, then R is called an SE (self extending)-ring. It is shown that with one exception, an abelian group G is the additive group of an IPQ-ring if and only if G is the additive group of an SE-ring. The one exception is the infinite cyclic group Z. The zeroring with additive group Z is an SE-ring, but a ring with infinite cyclic additive group is not an IPQ-ring. Since the structure of the additive groups of IPQ-rings is known, the structure of the additive groups of SE-rings is completely determined.     

Gradient flows in asymmetric metric spaces

This article is concerned with gradient flows in asymmetric metric spaces, that is, spaces with a topology induced by an asymmetric metric. Such an asymmetry appears naturally in many applications, e.g., in mathematical models for materials with hysteresis. A framework of asymmetric gradient flows is established under the assumption that the metric is weakly lower-semicontinuous in the second argument (and not necessarily on the first), and an existence theorem for gradient flows defined on an asymmetric metric space is given.     

ON THE SUSTAINABLE GROWTH IN AN ECONOMY WITH PERFECTLY SUBSTITUTABLE EXHAUSTIBLE RESOURCES

Abstract A model of sustainable economic growth in an economy with two types of exhaustible resources is analyzed. The resources are assumed to be perfect substitutes with marginal rate of substitution varying over time. The optimal control framework is used to characterize the optimal paths under the maximin criterion. It is shown that the resource with increasing productivity is not used before the constant productivity resource is depleted. Afterwards the resource with an increasing productivity is asymptotically depleted as well. The results are based on an assumption that transversality conditions hold. A new sufficient condition for the transversality conditions is derived. Finally, an analogue of Hartwick’s rule for this non‐autonomous case is established.     

Solvability of the vector problem by the linear criteria convolution algorithm

Conditions are found under which a multicriteria problem with a finite set of vector estimates is solvable by means of the linear criteria convolution (LCC) algorithm, that is, any Pareto optimum for the problem can be obtained as an optimum solution to a one-criterion problem with an aggregated criterion defined as an LCC. Also, an algorithm is suggested that is polynomial in dimension and reduces any problem with minimax and minimin criteria to an equivalent vector problem with the same Pareto set solvable by the LCC algorithm. Translated fromMatematicheskie Zametki, Vol. 62, No. 4, pp. 502–509, October, 1997. Translated by V. N. Dubrovsky     

Adaptive Inverse Control Using a Gradient-Projection Optimization Technique

As an application of an optimization technique, a gradient-projection method is employed to derive an adaptive algorithm for updating the parameters of an inverse which is designed to cancel the effects of actuator uncertainties in a control system. The actuator uncertainty is parametrized by a set of unknown parameters which belong to a parameter region. A desirable inverse is implemented with adaptive estimates of the actuator parameters. Minimizing an estimation error, a gradient algorithm is used to update such parameter estimates. To ensure that the parameter estimates also belong to the parameter region, the adaptive update law is designed with parameter projection. With such an adaptive inverse, desired control system performance can be achieved despite the presence of the actuator uncertainties.     

An effective asymptotic method in the axisymmetric frictionless contact problem for an elastic layer of finite thickness

A brief review of asymptotic methods to deal with frictionless unilateral contact problems for an elastic layer of finite thickness is presented. Under the assumption that the contact radius is small with respect to the layer thickness, an effective asymptotic method is suggested for solving the unilateral contact problem with a priori unknown contact radius. A specific feature of the method is that the construction of an asymptotic approximation is reduced to a linear algebraic system with respect to integral characteristics (polymoments) of the contact pressure. As an example, the sixth‐order asymptotic model has been written out. Copyright © 2015 John Wiley & Sons, Ltd.     

Optimal Control Problems of Phase Relaxation Models

This work is concerned with optimal control problems with convex cost criterion governed by the relaxed Stefan problem with or without memory. The existence of an optimal control is proved and necessary conditions for a given function to be an optimal control are found. Moreover, an asymptotic analysis is performed as the time relaxation parameter tends to zero.     

Approximative compactness of the algebraic sum of sets

Let X be a group with an invariant metric, A and B nonempty subsets of X with B compact. It is proved that if A is an existence set [1] (approximatively compact [2]) then A + B and B + A are existence sets (approximatively compact). An example is given of a one-dimensional linear metric space (with an invariant metric) in which there exist an approximatively compact set A and an element v such that A + v is not an existence set.Translated from Matematicheskie Zametki, Vol. 23, No. 1, pp. 55–60, January, 1978.     

Ordered *-Algebras with an Order Unit

We develop a theory of ordered *-algebras with an order unit. These are complex algebras equipped with a conjugate-linear vector space involution whose hermitian elements form an ordered real algebra with an order unit but not necessarily with a multiplicative identity. Our main result is a representation theorem for ordered *-algebras with an order unit. This can be viewed as the complex and the non-unital version of the representation theorem of Stone and Kadison for ordered real algebras containing an order unit which is a multiplicative identity. A key role in our approach is played by certain weighted function algebras.     

A sufficient condition for affine frames with matrix dilation

A sufficient condition for affine frame with an arbitrary matrix dilation is pre-sented. It is based on the univariate case by Shi, and generalizes the univariate results of Shi, Casazza and Christensen from one dimension with an arbitrary real number a (a>1) dilation to higher dimension with an arbitrary expansive matrix dilation.     

Concavity in a vintage capital model with nonlinear utility

An optimization problem in an economic vintage capital model with nonlinear utility is investigated. It is described by non-linear Volterra integral equations with an unknown in the limits of integration. The concavity of the problem is proven, the condition for an extremum is established, and their relevance to applications is demonstrated.     

Existence of Solutions for Impulsive Neutral Integro-Differential Inclusions with Nonlocal Initial Conditions via Fractional Operators

This paper is mainly concerned with existence of mild solutions for first-order impulsive neutral integro-differential inclusions with nonlocal initial conditions in α-norm. We assume that the undelayed part generates an analytic resolvent operator and transforms it into an integral equation. By using a fixed point theorem for condensing multivalued maps, a main existence theorem is established. As an application of this main theorem, a practical consequence is derived for the sublinear growth case. Finally, we present an application to a neutral partial integro-differential equation with Dirichlet and nonlocal initial conditions.     

On the index integral transformation with Nicholson's function as the kernel

The integral transformation, which is associated with the Nicholson function as the kernel, is introduced and investigated in the paper. This transformation is an integral, where integration is with respect to an index of the sum of squares of Bessel functions of the first and second kind. Composition representations and relationships with the Meijer K-transform, the Kontorovich-Lebedev transform, the Mellin transform, and the sine Fourier transform are given. We also present boundedness properties, a Parseval type equality, and an inversion formula.     

两类Cayley的向图的同构问题

证明了对m=1,2,3,有限广义双循环群B(Q8)是m-DCI群当且仅当它的极大交换子群L是m-DCI群且4|-1mm|L|;有限广义二面体群D是m-DCI群当且仅当它的极大交换子群K是m-DCI群且2|-1mm|K|.     

The existence results for optimal control problems governed by a variational inequality

In this paper, we establish the existence of the optimal control for an optimal control problem where the state of the system is defined by a variational inequality problem with monotone type mappings. Moreover, as an application, we get several existence results of an optimal control for the optimal control problem where the system is defined by a quasilinear elliptic variational inequality problem with an obstacle.     

An invariance principle for semimartingale reflecting Brownian motions in an orthant

Semimartingale reflecting Brownian motions in an orthant (SRBMs) are of interest in applied probability because of their role as heavy traffic approximations for open queueing networks. It is shown in this paper that a process which satisfies the definition of an SRBM, except that small random perturbations in the defining conditions are allowed, is close in distribution to an SRBM. This perturbation result is called an invariance principle by analogy with the invariance principle of Stroock and Varadhan for diffusions with boundary conditions. A crucial ingredient in the proof of this result is an oscillation inequality for solutions of a perturbed Skorokhod problem. In a subsequent paper, the invariance principle is used to give general conditions under which a heavy traffic limit theorem holds for open multiclass queueing networks. This revised version was published online in June 2006 with corrections to the Cover Date.     

Multiobjective linear programming with context-dependent preferences

Multiobjective linear programming algorithms are typically based on value maximization. However, there is a growing body of experimental evidence showing that decision maker behavior is inconsistent with value maximization. Tversky and Simonson provide an alternative model for problems with a discrete set of choices. Their model, called the componential context model, has been shown to capture observed decision maker behavior. In this paper, an interactive multiobjective linear programming algorithm is developed which follows the rationale of Tversky and Simonson. The algorithm is illustrated with an example solved using standard linear programming software. Finally, an interactive decision support system based on this algorithm is developed to field test the usefulness of the algorithm. Results show that this algorithm compares favorably with an established algorithm in the field.     

On measures ergodic with respect to an analytic equivalence relation

In this paper, we prove that the set of probability measures which are ergodic with respect to an analytic equivalence relation is an analytic set. This is obtained by approximating analytic equivalence relations by measures, and is used to give an elementary proof of an ergodic decomposition theorem of Kechris.

     

有使用限制的二台机器流水作业问题

本文研究了机器有使用限制的二台机器流水作业排序问题,目标为最小化最大完工时间,工件加工可以被机器的不可用时间段中断。我们讨论了两台机器上均有使用限制离线问题的可近似情形,并给出了性能比为3/2的近似算法。同时我们还考虑了在第二台机器上存在一个不可用时间段情况下的半在线问题,给出了一个竞争比为3/2的半在线算法。     

Adaptive Wavelet Solution to the Stokes Problem

This paper deals with the design and analysis of adaptive wavelet method for the Stokes problem. First, the limitation of Richardson iteration is explained and the multiplied matrix M0 in the paper of Bramble and Pasciak is proved to be the simplest possible in an appropiate sense. Similar to the divergence operator, an exact application of its dual is shown; Second, based on these above observations, an adaptive wavelet algorithm for the Stokes problem is designed. Error analysis and computational complexity are given; Finally, since our algorithm is mainly to deal with an elliptic and positive definite operator equation, the last section is devoted to the Galerkin solution of an elliptic and positive definite equation. It turns out that the upper bound for error estimation may be improved.