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.     

Degree of Approximation for Nonlinear Multivariate Sampling Kantorovich Operators on Some Functions Spaces

In this article, the problem of the order of approximation for the nonlinear multivariate sampling Kantorovich operators is investigated. The case of uniformly continuous and bounded functions belonging to Lipschitz classes is considered, as well as the case of functions in Orlicz spaces. In the latter setting, suitable Zygmung-type classes are introduced by using the modular functionals of the spaces. The results obtained show that the order of approximation depends on both the kernels of our operators and the engaged functions. Several examples of kernels are considered in special instances of Orlicz spaces, typically used in approximation theory and for applications to signal and image processing.     

On an optimal control problem involving first order hyperbolic systems with boundary controls

In this paper, we consider an optimal control problem involving a class of first order hyperbolic systems with boundary controls. A computational algorithm which generates minimizing sequences of controls is devised and the convergence properties of the algorithm are investigated. Moreover, a necessary and sufficient condition for optimality is derived and a result on the existence of optimal controls is obtained.     

Order acceptance/rejection policies in determining the sequence in mixed model assembly lines

This study presents a decision support system for order acceptance/rejection in a Make-to-Order production environment with the mixed model assembly line approach. Indeed, variety of orders is the parameter under investigation herein. When the company does not have sufficient capacity or the required resources to accept the entirety of all new arrival orders, the following steps are proposed: At first, the customers are prioritized based on their corresponding profit values (at present and in the future) whereas other orders are rejected by the top manager along with some undesirable ones. Then, prices and delivery dates of the non-rejected orders are determined via a mathematical programming model. Quality levels are also reported to the customers based upon which they are allowed to select their desired blend of main components. Afterwards, in the case of customer’s lack of satisfaction with the offered price and due date, further negotiation is proposed. Finally, if the negotiation leads to an agreement, the order is accepted and added to the production schedule of the shop floor. The schedule of accepted orders is performed based on minimizing the work overload. The present study presumes that the processing times of the tasks are affected by both learning effect and deterioration of the jobs, simultaneously. In the last section of the study afoot, numerical experiments as well as the corresponding methodology are presented in order to solve the models. Moreover, a simulated annealing algorithm is utilized to solve the problem in a large scale with little computational time. Numerical experiments confirm that the simulated annealing algorithm tends to yield rather fine results with little discrepancy compared to those of the exact algorithm in small and medium size.     

Zero-finder methods derived using Runge-Kutta techniques

In this paper some families of zero-finding iterative methods for nonlinear equations are presented. The key idea to derive them is to solve an initial value problem applying Runge-Kutta techniques. More explicitly, these methods are used to solve the problem that consists in a differential equation in what appears the inverse function of the one which zero will be computed and the condition given by the value attained by it at the initial approximation. Carrying out this procedure several families of different orders of local convergence are obtained. Furthermore, the efficiency of these families are computed and two new families using like-Newton’s methods that improve the most efficient one are also given.     

On L-Tychonoff spaces II

This paper is a sequel to the 1995 paper On L-Tychonoff spaces. The embedding theorem for L-topological spaces is shown to hold true for L an arbitrary complete lattice without imposing any order reversing involution (·)^′ on L. Some results on completely L-regular spaces and on L-Tychonoff spaces, which have previously been known to hold true for (L,^′) a frame, are exhibited as ones holding for (L,^′) a meet-continuous lattice. For such a lattice an insertion theorem for completely L-regular spaces is given. Some weak forms of separating families of maps are discussed. We also clarify the dependence between the sub-T₀ separation axiom of Liu and the L-T₀ separation axiom of Rodabaugh.     

Modeling of claim exceedances over random thresholds for related insurance portfolios

Large claims in an actuarial risk process are of special importance for the actuarial decision making about several issues like pricing of risks, determination of retention treaties and capital requirements for solvency. This paper presents a model about claim occurrences in an insurance portfolio that exceed the largest claim of another portfolio providing the same sort of insurance coverages. Two cases are taken into consideration: independent and identically distributed claims and exchangeable dependent claims in each of the portfolios. Copulas are used to model the dependence situations. Several theorems and examples are presented for the distributional properties and expected values of the critical quantities under concern.     

Composition of stochastic B-series with applications to implicit Taylor methods

In this article, we construct a representation formula for stochastic B-series evaluated in a B-series. This formula is used to give for the first time the order conditions of implicit Taylor methods in terms of rooted trees. Finally, as an example we apply these order conditions to derive in a simple manner a family of strong order 1.5 Taylor methods applicable to Itô SDEs.