Journal of Mathematical Extension
Volume:5 Issue: 2, Spring 2011

In this paper the Chebyshev finite difference method is em- ployed for finding the approximate solution of time varying constrained optimal control problems. This approach consists of reducing the op- timal control problem to a nonlinear mathematical programming prob- lem. To this end, the collocation points (Chebyshev Gauss-Lobatto nodes) are introduced then the state and control variables are approx- imated using special Chebyshev series with unknown parameters. The performance index is parameterized and the system dynamics and con- straints are then replaced with a set of algebraic equations. Numerical examples are included to demonstrate the validity and applicability of the technique.

In this paper, We extend the concept of semismoothness for functions to the Riemannian manifolds setting. Then, some properties of these functions are studied.

Let S be the matrix of residual sum of square in linear model Y = A + e, where the matrix of errors is distributed as elliptically contoured with unknown scale matrix . For Stein loss function, L1(ˆ,) = tr(ˆ −1)−log |ˆ−1|−p, and squared loss function, L2(ˆ,) = tr(ˆ−1 −I)2, we offer empirical Bayes estimators of , which dominate any scalar multiple of S, i.e., aS, by an effective amount. In fact, this study somehow shows that improvement of the empirical Bayes estimators obtained under the normality assumption remains robust under elliptically contoured model.

In this paper, a novel hybrid method based on fuzzy neu- ral network for estimate fuzzy coefficients (parameters) of fuzzy linear supply and demand function, is presented. Here a neural network is considered as a part of a large field called neural computing or soft computing. Moreover, in order to find the approximate parameters, a simple algorithm from the cost function of the fuzzy neural network is proposed.

In this paper we extend the concepts of two sided ideal and right quasi-duo ring. These ideals and rings are called totally fully in- variant and right strongly quasi-duo, respectively. Right strongly quasi- duo rings are always right quasi-duo. We investigate the properties of these rings and ideals and show among other things that right strongly quasi-duo rings are classical, directly finite and co-hopfian while right quasi duo, right duo or commutative rings do not have necessarily these properties.

In this paper, we introduce systems consisting of several production units, each of which include several subunits working in parallel. Meanwhile, each subunit is working independently. The input and output of each production unit are the sums of the inputs and outputs of its subunits, respectively. We consider each of these subunits as an independent decision making unit(DMU) and create the production possibility set(PPS) produced by these DMUs, in which the frontier points are considered as efficient DMUs. Then we introduce models for obtaining the efficiency of the production subunits. Using super-efficiency models, we categorize all efficient subunits into different efficiency classes. Then we follow by presenting the sensitivity analysis and stability problem for efficient subunits, including extreme efficient and non-extreme efficient subunits, assuming simultaneous perturbations in all inputs and outputs of subunits such that the efficiency of the subunit under evaluation declines while the efficiencies of other subunits improve.

In this paper we give some fixed point theorems in cone metric spaces and the purpose of this paper is the investigation of some manners for finding the fixed point of pointwise contraction and asymptotic pointwise contraction mappings.

In many cases of data envelopment analysis (DEA), decision making units (DMUs) can be separated into different components. These DMUs are called multi-component DMUs, and studying them is known as multi-component DEA. In multi-component DEA some inputs are shared among the components of a DMU, and some components involve into producing some outputs of the DMU. In this paper, we survey measuring the relative efficiency in multi-component DEA. It is shown that using common idea for measuring the efficiency of multi-component DMUs, the relative efficiency of an evaluating DMU may be not obtained. Therefore, present paper proposes a new DEA model which can obtain the relative efficiencies of multi-component DMUs. Some facts about the proposed approach are also provided by theorems. Moreover, the proposed DEA model is compared to another approach in literature utilizing a set of data about 19 bank branches.

In this paper, we focus on the bounded sequences of Fourier partial sums. Our interest is on the sequences which do not contain any rational multiple of 2¼. We construct a function on C[T] where its set of points is one of such sequences. We will show that this set is of the first category in R. Moreover the complement of this set in any arbitrary real closed interval form an uncountable set.

In the present paper, we characterize the eigenfunctions of a weighted composition operator on space of holomorphic function on the unit disk.