فصلنامه مدل سازی پیشرفته ریاضی
سال چهارم شماره 2 (پاییز و زمستان 1393)

In time of natural and man-made disasters, the supply of some commodities which are directly related to human life are very critical. In the real-world, supply systems are exposed to various disruptions in their facilities and these disruptions can essentially affect systems performance and can lead to shortage in the supply and importance of this subject is much more expressed in the blood supply case. In this paper, a multi–objective mathematical model is proposed for the collection of temporary blood facilities and allocation of blood donators to these places. The goals of the model are to minimize the maximum blood shortage in the blood bank and also to minimize the total cost in the worst case scenario in disruptions. In order to demonstrate the applicability of the proposed model, the epsilon constraint method is solved and analyzed on numerical examples.

The present study evaluates the portfolio optimization problem (as one of the fundamental problems in the field of investments) with respect to the concepts of risk based on credibility theory. So that, a possibilistic portfolio optimization model (Zadeh 1965-1978) associates a new probabilistic portfolio optimization model, and The latter model, which actually comes in the form of a passive investment approach, formed around a portfolio of active equity mutual funds in the Tehran Stock Exchange from 2011 until the end of January of 2013 puts. The results of the implementation of the approach by use of genetic algorithms, suggesting a similar performance composed of a portfolio of mutual funds (based on the Sharpe index) with the market.

Identifiablity is a necessary property for the adequacy of a statistical model‎. ‎When a model is not identifiable‎, ‎no amount of data cannot determine true parameter‎. ‎In this article‎, ‎well-known concept of identifiablity and it’s properties is reviewed‎. ‎Moreover‎, ‎since non-identifiablity problem in linear mixed effects models and generalized linear models with random effects is very common‎, ‎our main focus is on these models‎. ‎On the other hand‎, ‎statistical software‎, ‎after fitting non-identifiable models‎, ‎don’t usually indicate the problem and show invalid outputs‎. ‎Consequently‎, ‎it is useful to have a way to check model identifiability before fitting. In this regard‎, ‎some new theorems to check identifiability in generalized linear models with random effects are presented‎. ‎data from non-identifiable models are simulated and problems with model non-identifiablity are listed for showing advantages of the mentioned theorems.‎

Directional statistics are very useful tools to model the phenomenon that are characterized by the angles. Recently, various disciplines including biology, astronomy, meteorology and bioinformatics have paid attention to use these distributions. Particularly, it was shown in biological researches that there are two pair angles describing, relatively, the complete geometrical and spatial structures of a protein in the three dimensional space. There is a distribution, called bivariate Von-Mises, to represent the position of the atoms based upon the values of these angles in a probabilistic manner. In this paper, considering an especial case of this density (cosine model), the properties of distribution including the numbers of modes and its approximation by the bivariate normal distribution are first studied. Then, to estimate the parameters using the pseudo-likelihood method is described. The theoretical materials are evaluated in simulation studies and then the application of the cosine model in a real example is presented.

Let $LC_F(X)$ be the socle of $C(X)$ and $LC_F(X)={fin C(X): overline{S_f}=X}$, where $S_f$ is the union of all open subsets $U$ in $X$ such that $Ubackslash Z(f)| Keywords: socle, z, ideal, almost discrete space, locally socle, essential ideal