مجله علوم دانشگاه تهران
سال سی و سوم شماره 3 (پاییز 1386)

The spatial prediction of an unknown quantity at a specific site is one of the most important topics in the fuzzy spatial analysis. Under the assumption that covariance is known, optimal prediction and mean square error of predictor are determinable by using fuzzy kriging methods. When the parameters of the parametric covariance function are unknown, their estimates are usually replaced in optimal prediction as real values. But, determination of this predictor and its mean square error are usually difficult. Therefore, to solve this problem, in this paper the Bayesian approach is used to extend the fuzzy kriging to a new method, namely Bayesian fuzzy kriging. Then, in an applied example, its accuracy is compared with other spatial predictors.

In this paper the multicommodity network flow problem with equal flow on some predetermined arcs is considered. The equal flow constraints require that the amounts of arcs flow of some commodities on some subsets of predetermined arcs, are equal. For solving this problem, first, using the capacity allocation algorithm, we define a starting solution. Then by lagrangian relaxation technique on general constraints we find a lower bound on the objective function value. An upper bound is also found by using embedded network simplex method. Finally, The optimal or near optimal solution is found when the upper and lowers bounds are made close enough to each other.

For spatial data, that are correlated in terms of their locations in the underlined space, the moving block bootstrap method is usually used to estimate the precision measures of the estimators. But in this method, the boundary observations have less chance of presence in blocks resampling than the other observations. In this paper, an algorithm is given for separate block bootstrap to estimate the precision measures of kriging spatial predictor. Then, it is shown that the bias estimation of kriging with separate block bootstrap method is unbiased and the kriging variance estimator is consistent. Finally, in a simulation study, the efficiencies of the separate and moving block bootstrap methods are compared for measures of estimation precision.

Differential- algebraic equations (DAEs) play an important role in mathematical models. In this study, after discussing some difficulties involved in numerical solution to differential- algebraic equations we use sequential regularization method (SRM) for solving Hessenberg index-2 and index-3 DAEs. Then Navier-Stokes equations that have extensively used in fluid dynamics are considered as differential- algebraic equations and are solved with SRM. In contrast to the linear method for solving Navier-Stokes, initial values for pressure are not required and the problems are solved with less stiffness. In this paper we compare the above mentioned methods with predicted sequential regularizations method (PSRM) which significantly improves computational time over the SRM. Finally numerical results are given.

In regression analysis, it is usually assumed that the error terms are independent, but in practice we occasionally deal with many cases such as spatial data that the error terms in regression models are correlated and their correlation structure is a function of the observation locations. This type of models, namely spatial regression, are used for surface determination in geology, archaeology, epidemiology and image processing. In this paper, the Bayesian approach is used for spatial regression analysis with first order spatially autocorrelated errors. Because of computation difficulties of posterior distribution, MCMC methods are used for estimation of the posterior parameters. Then the efficiency of introduced method is considered in a simulation study for different sample and lattice sizes

In this note we discuss intertwined subsets of real line. We show that if two disjoint non-empty subsets and of real line possess the same boundary, then they are intertwined subsets if either and contain no intervals, or if they contain intervals, then they contain the end points of the intervals. In continue, by presenting new definition of intertwined sets of type two, we show that if and are intertwined sets, then either and are intertwined or they are intertwined sets of type two. Next we show that if is a function on with a unique infinite -limit set, then the -limit set is a cantor set. Finally, we discuss conditions that the set is dense in.

A hierarchical Bayes model for analysis of contingency tables is presented and, using it, inference about correlation parameter, logarithm of the odds ratio, is studied. For drawing random sample from the distribution of logarithm of the odds ratio, computational method of Gibbs sampling is used. For testing independence the use of the hierarchical Bayes in calculating the Bayes factor is introduced and in an applied example is employed.

The nonlinear Schrodinger equation (NLS) is one of the most important equations in quantum physics. It is frequently useful in describing the waveguide movement of minute particles, for example an electron in the atom. NLS can be divided into three different cases: critical, supercritical, and subcritical. In this paper we try to show numerical methods that solve critical case of NLS, for short CNLS, in two dimensions. We also study the effects of the discretization of the equation in the solutions. There are some initial conditions for which the solutions of CNLS become singular in the finite time interval, but by using the finite difference method for the discretization of the Laplacian term in the equation, it is shown that the resulting discrete NLS represents a more accurate discretized version of the modified CNLS equation which can have local solution as well. So, as such modified CNLS equations are simply obtained by inserting small perturbations in the original equation, evidently by using this method it is almost possible to avoid blowup in the numerical solutions of these equations.

In this paper for solving Toeplitz system by PCG, two parallel algorithms based on mesh and hypercube are given. We have shown that using these algorithms reduce of arithmetical operations. Also, we investigate speed up and efficiency for these algorithms.

In this paper, we introduce the complete hypergroup and -complete hypergroup. The hypergroup is called complete hypergroup if for every, we have we prove that if is a -complete hypergroup then =. If is a -complete hypergroup then is a complete hypergroup and we have =, . Finally we prove that is a - complete hypergroup if and only if it is an Abelian group.

Suppose G is the molecular graph of an achiral polyhex nanotorus and e is an edge of G. We denote by N1(e|G) the number of vertices of G lying closer to one end of e and by N2(e|G) the number of vertices of G lying closer to the other end of e. Then the Szeged index of G is defined as Sz(G) =? e?E(G)N1(e|G)N2(e|G), where E(G) is the set of all edges of G. The Wiener index of G is defined as W(G) = 1/2?{x,y}?V(G)d(x,y), where d(x,y) denotes the length of a minimal path between x and y. In this paper, the Wiener and Szeged indices of an achiral polyhex nanotorus are computed.