Iranian Journal of Mathematical Sciences and Informatics
Year:2006 | Volume:1 | Issue:1|Papers Count:6

On analyzing the Euclidean graph of fullerene C60, we have obtained the automorphism group of the Euclidean graphs of this molecule. It is proven that this group has order 120 and is isomorphic to Z2 x A5, where Z2 is a cyclic group of order 2 and A5 is the alternating group on five symbols.

A simple method is described, for calculation of character table for the symmetry group of molecules consisting of a number XHs groups attached to a rigid framework. For the full non-rigid group (f-NRG) of the trim ethylamine-BHs addend (BH3 free of rotation), with C3v symmetry we prove that it is a group of order 648 with 14 contumacy classes. The character tables of this group are calculated.

In this paper, we consider the fundamental relation b* as the smallest equivalence relation on a playgroup P such that the quotient P/b*, the set of all equivalence classes, is a group. The quotient P/b* is called the fundamental group. We give some interesting results about the fundamental groups.

When spatial data are realizations of a Gaussian model with parametric mean and covariance functions, then the function of observations that minimizes mean square prediction error depends on some unknown parameters. Usually, these parameters are replaced by their estimates to obtain the plug-in predictor. But, this method has some problems in estimation of the parameters and the optimality and mean square error of the spatial predictor. In this paper, the problems related to plug-in method are discussed and to avoid them, the Bayesian approach for spatial prediction is proposed. Then the Bayesian spatial prediction for Gaussian and trans Gaussian models according to observations, that may contain noise, are derived. Next, in a simulation study, the adequacy of Bayesian prediction is compared with plug-in prediction. Finally, a numerical example illustrates the Bayesian spatial prediction of rainfall in a region at the north of Iran.

Consider the measure space (X, A, m). Let S : X®X be a nonsingular transformation on this space and assume that is the Frobenius Perron operator associated with s . Also we will assume that Us is the Koopman operator corresponding to s. Properties of these two operators, namely Ps and Us have been considered by many authors. For more details see [5], [7], [8] and [9]. In this paper we will present some special aspects concerning the spectrum of Ps. Also it is shown that the spectrum of is a cyclic subset of the unit disk D. In connection with the Koopman operator Us it is shown that under certain conditions, if m is a regular measure, then Us from L¥(X) to itself is an isometric.

In this note we review briefly some topics on hyper Kalgebras.