Iranian Journal of Mathematical Sciences and Informatics
Year:2007 | Volume:2 | Issue:1|Papers Count:6

In this paper, it is shown that by exploiting the explicit parametric state feedback solution, it is feasible to obtain the ultimate solution to minimum sensitivity problem. A numerical algorithm for construction of a robust state feedback in eigenvalue assignment problem for a controllable linear system is presented. By using a generalized parametric vector companion form, the problem of eigenvalue assignment with minimum sensitivity is re-formulated as an unconstrained minimization problem. The derived explicit expressions of the solutions allow minimization of the sensitivity problem by using a powerful search technique.

Let T be a tree and n1(e½T) and n2(e½T) denote the number of vertices of T, lying on the two sides of the edge e. Suppose T1 and T2 are two trees with equal number of vertices, e Î T1 and f Î T2. The edges e and f are said to be equiseparable if either n1(e½T1) = n1(f½T2) or n1(e½T2) = n2(f½T2). If there is an one-to-one correspondence between the vertices of Tl and Tz such that the corresponding edges are equiseparable, then T1 and T2 are called equiseparable trees. Recently, Gutman, Arsic and Furtula investigated some equiseparable alkanes and obtained some useful rules (see J. Serb. Chern. Soc. (68)7 (2003), 549-555). In this paper, we use a combinatorial argument to find an equivalent definition for equiseparability and then prove some results about relation of equiseparability and isomorphism of trees. We also obtain an exact expression for the number of distinct alkanes on n vertices which three of them has degree one.

Reverse subdivision aims at constructing a coarser representation of an object given by a fine polygon mesh. In this paper, we first derive a mask for reverse Loop subdivision that can be applied to both regular and extraordinary vertices. The mask is parameterized, and thus can also be used in reversing variants of Loop subdivision, such as those proposed by Warren and Litke.We apply this mask not only to mesh geometry, but also to texture coordinates. This reverses the texture-mapping process described by DeRose, Kass and Truong, in which a texture originally defined for a coarse mesh was carried to the finer meshes obtained by subdivision. Combined with the forward subdivision, the proposed technique constitutes a multiresolution representation of textured subdivision surfaces. We illustrate its use with a set of examples.

In this paper we show that if G is a group acting on a tree X with inversions and if (T; Y ) is a fundamental domain for the action of G on X, then there exist a group G˜ and a tree X˜ induced by (T; Y ) such that G˜ acts on X˜ with inversions, G is isomorphic to G˜, and X is isomorphic to X˜. The pair (G˜; X˜) is called the quasi universal cover of (G;X) induced by the (T; Y).

An Euclidean graph associated with a molecule is defined by a weighted graph with adjacency matrix M = [dij], where for ij, dij is the Euclidean distance between the nuclei i and j. In this matrix dii can be taken as zero if all the nuclei are equivalent. Otherwise, one may introduce different weights for distinct nuclei. Balaban introduced some monster graphs and then Randic computed complexity indices of them (1973, 2001). In this paper, with a simple method, we calculate the automorphism group of some weighted graphs.

In this paper, a Bayesian hierarchical model is used to analyze the female breast cancer mortality rates for the State of Missouri from 1969 through 2001. The logit transformations of the mortality rates are assumed to be linear over the time with additive spatial and age effects as intercepts and slopes. Objective priors of the hierarchical model are explored. The Bayesian estimates are quite robustness in terms change of the hyperparamaters. The spatial correlations are appeared in both intercepts and slopes.