Fullerene chemistry is nowadays a well-established field of both theoretical and experimental investigations‎. This study considers the symmetry of small fullerenes cage C24 and C28‎. ‎Using PM3 program for C24 and C28 fullerenes, Oh and Td symmetry were confirmed, respectively‎. ‎ The mentioned algorithm to compute the automorphism group of these fullerenes with connectivity and geometry of th...

We assume that the “table head” of the ordinary character table of the sporadic simple Janko group J4 is known. That is, the conjugacy classes and their centralizer orders are known as well as all p-th power maps, for primes p up to the maximal element order in J4, which is 66. For the sake of simplicity, we take the table head of the character table contained in the GAP Character Table Library...

‎In our paper [A‎. ‎B‎. ‎M‎. ‎Basheer and J‎. ‎Moori‎, ‎On a group of the form $2^{10}{:}(U_{5}(2){:}2)$] we calculated the inertia factors‎, ‎Fischer matrices and the ordinary character table of the split‎ ‎extension $ 2^{10}{:}(U_{5}(2){:}2)$ by means of Clifford-Fischer‎ ‎Theory‎. ‎The second inertia factor group of $2^{10}{:}(U_{5}(2){:}2)$‎ ‎is a group of the form $2_{-}^{1+6}{:}((3^{1+2}{...

This paper presents a new probability table memory compression method based on mixture models and its application to N-tuple recognizers and N-gram character language models. Joint probability tables are decomposed into lower dimensional probability components and their mixtures. The maximum likelihood parameters of the mixture models are trained by the Expectation Maximization (EM) algorithm a...

the split extension group $a(4)cong 2^7{:}sp_6(2)$ is the affine subgroup of the symplectic group $sp_8(2)$ of index $255$‎. ‎in this paper‎, ‎we use the technique of the fischer-clifford matrices to construct the character table of the inertia group $2^7{:}(2^5{:}s_{6})$ of $a(4)$ of index $63$‎.

O n January 8, 2007, just before 9 in the morning, a computer finished writing to disk about sixty gigabytes of files containing the Kazhdan-Lusztig polynomials for the split real group G of type E8. Values at 1 of these polynomials are coefficients in characters of irreducible representations of G; so all irreducible characters were written down. The biggest coefficient appearing was 11,808,80...

It is well known that the complex adjacency algebra A of an association scheme has a specific module, namely the standard module, that contains the regular module of A as a submodule. The character afforded by the standard module is called the standard character. In this paper we first define the concept of standard character for C-algebras and we say that a C-algebra has the standard character...

‎in [u‎. ‎dempwolff‎, ‎on extensions of elementary abelian groups of order $2^{5}$ by $gl(5,2)$‎, ‎textit{rend‎. ‎sem‎. ‎mat‎. ‎univ‎. ‎padova}‎, ‎textbf{48} (1972)‎, ‎359‎ - ‎364.] dempwolff proved the existence of a group of the‎ ‎form $2^{5}{^{cdot}}gl(5,2)$ (a non split extension of the‎ ‎elementary abelian group $2^{5}$ by the general linear group‎ ‎$gl(5,2)$)‎. ‎this group is the second l...