In this paper, we study the relation between the cohomology of Coxeter groups and their parabolic subgroups of nite order. Let W be a Coxeter group and k a commutative ring with identity. We investigate the natural map : H (W; k) ! lim:inv: H (W F ; k), where W F runs all parabolic subgroups of nite order, and prove that the kernel and the cokernel of consist of nilpotent elements. This general...

The prime graph of a finite group $G$ is denoted by $Gamma(G)$ whose vertex set is $pi(G)$ and two distinct primes $p$ and $q$ are adjacent in $Gamma(G)$, whenever $G$ contains an element with order $pq$. We say that $G$ is unrecognizable by prime graph if there is a finite group $H$ with $Gamma(H)=Gamma(G)$, in while $Hnotcong G$. In this paper, we consider finite groups with the same prime gr...

Let $L = U_3(9)$ be the simple projective unitary group in dimension 3 over a field  with 92 elements. In this article, we classify groups with the same order and degree pattern as an almost simple group related to $L$. Since $Aut(L)equiv Z_4$ hence almost simple groups related to $L$ are $L$, $L : 2$ or $L : 4$. In fact, we prove that $L$, $L : 2$ and $L : 4$ are OD-characterizable.

Let $G$ be a finite group and $pi(G)$ be the set of all prime divisors of $|G|$. The prime graph of $G$ is a simple graph $Gamma(G)$ with vertex set $pi(G)$ and two distinct vertices $p$ and $q$ in $pi(G)$ are adjacent by an edge if an only if $G$ has an element of order $pq$. In this case, we write $psim q$. Let $|G= p_1^{alpha_1}cdot p_2^{alpha_2}cdots p_k^{alpha_k}$, where $p_1

We construct a space BDI(4) whose mod 2 cohomology ring is the ring of rank 4 mod 2 Dickson invariants. The loop space on BDI(4) is the rst example of an exotic nite loop space at 2. We conjecture that it is also the last one. From the point of view of homotopy theory a compact Lie group G has the following remarkable combination of properties: (1) G can be given the structure of a nite CW-comp...

We present a new method for solving numerically the equations associated with solvation continuum models, which also works when the solvent is an anisotropic dielectric or an ionic solution. This method is based on the integral equation formalism. Its theoretical background is set up and some numerical results for simple systems are given. This method is much more eeective than three dimensiona...

It is known that the entropy distance between two Gauss-ian measures is nite if, and only if, they are absolutely continuous with respect to one another. Shepp (1966) characterized the correlations corresponding to stationary Gaussian measures that are absolutely continuous with respect to the Wiener measure. By analyzing the entropy distance, we show that one of his conditions, involving the s...

The characteristics of di€raction radiation (DR), i.e. radiation of the charged particle moving near conducting target have been considered for an ultrarelativistic case. The simple expressions for DR ®elds for the semi-in®nite ideal conducting target have been derived. The close connection between transition radiation (TR) and DR has been shown. The e€ect of ®nite transversal sizes of target o...

We describe a few structural properties enjoyed by the policy space of problems such as in nite-horizon MDPs. From these properties we derive constraints limiting the number of iterations of algorithms such as the policy iteration algorithm for in nite-horizon MDPs and the Ho man-Karp algorithm for simple stochastic games. An open problem is to characterize the growth of the worst-case number o...

We show that dependent elds have no Artin-Schreier extension, and that simple elds have only a nite number of them.