topological analysis has been performed on the total electron density of the two forms of ozonemolecule,c2v and d3h ,to investigate the nature of chemical bonds ,molecular structure , atomiccharges and electrical properties. while these concepts have been completely discussed usingclassical models the emphasize in this work is based on quantum theory of atoms in molecules(qtaim). because the d3...

The form π is unique up to a character twist, while ν is simply the central character of Π. The central character ω of π may be chosen to be of finite order. Moreover, we may choose π such that, for any finite place v, πv is unramified, resp. Steinberg, when Πv ⊗ νv is unramified, resp. Steinberg. Here Ad(π) denotes the Adjoint of π, a selfdual automorphic form on GL(3)/F , defined to be sym2(π...

We deal with Boolean algebras and their cardinal functions: π-weight π and π-character πχ. We investigate the spectrum of π-weights of subalgebras of a Boolean algebra B. Next we show that the π-character of an ultraproduct of Boolean algebras may be different from the ultraproduct of the π-characters of the factors.

All spaces below are Tychonov. We define the pro-jective π-character p πχ(X) of a space X as the supremum of the values πχ(Y) where Y ranges over all continuous images of X. Our main result says that every space X has a π-base whose order is ≤ p πχ(X), that is every point in X is contained in at most p πχ(X)-many members of the π-base. Since p πχ(X) ≤ t(X) for compact X, this provides a signifi...

Let π be an irreducible representation of a real reductive group G. The global character θπ of π may be considered as a function on the regular semisimple elements of G. The global character determines π, and it is of great interest to compute it. For example Harish-Chandra found the discrete series representations of G by computing their characters. Fix a Cartan subgroup H of G and let D be th...

Let Fn be the set of cuspidal automorphic representations π GLn over a number field with unitary central character. We prove two unconditional large sieve inequalities for Hecke eigenvalues π∈Fn, one on integers and primes. The second leads to first zero density estimate family L-functions L(s,π) associated which we make log-free. As an application estimate, hybrid subconvexity bound L(12,π) su...

Consider the character of an irreducible admissible representation of a p-adic reductive group. The Harish-Chandra-Howe local expansion expresses this character near a semisimple element as a linear combination of Fourier transforms of nilpotent orbital integrals. Under mild hypotheses, we describe an explicit region on which the local character expansion is valid. We assume neither that the gr...