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...

Approximately fifty percent of Weyl’s theorem fails to transfer from Hilbert space operators to their tensor product. As a biproduct we find that the product of circles in the complex plane is a limaçon. 0. Introduction To say that “Weyl’s theorem holds”, for a bounded operator T ∈ B(X) on a Banach space X , is to assert [2],[4],[5] that 0.1 σ(T ) \ ωess(T ) = π 00 (T ) ≡ iso σ(T )∩π 0 (T ) : t...

Let F be a number field and ρ an irreducible Galois representation of Artin type, i.e., ρ is a continuous C-representation of the absolute Galois group ΓF . Suppose π is a cuspidal automorphic representation of GLn(AF ) such that the L-functions L(s, ρ) and L(s, π) agree outside a set S of primes. (Here, these L-functions denote Euler products over just the finite primes, so that we may view th...

Information Complexity Alexander Koza hinsky∗ ∗Mos ow State University, Fa ulty of Me hani s and Mathemati s kozla h mail.ru 2014 Abstra t We prove a version of "Reversed Newman Theorem" in ontext of information omplexity: every privateoin ommuni ation proto ol with information omplexity I and ommuni ation omplexity C an be repla ed by publi oin proto ol with the same behavior so that it's info...

Let Sp denote the category of p-local spectra for each prime number p and BP the Brown-Peterson spectrum at p. Then we have the Bousfield localization functor Ln : Sp → Sp with respect to v−1 n BP for the generator vn of BP∗ = Z(p)[vi : i > 0 ]. The category LnSp is easier to be understood than Sp itself and reflects some properties of it. LnSp is, in a sense, generated by the Ln-localized sphe...

The huge damage of denial of service attacks in security protocols attracts researchers’ attention and effort to analysis, verification and prevention of denial of service attacks. In order to model resistance of denial of service attacks, firstly, we extend applied pi calculus from both adversary context and processes aspects; secondly, the first computer-aided method of resistance of denial o...

The Intermediate Value Theorem is used to give an elementary proof of a Borsuk–Ulam theorem Adams, Bush and Frick [1] that if f : S 1 → R 2 k + $f: S^1\rightarrow {\mathbb {R}}^{2k+1}$ continuous function on the unit circle S1 in C ${\mathbb {C}}$ such ( − z ) = $f(-z)=-f(z)$ for all ∈ $z\in S^1$ , then there finite subset X diameter at most π / $\pi -\pi /(2k+1)$ (in standard metric which has ...

Dimensions are not units. Dimensions are fundamental physical quantities: length (L), time (T), mass (M), charge (Q), and so on. A set of units – such as SI units – define a conventional means by which to numerically measure these fundamental quantities. The choice of dimensions is not unique. For a given problem, it might be more convenient to use force (F), velocity (V), and frequency (Ω), fo...

E h(x)π(dx). Ibragimov and Linnik (1971) proved that if (Xn) is geometrically ergodic, then a central limit theorem (CLT) holds for h whenever π(|h|) < ∞, δ > 0. Cogburn (1972) proved that if a Markov chain is uniformly ergodic, with π(h) < ∞ then a CLT holds for h. The first result was re-proved in Roberts and Rosenthal (2004) using a regeneration approach; thus removing many of the technicali...