We use extensions to study the semi-simple quotient of the group ring FpAut(P ) of a finite p-group P . For an extension E : N → P → Q, our results involve relations between Aut(N), Aut(P ), Aut(Q) and the extension class [E] ∈ H(Q,ZN). One novel feature is the use of the intersection orbit group Ω([E]), defined as the intersection of the orbits Aut(N) · [E] and Aut(Q) · [E] in H(Q,ZN). This gr...

The main objective of this tutorial is to present the basic concepts on the instantaneous p-q Theory and them show its applicability for controlling switching converters connected in a micro-grid. These converters can be used for connecting renewable energy sources (solar, wind, and others) to the microgrids or for harmonic, reactive power or unbalance compensation, and even for voltage regulat...

We consider finite groups which have connected transversals to subgroups whose order is a product of two primes p and q. We investigate those values of p and q for which the group is soluble. We can show that the solubility of the group follows if q = 2 and p ≤ 61, q = 3 and p ≤ 31, q = 5 and p ≤ 11. We then apply our results on loop theory and we show that if the inner mapping group of a finit...

In the second self-creation theory of gravitation and in the general theory of relativity, Bianchi type VI0 cosmological model in the presence of viscous fluid is studied. An exact solution of the field equations is given by considering the cosmological model yields a constant decelerations parameter q=constant and the coefficients of the metric are taken as A(t)=[c1t+c<su...

the hydrogen abstraction reaction of oh radical with ch3ch2ocf2chf2 (hfe-374pc2) is investigated theoretically by semi-classical transition state theory. the stationary points on the potential energy surface of the reaction are located by using kmlyp density functional method along with 6-311++g(d,p) basis set. vibrational anharmonicity coefficients, xij, required for semi-classical transition ...

We analyse here the monadic theory of the rational order, the monadic theory of the real line with quantification over "small" subsets and models of these theories. We prove that the results are in some sense the best possible. ?0. Introduction. A chain is a linearly ordered set. A chain is short iff it embeds neither Wi nor O1. Shortness is expressible in the monadic language of order. For con...

This paper describes the calculation of the semileptonic Kl3 decay form factors at order p of chiral perturbation theory, which is the next-to-leading order correction to the well-known p result achieved by Gasser and Leutwyler. At order p the chiral expansion contains oneand two-loop diagrams which are discussed in detail. The irreducible two-loop graphs of the sunset topology are calculated n...

The concept of geometric-arithmetic indices was introduced in the chemical graph theory. These indices are defined by the following general formula:     ( ) 2 ( ) uv E G u v u v Q Q Q Q GA G , where Qu is some quantity that in a unique manner can be associated with the vertex u of graph G. In this paper the exact formula for two types of geometric-arithmetic index of Vphenylenic nanotube ar...

A type of rooted map called (p, q, n)-dipole, whose numbers on surfaces have some applications in string theory, are defined and the numbers of (p, q, n)-dipoles on orientable surfaces of genus 1 and 2 are given by Visentin and Wieler (The Electronic Journal of Combinatorics 14 (2007),#R12). In this paper, we study the classification of (p, q, n)-dipoles on nonorientable surfaces and obtain the...

We give an argument showing that in N=4 supersymmetric gauge theories there exists at least one bound state saturating the Bogomol’nyi bound with electric charge p and magnetic charge q, for each p and q relatively prime, and we comment on the uniqueness of such state. This result is a necessary condition for the existence of an exact S-duality in N=4 supersymmetric theories. On leave of absenc...