We review the application of the critical point large N f self-consistency method to QCD. In particular we derive the O(1/N f) d-dimensional critical exponents whose ǫ-expansion determines the perturbative coefficients in MS of the field dimensions, β-function and various twist-2 operators which occur in the operator product expansion of deep inelastic scattering.

In this paper, with the aid of symbolic computation we improve the extended F-expansion method described in Chaos, Solitons and Fractals 22, 111 (2004) to solve the (2 +1)-dimensional Korteweg de Vries equation. Using this method, we derive many exact non-travelling wave solutions. These are more general than the previous solutions derived with the extended F-expansion method. They include the ...

The unitary operators U(t), describing the quantum time evolution of systems with a time-dependent Hamiltonian, can be constructed in an explicit manner using the method of time-dependent invariants. We clarify the role of Lie-algebraic techniques in this context and elaborate the theory for SU(2) and SU(1,1). We show that the constructions known as Magnus expansion and Wei-Norman expansion cor...

several appliances have been used for palatal expansion for treatment of posterior cross bite. the purpose of this study was to evaluate the stress induced in the apical and crestal alveolar bone and the pattern of tooth displacement following expansion via removable expansion plates or fixed-banded palatal expander using the finite element method (fem) analysis.two 3d fem models were designed ...

We will pursue a way of building up an algebraic structure that involves, in a mathematical abstract way, the well known Grassmann variables. The problem arises when we tried to understand the grassmannian polynomial expansion on the scope of ring theory. The formalization of this kind of variables and its properties will help us to have a better idea of some algebraic structures and the way th...

The technique of relaxed power series expansion provides an efficient way to solve equations of the form F =Φ(F ), where the unknown F is a vector of power series, and where the solution can be obtained as the limit of the sequence 0,Φ(0),Φ(Φ(0)), . With respect to other techniques, such as Newton’s method, two major advantages are its generality and the fact that it takes advantage of possible...

Aim: the aim of this study was to compare cusp deflection, infraction and fracture in teeth filled with three temporary filling materials. Materials & method: Forty five extracted human premolar teeth were chosen. After root canal therapy and mesio-occluso-distal cavity preparation, samples were randomly divided into three groups , each contained 15 teeth and filled with three temporary filling...