We consider both primal and dual formulations of singular autonomous systems three different types fractional-order differential equations. present a comprehensive study which proves that by using the spectrum linear pencil, polynomial matrix first order, not pencil prime system, we will receive information for all properties its system. In addition, this spectrum, solutions can be obtained for...

This paper presents a synthesis methodology for parallel robots based on the dual quaternion synthesis of serial constrained robots, that is, serial robots with less than six degrees of freedom. This methodology uses a dual quaternion formulation of the kinematics equations. The goal of the synthesis problem is to determine the dimensions of the robot from a specification of its workspace. The ...

Compactly supported linear semiorthogonal B-spline wavelets together with their dual wavelets are developed to approximate the solutions of nonlinear Fredholm-Hammerstein integral equations. Properties of these wavelets are first presented; these properties are then utilized to reduce the computation of integral equations to some algebraic equations. The method is computationally attractive, an...

Analytical solutions of precise equations that describe the rf-coupling of two cavities through a co-axial cylindrical hole are given for various limited cases. For their derivation we have used the method of solution of an infinite set of linear algebraic equations, based on its transformation into dual integral equations.

Using recently proposed non-linearly realized supersymmetry in non-Abelian gauge theory corrected to O(α′), we derive the non-linear BPS equations in the background B-field for the U(2) monopoles and instantons. We show that these non-Abelian non-linear BPS equations coincide with the non-commutative anti-self-dual equations via the Seiberg-Witten map.

We compute complete leading logarithms in Φ4 theory with the help of Connes and Kreimer RG equations. These equations are defined in the Lie algebra dual to the Hopf algebra of graphs. The results are compared with calculations in parquet approximation. An interpretation of the new RG equations is discussed.

We give a formulation of the vacuum Einstein equations in terms of a set of volume-preserving vector fields on a four-manifold M. These vectors satisfy a set of equations which are a generalisation of the Yang-Mills equations for a constant connection on flat spacetime. It is known (Mason and Newman 1989) that the equations which describe self-dual Ricci-flat metrics can be derived from the sel...