Lecture 2. Index problem for manifolds with a boundary. Index of the Dirac operator and anomalies. Lecture 3. Spectral asymmetry and Riemannian geometry. Heat equation and asymptotic heat kernel. The η-and ζ-functions. Lecture 4. Two-component spinor calculus. Dirac and Weyl equations in two-component spinor form. Weyl equation with spectral or local boundary conditions. Potentials for massless...

in this work, a new iterative method is proposed for obtaining the approximate solution of a class of hammerstein type integral equations system. the main structure of this method is based on the richardson iterative method for solving an algebraic linear system of equations. some conditions for existence and unique solution of this type equations are imposed. convergence analysis and error bou...

In this paper we discuss the concept of cosymmetries and co–recursion operators for difference equations and present a co–recursion operator for the Viallet equation. We also discover a new type of factorisation for the recursion operators of difference equations. This factorisation enables us to give an elegant proof that the recursion operator given in arXiv:1004.5346 is indeed a recursion op...