Related papers: A note on the extension of the Dirac method
We expand the most general lattice Dirac operator D in a basis of simple operators. The Ginsparg-Wilson equation turns into a system of coupled quadratic equations for the expansion coefficients. Our expansion of D allows for a natural…
The article considers some concrete solutions to the Dirac equation coupled to a vector bundle with connection, arising in the study of Yang-Mills equations and vector bundles on Riemann surfaces.
We first study the linear eigenvalue problem for a planar Dirac system in the open half-line and describe the nodal properties of its solution by means of the rotation number. We then give a global bifurcation result for a planar nonlinear…
In this note, we describe a method to construct the Picard-Vessiot ring of a given linear differential equation.
It is shown that the Dirac equations in general higher dimensional Kerr-NUT-de Sitter spacetimes are separated into ordinary differential equations.
We consider a fractional generalization of gradient systems. We use differential forms and exterior derivatives of fractional orders. Examples of fractional gradient systems are considered. We describe the stationary states of these…
We describe a set of Gaussian Process based approaches that can be used to solve non-linear Ordinary Differential Equations. We suggest an explicit probabilistic solver and two implicit methods, one analogous to Picard iteration and the…
An important class of fractional differential and integral operators is given by the theory of fractional calculus with respect to functions, sometimes called $\Psi$-fractional calculus. The operational calculus approach has proved useful…
A method to calculate the adjoint solution for a large class of partial differential equations is discussed. It differs from the known continuous and discrete adjoint, including automatic differentiation. Thus, it represents an alternative,…
The objective of this paper is to investigate the existence and the forms of the pair of finite order entire and meromorphic solutions of some certain systems of Fermat-type partial differential-difference equations of several complex…
In recent papers we have introduced a method for the study of limit cycles of the Lienard system: dot{x}=y-F(x), dot{y}=-x, where F(x) is an odd polynomial. The method gives a sequence of polynomials R_n(x), whose roots are related to the…
We systematically introduce the idea of applying differential operator method to find a particular solution of an ordinary nonhomogeneous linear differential equation with constant coefficients when the nonhomogeneous term is a polynomial…
Applying domain decomposition to the lattice Dirac operator and the associated quark propagator, we arrive at expressions which, with the proper insertion of random sources therein, can provide improvement to the estimation of the…
In these informal lecture notes we outline different approaches used in doing calculations involving the Dirac equation in curved spacetime. We have tried to clarify the subject by carefully pointing out the various conventions used and by…
We determine a considerable class of nonlinear partial differential equation systems which have global regular solutions. Uniqueness is not a direct general consequence of this method. The scheme can be applied to the incompressible Navier…
We obtain a new general extension theorem in Banach spaces for operators which are not required to be symmetric, and apply it to obtain Harnack estimates and a priori regularity for solutions of fractional powers of several second order…
We present a numerical method for rigorous over-approximation of a reachable set of differential inclusions. The method gives high-order error bounds for single step approximations and a uniform bound on the error over the finite time…
The Dirac equation for an electron in an external electromagnetic field can be regarded as a singular set of linear equations for the vector potential. Radford's method of algebraically solving for the vector potential is reviewed, with…
By using a perturbation technique in critical point theory, we prove the existence of solutions for two types of nonlinear equations involving fractional differential operators.
We study conditions under which a partial differential operator of arbitrary order $n$ in two variables or ordinary linear differential operator admits a factorization with a first-order factor on the left. The factorization process…