Related papers: Exact Differential Equations and Harmonic Function…
We prove Euler-Lagrange fractional equations and sufficient optimality conditions for problems of the calculus of variations with functionals containing both fractional derivatives and fractional integrals in the sense of Riemann-Liouville.
We prove that every entire solution of the minimal graph equation that is bounded from below and has at most linear growth must be constant on a complete Riemannian manifold $M$ with only one end if $M$ has asymptotically non-negative…
To solve the problem of exact integration of the field equations or equations of motion of matter in curved spacetimes one can use a class of Riemannian metrics for which the simplest equations of motion can be integrated by the complete…
As a model of more general contour integration problems we consider the numerical calculation of high-order derivatives of holomorphic functions using Cauchy's integral formula. Bornemann (2011) showed that the condition number of the…
This paper concerns exact differential equations. First, I define two types of functions which I have named Basic Function of Type One and Basic Function of Type Two. I then derive the property and theorems of these functions. Finally, by…
We solve the Einstein vacuum-equations for the case of static and axisymmetric solutions in a system of coordinates different from the Weyl standard one. We prove that there exists a class of solutions with the appropriate asymptotical…
The differential constraints are applied to obtain explicit solutions of nonlinear diffusion equations. Certain linear determining equations with parameters are used to find such differential constraints. They generalize the determining…
In the present paper, we derive several conditions of linear combinations and convolutions of harmonic mappings to be univalent and convex in one direction, one of them gives a partial answer to an open problem proposed by Dorff. The…
This paper is a survey of uniqueness results for stochastic differential equations with jumps and regularity results for the corresponding harmonic functions.
In this paper, we define f-eikonal helix curves and f-eikonal V_{n}-slant helix curves in a n-dimensional Riemannian manifold. Also, we give the definition of harmonic curvature functions related to f-eikonal helix curves and f-eikonal…
Explicit harmonic and wave maps are typically available only in highly symmetric or constant-curvature settings, where additional symmetry or integrability structures are present. We develop a reduction framework for pseudo-Riemannian…
Asymptotic solutions are derived for inhomogeneous differential equations having a large real or complex parameter and a simple turning point. They involve Scorer functions and three slowly varying analytic coefficient functions. The…
We apply symmetry and invariance methods to analyse systems of difference equations. Non trivial symmetries are derived and their exact solutions obtained.
A method for finding exact solutions of nonlinear differential equations is presented. Our method is based on the application of the Newton polygons corresponding to nonlinear differential equations. It allows one to express exact solutions…
The problem of algebraic dependence of solutions to (non-linear) first order autonomous equations over an algebraically closed field of characteristic zero is given a `complete' answer, obtained independently of model theoretic results on…
We consider linear partial differential equations on resistance spaces that are uniformly elliptic and parabolic in the sense of quadratic forms and involve abstract gradient and divergence terms. Our main interest is to provide graph and…
We extend the equations of motion that describe non-relativistic elastic collision of two particles in one dimension to an arbitrary associative algebra. Relativistic elastic collision equations turn out to be a particular case of these…
We demonstrate how to explicitly calculate the QED path integral and associated Green functions, exactly, in curved spacetime, with retention of the boundary terms, to infinite order, for any and all spacetime manifolds with sufficient…
In the present work, an attempted was made to develop a numerical algorithm by the use of new orthogonal hybrid functions formed from hybrid of piecewise constant orthogonal sample-and-hold functions and piecewise linear orthogonal…
Accurate derivatives are important for efficiently locally traversing and converging in quantum optimization landscapes. By deriving analytically exact control derivatives (gradient and Hessian) for unitary control tasks, we show here that…