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An extension of the Laplace transform obtained by using the Laguerre-type exponentials is first shown. Furthermore, the solution of the Blissard problem by means of the Bell polynomials, gives the possibility to associate to any numerical…
We apply topological methods to the study of the set of harmonic solutions of periodically perturbed autonomous ordinary differential equations on differentiable manifolds, allowing the perturbing term to contain a fixed delay. In the…
In this study, a recursive solution technique in conjunction with generalized integrating factors is presented and applied to address first and second order linear differential equations. This approach demonstrates practical utility in…
Deviations from kinetic equilibrium of massive particles caused by the universe expansion are calculated analytically in the Boltzmann approximation. For the case of an energy independent amplitude of elastic scattering, an exact partial…
In this work we extend analytic signal theory to the multidimensional case when oscillations are observed in the $d$ orthogonal directions. First it is shown how to obtain separate phase-shifted components and how to combine them into…
The analytic and formal solutions to a family of singularly perturbed partial differential equations in the complex domain involving two complex time variables are considered. The analytic continuation properties of the solution of an…
We provide of a method to integrate first order non-linear systems of differential equations with variable coefficients. It determines approximate solutions given initial or boundary conditions or even for Sturm-Liouville problems. This…
The existence and analyticity of solutions to linear systems of moment differential equations with analytic coefficients is studied. The relation of solutions of such systems with respect to linear moment differential equations is…
The paper concerns the second-order generalized differentiation theory of variational analysis and new applications of this theory to some problems of constrained optimization in finitedimensional spaces. The main attention is paid to the…
The differential transform method is used to find numerical approximation of solution to a class of certain nonlinear differential algebraic equations. The method is based on Taylor's theorem. Coefficients of the Taylor series are…
In this note we extend the Dirac method to partial differential equations involving higher order roots of differential operators.
The method of variational completion allows one to transform an (in principle, arbitrary) system of partial differential equations -- based on an intuitive ``educated guess'' -- into the Euler-Lagrange one attached to a Lagrangian, by…
Tools of the intrinsic analysis on manifolds, helpful in solving the invariant inverse problem of the calculus of variations are being presented comprising a combined approach which consists in the simultaneous imposition of symmetry…
Functional equations satisfied by additive functions have a special interest not only in the theory of functional equations, but also in the theory of (commutative) algebra because the fundamental notions such as derivations and…
We identify conditions giving large natural classes of partial differential operators for which it is possible to construct a complete set of Laplace invariants. In order to do that we investigate general properties of differential…
This paper describes infinite sets of polynomial equations in infinitely many variables with the property that the existence of a solution or even an approximate solution for every finite subset of the equations implies the existence of a…
We perform an asymptotic evaluation of the Hankel transform, $\int_0^{\infty}J_{\nu}(\lambda x) f(x)\mathrm{d}x$, for arbitrarily large $\lambda$ of an entire exponential type function, $f(x)$, of type $\tau$ by shifting the contour of…
In this letter, we exploit the Damour-Deruelle solution to derive the analytical expression of the coordinate time in terms of the polar angle. This formula has advantageous applications in both pulsar timing and gravitational-wave theory.
The Euclidean algorithm makes possible a simple but powerful generalization of Taylor's theorem. Instead of expanding a function in a series around a single point, one spreads out the spectrum to include any number of points with given…
In the pattern matching approach to imaging science, the process of ``metamorphosis'' is template matching with dynamical templates. Here, we recast the metamorphosis equations of into the Euler-Poincare variational framework of and show…