Related papers: Generalized second-order partial derivatives of 1/…
A simple position probability density formulation is presented for the motion of a particle in a spherically symmetric potential. The approach provides an alternative to Newtonian methods for presentation in an elementary course, and…
We determine the most general scalar field theories which have an action that depends on derivatives of order two or less, and have equations of motion that stay second order and lower on flat space-time. We show that those theories can all…
Generalizations of some known results on the best, best linear and best one-sided approxima- tions by trigonometric polynomials of the classes of 2\pi - periodic functions presented in the form of convolutions to the case of set-valued…
There is a difficulty in finding an estimate of variance of the profile likelihood estimator in the joint model of longitudinal and survival data. We solve the difficulty by introducing the ``statistical generalized derivative''. The…
In a recent work [1, 2] Sjoberg remarked that generalization of the double reduction theory to partial differential equations of higher dimensions is still an open problem. In this note we have attempted to provide this generalization to…
We prove an extension of one direction in Marty's theorem where the spherical derivative is replaced by a more general quantity involving higher derivatives.
Fractional calculus allows one to generalize the linear, one-dimensional, diffusion equation by replacing either the first time derivative or the second space derivative by a derivative of fractional order. The fundamental solutions of…
A new method is presented for obtaining indefinite integrals of common special functions. The approach is based on a Lagrangian formulation of the general homogeneous linear ordinary differential equation of second order. A general integral…
It is shown that the renormalization group (RG) method for global analysis can be formulated in the context of the classical theory of envelopes: Several examples from partial differential equations are analyzed. The amplitude equations…
A generalization of the already studied transformations of the linear differential equation into a system of the first order equations is given. The proposed transformation gives possibility to get new forms of the N-dimensional system of…
In this paper, we extend to the case of spin 1 the method we have devised for deriving generalized spin quantities from first principles, and which we illustrated using the spin-1/2 case. Again, we not only derive from first principles the…
Lie's linearizability criteria for scalar second-order ordinary differential equations had been extended to systems of second-order ordinary differential equations by using geometric methods. These methods not only yield the linearizing…
A general explicit form for generating functions for approximating fractional derivatives is derived. To achieve this, an equivalent characterisation for consistency and order of approximations established on a general generating function…
We extend to the case l=2 the study of the new generalized spherical harmonics introduced recently, and worked out only for the case l=1. We present some of the properties of the new quantities and clarify how they are related to standard…
This short article contains the construction of a construction that generalizes the concept of the derivative of a function of one variable, using the theory of filters. The paper presents a new concept, demonstrates that it really…
Spherical radial basis functions are used to define approximate solutions to strongly elliptic pseudodifferential equations on the unit sphere. These equations arise from geodesy. The approximate solutions are found by the Galerkin and…
We derive global analytic representations of fundamental solutions for a class of linear parabolic systems with full coupling of first order derivative terms where coefficient may depend on space and time. Pointwise convergence of the…
Heuristic arguments and order of magnitude estimates for partial differential equations highlight essential features of the physics they describe. We present order of magnitude estimates, and their limitations, for the three classic second…
The general classical solution of the 3D electromagnetic pp-wave spacetime has been obtained. The relevant line element contains an arbitrary essential function providing an infinite number of in-equivalent geometries as solutions. A…
The generalized harmonic equations of general relativity are written in 3+1 form. The result is a system of partial differential equations with first order time and second order space derivatives for the spatial metric, extrinsic curvature,…