Results 101 to 110 of about 50,382 (139)

Functional equations for the functions of real variables

Moscow University Computational Mathematics and Cybernetics, 2014
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Addition theorems for $${\mathcal {C}}^k$$ real functions and applications in ordinary differential equations

Aequationes mathematicae, 2021
We say that a given function \(\varphi\) has an \textit{addition theorem} if the value of \(\varphi(x+y)\) can be expressed as a function of \(\varphi(x)\) and \(\varphi(y)\). In other words, for some \(G\) the formula \(G(\varphi(x),\varphi(y),\varphi(x+y))=0\) holds for all \(x,y\) from a given domain.
Francisco Crespo, Salomón Rebollo-Perdomo, Jorge L. Zapata   +2 more
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Real-space Green’s function calculation for the solution of the diffusion equation in stratified turbid media

Journal of the Optical Society of America A, 2000
We have derived the space-time Green's function for the diffusion equation in layered turbid media, starting from the case of a planar interface between two random scattering media. This new approach for working directly in real space permits highly efficient numerical processing, which is a decisive criterion for the feasibility of the inverse problem
J M, Tualle, J, Prat, E, Tinet, S, Avrillier   +3 more
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Elliptic partial differential equationsfor real analytic functions

Mathematische Zeitschrift, 2000
The problem of existence of a continuous linear right inverse operator for a given partial differential operators is studied. Suppose \(K\subset\mathbb{R}^N\) is a compact convex set with nonempty interior, \(\partial K\) is the boundary of \(K,\) \(A(K)\) is the space of all real analytic functions on \(K\) and the partial differential operator \(P(D):
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Real wave equations for positive-frequency electromagnetic fields and their Green’s function solutions

Journal of Mathematical Physics, 1992
A method is provided whereby solutions of the inhomogeneous wave equations that describe the propagation of positive-frequency photons in the forward tube of complex Minkowski space may be formally expressed in terms of integrals involving the tensor product of appropriate Green’s functions.
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Solvability Conditions for the Nonlocal Boundary-Value Problem for a Differential-Operator Equation with Weak Nonlinearity in the Refined Sobolev Scale of Spaces of Functions of Many Real Variables

Ukrainian Mathematical Journal, 2020
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Il'kiv, V. S., Strap, N. I., Volyanska, I. I.   +2 more
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Equilibrium Limit of Diffusion Equation for Interacting Particles:  Are Bifurcations and Multiplicity of Correlation Functions an Artifact or Real?

The Journal of Physical Chemistry B, 2007
The structure of a fluid is analyzed by taking the equilibrium limit of a diffusion equation including the Giacomin-Lebowitz term for intermolecular interactions. This equation represents the differential mass balance in fluids with the Metropolis algorithm for fluxes; it allows a new qualitative yet analytical approximation for the direct correlation ...
G L, Aranovich, M D, Donohue
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Quadratic forms as Liapunov functions for linear differential equations with real constant coefficients

Mathematical Proceedings of the Cambridge Philosophical Society, 1965
AbstractThis paper deals with the existence of a quadratic form as a Liapunov function for a linear homogeneous vector differential equation with constant coefficient matrix such that the total derivative of the Liapunov function is strictly negative semi-definite and not identically equal to 0 for every non-trivial solution of the given equation.
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