Results 141 to 150 of about 540,702 (189)

Functional integral for parabolic differential equations

Journal of Physics A: Mathematical and General, 1985
The proof of convergence of a discretisation procedure for path integrals associated with parabolic second-order differential equations is presented.
Alicki, Robert, Makowiec, Danuta
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Functional integral via functional equation

Letters in Mathematical Physics, 1994
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Integral Equations and Functionals

Mathematics Magazine, 1950
Introduction. It would be difficult to think of any two topics in mathematical analysis more central and more widely studied during the last fifty years than the theory of integral equations and functionals. Here we are using the word functional as a noun and not as an adjective.
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Functional Integral Equations

1999
Let X be an arbitrary Banach space with the norm ∥·∥. We denote the Euclidean norm in R n and the norm in the Banach space X by the same symbol. Elements of the space R n will be denoted by x = (x1, …, x n ), s = (s1, …, s n ). Let E ⊂ R + n be a compact set and G(x) = }ξ ∈ E:ξ≤x}. Assume that functions $$ E \in C\left( {E \times {X^m} \times X,\,X}
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Quintic spline functions and Fredholm integral equation

2021
Summary: A new six order method developed for the approximation Fredholm integral equation of the second kind. This method is based on the quintic spline functions (QSF). In our approach, we first formulate the Quintic polynomial spline then the solution of integral equation approximated by this spline.
Maleknejad, Khosrow, Rashidinia, Jalil, Jalilian, Hamed   +2 more
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Volterra Integral and Functional Equations

1990
The rapid development of the theories of Volterra integral and functional equations has been strongly promoted by their applications in physics, engineering and biology. This text shows that the theory of Volterra equations exhibits a rich variety of features not present in the theory of ordinary differential equations.
G. Gripenberg, S. O. Londen, O. Staffans
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Integral and functional equations

1960
An equation for a function u (x 1, x 2, ..., x n ) of n independent variables x 1, x 2, ..., x n , in the simplest case for a function y(x), is called an integral equation when it involves an integral with the function u appearing in its integrand and with at least one of the arguments of u among its variables of integration.
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Integrable solutions of a functional-integral equation

1992
A theorem about the existence of solutions of the functional-integral equation (1) \(x(t)=f\left(t,\int^ 1_ 0k(t,s)g(s,x(s))ds\right)\), \(t\in[0,1]\), is proved. The technique used in the proof depends on an interesting conjunction of the notions of the measure of weak noncompactness and the Schauder fixed point principle. It is worth while to mention
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Functional equations for path integrals

Journal of Statistical Physics, 1984
We consider the density matrices that arise in the statistical mechanics of the electron-phonon systems. In the path integral representation the phonon coordinates can be eliminated. This leads to an action that depends on pairs of points on a path, that depends explicitly on time differences, and that contains the phonon occupation numbers.
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Functional equations for Feynman integrals

Physics of Particles and Nuclei Letters, 2011
New types of equations for Feynman integrals are found. It is shown that the latter satisfy functional equations that relate integrals with different kinematics. A regular method for obtaining such relations is proposed. A derivation of the functional equations for one-loop two-, three-, and four-point functions with arbitrary masses and external ...
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