scholarly journals RELATIONSHIPS AMONG FOURIER-YEH-FEYNMAN TRANSFORM, CONVOLUTION AND THE FIRST VARIATION ON YEH-WIENER SPACE

2011 ◽  
Vol 33 (2) ◽  
pp. 207-221 ◽  
Author(s):  
Bong-Jin Kim ◽  
Byoung-Soo Kim
Keyword(s):  
Wiener Space ◽  
First Variation ◽  
The First Variation

scholarly journals Relationships among transforms, convolutions, and first variations

1999 ◽  
Vol 22 (1) ◽  
pp. 191-204 ◽  
Author(s):  
Jeong Gyoo Kim ◽  
Jung Won Ko ◽  
Chull Park ◽  
David Skoug
Keyword(s):  
Stochastic Integral ◽  
Wiener Space ◽  
Convolution Product ◽  
First Variation ◽  
The First Variation

In this paper, we establish several interesting relationships involving the Fourier-Feynman transform, the convolution product, and the first variation for functionalsFon Wiener space of the formF(x)=f(〈α1,x〉,…,〈αn,x〉),                                                      (*)where〈αj,x〉denotes the Paley-Wiener-Zygmund stochastic integral∫0Tαj(t)dx(t).

scholarly journals Parts formulas involving conditional Feynman integrals

2002 ◽  
Vol 65 (3) ◽  
pp. 353-369 ◽  
Author(s):  
Seung Jun Chang ◽  
David Skoug
Keyword(s):  
Basic Result ◽  
Feynman Integral ◽  
Wiener Space ◽  
Integration By Parts ◽  
Feynman Integrals ◽  
First Variation ◽  
Basic Formula ◽  
Analytic Feynman Integral ◽  
The First Variation

In this paper we first obtain a basic formula for the conditional analytic Feynman integral of the first variation of a functional on Wiener space. We then apply this basic result to obtain several integration by parts formulas for conditional analytic Feynman integrals and conditional Fourier-Feynman transforms.

scholarly journals A Change of Scale Formula for Wiener Integrals about the First Variation on the Product Abstract Wiener Space

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 12
Author(s):  
Young Sik Kim
Keyword(s):  
Feynman Integral ◽  
Wiener Space ◽  
Abstract Wiener Space ◽  
Wiener Integral ◽  
First Variation ◽  
Change Of Scale ◽  
Variation Of A Function ◽  
The First Variation

We shall prove the existence of the Wiener integral and the analytic Wiener and Feynman integral and we obtain those relationships and later, we prove the change of scale formula for the Wiener integral about the first variation of a function defined on the product abstract Wiener space. Later, we obtain those relationships in the Fresnel class as it’s corollaries.

scholarly journals Existence Results for the Conformal Dirac–Einstein System

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Chiara Guidi ◽  
Ali Maalaoui ◽  
Vittorio Martino
Keyword(s):  
Perturbation Methods ◽  
Existence Of Solutions ◽  
Coupled System ◽  
Existence Results ◽  
First Variation ◽  
The First Variation

AbstractWe consider the coupled system given by the first variation of the conformal Dirac–Einstein functional. We will show existence of solutions by means of perturbation methods.

scholarly journals On $L_1$-biharmonic timelike hypersurfaces in pseudo-Euclidean space $E_1^4$

2020 ◽  
Vol 51 (4) ◽  
pp. 313-332
Author(s):  
Firooz Pashaie
Keyword(s):  
Euclidean Space ◽  
Mean Curvature ◽  
Curvature Vector ◽  
Mean Curvature Vector ◽  
Principal Curvatures ◽  
First Variation ◽  
Chen’S Conjecture ◽  
The First Variation ◽  
Linearized Operator ◽  
Euclidean Submanifolds

A well-known conjecture of Bang Yen-Chen says that the only biharmonic Euclidean submanifolds are minimal ones. In this paper, we consider an extended condition (namely, $L_1$-biharmonicity) on non-degenerate timelike hypersurfaces of the pseudo-Euclidean space $E_1^4$. A Lorentzian hypersurface $x: M_1^3\rightarrow\E_1^4$ is called $L_1$-biharmonic if it satisfies the condition $L_1^2x=0$, where $L_1$ is the linearized operator associated to the first variation of 2-th mean curvature vector field on $M_1^3$. According to the multiplicities of principal curvatures, the $L_1$-extension of Chen's conjecture is affirmed for Lorentzian hypersurfaces with constant ordinary mean curvature in pseudo-Euclidean space $E_1^4$. Additionally, we show that there is no proper $L_1$-biharmonic $L_1$-finite type connected orientable Lorentzian hypersurface in $E_1^4$.

scholarly journals On solving the plateau problem in parametric form

1983 ◽  
Vol 6 (2) ◽  
pp. 341-361
Author(s):  
Baruch cahlon ◽  
Alan D. Solomon ◽  
Louis J. Nachman
Keyword(s):  
Minimal Surface ◽  
Numerical Method ◽  
Minimal Surfaces ◽  
Plateau Problem ◽  
Parametric Form ◽  
First Variation ◽  
Plateau’S Problem ◽  
Numerical Example ◽  
Plateau's Problem ◽  
The First Variation

This paper presents a numerical method for finding the solution of Plateau's problem in parametric form. Using the properties of minimal surfaces we succeded in transferring the problem of finding the minimal surface to a problem of minimizing a functional over a class of scalar functions. A numerical method of minimizing a functional using the first variation is presented and convergence is proven. A numerical example is given.

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