Results 221 to 230 of about 58,866 (264)
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Prentice’s Equation and Generalizations
Optometry and Vision Science, 2000ABSTRACT: The purpose of this note is to clarify confusion over the range of applicability of Prentice's equation for the calculation of prismatic effects in lenses. Making use of the concept of the ray transference in Gaussian and linear optics, the paper obtains generalized forms of Prentice'
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On generalized Rubel’s equation
Aequationes mathematicae, 2017Let \(G\) be an arbitrary domain of \(\mathbb C\) and denote by \(\mathcal{H}(G)\) the space of analytic functions in \(G\) equipped with the topology of compact convergence. Rubel posed and solved the problem of finding all pairs of linear continuous functionals \(L\) and \(M\) on \(\mathcal{H}(G)\) satisfying the relation \[ L(fg)=L(f)M(g)+L(g)M(f), \
Linchuk, S. S., Linchuk, Yu. S.
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On CIR Equations with General Factors
SIAM Journal on Financial Mathematics, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Michal Barski, Jerzy Zabczyk
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Il Nuovo Cimento, 1957
This note contains a derivation of a formally exact relation in the field theory between the elements of theS matrix corresponding to a given number of particles. This relation is similar in form to Low’s equation (1), but all elements of theS matrix associated with different numbers of particles but one distinguished are here eliminated (+).
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This note contains a derivation of a formally exact relation in the field theory between the elements of theS matrix corresponding to a given number of particles. This relation is similar in form to Low’s equation (1), but all elements of theS matrix associated with different numbers of particles but one distinguished are here eliminated (+).
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Equation generation for clustering
Proceedings of the third international conference on Industrial and engineering applications of artificial intelligence and expert systems - IEA/AIE '90, 1990Clustering events into useful classifications is an important part of problem solving in engineering. This paper discusses the role of clustering in engineering and why numerical and conceptual clustering techniques are not always adequate. The knowledge based equation generator system was constructed to overcome one of these shortfalls.
Bradley L. Whitehall +2 more
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Generalized master equations and the telegrapher's equation
Physica A: Statistical Mechanics and its Applications, 1990zbMATH Open Web Interface contents unavailable due to conflicting licenses.
HONGLER, MO, Streit, Ludwig
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Generalizing the Marcus equation
The Journal of Chemical Physics, 2020The Marcus equation for the rate of an electron-transfer reaction can be generalized to cover larger electronic-interaction matrix elements, irregular free-energy surfaces, and coupling to multiple vibrational modes and to recognize the different effects of vibrational relaxations and pure dephasing.
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Perturbation analysis of the generalized Sylvester equation and the generalized Lyapunov equation
International Journal of Computer Mathematics, 2010This paper is devoted to the perturbation analysis for the generalized Sylvester equation and the generalized Lyapunov equation. The explicit expressions and upper bounds of normwise, mixed and componentwise condition numbers for these equations are presented. The results are illustrated by numerical examples.
Yaoping Tang, Liang Bao, Yiqin Lin
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On the generalized Navier–Stokes equations
Applied Mathematics and Computation, 2003In this paper, we present a general Inodel of the classical Navier-Stokes equations. With the help of Laplace, Fourier Sine transforms, finite Fourier Sine transforms, and finite Hankel transforms, an exact solutions for three different special cases have been obtained.
Moustafa El-Shahed, Ahmed Salem 0007
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On The Generalized Cauchy Equation
Canadian Journal of Mathematics, 1967It is the purpose of this note to prove the following theorem: Let ƒ: G → R be a non-constant continuous function with G a locally compact connected topological group and with R the real numbers. Let C = ƒ(G) and suppose that F: C × C → C is a junction such thatThen ƒ is monotone and open and F is continuous.
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