Results 271 to 280 of about 15,169 (314)

Cauchy Problem for Dynamic Elasticity Equations

Differential Equations, 2020
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Makhmudov, O. I., Niyozov, I. E.
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Generalization of Cauchy–Riemann equations

Reports on Mathematical Physics, 1985
In view of the recently growing interest in applications of hypercomplex function theories to physical problems, the author discusses extensions of the analyticity notion to general composition algebras. Special stress is placed upon the case of an octonion algebra and upon the aim that the analyticity notion be suitable for re-establishing the main ...
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Additive Cauchy Equation

2011
The functional equation \(f(x+y)=f(x)+f(y)\) is the most famous among the functional equations. Already in 1821, A. L. Cauchy solved it in the class of continuous real-valued functions. It is often called the additive Cauchy functional equation in honor of A. L. Cauchy.
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Cauchy Type Integral Equations

2000
In this chapter we study various singular integral equations with kernels of the Cauchy type, starting from the most basic Cauchy type integral equation.
Ricardo Estrada, Ram P. Kanwal
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Cauchy's equation on Δ+

Aequationes Mathematicae, 1991
Recently R. C. Powers characterized the order automorphisms of the space of nondecreasing functions from one compact real interval to another [6, 7]. In this paper we show how his results, as well as the lattice-theoretic techniques which he employed, can be used to obtain solutions of Cauchy's equation for certain classes of semigroups (triangle ...
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Basic Equations: Cauchy and Pexider Equations

2009
In this chapter, Cauchy’s fundamental equations are studied, some algebraic conditions and generalizations are considered, and alternate equations, conditions on restricted domains, Jensen’s equation, some special cases of Cauchy’s equations, extensions of the additive equations, Pexider equations and their extensions, some applications in economics ...
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Generalized Additive Cauchy Equations

2011
It is very natural for one to try to transform the additive Cauchy equation into other forms. Some typically generalized additive Cauchy equations will be introduced. The functional equation \(f(ax+by)=af(x)+bf(y)\) appears in Section 3.1. The Hyers–Ulam stability problem is discussed in connection with a question of Th. M. Rassias and J. Tabor.
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The cauchy problem for laplace's equation

Siberian Mathematical Journal, 1992
See the review in Zbl 0773.31007.
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CAUCHY PROBLEM FOR NON-KOWALEVSKIAN EQUATIONS

International Journal of Mathematics, 1995
The paper deals with the well-posedness of the Cauchy problem for a class of non-Kowalevskian equations. The following Cauchy problem is considered: \[ Pu(t, x)= f(t, x)\quad\text{in }[- T, T]\times \mathbb{R}^n,\quad D^j_t u(0, x)= g_j(x),\quad 0\leq j\leq m- 1.
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Cauchy's equation on Δ+: Further results

Aequationes Mathematicae, 1992
In continuation of his paper [ibid. 41, No. 2/3, 192-211 (1991; Zbl 0733.39012)] the author deals under weak conditions with the functional equation \(\varphi(\tau_{T,L}(F,G))=\tau_{T,L}(\varphi(F),\varphi(G))\) for all probability distributions \(F,G\) of nonnegative random variables. Here \(T(x,y)=g^{(-1)}(g(x)+g(y))\), \(L(u,v)=f^{(-1)}(f(u)+f(v))\).
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