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1
Content available Measures of growth and approximation of entire harmonic functions in n-dimensional space in some Banach spaces
Kumar Devendra
Journal of Mathematics and Applications
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2021
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Vol. 44
57--70
EN
The relationship between the classical order and type of an entire harmonic function in space Rn, n≥3, and the rate of its best harmonic polynomial approximation for some Banach spaces of functions harmonic in the ball of radius R has been studied.
2
Content available Edge waves over a shelf
Dolai P., Dolai D. P.
International Journal of Applied Mechanics and Engineering
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2019
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Vol. 24, no. 2
453--460
EN
The problem considered in this paper is the derivation of properties of edge waves travelling along a submerged horizontal shelf. The problem is formulated within the framework of the linearized theory of water waves and Havelock expansions of water wave potentials are used in the mathematical analysis to obtain the dispersion relation for edge waves in terms of an integral. Appropriate multi-term Galerkin approximations involving ultra spherical Gegenbauer polynomials are utilized to obtain a very accurate numerical estimate for the integral and hence to derive the properties of edge waves over a shelf. The numerical results are illustrated in a table and curves are presented showing the variation of frequency of the edge waves with the width of the shelf.
3
Content available Scattering of oblique water waves by an infinite step
Dolai P., Dolai D. P.
International Journal of Applied Mechanics and Engineering
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2018
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Vol. 23, no. 2
327--338
EN
The present paper is concerned with the problem of scattering of obliquely incident surface water wave train passing over a step bottom between the regions of finite and infinite depth. Havelock expansions of water wave potentials are used in the mathematical analysis to obtain the physical parameters reflection and transmission coefficients in terms of integrals. Appropriate multi-term Galerkin approximations involving ultra spherical Gegenbauer polynomials are utilized to obtain very accurate numerical estimates for reflection and transmission coefficients. The numerical results are illustrated in tables.
4
Content available Oblique water wave diffraction by a step
Dolai P.
International Journal of Applied Mechanics and Engineering
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2017
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Vol. 22, no. 1
35--47
EN
This paper is concerned with the problem of diffraction of an obliquely incident surface water wave train on an obstacle in the form of a finite step. Havelock expansions of water wave potentials are used in the mathematical analysis to obtain the physical parameters reflection and transmission coefficients in terms of integrals. Appropriate multi-term Galerkin approximations involving ultraspherical Gegenbauer polynomials are utilized to obtain a very accurate numerical estimate for reflection and transmission coefficients which are depicted graphically. From these figures various interesting results are discussed.
5
Content available remote Generalized translation operators and Markov processes
Thu N.
Demonstratio Mathematica
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2001
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Vol. 34, nr 2
295-304
EN
We study the relationship between generalized translation operators and stochastic convolutions on locally compact spaces. We prove that stochastic convolution semigroups can generate Levy type processes which are strong Markov Feller processes and, as an example, we study the Bingham convolution and its dual on integers.
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