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1
Content available remote Unified elliptic-type integrals and asymptotic formulas
Chaurasia V., Pandey S.
Demonstratio Mathematica
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2008
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Vol. 41, nr 3
531-541
EN
The object of the present paper is to consider a unified and extended form of certain families of elliptic-type integrals, which have been discussed in number of earlier works on the subject due to their importance and applications in problems arising in radiation physics and nuclear technology. The results obtained are of general character and include the investigations carried out by several authors. We obtain asymptotic formulas for the unified elliptic-type integrals.
2
Content available remote Non-isothermal hydromagnetic convection in a porous medium with heat sink: hypergeometric function solutions
Beg O. A., Takhar H. S., Beg T. A., Singh A. K.
International Journal of Applied Mechanics and Engineering
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2007
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Vol. 12, no 2
337-351
EN
The present paper deals with the free convection laminar boundary layer flow and heat transfer of an incompressible, electrically conducting, viscous fluid through a porous medium caused by stretching a porous wall in the presence of a heat source and under the influence of uniform magnetic field. Exact solutions of the basic equations of momentu m and energy ar e obtained after reducing them i n to non-linear ordinary differential equations and using confluent hypergeometric functions. The variations in the velocity field and temperature distribution with the Prandtl number (Pr), hydromagnetic parameter (M), permeability param eter (K), suction parameter (N), wall temperature parameler (S), and the heat sink parameter (Q) are obtained and depicted graphically. The skin-friction at the wall is also derived, and the numerical values for various physical parameters are also tabulaled. Magnetic field (M) is seen to reduce both longitudinal and translational velocities and also lower temperalures, aiding in controlling momentum and heat transfer during materiaIs processing. Suction (N) posivitely influences the transverse velocity but depresses the longitudinal velocity magnitudes as we II as decreasing tempcratures. Suction therefore also assists in controlling heat transfer in Ihe boundary layer. Increasing permeability parameter (K) depresses the longitudinal velocity but elevates transverse velocities and increases the skin friction at the wall. Both rising temperature (non-isothermal wall) parameter (S) and heat sink parameter (Q) decrease temperature values. The model finds applications in nucIear engineering control systems and MHD energy systems.
3
Content available remote On certain subclasses of p-valently analytic functions of order alpha
Aouf M.
Demonstratio Mathematica
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2007
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Vol. 40, nr 2
317-330
EN
The object of the present paper is to derive various properties and char- acteristics of certain subclasses of p-valently analytic functions of order alpha in the open unit disc by using the techniques involving the Briot-Bouquet differential subordination.
4
Content available Run-Up of Linear Long Waves on Uniform Slope in Lagrangian Description
Chybicki W.
Archives of Hydro-Engineering and Environmental Mechanics
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2006
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Vol. 53, nr 2
97-104
EN
The case of linear, two-dimensional long waves on a uniform slope is considered. It is assumed that the fluid is nonviscous and incompressible. In the present paper the description of the long wave proposed by Wilde (Wilde, Chybicki 2004) is based on the fundamental assumption that the vertical material lines of fluid remain vertical during the entire motion. The equations of motion are derived with the help of a variational formulation of the problem. The Lagrangian is the difference between the kinetic and potential energy of the fluid. In the paper a correction followed from dispersion to the results obtained by Shuto is presented.
5
Content available remote Antilogarithms of second order in algebras with logarithms and their applications to special functions
Przeworska-Rolewicz D.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2004
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Vol. 44, nr spec.
167-191
EN
In the paper [PR5] it was shown that the so-called special functions of Mathematical Physics can be obtained by means of antilogarithms of the second order for the usual differential operator ^j. The same method applied to a right invertible operator D in a commutative Leibniz algebra with logarithms permits to determine eigenvectors of linear equations of order two in D with coefficients in the algebra X under consideration by a reduction to the generalized Sturm-Liouville operator. It seems that, in a sense, the proposed method is an answer for the question of Gian-Carlo Rota concerning a unified approach to special functions (cf. [Rl], problem 4). Section 6 of the present paper is devoted to some summations formulae expressing special functions by means of exponentials. Note that, in general, we do not need any assumption about the Hilbert structure of the algebra X.
6
On the subclassesof functions connected with some linear operators
Patel J., Sahoo P., Stankiewicz J.
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
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2001
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z. 25 [190]
151-165
EN
The object of the present paper is to introduce two subclasses Bk,p (a, c) and Ck,p (a, c) of analytic functions in the open unit disc involving a linear operator [...] (a, c) and derive some properties of these classes.
7
On a class of multivalent functions
Patel J., Mohanty A.
Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
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1999
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z. 23 [175]
85-91
EN
In the paper some special class of multivalent functions connected with the hypergeometric series are investigated.
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