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Random fixed point of mappings over a Hilbert space with a probability measure
M. Saha,L. Debnath 장전수학회 2009 Advanced Studies in Contemporary Mathematics Vol.18 No.1
In this paper an appropriate scheme of iteration have been presented for proving random xed point theorem for a class of mappings that includes semi non-expansive mapping over a Hilbert Space
INTERACTION BETWEEN THREE MOVING GRIFFITH CRACKS AT THE INTERFACE OF TWO DISSIMILAR ELASTIC MEDIA
Das, S.,Patra, B.,Debnath, L. 한국전산응용수학회 2001 The Korean journal of computational & applied math Vol.8 No.1
The paper deals with the interaction between three Griffith cracks propagating under antiplane shear stress at the interface of two dissimilar infinite elastic half-spaces. The Fourier transform technique is used to reduce the elastodynamic problem to the solution of a set of integral equations which has been solved by using the finite Hilbert transform technique and Cooke’s result. The analytical expressions for the stress intensity factors at the crack tips are obtained. Numerical values of the interaction efect have been computed for and results show that interaction effects are either shielding or amplification depending on the location of each crack with respect to other and crack tip spacing. AMS Mathematics Subject Classification : 73M25.
On a new nonlinear transformation and its applications to special functions
I. S. Gupta,L. Debnath 장전수학회 2007 Advanced Studies in Contemporary Mathematics Vol.15 No.2
A new nonlinear transformation is introduced by T = ÃMÁ : R[[x]] ! R[[x]]. Some simple examples and properties of T are discussed. Under certain restrictions, the inverse transformation is also introduced with examples. Many applications of this nonlinear transformation to special functions is studied with examples.
On some new nonlinear delay and weakly singular integral inequalities
Qing-hua Ma,L.Debnath 한국전산응용수학회 2008 Journal of applied mathematics & informatics Vol.26 No.5
This paper deals with some new nonlinear delay and weakly singular integral inequalities of Gronwall-Bellman type. These results generalize the inequalities discussed by Xiang and Kuang [19]. Several other inequalities proved by Medve\v d [15] and Ou-Iang [17] follow as special cases of this paper. This work can be used in the analysis of various problems in the theory of certain classes of differential equations, integral equations and evolution equations. A modification of the Ou-Iang type inequality with delay is also treated in this paper.
ON SOME NEW NONLINEAR DELAY AND WEAKLY SINGULAR INTEGRAL INEQUALITIES
Ma, Qing-Hua,Debnath, L. Korean Society of Computational and Applied Mathem 2008 Journal of applied mathematics & informatics Vol.26 No.5
This paper deals with some new nonlinear delay and weakly singular integral inequalities of Gronwall-Bellman type. These results generalize the inequalities discussed by Xiang and Kuang [19]. Several other inequalities proved by $Medve{\check{d}}$ [15] and Ou-Iang [17] follow as special cases of this paper. This work can be used in the analysis of various problems in the theory of certain classes of differential equations, integral equations and evolution equations. A modification of the Ou-Iang type inequality with delay is also treated in this paper.
PROPAGATION OF SURFACE WAVES ON IRREGULAR BED TOPOGRAPHY
WARKE, A. S.,DAS, S. K.,DEBNATH, L. 한국전산응용수학회 2006 Journal of applied mathematics & informatics Vol.20 No.1
This paper deals with the exact solution of surface gravity waves in an ocean with irregular bed topography. In order to obtain water surface elevation and run-up of infra-gravity waves when the bed is either wavy or exponential, closed form solutions are obtained. Numerical computations indicate that when solitary wave or sinusoidal wave conditions are applied at the boundary, water surface elevation attains near Gaussian profile.
A. Mondal,S. Chatterjee,A. McDonald Tariang,L. Prince Raj,K. Debnath Techno-Press 2023 Advances in aircraft and spacecraft science Vol.10 No.2
Drag reduction is significant research in aircraft design due to its effect on the cost of operation and carbon footprint reduction. Aircraft currently use conventional solid winglets to reduce the induced drag, adding extra structural weight. Fluidic on-demand winglets can effectively reduce drag for low-speed flight regimes without adding any extra weight. These utilize the spanwise airflow from the wingtips using hydraulic actuators to create jets that negate tip vortices. This study develops a computational model to investigate fluidic on-demand winglets. The well-validated computational model is applied to investigate the effect of injection velocity and angle on the aerodynamic coefficients of a rectangular wing. Further, the turbulence parameters such as turbulent kinetic energy (TKE) and turbulent dissipation rate are studied in detail at various velocity injections and at an angle of 30°. The results show that the increase in injection velocity shifted the vortex core away from the wing tip and the increase in injection angle shifted the vortex core in the vertical direction. Further, it was found that a 30° injection is efficient among all injection velocities and highly efficient at a velocity ratio of 3. This technology can be adopted in any aircraft, effectively working at various angles of attack. The culmination of this study is that the implementation of fluidic winglets leads to a significant reduction in drag at low speeds for low aspect ratio wings.