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The Classical Laplace Transform and Its q-Image of the Most Generalized Hypergeometric and Mittag-Leffler Functions
D. K. Jain,
Altaf Ahmad,
Renu Jain,
Farooq Ahmad
Issue:
Volume 2, Issue 1, March 2017
Pages:
1-5
Received:
23 December 2016
Accepted:
16 January 2017
Published:
9 February 2017
DOI:
10.11648/j.dmath.20170201.11
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Abstract: The q-Calculus has served as a bridge between mathematics and physics, particularly in case of quantum physics. The q-generalizations of mathematical concepts like Laplace and Fourier transforms, Hypergeometric functions etc. can be advantageously used in solution of various problems arising in the field of physical and engineering sciences. The present paper deals with some of the important results of q-Laplace transform of Fox-Wright and Mittag-Leffler functions in terms of well-known Fox’s H-function. Some special cases have also been discussed.
Abstract: The q-Calculus has served as a bridge between mathematics and physics, particularly in case of quantum physics. The q-generalizations of mathematical concepts like Laplace and Fourier transforms, Hypergeometric functions etc. can be advantageously used in solution of various problems arising in the field of physical and engineering sciences. The pr...
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Dirichlet Averages of Wright-Type Hypergeometric Function
Farooq Ahmad,
D. K. Jain,
Alok Jain,
Altaf Ahmad
Issue:
Volume 2, Issue 1, March 2017
Pages:
6-9
Received:
23 December 2016
Accepted:
21 January 2017
Published:
20 February 2017
DOI:
10.11648/j.dmath.20170201.12
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Abstract: In the present paper, the authors approach is based on the use of Dirichlet averages of the generalized Wright-type hyper geometric function introduced by Wright in like the functions of the Mittag-Leffler type, the functions of the Wright type are known to play fundamental roles in various applications of the fractional calculus. This is mainly due to the fact that they are interrelated with the Mittag-Leffler functions through Laplace and Fourier transformations.
Abstract: In the present paper, the authors approach is based on the use of Dirichlet averages of the generalized Wright-type hyper geometric function introduced by Wright in like the functions of the Mittag-Leffler type, the functions of the Wright type are known to play fundamental roles in various applications of the fractional calculus. This is mainly du...
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Wavelet-Based Numerical Homogenization for Scaled Solutions of Linear Matrix Equations
Issue:
Volume 2, Issue 1, March 2017
Pages:
10-16
Received:
6 January 2017
Accepted:
20 January 2017
Published:
20 February 2017
DOI:
10.11648/j.dmath.20170201.13
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Abstract: In this work we investigate the use of wavelet-based numerical homogenization for the solution of various closed form ordinary and partial differential equations, with increasing levels of complexity. In particular, we investigate exact and homogenized (scaled) solutions of the one dimensional Elliptic equation, the two-dimensional Laplace equation, and the two-dimensional Helmholtz equation. For the exact solutions, we utilize a standard Finite Difference approach with Gaussian elimination, while for the homogenized solutions, we applied the wavelet-based numerical homogenization method (incorporating the Haar wavelet basis), and the Schur complement) to arrive at progressive coarse scale solutions. The findings from this work showed that the use of the wavelet-based numerical homogenization with various closed form, linear matrix equations of the type: LU=F affords homogenized scale dependent solutions that can be used to complement multi-resolution analysis, and second, the use of the Schur complement obviates the need to have an a priori exact solution, while the possession of the latter offers the use of simple projection operations.
Abstract: In this work we investigate the use of wavelet-based numerical homogenization for the solution of various closed form ordinary and partial differential equations, with increasing levels of complexity. In particular, we investigate exact and homogenized (scaled) solutions of the one dimensional Elliptic equation, the two-dimensional Laplace equation...
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Fixed Point Theorem in Cone Metric Space
Issue:
Volume 2, Issue 1, March 2017
Pages:
17-19
Received:
19 December 2016
Accepted:
24 January 2017
Published:
22 February 2017
DOI:
10.11648/j.dmath.20170201.14
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Abstract: In this paper, we prove a unique common fixed point theorem for four self-mappings in cone metric spaces by using the continuity and commuting mappings. Our result extends,improvesthe results of [M. Abbas and G. Jungck, Common fixed point results for non commuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl. 341(2008) 416-420].
Abstract: In this paper, we prove a unique common fixed point theorem for four self-mappings in cone metric spaces by using the continuity and commuting mappings. Our result extends,improvesthe results of [M. Abbas and G. Jungck, Common fixed point results for non commuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl. 341(2008) 416...
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Correlation Matrices Design in the Spatial Multiplexing Systems
Sunil Chinnadurai,
Poongundran Selvaprabhu,
Abdul Latif Sarker
Issue:
Volume 2, Issue 1, March 2017
Pages:
20-30
Received:
13 January 2017
Accepted:
6 February 2017
Published:
24 February 2017
DOI:
10.11648/j.dmath.20170201.15
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Abstract: Channel correlation is closely related to the capacity of the multiple-input multiple-output (MIMO) correlated channel. Indeed, the high correlated channel degrades the system performance and the quality of wireless communication systems in terms of the capacity. Thus, we design an inverse-orthogonal matrix such as Toeplitz-Jacket matrix to design transmit and receive correlation matrices to mitigate the channel correlation of the MIMO systems. The numerical and simulation results are performed for both uncorrelated and correlated channel capacities in the case of single sided fading correlations.
Abstract: Channel correlation is closely related to the capacity of the multiple-input multiple-output (MIMO) correlated channel. Indeed, the high correlated channel degrades the system performance and the quality of wireless communication systems in terms of the capacity. Thus, we design an inverse-orthogonal matrix such as Toeplitz-Jacket matrix to design ...
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