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Search Results: 1 - 10 of 486704 matches for " R S Pathak "
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The pseudodifferential operator
R. S. Pathak,S. Pathak
International Journal of Mathematics and Mathematical Sciences , 2004, DOI: 10.1155/s0161171204212388
Abstract: The pseudodifferential operator (p.d.o.) A(x,D), associated with the Bessel operator d2/dx2
Asymptotic Expansions of the Wavelet Transform for Large and Small Values of b
R. S. Pathak,Ashish Pathak
International Journal of Mathematics and Mathematical Sciences , 2009, DOI: 10.1155/2009/270492
Abstract: Asymptotic expansions of the wavelet transform for large and small values of the translation parameter are obtained using asymptotic expansions of the Fourier transforms of the function and the wavelet. Asymptotic expansions of Mexican hat wavelet transform, Morlet wavelet transform, and Haar wavelet transform are obtained as special cases. Asymptotic expansion of the wavelet transform has also been obtained for small values of when asymptotic expansions of the function and the wavelet near origin are given.
Asymptotic expansion of the wavelet transform for small a
R S Pathak,Ashish Pathak
Mathematics , 2014,
Abstract: Asymptotic expansion of the wavelet transform for small values of the dilation parameter a is obtained using asymptotic expansion of the Mellin convolution technique ofWong. Asymptotic expansions of Morlet wavelet transform, Mexican hat wavelet transform and Haar wavelet transform are obtained as special cases.
Asymptotic expansion of the wavelet transform with error term
R S Pathak,Ashish Pathak
Mathematics , 2014,
Abstract: UsingWong's technique asymptotic expansion for the wavelet transform is derived and thereby asymptotic expansions for Morlet wavelet transform, Mexican Hat wavelet transform and Haar wavelet transform are obtained.
Moment Asymptotic Expansions of the Wavelet Transforms
R S Pathak,Ashish Pathak
Mathematics , 2014,
Abstract: Using distribution theory we present the moment asymptotic expansion of continuous wavelet transform in different distributional spaces for large and small values of dilation parameter $a$. We also obtain asymptotic expansions for certain wavelet transform.
Calderón's reproducing formula for Hankel convolution
R. S. Pathak,Gireesh Pandey
International Journal of Mathematics and Mathematical Sciences , 2006, DOI: 10.1155/ijmms/2006/24217
Abstract: Calderón-type reproducing formula for Hankel convolution is established using the theory of Hankel transform.
Expansions of distributions in terms of generalized heat polynominals and their Appell transforms
R. S. Pathak,Lokenath Debnath
International Journal of Mathematics and Mathematical Sciences , 1980, DOI: 10.1155/s0161171280000567
Abstract: This paper is concerned with expansions of distributions in terms of the generalized heat polynomials and of their Appell transforms. Two different techniques are used to prove theorems concerning expansions of distributions. A theorem which provides an orthogonal series expansion of generalized functions is also established. It is shown that this theorem gives an inversion formula for a certain generalized integral transformation.
Yield Evaluation of a Wheat Line with Combined Resistance to Russian Wheat Aphid and Stem Rust Race “Ug99” in Kenya  [PDF]
F. O. Amulaka, J. N. Maling’a, R. S. Pathak, M. Cakir, R. M. S. Mulwa
American Journal of Plant Sciences (AJPS) , 2013, DOI: 10.4236/ajps.2013.47181
Abstract:

InKenya, Russian wheat aphid (RWA) and stem rust race TTKS (“Ug99”) are the most devastating pests of wheat. Severe infestations by RWA result in yield losses of up to 90% while epidemics of “Ug99”can cause up to 100% loss. The two pests combined have seriously affected farmer incomes forcing them to rely heavily on pesticides and increasing the cost of production. This study sought to evaluate a wheat line that has been developed to be resistant to both RWA and “Ug99”by pyramiding two major resistance genes. Three varieties were used in this study: Kwale, a Kenyan high yielding commercial variety but susceptible to both RWA and “Ug99”; Cook, an Australian variety carrying stem rust resistance gene Sr36 conferring immunity to “Ug99”; and KRWA9”, a Kenyan line resistant to RWA but with poor agronomic attributes. The F1 of the double cross (DC F1) was obtained by crossing the F1 of Kwale × Cook and the F1 of Kwale × KRWA9”. The DC F1 population was subjected to sequential screening for both RWA and “Ug99”resistance. The surviving DC F

Abelian theorems for Whittaker transforms
Richard D. Carmichael,R. S. Pathak
International Journal of Mathematics and Mathematical Sciences , 1987, DOI: 10.1155/s0161171287000504
Abstract: Initial and final value Abelian theorems for the Whittaker transform of functions and of distributions are obtained. The Abelian theorems are obtained as the complex variable of the transform approaches 0 or ¢ in absolute value inside a wedge region in the right half plane.
A distributional Hardy transformation
R. S. Pathak,J. N. Pandey
International Journal of Mathematics and Mathematical Sciences , 1979, DOI: 10.1155/s0161171279000521
Abstract: The Hardy's F-transform F(t)= ¢ 0 ¢ Fv(ty)yf(y)dy is extended to distributions. The corresponding inversion formula f(x)= ¢ 0 ¢ Cv(tx)tF(t)dt is shown to be valid in the weak distributional sense. This is accomplished by transferring the inversion formula onto the testing function space for the generalized functions under consideration and then showing that the limiting process in the resulting formula converges with respect to the topology of the testing function space.
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