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Salehbhai, Ibrahim A.,Prajapati, Jyotindra C.,Shukla, Ajay K. Korean Mathematical Society 2013 대한수학회논문집 Vol.28 No.1
Operational techniques have drawn the attention of several researchers in the study of sequence of functions and polynomials. An attempt is made to introduce a new sequence of functions by using operational techniques. Some generating relations and finite summation formulae have been obtained. The corresponding MAPLE code for obtaining above sequence of functions for different values of parameters was also discussed.
SOME PROPERTIES OF GENERALIZED HYPERGEOMETRIC FUNCTION
Rao, Snehal B.,Patel, Amit D.,Prajapati, Jyotindra C.,Shukla, Ajay K. Korean Mathematical Society 2013 대한수학회논문집 Vol.28 No.2
In present paper, we obtain functions $R_t(c,{\nu},a,b)$ and $R_t(c,-{\mu},a,b)$ by using generalized hypergeometric function. A recurrence relation, integral representation of the generalized hypergeometric function $_2R_1(a,b;c;{\tau};z)$ and some special cases have also been discussed.
Timothy H. Bell,Ioan V. Sanislav,Jyotindra Sapkota 한국지질과학협의회 2018 Geosciences Journal Vol.22 No.1
Multiple generations of sub-vertical and sub-horizontal foliations preserved as inclusion trails in garnet in mylonitic rocks from the hanging wall of the Main Central Thrust in the Himalayas indicate that these porphyroblasts did not rotate during thrusting. This result is predicated by (i) a consistent succession of 5 changes in FIA trend (foliation inflection/intersection axes in porphyroblasts) for samples where the orientation changes from porphyroblast cores to rims; (ii) sub-vertical and sub-horizontal foliations occur as inclusion trails around each of the 5 FIAs in the succession, which would not be the case if the garnet porphyroblasts rotated during subsequent phases of deformation as tectonism continued; (iii) a change in inclusion trail asymmetry immediately prior to the commencement of mylonitzation indicates top to the south thrusting only if the porphyroblasts had not rotated as they grew; (iv) the latter asymmetry matches truncated crenulation relics preserved within the mylonitic matrix foliation that indicate top to the south thrusting as the latter foliation formed. Partitioning of deformation into shortening and shearing components stops rotation of porphyroblasts during their growth and during following periods of ductile tectonism. This can be replicated via computer modelling by duplicating the crenulation-hinge-like coaxial environment in which porphyroblasts nucleate and grow before the strain intensifies. This was done using Drucker-Prager constitutive models with temperature-dependent strain softening behaviour and resulted in no porphyroblast rotation when followed by non-coaxial deformation no matter how intense. Furthermore, strain localization in the model containing competent objects of variable size, shape and orientation, produced no rotation during deformation involving components of shortening and shearing. These approaches to modelling mechanically resolve the sub-vertical/sub-horizontal foliations defined by inclusion trails and consistent FIA trend successions obtained from the Main Central Thrust rocks as well as in orogens elsewhere.
SOME INTEGRAL TRANSFORMS INVOLVING EXTENDED GENERALIZED GAUSS HYPERGEOMETRIC FUNCTIONS
Choi, Junesang,Kachhia, Krunal B.,Prajapati, Jyotindra C.,Purohit, Sunil Dutt Korean Mathematical Society 2016 대한수학회논문집 Vol.31 No.4
Using the extended generalized integral transform given by Luo et al. [6], we introduce some new generalized integral transforms to investigate such their (potentially) useful properties as inversion formulas and Parseval-Goldstein type relations. Classical integral transforms including (for example) Laplace, Stieltjes, and Widder-Potential transforms are seen to follow as special cases of the newly-introduced integral transforms.
SOME INTEGRAL TRANSFORMS AND FRACTIONAL INTEGRAL FORMULAS FOR THE EXTENDED HYPERGEOMETRIC FUNCTIONS
Agarwal, Praveen,Choi, Junesang,Kachhia, Krunal B.,Prajapati, Jyotindra C.,Zhou, Hui Korean Mathematical Society 2016 대한수학회논문집 Vol.31 No.3
Integral transforms and fractional integral formulas involving well-known special functions are interesting in themselves and play important roles in their diverse applications. A large number of integral transforms and fractional integral formulas have been established by many authors. In this paper, we aim at establishing some (presumably) new integral transforms and fractional integral formulas for the generalized hypergeometric type function which has recently been introduced by Luo et al. [9]. Some interesting special cases of our main results are also considered.
CERTAIN INTEGRAL FORMULAS ASSOCIATED WITH ALEPH (ℵ)-FUNCTION
Agarwal, Praveen,Jain, Shilpi,Karimov, Erkinjon T.,Prajapati, Jyotindra C. Korean Mathematical Society 2017 대한수학회논문집 Vol.32 No.2
Recently many authors have investigated so-called Aleph (${\aleph}$)-function and its various properties. Here, in this paper, we aim at establishing certain integral formulas involving the Aleph (${\aleph}$)-function. Precisely, integrals with product of Aleph (${\aleph}$)-function with Jacobi polynomials, Bessel Maitland function, general class of polynomials were under consideration. Some interesting special cases of our main result are also considered and shown to be connected with certain known ones.
Synthesis of Novel Pyrazolines of Medicinal Interest
Gol, Ravindra M.,Khokhani, Kamlesh M.,Khatri, Taslimahemad T.,Bhatt, Jyotindra J. Korean Chemical Society 2014 대한화학회지 Vol.58 No.1
Different pyrazoline derivatives (6a-h and 7a-h) were synthesized by cyclization of substituted chalcones with hydrazine hydrate in acidic as well as basic conditions. Both the reactions were performed under conventional heating and microwave irradiation and percentage yields were compared. All the reactions were accelerated in acidic and basic conditions under microwave irradiation, with higher yields. All the synthesized compounds were characterized by their spectral study (IR, MS, $^1H$ and $^{13}C$ NMR) and were tested for their antibacterial and antifungal activity. The compounds 6g and 7g exhibited significant activity against S. aureu, 7g against E. faecalis, 6b and 7b against E. coli and 6b, 6c, 7b, 7c against S. typhi. The compounds 6d and 7d exhibited significant activity against C. albicans and 6c against M. luteus. Rest of the synthesized compounds showed moderate to poor activity against tested species with compared to standard.