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Banerji, P. K.
- On the Exchange Property for the Laplace Transform
Authors
1 Department of Mathematics, Faculty of Science, J.N.V. University, Jodhpur - 342 005, IN
Source
Indian Journal of Science and Technology, Vol 3, No 2 (2010), Pagination: 196-198Abstract
In this paper we investigate the exchange property for the Laplace transform by using the relation between the Fourier transform and the Laplace transform. Simplified construction of tempered Boehmians is also presented.Keywords
Distribution, Boehmians, Tempered Distribution, Tempered Boehmians, Laplace TransformFull Text
References
- Atanasiu D and Mikusinski P (2005) On the Fourier transform and the exchange property. Intl. J. Math. Math. Sci. 16, 2579-2584.
- Banerji PK and Loonker D (2006) Laplace transform for Integrable Boehmians. Bull. Cal. Math. Soc. 98 (5), 465-470.
- Boehme TK (1973) The support of Mikusinski operators. Trans. Amer. Math. Soc. 176, 319-334.
- Mikusinski P (1995) Tempered Boehmians and ultradistributions. Proc. Amer. Math. Soc. 123, 813-817.
- Zemanian AH (1987) Distribution theory and transform analysis, Dover Publ., Inc., NY.
- Distributional Dual Series Equations and Fractional Calculus
Authors
1 Department of Mathematics, Faculty of Science, JNV Univerity, Jodhpur- 342 005, IN
Source
Indian Journal of Science and Technology, Vol 6, No 1 (2013), Pagination: 3892-3897Abstract
Solutions of dual series equations are devised by multiplying factor technique and Abel integral equations and are reduced using fractional integral and derivatives and further, written in fractional calculus form the solution are employed for the distribution spaces.Keywords
Dual Series Equations, k-Bateman's Function, Fractional Integrals and Derivatives, Distribution SpacesFull Text
References
- Askey, R. (1968) Dual equations and orthogonal polynomials, J. Math. Anal. Appl. 24, 677-685.
- Erdélyi, A. (1972) Fractional integrals of generalized functions, J. Austral. Math. Soc. 14, 30-37.
- Erdélyi, A.(1975) Fractional integrals of generalized functions, In the Proceedings of International Conference held at the University of New Haven, 1974, “Fractional Calculus and its Applications” (Ed. Ross, B.), Lecture Notes in Mathematics # 457, Springer-Verlag, Berlin, New York, pp. 151-170
- Erdélyi, A. and McBride, A. C. (1970) Fractional integrals of distributions, SIAM J. Math. Anal. 1 , 547- 557.
- Lowndes, J. S. (1968) Some dual series equations involving Laguerre polynomials, Pacific J. Math. 25, 123-127.
- McBride, A. C. (1975) A theory of fractional integration for generalized functions, SIAM J. Math. Anal. 6 (3), 583-599.
- Miller, K. S. (1975) The Weyl fractional calculus, In the Proceedings of International Conference held at the University of New Haven, 1974, “Fractional Calculus and its Applications” (Ed. Ross, B.), Lecture Notes in Mathematics # 457, Springer-Verlag, Berlin, New York, pp. 80-89.
- Noble, B. (1963) Some dual series equations involving Jacobi polynomials, Proc. Cambridge Philos. Soc. 59, 363-371.
- Sneddon, I. N. (1975) The use in mathematical physics of Erdelyi-Kober operators and of some of their generalizations, In the Proceedings of International Conference held at the University of New Haven, 1974, “Fractional Calculus and its Applications” (Ed. Ross, B.), Lecture Notes in Mathematics # 457, Springer-Verlag, Berlin, New York, pp. 37-99.
- Sneddon, I. N. and Srivastava, R. P. (1964) Dual series relations I : Dual series involving Fourier - Bessel series, Proc. Royal Soc. Edinburgh Sec. A., 66, 161- 172.
- Srivastava, H. M. (1972) A pair of dual series equations involving generalized Bateman k - function, Koninkl. Nederl. Akad. Wetensch. Proc. Ser. A 75 (1) = Indag. Math. 34 (1) , 53-61.
- Srivastava, K. N. (1966) On dual series relations involving generalized Bateman k - function. Proc. Amer. Math. Soc. 17, 796-802.
- Samko, S. G., Kilbas, A. A. and Marichev, O. I. (1993) Fractional integrals and derivatives, Theory and Applications, Gordon and Breach Publishers, Switzerland, Australia, India..
- Ngoc, Nguyen Van (1982) Some results on the dual series equations, Acta Mathematica Vientamica 7 (1), 107-116.
- Zemanian, A. H. (1968) Generalized Integral Transformations, Interscience Publishers, New York, London, Sydney.
- Impact Factor and Mathematics : a Debate
Authors
1 Department of Mathematics, Faculty of Science, JNV Univerity, Jodhpur- 342 005, IN
Source
Indian Journal of Science and Technology, Vol 6, No 1 (2013), Pagination: 3957-3959Abstract
No AbstractKeywords
Impact FactorFull Text
References
- Krantz, S. G. How to write your first paper, NOTICES, Amer. Math. Soc. 54 (11) (2007), 1507-1511.
- Milman, Vitali. Impact factor and how it relates to quality of journals, NOTICES, Amer. Math. Soc. 53 (3) (2006), 351-352.
- Mustaq, Qaiser. The misuse of the impact factor, NOTICES, Amer. Math. Soc. 54 (7) (2007), 821.
- Seglen, Per O., Judging Journals : How One Measures Impact, http://www.ams.org/ewing/Documents/Judgingjournals.pdf.
- Inverted Metamorphism in the Sikkim-Darjeellng, Himalaya, India
Authors
1 Geological Survey of India. Orissa Circle (N) 31, Budha Nagar, Bhubaneshwar 14, IN
Source
Journal of Geological Society of India (Online archive from Vol 1 to Vol 78), Vol 21, No 7 (1980), Pagination: 330-342Abstract
Inverted metamorphic sequences from chlorite zone phyllites grading progressively upwards into staurolitc/kyanite zone schists and gneisses with associated granitic bodies occur intermittently in the Lower Himalaya from Kumaon to Sikkim. In Sikkim-Darjeeling area, this progressive metamorphism is broadly late-kinematic with respect to the polyphase fabric elements in the metasedimentaries and is broadly coeval with the emplacement of metasomatic/anatectic granitic masses, which occur as low to moderately dipping sheets within both greenschist and amphibolite facies metasediments and carry I-type enclaves. Locally, strong, gravity induced polarity has concentrated metasomatic transformations along the hanging wall sections of the granite.
This 'inverted' metamorphism, as well as positive gravity anomaly gradients and shallow focus seismicity in this sector, are correlative with differential vertical displacements, which have exposed the naturally inverted metamorphic sequences along footwall sections of moderately dipping intrusive masses. LANDSAT and air photo interpretations of various types of linears and lineaments with supporting indications from the location of hot springs, lakes, water falls, abrupt changes in river gradient, truncation of marker bands and erraticity in terrace distribution, suggest that the area has been witnessing differential uplift along a number of regional and local sub-vertical fault surfaces including a number of geofaults, some of which are transverse to the axis of the range in a crypto-aulacogen style. This tectonic regime appears to be an integral part of postorogenic processes in Sikkim-Kumaon Himalaya possibly extending eastwards up to Arunachal Pradesh.
- The Khondalites of Orissa, India - A Case Confusing Terminology
Authors
1 Geological Survey of India, Orissa Circle, Bhubhaneswar 751 014, IN
Source
Journal of Geological Society of India (Online archive from Vol 1 to Vol 78), Vol 23, No 4 (1982), Pagination: 155-159Abstract
The paper traces the progressive metamorphosis of the term 'Khondalite' from 1902 to 1975 from a specific rock name to the collective group name of a suite of high grade metamorphic and metasomatic rocks and presents examples of the extent of compositional variations of these rocks from Dhenkanal, Angul and Tikarpara areas of Orissa. It is recommended that prevalent usage of the term 'Khondalite' as a mapping unit should be discontinued by general consensus, since the term can now be used only in the sense of a 'group'.- Behaviour of Elements in Tropical Weathering Profiles
Authors
1 Geological Survey of India, Orissa Circle, Bhubaneswar 751 012, IN
Source
Journal of Geological Society of India (Online archive from Vol 1 to Vol 78), Vol 25, No 12 (1984), Pagination: 809-809Abstract
No Abstract.Full Text
- Secondary Geochemical Dispersion in the Lateritic Tracts Over Two Copper Sulphide Deposits in Orissa, India
Authors
1 Geological Survey of India, IN
Source
Journal of Geological Society of India (Online archive from Vol 1 to Vol 78), Vol 31, No 4 (1988), Pagination: 404-416Abstract
Host rocks are kyanite-quartzite at Kesarpur and uralitised garnet-diopside granulite (± scapolite) at Adash. Primary sulphides include chalcopyrite, pyrite and pyrrhotite with small but variable amounts of bornite. The ore bodies are lenticular and carry variable trace constituents of Ag. Au, Ni and Co. Supergene minerals occur only in thin stretches and include covellite, marcasite and violarite. No discrete zone of supergene enrichment is noted in the boreholes. Oxidised zones at the top are 15-45m. thick and analyse in Adash up to 2.27% Cu plus 0.4% Zn over 3-4 m width. Goethite, haematite, malachite, azurite and chrysocolla are the constituent minerals.
Feeble to strong anomalies are present in pedogenetic laterites over orc bodies. but spurious anomalies locally with 1 % Mn are common. Laterites in Adash are polycyclic and anomaly values are locally erratic. Over groundwater laterites of Kesarpur. very feeble secondary anomalies are confined to only 100 m from the ore zone.
Stream sediment signals are confined to first order seasonal drainge courses and are traceable for only 2-3 km from the source down stream. Such limited anomaly dispersion is due to differential block movements in this area.
Landforms developing under this dynamic system have not given rise to widespread and strong stream sediment dispersion patterns of chalcophile elements. Systematic search for small ore bodies in such tracts has, therefore, to be hased only on sampling the sediments of first order drainage courses.
- On Distributional Abel Integral Equation for Distributional Elzaki Transform
Authors
1 Department of Mathematics, Faculty of Science, J. N. V. University, Jodhpur - 342 005, IN
Source
The Journal of the Indian Mathematical Society, Vol 81, No 1-2 (2014), Pagination: 87-96Abstract
In this paper Elzaki transform is defined for distribution spaces. Solution of the Abel integral equation is obtained using distributional Elzaki transform is proved in distributional sense. The fractional integral and derivatives (as form of the integral equation) is also employed on distribution spaces.Keywords
Elzaki Transform, Laplace Transform, Abel Integral Equation, Distribution Spaces, Fractional Integrals and Derivatives.- Fractional Integration and Dual Integral Equations
Authors
1 Department of Mathematics, University of Jodhpur, Jodhpur, IN
Source
The Journal of the Indian Mathematical Society, Vol 38, No 1-4 (1974), Pagination: 359-363Abstract
Following a method of fractional integration operators, we have presented a formal solution of the set of dual integral equations involving the ordinary Bessel function.- Applications of Fractional Derivative to Study the Mapping Properties of Starlike Functions and the Convexity of Analytic Functions-II
Authors
1 Department of Mathematics, JNV University, Jodhpur-342005, IN
Source
The Journal of the Indian Mathematical Society, Vol 70, No 1-4 (2003), Pagination: 25-32Abstract
In the present paper a function is introduced using certain modified fractional derivative operator and the convolutions of three functions, analytic in the unit disc, are mentioned. Also investigated are the characterization properties of the said function in the open unit disc, in order to establish its belongingness to some subclasses of analytic functions and finally, some associations of the said properties with the convolution are mentioned.Keywords
Convex Functions, Starlike Functions, Fractional Derivative Operator, Convolution.- Application of N-Fractional Calculus to Obtain Generating Functions
Authors
1 Department o f Mathematics, J.N.V. University, Jodhpur-342 005, IN
2 Department of Mathematics, University of Aden, Aden, YE
Source
The Journal of the Indian Mathematical Society, Vol 71, No 1-4 (2004), Pagination: 61-68Abstract
In this paper we apply the concept of Nishimoto’s fractional calculus (N-fractional calculus) to obtain some linear, bilinear and bilateral generating functions involving hypergeometric functions of two and three variables. Some particular cases are mentioned too.Keywords
Generating Functions, Hypergeometric Functions, Appell’s Functions, Lauricella’s Functions, Fractional Derivative.- Inequalities for Multivalent Functions Defined by Ruscheweyh Derivative
Authors
1 Department of Mathematics, Walchand College of Engineering, Sangli-416 415, IN
2 Department of Mathematics, J.N.V. University, Jodhpur-342 005, IN