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New Modular Relations for the Ratio’s of Ramanujan Function χ(−q) of degree 9
B. N. DHARMENDRA,P. S. Guruprasad 장전수학회 2020 Proceedings of the Jangjeon mathematical society Vol.23 No.3
In this paper, we establish some new modular equations of Ramanujan’s function χ(−q) of degree 9. Further, we obtain some explicit evaluations of class invariant gn from them.
Special Case on Rogers-Ramanujan Type Continued Fraction Identity
B. N. DHARMENDRA 장전수학회 2020 Proceedings of the Jangjeon mathematical society Vol.23 No.3
In this article, we derive a new continued fraction d(q) by using a general continued fraction in Ramanujan's lost notebook. By using this continued fraction d(q), we establish modular relation between d(q) and d(qn), where n = 2, 3, 4, 5, 7, 11. We also establish some explicit values of d(q) by using Ramanujan's class invariant.
SOME MODULAR RELATIONS BETWEEN RAMANUJAN’S FUNCTION V(q) AND V(qn)
B. N. DHARMENDRA,M. C. MAHESH KUMAR 장전수학회 2020 Proceedings of the Jangjeon mathematical society Vol.23 No.3
In his ‘lost’ notebook, S. Ramanujan introduced the parameter k(q) :=R(q)R2(q2) and v(q) := R2(q½)R(q)/R(q2) related to the Rogers-Ramanujan continued fraction R(q). In this paper, we establish some new modular relations connecting k(q) with v(qn) and v(q) with v(qn) for n = 6, 8 and 10.
Some Result on Analogous to Ramanujan’s Remarkable Product of Theta Function
B. N. DHARMENDRA,R. Raghavendra 장전수학회 2020 Proceedings of the Jangjeon mathematical society Vol.23 No.3
In this paper, we study the analogous of Ramanujan's Remarkable product of theta-function of degree 9 and their explicit values.
New ramanujan’s remarkable product of Theta-function and their explicit evaluations
B. N. DHARMENDRA 장전수학회 2019 Proceedings of the Jangjeon mathematical society Vol.22 No.4
In this article, we dene dm;n for any positive real numbers m and n involving Ramanujan's product of theta-functions (q) and f( q2), which is analogous to Ramanujan's remarkable product of theta-functions and establish its several properties by Ramanujan. We establish general theorems for the explicit evaluations of dm;n and its explicit values.
Vijai Singh,Dharmendra Kumar Chaudhary,Indra Mani,Rohan Jain,B.N. Mishra 한국미생물학회 2013 The journal of microbiology Vol.51 No.3
Aeromonas hydrophila is an opportunistic bacterial pathogen that is associated with a number of diseases in fish, amphibians, reptiles, and humans. In fish it causes several disease symptoms including tail and skin rot, and haemorrhagic septicemia; in human it causes soft-tissue wound infection and diarrhoea. The pathogenesis of A. hydrophila is multifactorial, but the mechanism is unknown so far. It is considered to be mediated by expression and secretion of extracellular proteins such as aerolysin, lipase, chitinase, amylase, gelatinase, hemolysins, and enterotoxins. A number of the putative virulence-protein-encoding genes that are present in the genome of A. hydrophila have been targeted by PCR for molecular diagnosis. These significant genes are also targeted for over-production of proteins by cloning and expression methods. In this review, we emphasize recent progress in the cloning, expression, and regulation of putative virulence-protein-encoding genes of A. hydrophila for a better understanding of the pathogenesis and also help to provide effective strategies for control of diseases.