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General Formulas for Evaluation of Singular Modulus of the Complete Elliptic Integral
K. R. Vasuki,G. Sharath,N. Bhaskar 장전수학회 2010 Advanced Studies in Contemporary Mathematics Vol.20 No.1
The complete elliptic integral of the first kind K(k) is defined for 0 < k < 1 by K(k) := π /2Ɵ=0dƟ/√1 − k2 sin2 ƟThe real number k is called the modulus of the elliptic integral. The complementary modulus is k' = √1 − k2 (0 < k' < 1). Let ⋋ be a positive integer. The equation K(k') = √K(k),defines a unique real number k(k') (0 < k' < 1) called the singular modulus of K(k). In this paper, we establish certain general formulas for evaluating k(λ), by employing Ramanujan’s modular equation.
On Certain Continued Fractions Related To 3ψ3 Basic Bilateral Hypergeometric Functions
K. R. Vasuki,G. Sharath,Abdulrawf A. A. Kahtan 장전수학회 2010 Advanced Studies in Contemporary Mathematics Vol.20 No.3
In this paper, we obtain several new continued fraction expansions for the ratios of the basic bilateral hypergeometric series 3ψ3 with its contigu-ous functions. Further, as special cases of these identities, we generate several classical and some new continued fraction expansions.
On certain Ramanujan's modular equations of degree 7
K. R. Vasuki,R. G. veeresha 장전수학회 2016 Advanced Studies in Contemporary Mathematics Vol.26 No.1
In this paper, we give alternative proofs of Ramanujan's modular equations of degree 7, by employing certain theta-function identities.
On certain continued fraction expansions for ratios of basic hypergeometric series
K. R. Vasuki,K. R. Rajanna 장전수학회 2007 Proceedings of the Jangjeon mathematical society Vol.10 No.2
In this paper, we establish three new continued fraction expansions for the ratios of the basic hypergeometric series 2'1 by employing four q-difference equations. As particular case of these, we obtain certain new continued fractions including the continued fractions for the quotient of Ramanujan-G¨ollnitz-Gordon function.
On Certain New Modular Relations for the Rogers-Ramanujan type functions of order Twelve
K. R. Vasuki,P. S. Guruprasad 장전수학회 2010 Advanced Studies in Contemporary Mathematics Vol.20 No.3
In this paper, we define the Rogers-Ramanujan type functions M(q) and N(q) of order twelve and obtain some modular relations involving these identities, which are analogues to Ramanujan’s well known forty identities for Rogers-Ramanujan functions. Further, we establish certain color partition identities from them.
Amperometric hydrogen peroxide sensor based on the use of CoFe2O4 hollow nanostructures
Vasuki, K.,Babu, K. J.,Sheet, S.,Siva, G.,Kim, A. R.,Yoo, D. J.,kumar, G. G. Springer Science + Business Media 2017 Mikrochimica acta Vol.184 No.8
<P>The authors report on the preparation of a hollowstructured cobalt ferrite (CoFe2O4) nanocomposite for use in a non-enzymatic sensor for hydrogen peroxide ( H2O2). Silica (SiO2) nanoparticles were exploited as template for the deposition of Fe3O4/CoFe2O4 nanosheets, which was followed by the removal of SiO2 template under mild conditions. This leads to the formation of hollow-structured Fe3O4/CoFe2O4 interconnected nanosheets with cubic spinel structure of high crystallinity. The material was placed on a glassy carbon electrode where it acts as a viable sensor for non-enzymatic determination of H2O2. Operated at a potential of -0.45 V vs. Ag/AgCl in 0.1 M NaOH solution, the modified GCE has a sensitivity of 17 nA mu M-1 cm(-2), a linear response in the range of 10 to 1200 mu M H2O2 concentration range, and a 2.5 mu M detection limit. The sensor is reproducible and stable and was applied to the analysis of spiked urine samples, where it provided excellent recoveries.</P>