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Articles by K. Shankar
Total Records ( 3 ) for K. Shankar
  K. Shankar and C. Sormani
  In this paper we extend the concept of a conjugate point in a Riemannian manifold to geodesic spaces. In particular, we introduce symmetric conjugate points and ultimate conjugate points and relate these notions to prior notions developed for more restricted classes of spaces. We generalize the long homotopy lemma of Klingenberg to this setting as well as the injectivity radius estimate also due to Klingenberg which was used to produce closed geodesics or conjugate points on Riemannian manifolds. We close with applications of these new kinds of conjugate points to CBA(κ) spaces: proving both known and new theorems. In particular we prove a Rauch comparison theorem, a Relative Rauch Comparison Theorem, the fact that there are no ultimate conjugate points less than π apart in a CBA(1) space and a few facts concerning closed geodesics. This paper is written to be accessible to students and includes open problems.
  A. Thirunavukkarasu , S. Rajendran , B. Poovalinga Ganesh , K. Shankar , S. Raja , M. Rajamanickam and K. Maharani
  The present study is an attempt to understand the mineralogical and geochemical characteristics of iron formations especially, the ferried group of elements and their significance in the origin to selected iron formations of northern districts of Tamil Nadu. Fourier Transform Infrared (FTIR) spectroscopy and ore microscopic investigation reveals that, the banded magnetite quartzite samples consist of magnetite and quartz as major minerals with hematite, grunerite, hornblende, hypersthene, goethite and chlorite as accessory minerals. About 36 magnetite quartzite samples were analyzed for the ferride group of elements of study regions. The results of chemical analyses of ferride group elements like Mn, Ni, Ti, Co, Cr and V in the iron formations of different regions are presented and interpreted. Lower concentration of these elements in the iron formations indicate that source of materials derived from weathering of landmasses. Further enrichment of Ti and Cr compared to other elements suggest the BIF’s are of metasedimentary in origin.
  K. Shankar , L. Chavan , S. Shinde and B. Patil
  Molecular study of plants relies on high quality and yield of the DNA obtained. The leaf of banana contains high levels of polysaccharides, polyphenols and secondary metabolites. Hence, we developed an easy and efficient protocol for isolation of genomic DNA from leaves of four banana cultivars (Grand Naine, Poovan, Nendran and Red Banana). The method prevents solubilization of polysaccharides and polyphenols using high concentration of salt in combination with polyvinyl pyrrolidone and Cetyl trimethyl ammonium bromide. The purity of DNA was confirmed by 260/280 ratio from spectrophotometer readings and further by restriction digestion of the isolated DNA using Hind III and EcoRI. The yield of DNA ranged from 712-808 μg g-1 and the purity ratio was ranging from 1.7 to 1.8 showing minimal level of secondary metabolite contamination. Thus, this protocol proved amenable for PCR analysis and can be applicable to other plant related species also. Further more this protocol was suitable for randomly amplified polymorphic DNA analysis to study genetic variation in four banana cultivars.
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