This paper deals with the basic notions of k-tautimmersions . These notions come from two special cases; that is, tight and taut immersions. Tight and taut based on high and distance functions respectively and their basic notions are normal bundle, endpoint map, focal point, critical normal. We generalize hight and distance functions to cylindrical function and define basic notions of k-taut ...

this paper deals with the basic notions of k-tautimmersions . these notions come from two special cases; that is, tight and taut immersions. tight and taut based on high and distance functions respectively and their basic notions are normal bundle, endpoint map, focal point, critical normal. we generalize hight and distance functions to cylindrical function and define basic notions of k-taut im...

The theory of  continuous frames in Hilbert spaces is extended, by using the concepts of measure spaces, in order to get the results of a new application of operator theory.  The $K$-frames were  introduced by G$breve{mbox{a}}$vruta (2012) for Hilbert spaces to study atomic systems with respect to a bounded linear operator. Due to the structure of  $K$-frames, there are many differences between...

One of the most practical routine tests for convergence of a positive series makes use of the ratio test. If this test fails, we can use Rabbe's test. When Rabbe's test fails the next sharper criteria which may sometimes be used is the Bertrand's test. If this test fails, we can use a generalization of Bertrand's test and such tests can be continued innitely. For simplicity, we call ratio test,...