given a mapping $f:xto x$ we naturally associate to it a monotonic map $gg_f:exp xto exp x$ from the power set of $x$ into itself, thus inducing a generalized topology on $x$. in this paper we investigate some properties of generalized topologies which are defined by such a procedure.

Nihar B. Shah† [email protected] Sivaraman Balakrishnan# [email protected] Joseph Bradley† [email protected] Abhay Parekh† [email protected] Kannan Ramchandran† [email protected] Martin J. Wainwright† ? [email protected] † Department of Electrical Engineering and Computer Sciences ? Department of Statistics, University of California, Berkeley Berkeley, CA-94720...

These notes were taken during Math 155 (Analytic Number Theory) taught by Kannan Soundararajan in Spring 2012 at Stanford University. They were live-TEXed during lectures in vim and compiled using latexmk. Each lecture gets its own section. The notes are not edited afterward, so there may be typos; please email corrections to [email protected]. 1. 4/3 1.

In this letter, we revisit the orbit problem, which was studied in [1,2,3]. In [3], Kannan and Lipton proved that this problem is decidable in polynomial time. In this paper, we study the approximate orbit problem, and show that this problem is decidable except for one case.

Some interesting properties of dislocated quasi-metric are obtained. Using these properties some fixed point theorems for contractions and Kannan mappings are derived dropping continuity condition imposed by F. M. Zeyada et al (The Arabian Journal for Science and Engineering, Volume 31, Number 1A, (2005), 111–114), C. T. Aage and J. N. Salunke (Applied Mathematical Sciences, Vol. 2,59 (2008) 29...

J. Santamaria,* M.-E. Gomez, M.-C. Cyrille, C. Leighton, Kannan M. Krishnan, and Ivan K. Schuller Department of Physics, University of California–San Diego, La Jolla, California 92093-0319 Materials Sciences Division, National Center for Electron Microscopy, Lawrence Berkeley Laboratory, University of California–Berkeley, Berkeley, California 94720 ~Received 14 August 2001; published 3 December...