In this paper, we answer as follows: the latter problem is nothing but a 2dimensional word problem in a “2-monoid”, which leads to the syntactical study of a 3-category. This crucial observation leads to the general problem for n-paths in an n-category, or even in an ∞-category. A lot of computations made by category theorists are 1-, 2or 3-dimensional, and in fact, n-dimensional computations t...

The use of tabling in logic programming has been recognized as a powerful evaluation technique. Currently available tabling systems are mostly based on variant checks and hence are limited in their ability to recognize reusable subcomputations. Tabling systems based on call subsumption can yield superior performance by recognizing a larger set of reusable computations. However, a straightforwar...

This paper presents a novel topology of single-phase multilevel inverter for low and high power applications. It consists of polarity (Level) generation circuit and H Bridge. The proposed topology can produce higher output voltage levels by connecting dc voltage sources   in series and parallel. The proposed topology utilizes minimum number of power electronic devices which helps in reduction o...

Deligne has defined a category which interpolates among the representations of the various symmetric groups. In this paper we show Deligne’s category admits a unique nontrivial family of modified trace functions. Such modified trace functions have already proven to be interesting in both low-dimensional topology and representation theory. We also introduce a graded variant of Deligne’s category...

Lecture notes from M275 at SJSU, a graduate-level course at SJSU in Algebraic Topology taught by Professor Richard Kulbelka. These notes were taken using Vim and/or GVim equipped with L A T E X-Suite, which sped up typesetting significantly; latexmk with the flag-pvc was useful for compiling these notes in real-time. 1.1 The Question Question. Given two topological spaces, can we determine if t...