In this paper, I define and study an abstract algebraic structure, the dimensive algebra, which embodies the most general features of the algebra of dimensional physical quantities. I prove some elementary results about dimensive algebras and suggest some directions for future work. Copyright © 2003 Mark F. Sharlow. Updated 2009.

The Multiple Zeta Values (or ‘MZVs’) have been investigated a great deal in recent years, yielding a wealth of interesting results and exciting conjectures. The aim of this report is to introduce the MZVs and their relations, and to display some of the techniques being used in modern research to describe them. We being with an emphasis on the combinatorial methods of describing the MZVs, and th...

In [2] Kriz and May introduced partial algebras over an operad. In this paper we prove that, in the category of chain complexes, partial algebras can be functorially replaced by quasi-isomorphic algebras. In particular, partial algebras contain all of the important homological and homotopical information that genuine algebras do. Applying this result to McClure’s partial algebra in [6] shows th...

Non-commutative Poisson algebras are the algebras having an associative algebra structure and a Lie algebra structure together with the Leibniz law. For finite-dimensional ones we show that if they are semisimple as associative algebras then they are standard, on the other hand, if they are semisimple as Lie algebras then their associative products are trivial. We also give the descriptions of ...

In this paper we construct a tilting sheaf for SeveriBrauer Varieties and Involution Varieties. This sheaf relates the derived category of each variety to the derived category of modules over a ring whose semisimple component consists of the Tits algebras of the corresponding linear algebraic group.

We investigate classes of Boolean algebras related to the notion of forcing that adds Cohen reals. A Cohen algebra is a Boolean algebra that is dense in the completion of a free Boolean algebra. We introduce and study generalizations of Cohen algebras: semi-Cohen algebras, pseudo-Cohen algebras and potentially Cohen algebras. These classes of Boolean algebras are closed under completion.

We study the combinatorics of fully commutative elements in Coxeter groups of type H n for any n > 2. Using the results, we construct certain canonical bases for non-simply-laced generalized Temperley{Lieb algebras and show how to relate them to morphisms in the category of decorated tangles.

ABSTRACT We describe efficient interior-point methods for the design of filters with constraints on the magnitude spectrum, for example, piecewise-constant upper and lower bounds, and arbitrary phase. Several researchers have observed that problems of this type can be solved via convex optimization and spectral factorization. The associated optimization problems are usually solved via linear pr...

In this paper, we propose a new infeasible interior-point algorithm with full NesterovTodd (NT) steps for semidefinite programming (SDP). The main iteration consists of a feasibility step and several centrality steps. We used a specific kernel function to induce the feasibility step. The analysis is more simplified. The iteration bound coincides with the currently best known bound for infeasibl...