We study the cohomology of the Schwinger term arising in second quantization of the class of observables belonging to the restricted general linear algebra. We prove that, for all pseudodifferential operators in 3+1 dimensions of this type, the Schwinger term is equivalent to the " twisted " Radul cocycle, a modified version of the Radul cocycle arising in non-commutative differential geometry....

We present a new approach to the covariant canonical formulation of EinsteinCartan gravity that preserves the full Lorentz group as the local gauge group. The method exploits lessons learned from gravity in 2+1 dimensions regarding the relation between gravity and a general gauge theory. The dynamical variables are simply the frame field and the spin-connection pulled-back to the hypersurface, ...

The Cunningham project seeks to factor numbers of the form bn±1 with b = 2, 3, . . . small. One of the most useful techniques is Aurifeuillian Factorization whereby such a number is partially factored by replacing bn by a polynomial in such a way that polynomial factorization is possible. For example, by substituting y = 2k into the polynomial factorization (2y2)2+1 = (2y2−2y+1)(2y2+2y+1) we ca...

Considering a commutative unital quantale L as the truth value table and using the tool of L-generalized convergence structures of stratified L-filters, this paper introduces a kind of fuzzy upper topology, called fuzzy S-upper topology, on L-preordered sets. It is shown that every fuzzy join-preserving L-subset is open in this topology. When L is a complete Heyting algebra, for every completel...

Modern computer algebra systems use heuristics and algorithms for the fast computation with mathematical formulas. General purpose computer algebra systems like Axiom [12], Derive [20], Macsyma [17], Maple [5], Mathematica [23] or Reduce [11] are for example great with integrals. Even a small system like Derive computes all explicitly given integrals of Bronshtein and Semedyayev’s integral tabl...

It is shown that the quantised enveloping algebra of sl(n) contains a quantum Lie algebra, deened by means of axioms similar to Woro-nowicz's. This gives rise to Lie algebra-like generators and relations for the locally nite part of the quantised enveloping algebra, and suggests a canonical Poincar e-Birkhoo-Witt basis.

MathGirls is computer-based algebra designed for high school girls learning algebra I. Given that girls are in general more interested in interactive computing and more positive about the social presence of pedagogical agents, the primary goal of MathGirls is to provide a girl-friendly learning environment that helps enhance girls’ self-efficacy beliefs in and motivation towards learning algebr...

first we show that the cosets of a fuzzy ideal μ in a bck-algebrax form another bck-algebra  x/μ (called the fuzzy quotient bck-algebra of x by μ). also we show thatx/μ is a fuzzy partition of x and we prove several some isomorphism theorems. moreover we prove that if the associated fuzzy similarity relation of a fuzzy partition p of a commutative bck-algebra iscompatible, then p is a fuzzy quo...

Algebra is defined as the manipulation of symbols. Today, algebra is commonly known as abstract algebra or modern algebra. Algebra is mainly used to describe the symmetries or patterns in the mathematics. Operations that made on algebraic structures are basic thing in the computer algebra algorithms. Set, functions (arithmetic, numerical, symbolic), field, group, semi-group, abelian group and r...