In this paper we introduce the notion of classical quasi-primary submodules that generalizes the concept of classical primary submodules. Then, we investigate decomposition and minimal decomposition into classical quasi-primary submodules. In particular, existence and uniqueness of classical quasi-primary decompositions in finitely generated modules over Noetherian rings are proved. More...

Fractional order partial differential equations are generalizations of classical partial differential equations. Increasingly, these models are used in applications such as fluid flow, finance and others. In this paper we examine some practical numerical methods to solve a class of initial- boundary value fractional partial differential equations with variable coefficients on a finite domain. S...

Let F = 〈a, b〉 be a rank two free group. A word W (a, b) in F is primitive if it, along with another group element, generates the group. It is a palindrome (with respect to a and b) if it reads the same forwards and backwards. It is known that in a rank two free group any primitive element is conjugate either to a palindrome or to the product of two palindromes, but known iteration schemes for ...

The Wheeler-DeWitt equation is based on the use of canonical quantization rules that may be inconsistent for constrained dynamical systems, such as Einstein’s gravitational field equations. The resulting quantum dynamics has no classical limit, and it suffers from the infamous “problem of time.” In this article, it is shown how a dynamical time (an internal “clock”) can be constructed by means ...

The chiral glass behaviour of the nearest-neighbour random-bond XY spin glass in four dimensions is studied by Monte Carlo simulations. A chiral glass transition at T cg = 0.90 ± 0.05 is found by a finite-size scaling analysis of the results. The associated chiral correlation-length exponent is estimated to be ν cg = 0.6 ± 0.1 and η cg ∼ 0.25. The values for the chiral critical temperature and ...

Three-dimensional spin models of the Ising and XY universality classes are studied by a combination of high-temperature expansions and Monte Carlo simulations applied to improved Hamiltonians. The critical exponents and the critical equation of state are determined to very high precision.

Representations of the quantum superalgebra U q [osp(1/2)] and their relations to the basic hypergeometric functions are investigated. We first establish Clebsch-Gordan decomposition for the superalgebra U q [osp(1/2)] in which the representations having no classical counterparts are incorporated. Formulae for these Clebsch-Gordan coefficients are derived, and it is observed that they may be ex...

The Heisenberg model is described. Some of the interesting behavior of Heisenberg antiferromagnets and its behavior as a function of dimension is described. One dimensional systems have no long range order, two dimensional systems order magnetically only at zero temperature, and three dimensional systems have a non-zero critical temperature. Assembling lower dimensional pieces into ladders and ...