A b s t r a c t In this paper, we briefly discuss the dynamic and functional approach to computer symbolic tensor analysis. The ccgrg package for Wolfram Language/Mathematica is used to illustrate this approach. Some examples of applications are attached.

In this article, we propose a fuzzy class relation assigning to each pair of finite fuzzy sets a degree to which they are equipollent, which indicates that they have the same number of elements. The concepts of fuzzy sets and fuzzy classes in the class of all countable sets are introduced, and several standard relations and constructions, such as the fuzzy power set and exponentiation, are defi...

We show that dynamical symmetry methods can be applied to Hamiltonians with periodic potentials. We construct dynamical symmetry Hamiltonians for the Scarf potential and its extensions using representations of su(1, 1) and so(2, 2). Energy bands and gaps are readily understood in terms of representation theory. We compute the transfer matrices and dispersion relations for these systems, and fin...

The periodic event scheduling problem (PESP) is a well studied problem known as intrinsically hard, but with important applications mainly for finding good timetables in public transportation. In this paper we consider PESP in public transportation, but in a reduced version (r-PESP) in which the driving and waiting times of the vehicles are fixed to their lower bounds. This results in a still N...

Unlike commonly used methods, in this paper, we have introduced a new approach for designing fuzzy controllers. In this approach, we have simultaneously optimized both objective functions of a supply chain over a two-dimensional space. Then, we have obtained a spectrum of optimized points, each of which represents a set of optimal parameters which can be chosen by the manager ...

we present a numerical study of a one-dimensional version of the burridge-knopoff model [16] of n-site chain of spring-blocks with stick-slip dynamics. our numerical analysis and computer simulations lead to a set of different results corresponding to different boundary conditions. it is shown that we can convert a chaotic behaviour system to a highly ordered and periodic behaviour by making on...

We present a set of problem frames specialized to the area of geographic applications. Problem frames describe the elements of common problems, and help a specifier understand and decompose a complex problem into simpler subproblems for which a solution is often known. We provide an overview of the main issues in geographic applications, and present twelve frames that address many of the proble...

The present article argues for what is essentially a return to the functionalist approach to investigation of memory. Two experiments demonstrate that the effects of level of processing depend on scaled meaningfulness of the material and study time. Data from those experiments along with data currently in the literature are then reanalyzed to examine the effect of repetitions. Of particular int...