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...

The present study attempts to establish a new framework to speculate customer lifetime value by a stochastic approach. In this research the customer lifetime value is considered as combination of customer’s present and future value. At first step of our desired model, it is essential to define customer groups based on their behavior similarities, and in second step a mechanism to count current ...

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...

To evaluate and predict component-based software security, a two-dimensional model of software security is proposed by Stochastic Petri Net in this paper. In this approach, the software security is modeled by graphical presentation ability of Petri nets, and the quantitative prediction is provided by the evaluation capability of Stochastic Petri Net and the computing power of Markov chain. Each...

In this article, the continuum-based high-cycle fatigue analysis method, introduced by Ottosen, Stenström and Ristinmaa in 2008, is extended to cases where stress history a stochastic process. The basic three-parameter Ornstein–Uhlenbeck process chosen for description. As practical example, theory applied both finite infinite life cases. A definition safety factor introduced, which reduced mini...