The problem of the transformation of microscopic information to the macroscopic level is an intriguing challenge in computational neuroscience, but also of general mathematical importance. Here, a phenomenological mathematical model is introduced that simulates the internal information processing of brain compartments. Synaptic potentials are integrated over small number of realistically couple...

Wide classes of nonlinear mathematical physics equations are described that admit order reduction through the use of the von Mises transformation, with the unknown function taken as the new independent variable and an appropriate partial derivative taken as the new dependent variable. RF-pairs and associated Bäcklund transformations are constructed for evolution equations of general form (speci...

The contribution describes the formulation of study activities within the selected LMS particular from the mathematical task point of view. The field activities are based primarily on tests drawn from the automatically generated online questions. The paper demonstrates solutions to several problems related to the creation of parameterized questions for the domain of math/science. These are main...

The paper presents a mathematical model and steady-state operational characteristics of a Unified Power Flow Controller (UPFC). The mathematical description is based on the transformation of a three-phase system into an orthogonal synchronously rotating coordinate system, in which, under steady-state conditions, all the system quantities are constant values. Thus, at given parameters, it is gen...

The Fitzhugh-Nagumo (fn) mathematical model characterizes the action potential of the membrane. The dynamics of the Fitzhugh-Nagumo model have been extensively studied both with a view to their biological implications and as a test bed for numerical methods, which can be applied to more complex models. This paper deals with the dynamics in the (FH) model. Here, the dynamics are analyzed, qualit...

The appropriate mathematical model for the problem space of tower transformation tasks is the state graph representing positions of discs or balls and their moves. Graph theoretical quantities like distance, eccentricities or degrees of vertices and symmetries of graphs support the choice of problems, the selection of tasks and the analysis of performance of subjects whose solution paths can be...

Mathematical Morphology (MM) is a nonlinear approach to image processing that relies on a fundamental structure, the complete lattice L [7] (a nonempty set equipped with an ordering relation). With the complete lattice theory, it is possible to define morphological operators for any type of data once a proper ordering is established [1]. If Mathematical Morphology is well defined for binary and...

We introduce the concepts of closed sets and closure operators as mathematical tools for the study of social networks. Dynamic networks are represented by transformations. It is shown that under continuous change/transformation, all networks tend to “break down” and become less complex. It is a kind of entropy. The product of this theoretical decomposition is an abundance of triadically closed ...

Novel discrete orthogonal transforms are introduced in this paper, namely the unified complex Hadamard transforms. These transforms have elements confined to four elementary complex integer numbers which are generated based on the Walsh–Hadamard transform, using a single unifying mathematical formula. The generation of higher dimension transformation matrices are discussed in detail.

A class of Cohen-Grossberg-type BAM neural networks with distributed delays and impulses are investigated in this paper. Sufficient conditions to guarantee the uniqueness and global exponential stability of the periodic solutions of such networks are established by using suitable Lyapunov function, the properties of M-matrix, and some suitable mathematical transformation. The results in this pa...