DIGITAL CULTURE – A HISTORICAL STAGE IN THE DEVELOPMENT OF THE INFORMATION CULTURE OF SOCIETY

Different scientific approaches to digital culture have been analysed in the article: digital culture is considered as a special form of being, a special integral design that includes audiovisual, semiotic, technological, logical, communication, network and other subsystems that exists at five levels: material, functional, symbolic, mental and spiritual; and as a set of values ofmodern society based on digital coding; and as a system of changes in practices, products of human activity associated with the culture of the digital age; and as a special level of digital literacy and competency. The anthropological aspect of digital culture has been emphasized. The main causes and stages of the development of digital culture as a modern stage in the development of the information culture of society also have been considered.

On some degenerate pseudodifferential operators

In this paper, a new class of degenerate pseudo-differential operators is investigated, with a variable symbol depending on the complex parameter. Pseudodifferential operators are constructed by a special integral transform. Theorems on the composition and boundedness of these operators in special weighted spaces are proved. The behavior of these operators on hyperplanes of degeneration is investigated. The theorems on the commutation of these operators with differentiation operators are established. A adjoint operator is constructed and an analogue of Goring inequality for degenerate pseudodifferential operators is proved.

An Optimal Identification of the Input-Output Disturbances in Linear Dynamic Systems by the Use of the Exact Observation of the State

A new methodology for the identification of the values of unknown disturbance signals acting in the input and output measurements of the dynamic linear system is presented. For the solution of this problem, the new idea of the use of two different state observers, which are coworking simultaneously in parallel, was elaborated. Special integral type observers are operating on the same finite time window of the width T and both can reconstruct the exact value of the vector state x(T) on the basis of input-output measurements in this interval [0, T]. If in the input-output signals the disturbances are absent (measurements of I/O signals are perfect) then both observers (although they are different) reconstruct the exact and the same state x(T). However, if in the measurement signals the disturbances are present then these observers will reconstruct the different values of the final states x1(T)=x(T)+e1(T) and x2(T)=x(T)+e2(T). It is because they have different norms and hence they generate different errors in both estimated states. Because of the disturbances, the real state x(T) is unknown, but it is easy to calculate the state difference: x1(T)-x2(T)=e1(T)-e2(T). It occurs that, based on this difference, the values of all the disturbances acting during the control process can be identified. In the paper, the theory of the exact state observation and application of such observers in online mode is recalled. The new methodology for disturbances identification is presented.

SPECIAL SPLINES OF HYPERBOLIC TYPE FOR THE SOLUTIONS OF HEAT AND MASS TRANSFER 3-D PROBLEMS IN POROUS MULTI-LAYERED AXIAL SYMMETRY DOMAIN

In this paper we study the problem of the diffusion of one substance through the pores of a porous multi layered material which may absorb and immobilize some of the diffusing substances with the evolution or absorption of heat. As an example we consider circular cross section wood-block with two layers in the radial direction. We consider the transfer of heat process. We derive the system of two partial differential equations (PDEs) - one expressing the rate of change of concentration of water vapour in the air spaces and the other - the rate of change of temperature in every layer. The approximation of corresponding initial boundary value problem of the system of PDEs is based on the conservative averaging method (CAM) with special integral splines. This procedure allows reduce the 3-D axis-symmetrical transfer problem in multi-layered domain described by a system of PDEs to initial value problem for a system of ordinary differential equations (ODEs) of the first order.

Majorization problems and integral transforms for a Class of Univalent Functions with missing coefficients

In 2005, Ponnusamy and Sahoo have introduced a special subclass of univalent functions Un(\lambda) (n 2 N, > 0) and obtained some geometrical properties, including strongly starlikeness and convexity, for the functions of this subclass Un(). Moreover, they have studied some important properties of an integral transform connected with these subclasses. The aim of the present paper is to investigate another important concept of majorization for the functions belonging to the class Un(\lambda) (0 <\lambda=< 1). We shall also discuss a majorization problem for some special integral transforms.