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This article presents approaches, methods, and algorithms for the intellectualization of existing systems and development of fundamentally new systems of transformation of information into forms convenient for human perception. Interfaces with computer environments are proposed for text, voice, and visual ways of communication and their interaction. Information technologies are developed to create tools for training people with hearing impairments, communication with people with disabilities, in medicine, etc.

A new generalized model of propagation of a medicine in tissue is considered. Instead of the traditional diffusion model described by a parabolic equation, the model described by a more general hyperbolic equation is postulated, which predicts finite velocity of disturbance propagation. As a result, the medicine is delivered to the invaded tissue with a finite velocity. The first disturbance (precursor) carries information from the injection to any point in the tissue and, what is important, to the affected zone, wherefrom information arrives at the brain in the form of neurological disorder. The generalized solution of the problem is considered. A brief generalization of the Bellman problem is given concerning the injection of medicine with respect to the time of injection.

This paper investigates the intellectualization of text input using a system for accelerated input of texts into digital devices with a view to constructing a model of a corpus of the Ukrainian spoken language and a text typing system based on this model. Such a system uses a smaller number of commands to input letters and predicts variants of words on the basis of the corpus of words and word combinations for communication. It is experimentally shown that the input of texts using four and six command keys is rather efficient for the constructed corpus.

We investigate the dynamics of a bypass in terms of determining the optimal parameters of shunt operation. The equations that describe the propagation of pressure pulse waves in blood vessels are presented in differential form and in approximate form for the averaged values based on the conservation laws. The correspondence of these forms is shown from the solution of the initial---boundary-value problem for vascular junction. The influence of the parameters such as various diameters, wall thicknesses, and elastic properties of blood vessels on the shunt effectiveness is investigated. In particular, we investigate the influence of the shunt form and junction area, as well as the angle of the shunt connection with the vessel, on the passage of the coronary vessels and blood coagulation. On the basis of the calculations, conclusions about the influence of various parameters on the dynamics of bypass are made.

This paper presents an information technology based on modern IT devices (netbooks, tablets, phones, etc) and supporting an alternative communication for persons with (temporary or permanent) verbal communication disorders. It is proposed to implement this communication through the intellectualization of the process of entering text data with applying a limited number of relevant controls specified by a person's hand. A human skeleton model is investigated with a view to determining a limited number of hand configurations and motions reliably identified by recognition tools of IT devices.

The authors consider current problems of the modern theory of dynamic systems on manifolds, which are actively developing. A brief review of such trends in the theory of dynamic systems is given. The results of the algebra of dual numbers, quaternionic algebras, biquaternions (dual quaternions), and their application to the analysis of infinitesimal neighborhoods and infinitesimal deformations of manifolds (schemes) are presented. The theory of differential---algebraic equations over the field of real numbers and their dynamics, as well as elements of trajectory optimization of respective dynamic systems, are outlined. On the basis of connection in bundles, the theory of differential---algebraic equations is extended to algebraic manifolds and schemes over arbitrary fields and schemes, respectively.

This article presents new results on the solution of the problem of definition of efficient features and synthesis of an optimal band-separating classifier for elements of the dactyl alphabet of deaf sign language. Approaches to the qualitative evaluation of the separability of elements of dactyl alphabet for different feature spaces are considered. An algorithm is proposed for obtaining a hyperplane classifier separating groups of dactylemes in a feature space.

The authors formulate the initial---boundary-value problem of step pulse propagating from input to output on the basis of a hyperbolic equation with dissipation, which describes the propagation of waves with a finite speed. Exact analytical solution is obtained in the Laplace transform space. Numerical inversion of the Laplace transform by using Euler's method is carried out and the results are analyzed.

Degeneration in a small spatial coordinate of the original initial---boundary-value problem for hyperbolic equations is considered in order to construct simpler models. The problem is investigated in a domain whose one spatial scale is much less than the other scales. This makes it possible to expand the desired functions in power series and hence to reduce the dimension of the problem. However, this comes at the cost of degeneration of the spectrum of the original three-dimensional problem.

The authors present new results in solving problems of concatenative segment synthesis of voice information with prosody and vocal utterance, computer modeling of human voice signals based on joint models of human voice source and vocal tract, and speech signal preprocessing for automated documenting systems. The experiments show the efficiency of the proposed approaches.

This article proposes mathematical models and an information technology for constructing movements of a virtual person and reproducing a sign language based on a set of gesture units and transitions between them. The implementation of movement reproduction in a virtual model allows obtaining a real-time animation of sign information. The efficiency of the proposed approach is illustrated by an example of modelling and identifying dactyl information.

Information and mathematical models are proposed for the animation of sign language communication based on a virtual human model. A model is developed to fix sign language morphemes and is used to create a technology and software to generate, store, and reproduce gestures. Algorithmic solutions are proposed for the computation of human-like trajectories of hand and body movements in passing from a gesture to another and also facial expressions and articulation.