Multimedia as a modernization direction in the course of teaching "History of Ukraine"

Використання мультимедійних презентацій в системі сучасної освіти займає все більше місце та стає певною повсякденністю. Мультимедія під час викладання дисципліни "Історія України" є важливим елементом освітнього процесу, яка покликана мотивувати студентів до навчання, поліпшити сприйняття інформації, зробити навчальний процес сучасним, цікавим та продуктивним. Мультимедійні презентації створені викладачами та студентами постійно вдосконалюються та являються модернізаційним напрямком навчання та комунікації.The use of multimedia presentations in the system of modern education takes up an increasing number of places and becomes a "daily routine". Multimedia during the teaching of the discipline "History of Ukraine" is an important element of the educational process. During lectures and seminars, using the multimedia technologies is a topical issue today. Multimedia is designed to motivate students to study, improve perceptions of information, make the learning process interesting and productive. Multimedia presentations created by lecturers and students serve as a kind of communication. They are constantly improving and being a modernization training area

Approximation of Parametric Derivatives by the Empirical Interpolation Method

We introduce a general a priori convergence result for the approximation of parametric derivatives of parametrized functions. We consider the best approximations to parametric derivatives in a sequence of approximation spaces generated by a general approximation scheme, and we show that these approximations are convergent provided that the best approximation to the function itself is convergent. We also provide estimates for the convergence rates. We present numerical results with spaces generated by a particular approximation scheme—the Empirical Interpolation Method—to confirm the validity of the general theory

A generalized empirical interpolation method : application of reduced basis techniques to data assimilation

In an effort to extend the classical lagrangian interpolation tools, new interpolating methods that use general interpolating functions are explored. The method analyzed in this paper, called Generalized Empirical Interpolation Method (GEIM), belongs to this class of new techniques. It generalizes the plain Empirical Interpolation Method by replacing the evaluation at interpolating points by application of a class of interpolating linear functions. The paper is divided into two parts: first, the most basic properties of GEIM (such as the well-posedness of the generalized interpolation problem that is derived) will be analyzed. On a second part, a numerical example will illustrate how GEIM, if considered from a reduced basis point of view, can be used for the real-time reconstruction of experiments by coupling data assimilation with numerical simulations in a domain decomposition framework

Analiza i modeliranje dinamičkih svojstava interaktivnog pogonskog sustava

The recent drive systems are considered as interactive systems containing a range of subsystems with different physical nature. This contribution deals with the modelling of mechatronic drive systems using numerical package DYNAST. The theoretical general observations are demonstrated on particular experiments on real system.Moderni pogonski sustavi smatraju se interaktivnim sustavima koji sadržavaju podsustave različitih fizikalnih svojstava. Ovaj dokument prikazuje modeliranje mehatroničkog pogonskog sustava korištenjem numeričkog paketa DYNAST. Načelna teorijska razmatranja demonstrirana su pomoću konkretnih eksperimenata na realnom sustavu

Reduced Basis Approximation and A Posteriori Error Estimation: Applications to Elasticity Problems in Several Parametric Settings

In this work we consider (hierarchical, Lagrange) reduced basis approximation and a posteriori error estimation for elasticity problems in affinley parametrized geometries. The essential ingredients of the methodology are: a Galerkin projection onto a low-dimensional space associated with a smooth "parametric manifold" - dimension reduction, an efficient and effective greedy sampling methods for identification of optimal and numerically stable approximations - rapid convergence, an a posteriori error estimation procedures - rigorous and sharp bounds for the functional outputs related with the underlying solution or related quantities of interest, like stress intensity factor, and Offline-Online computational decomposition strategies - minimum marginal cost for high performance in the real-time and many-query (e.g., design and optimization) contexts. We present several illustrative results for linear elasticity problem in parametrized geometries representing 2D Cartesian or 3D axisymmetric configurations like an arc-cantilever beam, a center crack problem, a composite unit cell or a woven composite beam, a multi-material plate, and a closed vessel. We consider different parametrization for the systems: either physical quantities - to model the materials and loads - and geometrical parameters - to model different geometrical configurations - with isotropic and orthotropic materials working in plane stress and plane strain approximation. We would like to underline the versatility of the methodology in very different problems. As last example we provide a nonlinear setting with increased complexity

A Two-Step Certified Reduced Basis Method

In this paper we introduce a two-step Certified Reduced Basis (RB) method. In the first step we construct from an expensive finite element “truth” discretization of dimension N an intermediate RB model of dimension N≪N . In the second step we construct from this intermediate RB model a derived RB (DRB) model of dimension M≤N. The construction of the DRB model is effected at cost O(N) and in particular at cost independent of N ; subsequent evaluation of the DRB model may then be effected at cost O(M) . The DRB model comprises both the DRB output and a rigorous a posteriori error bound for the error in the DRB output with respect to the truth discretization. The new approach is of particular interest in two contexts: focus calculations and hp-RB approximations. In the former the new approach serves to reduce online cost, M≪N: the DRB model is restricted to a slice or subregion of a larger parameter domain associated with the intermediate RB model. In the latter the new approach enlarges the class of problems amenable to hp-RB treatment by a significant reduction in offline (precomputation) cost: in the development of the hp parameter domain partition and associated “local” (now derived) RB models the finite element truth is replaced by the intermediate RB model. We present numerical results to illustrate the new approach.United States. Air Force Office of Scientific Research (AFOSR Grant number FA9550-07-1-0425)United States. Department of Defense. Office of the Secretary of Defense (OSD/AFOSR Grant number FA9550-09-1-0613)Norwegian University of Science and Technolog

Comparison of some Reduced Representation Approximations

In the field of numerical approximation, specialists considering highly complex problems have recently proposed various ways to simplify their underlying problems. In this field, depending on the problem they were tackling and the community that are at work, different approaches have been developed with some success and have even gained some maturity, the applications can now be applied to information analysis or for numerical simulation of PDE's. At this point, a crossed analysis and effort for understanding the similarities and the differences between these approaches that found their starting points in different backgrounds is of interest. It is the purpose of this paper to contribute to this effort by comparing some constructive reduced representations of complex functions. We present here in full details the Adaptive Cross Approximation (ACA) and the Empirical Interpolation Method (EIM) together with other approaches that enter in the same category

Morphological variation and sensitivity to frequency of forms among native speakers of Czech

This article looks at inter-speaker variation in two environments: the genitive and locative singular cases of masculine ‘hard inanimate’ nouns in Czech, using a large-scale survey of native speakers that used two tasks to test their preferences for certain forms (acceptability) and their choices (gap filling). Our hypothesis that such variation exists was upheld, but only within limited parameters. Most biographical data (age, gender, education) played no role in respondents’ choices or preferences. Their region of origin played a small but significant role, although not the one expected. Relating the two types of tasks to each other, we found that respondents’ use of the ratings scale did not correlate to their choice of forms, but their overall strength of preference for one form over another did correlate with their choices. Inter-speaker variation does thus go some way to explaining the persistent diversity in this paradigm and arguably may contribute to its maintenance