MatSciNet: Mathematical Reviews

A study of a novel multi-degree-of-freedom piezoelectric actuator is given in the paper. Design of the actuator is based on the implementation of bending vibrations of a circular plate. The actuator consists of a vibrating disc with the driving tip mounted at the disc centre and a piezoceramic disc. This actuator can move a slider in two perpendicular directions in the plane and achieve a curvilinear or rotational motion of the positioned object depending on the excitation scheme of the electrodes. Numerical modelling based on the finite element method was performed to find resonant frequencies and modal shapes of the actuator and to calculate the trajectories of contact point's movements under different excitation schemes. The transient dynamic analysis of the actuator was performed to simulate the motion of the slider. A contact between the driving tip, slider and slider-way was taken into account in the finite element model. A prototype actuator was made and measurement results of actuator's top surface's oscillations are given. Results of the numerical and experimental investigation are analysed and discussed.

This paper deals with the description of a theoretical background of systematic computer algebra methods for analyzing the real-time dynamics of robots with a large numbers of joints. Many numerical methods based on different principles of mechanics were developed to obtain the equations that model the dynamic behavior of robots. In this paper, the efficiency of computer algebra application was compared with the most popular methods of forming the dynamic equations of robots in real time. To this end, the computer algebra system VIBRAN was used. A real-time dynamic model in closed form of the robots with large numbers of joints has been developed, using the computer algebra technique with the following automatic program code generation.

Walras theory is well known and widely used in models of market economy. Various iterative methods are developed to search for the equilibrium conditions. In this paper a new approach is proposed and implemented where the search for Walras equilibrium is defined as a stochastic global optimization problem. This way random nature of customer arrivals is represented and the convergence to equilibrium is provided if equilibrium exists. This paper describes a part of a Web-based integrated system for scientific cooperation and distance graduate studies of theories of optimization, games and markets which aim is to provide researchers and graduate students with hands-on experience on effective use of software. The objectives are to provide a tool for scientific collaboration and to stimulate creative abilities of graduate students to work as independent researchers. The web-site http://soften.ktu.lt/(similar to)mockus includes a family of economic and financial models regarding them all as examples of the the general optimization theory.

The analysis of the parallel varinats of a probability task are presented. The results of testing by Vilnius Gediminas Technical University second year students are proposed.