Rational approximation near zero sets of functions

The paper deals with the relation between global rational approximation and local approximation off the zero set. Also connections with the problem f2 Є R(X) => f Є R(X) are studied

On radial limit functions for entire solutions of second order elliptic equations in

Given a homogeneous elliptic partial di®erential operator L of order two with constant complex coe±cients in R2, we consider entire solutions of the equation Lu = 0 for whic

State-Selective Control For Vibrational Excitation and Dissociation of Diatomic Molecules With Shaped Ultrashort Laser Pulses

Ultrafast state-selective dynamics of diatomic molecules in the electronic ground state under the control of infrared picosecond and femtosecond shaped laser pulses is investigated for the discrete vibrational bound states and for the dissociative continuum states. Quantum dynamics in a classical laser field is simulated for a one-dimensional nonrotating dissociative Morse oscillator, representing the local OH bond in the H2O and HOD molecules. Computer simulations are based on two approaches - exact treatment by the time-dependent Schrödinger equation and approximate treatment by integro-differential equations for the probability amplitudes of the bound states only. Combination of these two approaches is useful to reveal mechanisms underlying selective excitation of the continuum states and above-threshold dissociation in a single electronic state and for designing optimal laser fields to control selective preparation of the high-lying bound states and the continuum states. Optimal laser fields can be designed to yield almost 100% seletive preparation of any prescribed bound state, including those close to the dissociation threshold. State-selective preparation of the highest bound state may be accompanied by the appearance of a quasi-bound molecular state in the continuum with the kinetic energy of the fragments being close to zero. The respective above-threshold dissociation spectrum containes an additional, zero-order peak. The laser-induced dissociation from selectively prepared high-lying bound states is shown to be very efficient, with the dissociation probability approaching the maximal value. Flexible tools of state-selective laser control are developed which enable one to achieve selective control of the dissociation spectra resulting in time-selective and space-selective control of the dissociation fragments

ADAPTIVE ROBUST DISTURBANCE COMPENSATION IN LINEAR SYSTEMS WITH DELAY

Subject of Research. The paper considers the problem of disturbance compensation for the class of linear time-invariant plants with known parameters and delay.Method. The disturbance is presented as a sum of irregular and regular components. An irregular component is treated as an unknown bounded time function. A regular component is described as unmeasurable output of linear autonomous model (exosystem) with known order and unknown parameters. The problem is resolved with the use of parametrized representation of disturbance designed by means of exosystem state observer and predictor of this state that finally allows applying certainty equivalence principle. In order to remove undesirable influence of delay, a modified adaptation algorithm is created. The algorithm is based on augmentation of the plant state vector and generates advanced adjustable parameters for control. Robust modification of adaptive algorithm is used for keeping stability of closed-loop system in the presence of irregular disturbance. As distinct from widespread approaches the proposed algorithm does not require identification of disturbance parameters and gives the possibility to discard from the control system such restrictions as adaptation gain margin and time delay margin. Main Results. Simulation results obtained in MATLAB/Simulink environment are presented to demonstrate the performance of the proposed approach. The results illustrate the boundedness of all signals in the closed-loop system in the presence of external disturbance. It is shown that the proposed idea enables keeping system stability for different values of input delay. Practical Relevance. Thealgorithm of adaptive compensation is recommended for application in such problems as: the problem of control for active vibration protection devices wherein several dominating harmonics can be taken from the spectrum of vibration signal, control problems of robotic systems with periodical behavior, the problems of ship roll compensation, control problems of space plants in the presence of uncontrollable rotation

Settlements of Neighboring Buildings During Piling Works

Two case histories of heavy damaging the neighbouring buildings in Sankt-Petersburg during construction the bored piles are presented. The analysis of causes of the damages has shown that ground inflow into the housing tubes due to low strength properties of water saturated liquid-plastic loams is the main cause of additional settlements of existing houses during construction the bored piles of large diameter close to them