A Miura of the Painlevé I Equation and Its Discrete Analogs

We present Miura transformations for the continuous and several discrete Painlev\'e I equations. In the case of the continuous P_I, we use the Hamiltonian formulation of the Painlev\'e equations and show that there exists a Miura transformation between P_I and the binomial, second degree, equation of Cosgrove SD_V. In the case of the discrete P_I's we obtain two different kinds of Miuras. One kind relates a d-P_I to some other d-P_I while the other leads to discrete four-point equations which are the discrete analogs of the derivative of Cosgrove's equation SD_V.     

Numerical modeling of a XeCl laser excited by microwave discharge

12 , 169 (1987). Reasonably good agreements in the peak output power and laser efficiency have been achieved. Model calculations also predict that an efficiency as high as 2.7% can be obtained once the conditions of the above-mentioned experiments have been optimized. From the consideration that the skin depth effectively limits the absorption length of the microwave pumping and hence the excitable volume, it is concluded that high input power densities (>2 MW/cm³) and higher gas pressures (between 3 and 10 atm) are the preferable conditions to achieve higher efficiency. Preliminary calculations on CCl₄ containing XeCl gas mixtures show that improvement in laser efficiency by several folds may be achieved as a result of the higher intrinsic efficiency of excimer formation. Received: 23 September 1996 / Revised version: 25 March 1997     

Quenching of fluorescence from Na(32P) and K(42P) atoms following photodissociation of NaCl and KCl at 193 nm

 Quenching of fluorescence from Na(3² P) and K(4² P) atoms by various collision partners was studied at 973 and 1273K. Excited alkali atoms were produced photolytically by excimer laser light at 193nm. For each collision pair, the appropriate relative velocity was computed and used to evaluate the quenching cross-section from the measured rate constants. Cross sections for CO₂, O₂ and N₂ are large (10–60Ų) while for Ar, the values are <1 Ų. The results are compared with those of previous investigations as a function of relative velocity. Finally, implications for combustion diagnostics are briefly discussed. Received: 29 March 1996     

Determination of the largest lyapunov index for short chaotic time sequences in self-oscillating chemical reactions

A method was developed for the determination of largest Lyapunov index for short chaotic time sequences with allowance for the presence of noise in the response of the system. For this purpose a simple unidimensional representation modelling the dynamics of irregular self-oscillations was investigated. Conditions were found for adequate determination of the largest Lyapunov index from the noise-distorted signals. The results were used to obtain the largest Lyapunov index for the Belousov—Zhabotinskii reaction taking place in an ideal-mixing closed reactor and in a constant-mixing flow-type reactor. Institute of Organic Chemistry, National Academy of Sciences of Ukraine. Translated from Teoreticheskaya i éksperimental’naya Khimiya, Vol. 33, No. 3, pp. 136–142, May–June, 1997.     

Influence of the domain structure on the permeability of planar hexaferrites in the natural ferrimagnetic resonance region

A calculation is presented of the permeability of hexaferrites with an easy magnetization plane in the region of natural ferrimagnetic resonance and in the presence of a domain structure. It is shown that the domain structure strongly influences both the magnitude of the permeability and the natural ferrimagnetic resonance frequency. The expressions obtained are compared with the results of calculations of the natural ferrimagnetic resonance spectra of single-domain planar hexaferrites. State University, Tomsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 53–57, February, 1997.     

Pseudoparabolic variational inequalities without initial conditions

We consider a pseudoparabolic variational inequality in a cylindrical domain semibounded in a variable t. Under certain conditions imposed on the coefficients of the inequality, we prove theorems on the unique existence of a solution for a class of functions with exponential growth as t → ∞. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 7, pp. 919–929, July, 1998.     

Criteria for controllability and observability in complex domain models of stationary systems

We propose criteria for controllability and observability of stationary systems specified by complex domain models. Conclusions concerning controllability and observability are made on the basis of coefficients in the corresponding transfer functions. Translated fromDinamicheskie Sistemy, Vol. 12, pp. 120–126, 1993.