Algorithms of motion planning for a six-legged walking machine

This paper investigates algorithms of motion planning for a six-legged walking machine over complex terrain. Application of the Rodrigues-Hamilton parameters for describing the orientation of the body enables one to develop algorithms of motion planning for the body and legs in an absolute coordinate frame with automatic adaptation to the surface. Experiments with a laboratory scale walking machine have demonstrated the efficiency of proposed algorithms. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 7, pp. 197–206, 2005.     

Kinetics of Heterogeneous Reduction of Red-Brown Zh Vat Dye with Rongalite in the Absence of Diffusion Hindrance

The kinetics of heterogeneous reduction of red-brown Zh vat dye with formaldehyde sodium sulfoxylate (rongalite) was studied. The dye was reduced in the form of nonporous disk, which eliminates the effect of mass transfer on the reaction rate. The stages of the reduction mechanism and the reaction rate equations are proposed.     

X-ray electron probe microanalysis of the reaction zone of thermally stimulated heterovalent anion substitution in the Ga 2III Se 3VI -GaAs solid-phase system

X-ray electron probe microanalysis (EPMA) was used to study the concentration profiles of the main reaction components in the Ga₂Se₃-GaAs heterojunction obtained as a result of thermally stimulated heterovalent anion substitution. It has been found that the quasi-equilibrium and quasi-steady diffusion modes for delivery of chalcogen to the reaction zone are different with respect to the kinetics of the A₂^IIIC₃^VI layer growth. Independent of this, the concentration profiles of the reaction elements are self-organized with time, which allows heterostuctures with a sharp interphase boundary to be reproduced.     

Methods of Weyl representation of the phase space and canonical transformations. I

Conclusions Thus, we have shown that the solutions (24) and (36) of the basic equation (17) for the symbol of the intertwining operator of general linear canonical transformations are convenient for constructing the Green's functions of quadratic systems and studying group representations; this makes it possible to dispense completely with the technique of coherent states. For example, for a parametrically excited oscillator we have (34), a simple expression for the symbol of the Green's function in terms of fundamental solutions of the classical equation. This fact is not fortuitous: For it is only by virtue of the characteristic property (13) of the Weyl ordering that the invariance group of the symbol, realized by unitary transformations, is identical to the dynamical symmetry groupH(2n, R) Sp(2n, R) of the classical quadratic Hamiltonians. Therefore, it is convenient to use the classification methods for diagonalizing classical systems in the symbol itself. In this way, we have been able to show that the unique -functional singularities of the symbol (24) determine the sliding mappings (27)–(28) on invariant subspaces, and we have also obtained the symbols (37)–(41) of the spectral projectors of arbitrary quadratic systems. Note that every irreducible subspace and the projectors acting on it are ultimately determined by the type of some Jordan cell of the matrix of the classical Hamiltonian, and therefore, the theory of canonical Jordan-Arnol'd forms [31] for many-parameter quadratic systems finds a natural quantum-mechanical realization in the formalism we have proposed.Institute of High Energy Physics, Serpukhov. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 61, No. 3, pp. 347–363, December, 1984.     

Kinetics of Liquid-Phase Redox Reactions Involving Hydroxy- and Aminoalkanesulfinates

The mechanisms and kinetics of practically important redox reactions proceeding under the action of hydroxy- and aminoalkanesulfinates are analyzed. The general features allowing forecasting of the rates of reactions involving the above reducing agents are elucidated.     

Analysis of nonexponential capacitance relaxation signals

The kinetics of charge transfer by deep energy levels of the semiconductor gap, describing nonexponential shape of capacitance relaxation signals, is suggested. A method of analysis of these signals, possessing higher accuracy and resolution in comparison with the conventional methods based on the relaxation-time approximation, is developed.