Integration of differential forms on manifolds with locally-finite variations. II

In part I of the paper, we have defined n-dimensional C⁰-manifolds in ℝⁿ(m ≥ n) with locally-finite n-dimensional variations (a generalization of locally-rectifiable curves to dimensionn > 1) and integration of measurable differential n-forms over such manifolds. The main result of part II states that an n-dimensional manifold that is C¹-embedded into ℝ^m has locally-finite variations and the integral of a measurable differential n-form defined in part I can be calculated by the well-known formula. Bibliography: 5 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 333, 2006, pp. 66–85.     

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.     

Slow cyclotron instability in a high-power backward-wave oscillator

The linear dispersion relation of a backward-wave oscillator (BWO), derived earlier by the authors, is modified to include effects of RF surface current at the beam-vacuum interface. This modified dispersion relation results in an unstable interaction between the slow cyclotron mode (SCM) and the structure mode in addition to the conventional Cherenkov instability caused by the slow space charge mode. Numerical analysis is then carried out using parameters of a BWO experiment at University of Maryland. Fine structure of the SCM instability is elucidated. The analysis indicates that BWO radiation would not be suppressed near cyclotron absorption in an infinitely long system.     

Diffuse x-ray scattering study of the formation of microdefects in heat-treated dislocation-free large-diameter silicon wafers

Diffuse x-ray scattering (DXS) is used to study the formation of microdefects (MDs) in heat-treated dislocation-free large-diameter silicon wafers with vacancies. The DXS method is shown to be efficient for investigating MDs in silicon single crystals. Specific defects, such as impurity clouds, are found to form in the silicon wafers during low-temperature annealing at 450°C. These defects are oxygen-rich regions in the solid solution with diffuse coherent interfaces. In the following stages of decomposition of the supersaturated solid solution, oxide precipitates form inside these regions and the impurity clouds disappear. As a result of the decomposition of the supersaturated solid solution of oxygen, interstitial MDs form in the silicon wafers during multistep heat treatment. These MDs lie in the {110} planes and have nonspherical displacement fields. The volume density and size of MDs forming in the silicon wafers at various stages of the decomposition are determined.