Pseudospark switches for the power supply circuits of pulsed lasers

A family of sealed-off low-pressure spark gap switches developed at the Institute of High Current Electronics (Tomsk) and at the Plasma Scientific Research Institute (Ryazan) with participation of researchers from the Physical Institute of the University of Erlangen (Germany) is described. The devices are of cermet construction, are capable of switching pulsed currents over wide ranges of amplitudes and durations, and have a number of unique characteristics. The principle of operation of the spark gap switches is described and their designs are given. The triggering circuits of the switches are considered. Institute of High-Current Electronics, Siberian Division of the Russian Academy of Sciences. Plazma Scientific Research Institute of Gas-Discharge Devices. Physical Institute of the University of Erlangen. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 97–105, April, 2000.     

Isoperimetric balls in cones over tori

In the cone over a cubic three-torus T ³, balls about the vertex are isoperimetric if the volume of T ³ is less than π/16 times the volume of the unit three-sphere. The conjectured optimal constant is 1.     

On representations,inversions, and approximations of laplace transforms in banach spaces

The paper extend's some of the basic results of classical Laplace transform theory to the Laplace transform of bounded Bochner integrable functions and the Laplace-Stieltjes transform of Lipschitz continuous functions with values in a Banach space.     

Electron energy-loss spectroscopy at incommensurately modulated crystalline and glassy Ba2TiGe2O8

Based on cluster molecular orbital calculations, high-energy resolution (ΔE?～ 0.4?eV) Ti–L_2,3 electron energy loss near-edge structures of single-crystalline and glassy Ba₂TiGe₂O₈ are interpreted. The finding that the Ti–L_2,3 near-edge structure of the Ba₂TiGe₂O₈ single crystal possesses less pronounced peaks than the glass under identical experimental conditions can be attributed to distinct distortions of the titanium environment caused by the very strong one-dimensional structural modulation hosted by the Ba₂TiGe₂O₈ crystal lattice. As lattice periodicity is absent in the glass, the titanium environment is more regular in the vitreous surroundings. Moreover, the modulation in crystalline Ba₂TiGe₂O₈ is responsible for the virtually indiscernible O–K near-edge structures of the glassy and crystalline samples.     

Continuous location of an assembly station

Demand existing at client points in the plane for several products should be met. Products have to be assembled from different components obtainable at given prices at various sources with known production capacities. The optimal design of the resulting supply chain must be determined, including the location of a central assembly station in the plane, so as to minimize the total operational cost comprising buying and transport of components as well as transport of final products. This problem leads to a difficult nonlinear and non-convex optimization problem for which a locally convergent algorithm is proposed. Some computational results are presented.     

Weakly coupled bound states of Pauli operators

We consider the two-dimensional Pauli operator perturbed by a weakly coupled, attractive potential. We show that besides the eigenvalues arising from the Aharonov?CCasher zero modes there are two or one (depending on whether the flux of the magnetic field is integer or not) additional eigenvalues for arbitrarily small coupling and we calculate their asymptotics in the weak coupling limit.