Bounds on the index of rotationally symmetric self-shrinking tori

Geometriae Dedicata - A closed surface evolving under mean curvature flow becomes singular in finite time. Near the singularity, the surface resembles a self-shrinker, a surface that shrinks by...     

Interlaboratory comparisons and improvements of methods for acid number determination in used motor oils

The results of two interlaboratory comparisons of acid number determinations in used motor oils are discussed. It is shown that the comparability of the measurement results is not as good as that required by known standards for petroleum products. The problem is motor oil contaminants which accumulated during use, and which are the source of a matrix effect in the acid number determination. The standard methods’ drawbacks are analyzed and some improvements are proposed. Repeatability and accuracy of the improved methods are evaluated. Received: 11 December 2001 Accepted: 15 February 2002     

Structure studies on porous titanium nickelide made by high-temperature self-propagating synthesis

Structure studies are reported on martensite transformations in porous TiNi alloy made by high-temperatures self-propagating synthesis. The transformations occur over a large temperature range and are incomplete. The structure data are used in reconstructing the heat release during the transition, where it is shown that it is determined by the superposition of martensite transformations occurring locally at various temperatures. Tomsk State Architectural and Building Academy. Kuznetsov Siberian Technical Physics Institute, Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 20–24, January, 1997.     

Lefschetz–Verdier Trace Formula and a Generalization of a Theorem of Fujiwara

The goal of this paper is to generalize a theorem of Fujiwara (Deligne’s conjecture) to the situation appearing in a joint work [KV] with David Kazhdan on the global Langlands correspondence over function fields. Moreover, our proof is more elementary than the original one and stays in the realm of ordinary algebraic geometry, that is, does not use rigid geometry. We also give a proof of the Lefschetz–Verdier trace formula and of the additivity of filtered trace maps, thus making the paper essentially self-contained. The work was supported by the Israel Science Foundation (Grant No. 555/04) Received: May 2005 Accepted: August 2005     

Resonant Phenomena in Slowly Irregular Rectangular Waveguides

A waveguide with a rectangular cross section of size and orientation slowly changing along the length of the waveguide is considered. Methods of the canonical perturbation theory are used to describe the ray dynamics in the waveguide. As the size and orientation of the cross section slowly change along the ray trajectory, certain resonance conditions may be satisfied. The phenomena of scattering on resonance and capture into resonance is studied. These phenomena lead to destruction of the adiabatic invariance in the system. Bibliography: 12 titles.__________Published in Zapiski Nauchnykh Seminarov POMI, Vol. 300, 2003, pp. 173–179     

Distribution of energy levels of quantum free particle on the Liouville surface and trace formulae

We consider the Weyl asymptotic formula

Magnetic properties of nanosized hexaferrite powders

Hexagonal ultradispersed ferrites were obtained in a high energy planetary mill by mechanochemical treatment. Their structural characteristics — average size and internal stress — were studied. Fundamental magnetic characteristics — saturation magnetization and effective fields of crystal anisotropy — were examined in pulse magnetic fields with the law of approach to saturation, as well as by ferromagnetic resonance technique in the 26–53 GHz frequency range. It was demonstrated that size reduction of powders to a few tens of nanometers influenced significantly the effective anisotropy field. A model accounting for anisotropy contribution from the disturbed subsurface layer and magnetoelastic interactions was suggested. Mechanical activation was shown to be an alternative to chemical substitution for magnetic anisotropy control.     

Annulation of pyrrole ring in 4-acylpyridine-3,5-dicarbonitriles in the presence of ammonia

Chemistry of Heterocyclic Compounds - 4-Acyl-2-amino-6-chloropyridine-3,5-dicarbonitriles underwent heterocyclization in the presence of ammonia in aqueous dioxane medium, involving the...     

On a borderline between the NP-hard and polynomial-time solvable cases of the flow shop with job-dependent storage requirements

The paper is concerned with the two-machine flow shop, where each job requires an additional resource (referred to as storage space) from the start of its first operation till the end of its second operation. The storage requirement of a job is determined by the processing time of its first operation. At any point in time, the total consumption of this additional resource cannot exceed a given limit (referred to as the storage capacity). The goal is to minimise the makespan, i.e. to minimise the time needed for the completion of all jobs. This problem is NP-hard in the strong sense. The paper analyses how the parameter - a lower bound on the storage capacity specified in terms of the processing times, affects the computational complexity.