Spectral asymptotics for the Schrödinger operator with potential which steadies at infinity

We consider the discrete spectrum of the selfadjoint Schrödinger operatorA _h =–h ² +V defined inL ²(^m) with potentialV which steadies at infinity, i.e.V(x)=g+|x|^– f(1+o(1)) as |x| for>0 and some homogeneous functionsg andf of order zero. Let _h (),0, be the total multiplicity of the eigenvalues ofA _h smaller thanM–, M being the minimum value ofg over the unit sphereS ^m–1 (hence,M coincides with the lower bound of the essential spectrum ofA _h ). We study the asymptotic behaviour of ₁() as0, or of _h () ash0, the number0 being fixed. We find that these asymptotics depend essentially on the structure of the submanifold ofS ^m–1, where the functiong takes the valueM, and generically are nonclassical, i.e. even as a first approximation (2) ^m _h () differs from the volume of the set {(x, )^2m:h ²||²+V(x)<M–}.Partially supported by Contract No. 52 with the Ministry of Culture, Science and Education     

Homogeneous spaces and invariant tensors

In the present survey a method is presented for the construction of invariant tensors (with respect to a given representation) called the inclusion principle and the possibility of applying the cited method to various problems of algebra, topology, geometry, and analysis.Translated from Itogi Nauki i Tekhniki, Seriya Problemy Geometrii, Vol. 18, pp. 105–142, 1986.     

Minimum audible movement angle as a function of signal frequency and the velocity of the source

Thresholds for the detection of the direction of travel of a moving sound source were determined in a single-interval, forced-choice paradigm. Both the rate at which the sound source is displaced (8 degrees-128 degrees/s) and the frequency of the signal to be localized (500-3700 Hz) affect dynamic spatial resolution. There is an inverse relationship between spatial resolution and the rate of travel, a finding that replicates an earlier observation on performance with sources displaced at high velocities [Perrott and Musicant, J. Acoust. Soc. Am. 62, 1463-1466 (1977)]. However, the magnitude of this effect depends on the actual velocities employed. Relatively small changes in spatial resolution are apparent for velocities below approximately 32 degrees/s. The significant frequency effect can be summarized as follows: Dynamic spatial resolution is better for signals below 1000 Hz than for signals above this value (within the range tested). Particularly poor resolution is evident for signals between 1300-2000 Hz. The present results indicate that signal frequency affects dynamic spatial resolution in a fashion similar to that which has been observed in the more common "static" localization test situation. There is no indication of an interaction between these two variables. These results provide additional support for the hypothesis that both static and dynamic spatial discrimination functions are dependent upon the same underlying mechanisms. The effects of velocity upon the spatial resolution problem, a unique aspect of the dynamic paradigm, can probably be explained without the necessity of additional hypothetical mechanisms in the auditory system (e.g., a specialized motion detector).     

Ultra'soft X-ray diagnostics of short-living plasmas

Ultrasoft X-ray plasma diagnostics in IPP is realized by using X-ray diodes with Al photocathodes and submicrometer nitrocellulose filters. The X-ray detections system is suitable for measurements in a relatively broad range of radiation intensities in the spectral interval of (10–1000) eV with the time resolution of (1–10) ns under various plasma conditions. Construction, calibration and characteristic properties of the measuring apparatus are described. To illustrate its use, some results of the diagnostics of REB-heated plasma are presented.We would like to acknowledge Dr. P. unka for many helpful discussions and Dr. J. Ullschmied for cooperation in REB-heated plasma diagnostics interpretation.     

Pervasiveness of cluster excitations as seen in the Mössbauer spectra of magnetic materials

Magnetic cluster excitations in various physical systems (e.g., soliton bearing one-dimensional solids, metallic alloys, amorphous materials, small particle aggregates, magnetically ordered substances near T_C, transition metal di-chloride graphite intercalation compounds, etc.) are described. Use of Fe-57 Mössbauer effect spectroscopy as a probe of the spin dynamics for inverse autocorrelation times between 10⁷Hz to 10¹⁰ Hz is emphasized. Particular attention is given to systems which exhibit local or long range magnetic order and whose Mössbauer spectra must therefore be described by more than one autocorrelation (or dwell) time for fluctuations between different allowed hyperfine field directions on a given site.     

The search for top quarks at hadron colliders: a realistic appraisal

We study means of identifying top quarks of mass in the range 70–120 GeV at the CERN and FNAL \(\bar pp\) colliders. We show that “W+dijet” production presents a serious background to the conventional “isolated electron+dijet” signature of top. We study an improved signature, calculate the expected event rates, and discuss the determination of the mass of the top quark.     

2-Amino-4,4-disubstituted-5-carboxymethyl-Δ2-1,3,4-oxadiazolin-4-ium chlorides and their recyclization in acetic anhydride

2-Methylamino-4,4-disubstituted-5-carboethoxymethyl-²-1,3,4-oxadiazolin -4-ium chlorides were obtained from the reaction of 1,1-disubstituted-4-methylsemicarbazides with ethyl propiolate in the presence of hydrochloric acid. After hydrolysis of the ester these chlorides recyclize in acetic anhydride to 1-substituted-3-acetoxy-1H-pyrazoles. The difference in the direction of ring opening with acetic anhydride in the betaines of 1,3,4-oxadiazolin-5-acetic acids and their thia-analogs has been demonstrated.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 12, pp. 1685–1688, 1992.     

Pseudo-cross-conjugated mesomeric betaines. 1. Synthesis of pseudo-cross-conjugated mesomeric betaines from quinoxaline derivatives

A new method for the synthesis of pseudo-cross-conjugated mesomeric betainic heterocyclic compounds with an angular nitrogen atom has been developed consisting in the reaction of 1,4-dielectrophile — -carbethoxy-2-(3-chloro)quinoxalylacetonitrile with azoles. Experimental regularities have been studied and a reaction mechanism has been proposed including the stage of formation of an ylide from a quaternary azolium salt. A pseudo-crossconjugated mesomeric betainic heterocyclic compound containing a thiazole ring compound has been synthesized for the first time.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 11, pp. 1528–1533, November, 1992.