Can one see the fundamental frequency of a drum?

We establish two-sided estimates for the fundamental frequency (the lowest eigenvalue) of the Laplacian in an open subset G of R^n with the Dirichlet boundary condition. This is done in terms of the interior capacitary radius of G which is defined as the maximal possible radius of a ball B which has a negligible intersection with the complement of G. Here negligibility of a subset F in B means that the Wiener capacity of F does not exceed gamma times the capacity of B, where gamma is an arbitrarily fixed constant between 0 and 1. We provide explicit values of constants in the two-sided estimates.Comment: 18 pages, some misprints correcte

A One-Parameter Family of Hamiltonian Structures for the KP Hierarchy and a Continuous Deformation of the Nonlinear \W_{\rm KP} Algebra

The KP hierarchy is hamiltonian relative to a one-parameter family of Poisson structures obtained from a generalized Adler map in the space of formal pseudodifferential symbols with noninteger powers. The resulting \W-algebra is a one-parameter deformation of \W_{\rm KP} admitting a central extension for generic values of the parameter, reducing naturally to \W_n for special values of the parameter, and contracting to the centrally extended \W_{1+\infty}, \W_\infty and further truncations. In the classical limit, all algebras in the one-parameter family are equivalent and isomorphic to \w_{\rm KP}. The reduction induced by setting the spin-one field to zero yields a one-parameter deformation of \widehat{\W}_\infty which contracts to a new nonlinear algebra of the \W_\infty-type.Comment: 31 pages, compressed uuencoded .dvi file, BONN-HE-92/20, US-FT-7/92, KUL-TF-92/20. [version just replaced was truncated by some mailer

Study of KS KL Coupled Decays and KL -Be Interactions with the CMD-2 Detector at VEPP-2M Collider

The integrated luminosity about 4000 inverse nanobarn of around phi meson mass ( 5 millions of phi mesons) has been collected with the CMD-2 detector at the VEPP-2M collider. A latest analysis of the KS KL coupled decays based on 30 % of available data is presented in this paper. The KS KL pairs from phi meson decays were reconstructed in the drift chamber when both kaons decayed into two charged particles. From a sample of 1423 coupled decays a selection of candidates to the CP violating KL into pi+ pi- decay was performed. CP violating decays were not identified because of the domination of events with a KL regenerating at the Be beam pipe into KS and a background from KL semileptonic decays. The regeneration cross section of 110 MeV/c KL mesons was found to be 53 +- 17 mb in agreement with theoretical expectations. The angular distribution of KS mesons after regeneration and the total cross section of KL for Be have been measured.Comment: 14 pages, 8 figure

New precise determination of the \tau lepton mass at KEDR detector

The status of the experiment on the precise $\tau$ lepton mass measurement running at the VEPP-4M collider with the KEDR detector is reported. The mass value is evaluated from the $\tau^+\tau^-$ cross section behaviour around the production threshold. The preliminary result based on 6.7 pb$^{-1}$ of data is $m_{\tau}=1776.80^{+0.25}_{-0.23} \pm 0.15$ MeV. Using 0.8 pb$^{-1}$ of data collected at the $\psi'$ peak the preliminary result is also obtained: $\Gamma_{ee}B_{\tau\tau}(\psi') = 7.2 \pm 2.1$ eV.Comment: 6 pages, 8 figures; The 9th International Workshop on Tau-Lepton Physics, Tau0

ЧЕТЫРЕ ГЕНСЕКА АФРИКАНСКОГО НАЦИОНАЛЬНОГО КОНГРЕССА ЮЖНОЙ АФРИКИ

The article is devoted to four secretaries-general of the African National Congress of South Africa: Alfred Nzo, who has held this position for more than 20 years, and after the elimination of the apartheid regime, became the foreign minister of democratic South Africa, Cyril Ramaphosa, the current president of South Africa, Kgalema Motlanthe, who also served as interim president and Gwede Mantashe, one of the leading members of the government elected at the last conference by the National Chairman of the ANC.Статья посвящена четырем генеральным секретарям Африканского национального конгресса Южной Африки: Альфреду Нзо, находившемуся на этой должности более 20 лет, а после устранения режима апартеида ставшему министром иностранных дел демократической Южной Африки, Сирилу Рамапосе, нынешнему президенту ЮАР, Кхалеме Мотланте, также занимавшему пост президента и Гведе Манташе, одному из ведущих членов правительства, избранному на последней конференции Национальным председателем АНК

Redox reactions between acetonitrile and nitrogen dioxide in the interlayer space of fluorinated graphite matrices

The interlayer space of 2D materials can be a slit reactor where transformations not typical for the gas phase occur. We report redox reactions involving acetonitrile and nitrogen oxide guests in galleries of fluorinated graphite. Fluorinated graphite intercalation compounds with acetonitrile are treated with dinitrogen tetraoxide and the synthesis products are studied by a set of experimental methods. Data analysis reveals that N2O4 dissociates in fluorinated graphite matrices to form nitrogen containing species NO3, NO2, NO, and N2. The interaction of NO3 with acetonitrile yields HNO3, which predominates as a guest in the synthesis products independently of the fluorination degree of the matrix. This reaction is accompanied by the removal of fluorine atoms weakly bonded to the graphite layers, leading to partial defluorination of the matrices. Our work demonstrates the possibility of using fluorinated graphite as a test nanoreactor whose dimension can be controlled by fluorination of the layers