Recu 7 dicembre 1978, pvisentation dPfinitive 30 mars I979 Rbsumb Un cryostat a rkgulation de temperature a ktk construit pour l'etude par spectromktrie infrarouge des transitions de phase des molkcules adsorbkes sur des halogenures alcalins prepares par Cvaporation sous vide selon la mkthode de Kozirovski et Folman. La rkgulation s'effectue a 0.1 K prks et la temperature peut &re maintenue constante a 0.5 K en moyenne pendant 12 h dans le domaine 80-300 K. Ce cryostat peut kgalement &re utili& comme cellule a tempkrature variable pour liquides, solides, m6me formes par condensation de vapeurs (matrices) et, eventuellement, comme cellule a gaz.
Variable-temperature infrared cell for studies of adsorption on alkali halides and other usesAbstract A low-temperature infrared cell is described for phase transition studies of adsorbed molecules on alkali halides prepared by the technique of Kozirovski and Folman : i.e., under vacuum, halide is evaporated and condensed on a cold window. The cell temperature is automatically controlled throughout the range 80-300 K with a precision of 0.1 K and is constant with an average accuracy of 0.5 K for 12 h. This cell can be used also as a variabletemperature cell for liquids and solids, for studies of solids condensed from vapour (matrix studies, for example) and, possibly, as a gas cell.
Abstract. In 1947, Lehmer conjectured that the Ramanujan's tau function τ (m) never vanishes for all positive integers m, where τ (m) is the m-th Fourier coefficient of the cusp form ∆ 24 of weight 12. The theory of spherical t-design is closely related to Lehmer's conjecture because it is shown, by Venkov, de la Harpe, and Pache, that τ (m) = 0 is equivalent to the fact that the shell of norm 2m of the E 8 -lattice is a spherical 8-design. So, Lehmer's conjecture is reformulated in terms of spherical t-design.Lehmer's conjecture is difficult to prove, and still remains open. However, Bannai-Miezaki showed that none of the nonempty shells of the integer lattice Z 2 in R 2 is a spherical 4-design, and that none of the nonempty shells of the hexagonal lattice A 2 is a spherical 6-design. Moreover, none of the nonempty shells of the integer lattices associated to the algebraic integers of imaginary quadratic fields whose class number is either 1 or 2, except for Q( √ −1) and Q( √ −3) is a spherical 2-design. In the proof, the theory of modular forms played an important role.Recently, Yudin found an elementary proof for the case of Z 2 -lattice which does not use the theory of modular forms but uses the recent results of Calcut. In this paper, we give the elementary (i.e., modular form free) proof and discuss the relation between Calcut's results and the theory of imaginary quadratic fields.
It is proved that the minimum of the potential energy of 24 unit charges placed on the sphere in R 8 is equal to 637975/72. This minimum is attained on the minimal vectors of the lattice ES.
We present a method of covering a multidimensional sphere by spherical caps based on spherical designs. The following extremal problem is solved: for which greatest η a polynomial over the Gegenbauer system with the zero coefficient equal to 0 is non-negative on
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