Form factors and action of U_{\sqrt{-1}}(sl_2~) on infinite-cycles

Let ${\bf p}=\{P_{n,l}\}_{n,l\in\Z_{\ge 0}\atop n-2l=m}$ be a sequence of skew-symmetric polynomials in $X_1,...,X_l$ satisfying $\deg_{X_j}P_{n,l}\le n-1$, whose coefficients are symmetric Laurent polynomials in $z_1,...,z_n$. We call ${\bf p}$ an $\infty$-cycle if $P_{n+2,l+1}\bigl|_{X_{l+1}=z^{-1},z_{n-1}=z,z_n=-z} =z^{-n-1}\prod_{a=1}^l(1-X_a^2z^2)\cdot P_{n,l}$ holds for all $n,l$. These objects arise in integral representations for form factors of massive integrable field theory, i.e., the SU(2)-invariant Thirring model and the sine-Gordon model. The variables $\alpha_a=-\log X_a$ are the integration variables and $\beta_j=\log z_j$ are the rapidity variables. To each $\infty$-cycle there corresponds a form factor of the above models. Conjecturally all form-factors are obtained from the $\infty$-cycles. In this paper, we define an action of $U_{\sqrt{-1}}(\widetilde{\mathfrak{sl}}_2)$ on the space of $\infty$-cycles. There are two sectors of $\infty$-cycles depending on whether $n$ is even or odd. Using this action, we show that the character of the space of even (resp. odd) $\infty$-cycles which are polynomials in $z_1,...,z_n$ is equal to the level $(-1)$ irreducible character of $\hat{\mathfrak{sl}}_2$ with lowest weight $-\Lambda_0$ (resp. $-\Lambda_1$). We also suggest a possible tensor product structure of the full space of $\infty$-cycles.Comment: 27 pages, abstract and section 3.1 revise

Preliminary results of measurements by automated probes Vega 1 and 2 or particle concentration in clouds of Venus at heights 47-63 KM

Results of the preliminary processing of the Vega 1 and 2 descender data on the cloud layer structure of the Venusian atmosphere are discussed. A photoelectric counter for aerosol particles is described together with its optical and pneumatic circuits and operation algorithm. Vertical profiles of concentrations of particles with a diameter of 0.4 microns agree quantitatively with the Pioneer-Venus and Venera 9 and 10 data. Concentrations of these particles are: in the B layer, up to 190/cu cm; in the C layer, up to 10/cu cm; and in the D layer, up to 130/cu cm. Layers have sharp boundaries with a significant vertical heterogeneity of the aerosol concentration field inside them

A monomial basis for the Virasoro minimal series M(p,p') : the case 1<p'/p<2

Quadratic relations of the intertwiners are given explicitly in two cases of chiral conformal field theory, and monomial bases of the representation spaces are constructed by using the Fourier components of the intertwiners. The two cases are the (p,p')-minimal series for the Virasoro algebra where 1<p'/p<2, and the level k integrable highest weight modules for the affine Lie algebra \hat{sl}_2.Comment: Latex, 29 page

Authored Lexical Syntagmatics in a Systematic Interpretation

В статье рассматривается стилометрическая модель системного представления авторской лексической синтагматики в русской литературе XIX в.The article considers a stylometric model of systematic interpretation of authored lexical syntagmatics(lexical compatibility) in the classical prose of the 19th century

Author’s Thesaurus and Word Compatibility: Lexicostatistical Models of Individual Style

The article considers the possibilities of comparative lexicostatistical analysis to study the individualstyle (idiostyle) of a literary text author. Within the framework of the concept of idiostyle as a two-dimensionalessence two research models connected with the identification of individual-author lexicon andpeculiarities of an author’s lexicon compatibility are discussed.В статье рассматриваются возможности сравнительного лексико-статистического анализа, применяемого для изучения индивидуального стиля (идиостиля) автора художественного текста