Vibrational spectra and structure of antimony (III) trialkoxides

1. According to their vibrational spectra, antimony trialkoxides of formula Sb(OR)3 with R=CH3, C2H5, n-C3H7, and i-C4H9 are associated; no signs of association are observed for the compounds with R=i-C3H7 and t-C4H9. 2. The molecules of antimony tri-t-butoxide in the liquid state at 20°C exist in the form of rotational isomers having C1 (Cs) and C3 (C3v) symmetry, with the C1 (Cs) conformer predominating. Upon freezing, the C3 (C3v) conformer remains in the crystal. © 1981 Plenum Publishing Corporation

Production of some derivatives of 1,3,2-dioxastibinane and their vibrational spectra

1. 2-Chloro-, 2-methoxy-, and 2-tert-butoxy-4,6,6-trimethyl-1,3,2-dioxastibinanes and 2-tert-butoxy-5,5-dimethyl-and 2-tert-butoxy-4-methyl-1,3,2-dioxastibinanes were synthesized by the transetherification of chlorodiethoxy-, trimethoxy-, and tri-tert-butoxyantimony with the respective glycols. 2. According to the data on the vibration spectra, the 2-chloro and 2-alkoxy derivatives of 1,3,2-dioxastibinane are associated at the Sb-O bonds in the crystalline phase. The degree of association is determined by steric factors. 2-tert-Butoxy-4,6,6-trimethyl-1,3,2-dioxastibinane exists in the monomeric form. © 1985 Plenum Publishing Corporation

Preparation and vibrational spectra of various esters and chlorides of antimonous acid

1. 2-Methoxy-, 2-methoxy-4-methyl-, 2-methoxy-5,5-dimethyl-, 2-chloro-, 2-chloro-4-methyl-, and 2-chloro-5,5-dimethyl-1,3,2-dioxastibinanes have been prepared. 2. The bands due to the group vibrations ν (Sb-O) and ν (Sb-Cl) have been identified in the infrared and Raman spectra of the acyclic and cyclic esters and chlorides of antimonous acid obtained. © 1976 Plenum Publishing Corporation

Vibrational spectra of solutions of some derivatives of 1,3,2-dioxastibinane and their structure

1. The vibrational spectra of the 2-chloro and 2-alkoxy derivatives of 1,3,2-dioxastibinane in various phase states indicate they are capable of self-association through Sb-O...Sh and Sb-Cl...Sb bridges of various types, determined by the steric strain in the molecules. 2. In the crystalline phase polymers with strong and weak coordination bonds, dimers, and monomers are formed, depending on the type of substitution in the six-membered ring. In the series of the investigated compounds concentration-dependent signs of a polymer ⇄ dimer ⇄ monomer equilibrium are observed in the melts and the solutions. © 1986 Plenum Publishing Corporation

Synthesis and vibrational spectra of some 2-alkoxy-5,6-benzo-1,3,2-dioxastibepines

1) Tranesterification of the respective antimony trialkoxides with phthalyl alcohol have 2-methoxy-, 2-ethoxy-, and 2-tert-butoxy-5,6-benzo-1,3,2-dioxastibepines. 2) According to the IR and Raman spectra, 2-ethoxy- and 2-tert-butoxy-5,6-benzo-1,3,2-dioxastibepines are polymerized in the crystalline phase; the νSb-O frequencies are at least 100 cm-1 higher in melt and in solution than in the crystalline phase; they exist both as dimer and monomer. 2-tert-butoxy-5,6-benzo-1,3,2-dioxastibepine exists predominantly in the chair conformation. © 1987 Plenum Publishing Corporation

Challenges of beta-deformation

A brief review of problems, arising in the study of the beta-deformation, also known as "refinement", which appears as a central difficult element in a number of related modern subjects: beta \neq 1 is responsible for deviation from free fermions in 2d conformal theories, from symmetric omega-backgrounds with epsilon_2 = - epsilon_1 in instanton sums in 4d SYM theories, from eigenvalue matrix models to beta-ensembles, from HOMFLY to super-polynomials in Chern-Simons theory, from quantum groups to elliptic and hyperbolic algebras etc. The main attention is paid to the context of AGT relation and its possible generalizations.Comment: 20 page

On "Dotsenko-Fateev" representation of the toric conformal blocks

We demonstrate that the recent ansatz of arXiv:1009.5553, inspired by the original remark due to R.Dijkgraaf and C.Vafa, reproduces the toric conformal blocks in the same sense that the spherical blocks are given by the integral representation of arXiv:1001.0563 with a peculiar choice of open integration contours for screening insertions. In other words, we provide some evidence that the toric conformal blocks are reproduced by appropriate beta-ensembles not only in the large-N limit, but also at finite N. The check is explicitly performed at the first two levels for the 1-point toric functions. Generalizations to higher genera are briefly discussed.Comment: 10 page

Introduction to Integral Discriminants

The simplest partition function, associated with homogeneous symmetric forms S of degree r in n variables, is integral discriminant J_{n|r}(S) = \int e^{-S(x_1 ... x_n)} dx_1 ... dx_n. Actually, S-dependence remains the same if e^{-S} in the integrand is substituted by arbitrary function f(S), i.e. integral discriminant is a characteristic of the form S itself, and not of the averaging procedure. The aim of the present paper is to calculate J_{n|r} in a number of non-Gaussian cases. Using Ward identities -- linear differential equations, satisfied by integral discriminants -- we calculate J_{2|3}, J_{2|4}, J_{2|5} and J_{3|3}. In all these examples, integral discriminant appears to be a generalized hypergeometric function. It depends on several SL(n) invariants of S, with essential singularities controlled by the ordinary algebraic discriminant of S.Comment: 36 pages, 19 figure

First Measurement of Coherent Elastic Neutrino-Nucleus Scattering on Argon

We report the first measurement of coherent elastic neutrino-nucleus scattering (\cevns) on argon using a liquid argon detector at the Oak Ridge National Laboratory Spallation Neutron Source. Two independent analyses prefer \cevns over the background-only null hypothesis with greater than $3\sigma$ significance. The measured cross section, averaged over the incident neutrino flux, is (2.2 $\pm$ 0.7) $\times$10$^{-39}$ cm$^2$ -- consistent with the standard model prediction. The neutron-number dependence of this result, together with that from our previous measurement on CsI, confirms the existence of the \cevns process and provides improved constraints on non-standard neutrino interactions.Comment: 8 pages, 5 figures with 2 pages, 6 figures supplementary material V3: fixes to figs 3,4 V4: fix typo in table 1, V5: replaced missing appendix, V6: fix Eq 1, new fig 3, V7 final version, updated with final revision