Spectral characteristics of elliptic solitons

Translated from Matematicheskie Zametki, Vol. 53, No. 3, pp. 62–71, March, 1993.     

Non-linear strings in two-dimensional U(∞) gauge theory

A non-singular version of the Makeenko-Migdal equation for the Wilson loop average in two-dimensional U(N) gauge theory is derived. In the limit N→∞ the exact solution is obtained for an arbitrary (with any self-intersections) closed loop.     

Lifetime measurements and particle-core coupling calculations in144Sm

Applying the generalized centroid shift method in the¹⁴²Nd(α, 2n)¹⁴⁴Sm reaction the following half-lives have been measured:T _1/2(3,376 keV)=(1.6±0.2) ns,T _1/2(3,460 keV) =(0.5±0.2) ns andT _1/2(5,150 keV)≦0.3 ns. Level energies and electromagnetic transition rates have been calculated within a particle-core coupling approach that is based on the shell model with configuration mixing. The persistence ofl-forbiddenness of M1 transitions between rather complex configurations could be confirmed.     

Quasi-periodic solutions of the integrable dynamical systems related to Hill's equation

We present finite-gap solutions to the Garnier system and to the g-dimensional anisotropic harmonic oscillator in a radial quartic potential. The relationship between these solutions and solutions of Neumann-type dynamical systems is discussed.     

Original fluorinated surfactants potentially non-bioaccumulable

This minireview updates non-exhaustive recent strategies of synthesis of original fluorosurfactants potentially non-bioaccumulable. Various strategies have been focused on (i) the preparation of CF₃–X–(CH₂)_n–SO₃Na (with X = O, C₆H₄O or N(CF₃) and n = 8–12), (ii) the oligomerization of hexafluoropropylene oxide (HFPO) to further synthesize oligo(HFPO)–CF(CF₃)CO–R_H (where R_H stands for an hydrophilic chain); (iii) the telomerization of vinylidene fluoride (VDF) with 1-iodopentafluoroethane or 1-iodononafluorobutane to produce C_nF_2n+1–(VDF)₂–CH₂CO₂R (n = 2 or 4, R = H or NH₄), (iv) the radical telomerization of 3,3,3-trifluoropropene (TFP) with isoperfluoropropyliodide or diethyl hydrogenophosphonate to prepare (CF₃)₂CF(TFP)_x–R_H or CF₃–CH₂–CH₂–(TFP)_y–P(O)(OH)₂, and (v) the radical cotelomerization of VDF and TFP, or their controlled radical copolymerization in the presence of (CF₃)₂CFI or a fluorinated xanthate. In most cases, the surface tensions versus the surfactant concentrations have been assessed. These above strategies led to various highly fluorinated (but yet not perfluorinated) telomers whose chemical changes enabled to obtain original surfactants as novel alternatives to perfluorooctanoic acid (PFOA), ammonium perfluorooctanoate (APFO), or perfluorooctylsulfonic acid (PFOS) regarded as bioaccumulable, persistent, and toxic.     

Miniaturized 96-well ELISA chips for staphylococcal enterotoxin B detection using portable colorimetric detector

A previously developed fluorescence sensing platform, combining spatial illumination using electroluminescence (EL) semiconductor strips with charge coupled device (CCD)-based detection (EL-CCD), was adapted to a new 96-well chip for colorimetric immunological assays, enhancing the capabilities of the EL-CCD platform. The modified system was demonstrated using a colorimetric-based enzyme linked immunosorbent assay (ELISA) for detection of staphylococcal enterotoxin B (SEB). Limits of detection (LODs) of 3.9 ng/mL (±2.4 ng/mL) SEB were determined with the ELISA chip measured using the EL-CCD platform, following a standard 4-h ELISA protocol. The LODs were comparable to those obtained using standard 96-well ELISA plates measured using a standard laboratory 96-well plate reader. The miniature 96-well ELISA chip however required as little as 5-μL samples, representing a tenfold reduction in sample volume compared to a standard 96-well ELISA plates. The ELISA chip also demonstrated detection of SEB spiked into various food matrices (milk, mushrooms, and mayonnaise) using limited-to-no sample preparation, with LODs ranging from 3.9 to 18.5 ng/mL depending on the matrix. The EL-CCD platform is versatile, capable of multi-mode detection (e.g., fluorescent and colorimetric along with solution and solid phase assays), and could readily be applied to other field portable or point-of-care applications. Figure Detection of SEB using miniature ELISA chips coupled with a portable electroluminiscent-charge couple device (EL-CCD) detection system. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Matrix models as CFT: Genus expansion

We show how the formulation of the matrix models as conformal field theories on a Riemann surfaces can be used to compute the genus expansion of the observables. Here we consider the simplest example of the Hermitian matrix model, where the classical solution is described by a hyperelliptic Riemann surface. To each branch point of the Riemann surface we associate an operator which represents a twist field dressed by the modes of the twisted boson. The partition function of the matrix model is computed as a correlation function of such dressed twist fields. The perturbative construction of the dressing operators yields a set of Feynman rules for the genus expansion, which involve vertices, propagators and tadpoles. The vertices are universal, the propagators and the tadpoles depend on the Riemann surface. As a demonstration we evaluate the genus-two free energy using the Feynman rules.     

On realizability of sign patterns by real polynomials

The classical Descartes’ rule of signs limits the number of positive roots of a real polynomial in one variable by the number of sign changes in the sequence of its coefficients. One can ask the question which pairs of nonnegative integers (p, n), chosen in accordance with this rule and with some other natural conditions, can be the pairs of numbers of positive and negative roots of a real polynomial with prescribed signs of the coefficients. The paper solves this problem for degree 8 polynomials.     

Interlacing properties and the Schur-Szegő composition

Each degree n polynomial in one variable of the form (x+1)(x ^n?1+c ₁ x ^n?2+???+c _n?1) is representable in a unique way as a Schur-Szeg? composition of n?1 polynomials of the form (x+1) ^n?1(x+a _i ), see Kostov (2003), Alkhatib and Kostov (2008) and Kostov (Mathematica Balkanica 22, 2008). Set $\sigma _{j}:=\sum _{1\leq i_{1}<\cdots <i_{j}\leq n-1}a_{i_{1}}\cdots a_{i_{j}}$ . The eigenvalues of the affine mapping (c ₁,…,c _n?1)?(σ ₁,…,σ _n?1) are positive rational numbers and its eigenvectors are defined by hyperbolic polynomials (i.e. with real roots only). In the present paper we prove interlacing properties of the roots of these polynomials.