Heat kernel expansions on the integers and the Toda lattice hierarchy

We consider the heat equation u _t = Lu where L is a second-order difference operator in a discrete variable n. The fundamental solution has an expansion in terms of the Bessel functions of imaginary argument. The coefficients α _k (n, m) in this expansion are analogs of Hadamard’s coefficients for the (continuous) Schr?dinger operator. We derive an explicit formula for α _k in terms of the wave and the adjoint wave functions of the Toda lattice hierarchy. As a first application of this result, we prove that the values of these coefficients on the diagonals n = m and n = m + 1 define a hierarchy of differential-difference equations which is equivalent to the Toda lattice hierarchy. Using this fact and the correspondence between commutative rings of difference operators and algebraic curves we show that the fundamental solution can be summed up, giving a finite formula involving only two Bessel functions with polynomial coefficients in the time variable t, if and only if the operator L belongs to the family of bispectral operators constructed in [18].     

Electrochemical Studies of Intramolecular Electron Transfer in Laccase from Trametes versicolor

This paper describes electrochemical behavior of laccase from the fungus Trametes versicolor. The issues related to discrimination of the redox potentials corresponding to copper centers T1 and T2/T3 in the active site and possible mechanism of intramolecular electron transfer have been discussed. The electron‐transfer rate constant for laccase immobilized on carbon electrode is 3.4 s^?1. The bioelectrocatalytic activity of the enzyme was studied in the presence of 1,4‐hydroquinone (HQ). The kinetics of HQ oxidation is very fast (K_M=3.8 μM). However, the catalytic activity of laccase in the presence of high concentration of HQ decreases drastically. It is suggested that the T2/T3 copper center is able to accept electrons from HQ molecules directly via intramolecular channel.     

Mechanical properties and structural characteristics of plastically deformed peridotites

The paper reports on experimental study of peridotites with different average grain sizes. It is shown that coarse-crystalline peridotite undergoes multiple bulk fracture along all large fragments, whereas fracture of fine-crystalline peridotite is localized in the centre and develops in a direction close to the compression axis with the only slight deflection toward maximum tangential stresses in the upper and lower parts in which the strain localization zone is bifurcated. It is found that by the onset of fracture, the lateral to axial strain ratio for the coarse- and fine-crystalline specimens is 1.36 and 0.76, respectively.     

Real Hamiltonian forms of affine Toda field theories: Spectral aspects

Theoretical and Mathematical Physics - The paper is devoted to real Hamiltonian forms of $$2$$ -dimensional Toda field theories related to exceptional simple Lie algebras, and to the spectral...     

Wave dynamics of cracks and multiple contact surface interaction

This work considers the numerical simulation of crack behavior involving contact surfaces. A surface-slipping algorithm is developed to obtain the deformation of solids containing one or several cracks under dynamic loading. A shear-loading-induced crack is also considered.     

Well-posedness and small data scattering for the generalized Ostrovsky equation

We consider the generalized Ostrovsky equation utx=u+(up)_xx. We show that the equation is locally well posed in Hs, s>3/2 for all integer values of p?2. For p?4, we show that the equation is globally well posed for small data in H⁵∩W3,1 and moreover, it scatters small data. The latter results are corroborated by numerical computations which confirm the heuristically expected decay of ‖uLr_‖∼t−(r−2)/(2r).     

Syrian hamster embryo (SHE) assay (pH 6.7) coupled with infrared spectroscopy and chemometrics towards toxicological assessment

The Syrian hamster embryo (SHE) assay (pH 6.7) is an in vitro candidate to replace in vivo carcinogenicity tests. However, the conventional method of visual scoring of foci (non-transformed vs. transformed colonies) can be time-consuming and is open to subjectivity. Infrared (IR) spectroscopy has the potential to provide objective assessment of such SHE colonies with the added advantage of potentially providing mechanistic information. In this study, SHE cells were treated with one of eight different chemical regimens, allowed in culture to attach and form foci on IR-reflective glass slides; these were subsequently interrogated by attenuated total reflection (ATR) Fourier-transform IR (FTIR) spectroscopy. Derived mid-IR spectra (n = 13,406) were subjected to chemometric analysis focusing primarily on the extraction of biochemical information related to test agent treatment and/or morphological transformation. The use of ATR-FTIR spectroscopy with chemometrics to analyze the SHE assay is a novel approach to toxicological assessment.     

Accurate and efficient evaluation of Schur and Jack functions

We present new algorithms for computing the values of the Schur and Jack functions in floating point arithmetic. These algorithms deliver guaranteed high relative accuracy for positive data ( 0$">) and run in time that is only linear in .

     

The central polynomials for the Grassmann algebra

In this paper we describe the central polynomials for the infinite-dimensional unitary Grassmann algebra G over an infinite field F of characteristic ≠ 2. We exhibit a set of polynomials that generates the vector space C(G) of the central polynomials of G as a T-space. Using a deep result of Shchigolev we prove that if charF = p > 2 then the T-space C(G) is not finitely generated. Moreover, over such a field F, C(G) is a limit T-space, that is, C(G) is not a finitely generated T-space but every larger T-space W ≩ C(G) is. We obtain similar results for the infinite-dimensional nonunitary Grassmann algebra H as well.