A differential Azumaya algebra, and in particular a differential matrix algebra, over a differential field K with constants C is trivialized by a Picard–Vessiot (differential Galois) extension E. This yields a bijection between isomorphism classes of differential algebras and Picard–Vessiot cocycles Z(G(E/K), PGLn(C)) which cobound in Z (G(E/K), PGLn(E)).

It is proved that a compactly supported (or decaying faster than any exponential) spherically symmetric potential is uniquely determined by the phase shift δ(k) known for all k ∈ (a, b), 0 ≤ a < b < ∞. Here the phase shift δ(k) corresponds to the s-wave. No information about bound states energies and normalizing constants is assumed known

We consider a compact set K in the form of a sequence of segments. By means of nearly Chebyshev polynomials for K, the modulus of continuity of the Green functions gC\K is estimated. Markov’s constants of the corresponding set are evaluated.

Actin is an abundant protein that constitutes a main component of the eukaryotic cytoskeleton. Its polymerization and depolymerization are regulated by a variety of actin-binding proteins. Their functions range from nucleation of actin polymerization to sequestering G-actin in 1∶1 complexes. The kinetics of forming these complexes, with rate constants varying at least three orders of magnitude,...

Expressions for a K-adiabatic master equation for a bimolecular recombination rate constant krec are derived for a bimolecular reaction forming a complex with a single well or complexes with multiple well, where K is the component of the total angular momentum along the axis of least moment of inertia of the recombination product. The K-active master equation is also considered. The exact analy...

Immıscible polymethyl methacrylate/polystyrene (PMMA/PS) mixtures with various maleic anhydride-styrene-methyl methacrylate (MAStMMA) compatibilizer ratio (0, 2, 4, 6, 8 and 10) % were obtained by solution casting. The spectral results showed that the optical constants such as refractive index (n), extinction coefficient (k) absorption increase increasing terpolymer ratio. On other hand, energy...

We investigate the problem of equivalence Lq-Sobolev norms in Malliavin spaces for q∈[1,∞), focusing on graph norm k-th derivative operator and full Sobolev involving all derivatives up to order k, where k is any positive integer. The case q=1 infinite-dimensional setting challenging, since at such extreme standard approach Meyer's inequalities fails. In this direction, we are able establish me...

The pH profiles of the apparent biomolecular rate constants for the reaction f free EO with [2-'H]and [22H]phenylalanine (evaluated as (kr)H and (kr)H*, respectively, from rapid kinetic measurements and as the equivalent steady state coefficients ( & l ) ~ and (+I-')"*) show that k , = k', k2 >> k-' << k2* and that the ionization controlled by K', (= kL,/k,) is at virtual equilibrium. The expre...

The pH profiles of the apparent biomolecular rate constants for the reaction f free EO with [2-'H]and [22H]phenylalanine (evaluated as (kr)H and (kr)H*, respectively, from rapid kinetic measurements and as the equivalent steady state coefficients ( & l ) ~ and (+I-')"*) show that k , = k', k2 >> k-' << k2* and that the ionization controlled by K', (= kL,/k,) is at virtual equilibrium. The expre...

The magnetic properties of nitride clusterfullerenes GdxSc3-xN@C80 (x = 1-3) are studied as a function of the number of Gd atoms in the cluster. The intracluster interaction of the Gd ions in Gd2ScN@C80 and Gd3N@C80 is ferromagnetic with exchange constants of -1.2 K ± 0.1 K and -0.6 K ± 0.1 K, respectively. At 2 K, the magnetization curves exhibit noticeable deviations from the Heisenberg model...