Generalized covariance inequalities

We prove some inequalities for the difference between a joint distribution and the product of its marginals for arbitrary absolutely continuous random variables. Some applications of the obtained inequalities are also presented.     

Good and viscosity solutions of fully nonlinear elliptic equations

We introduce the notion of a ``good" solution of a fully nonlinear uniformly elliptic equation. It is proven that ``good" solutions are equivalent to -viscosity solutions of such equations. The main contribution of the paper is an explicit construction of elliptic equations with strong solutions that approximate any given fully nonlinear uniformly elliptic equation and its -viscosity solution. The results also extend some results about ``good" solutions of linear equations.

     

Breit–Wigner Approximation and the Distribution¶of Resonances

For operators with a discrete spectrum, {λ _j ²}, the counting function of λ _j 's, N (λ), trivially satisfies N ( λ+δ ) −N ( λ−δ ) =∑ _j δ_{λ j} ((λ−δ,λ+δ]). In scattering situations the natural analogue of the discrete spectrum is given by resonances, λ _j ∈ℂ₊, and of N (λ), by the scattering phase, s(λ). The relation between the two is now non-trivial and we prove that

About some problems of spectral synthesis

For a given pair $\text{(A,b)∈}\text{R}{}^{\mathrm{n\times n}}\text{×}\text{R}{}^{\mathrm{n\times 1}}$ such that A is cyclic and b is a cyclic generator (with respect to A) of $\text{R}{}^{\mathrm{n\times 1}}$, it is shown that for every nonnegative integer m we can find a nonnegative integer t and a sequence $\text{{f}{}_{\mathrm{j\}}}{}^{\mathrm{t}}{}_{\mathrm{j=0}}\text{,f}{}_{\mathrm{j}}\text{∈}\text{R}{}^{\mathrm{1\times n}}$,so that a the zeros of the rational function det P(z), where $\text{P(z) = zI ? A ? ∑}{}^{\mathrm{t}}{}_{\mathrm{j=0}}\text{z}{}^{\mathrm{-(m+j)}}\text{b?}$_f, lie in the open unit disc in the complex plane. The result is directly applicable to a stabilizability problem for linear systems with a time delay in control action.     

Capacities of quantum channels for massive bosons and fermions

We consider the capacity of classical information transfer for noiseless quantum channels carrying a finite average number of massive bosons and fermions. The maximum capacity is attained by transferring the Fock states generated from the grand-canonical ensemble. Interestingly, the channel capacity for a Bose gas indicates the onset of Bose-Einstein condensation, by changing its qualitative behavior at the criticality, while for a channel carrying weakly attractive fermions, it exhibits the signatures of Bardeen-Cooper-Schrieffer transition. We also show that, for noninteracting particles, fermions are better carriers of information than bosons.     

Heavy-to-light-quark decays with two-loop accuracy

We present a determination of a new class of three-loop Feynman diagrams describing heavy-to-light transitions. We apply it to find the O(alpha2(s)) corrections to the top quark decay t --> bW and to the distribution of lepton invariant mass in the semileptonic b quark decay b --> ulnu. We also confirm the previously determined total rate of that process as well as the O(alpha2) corrections to the muon lifetime.     

May GSH and L-His contribute to intracellular binding of zinc? Thermodynamic and solution structural study of a ternary complex

GSH and L-His are abundant biomolecules and likely biological ligands for Zn(II) under certain conditions. Potentiometric titrations provide evidence of formation of ternary Zn(II) complexes with GSH and L-His or D-His with slight stereoselectivity in favour of L-His (ca. 1 log unit of stability constant). The solution structure of the ZnH(GSH)(L-His)(H2O) complex at pH 6.8, determined by NMR, includes tridentate L-His, monodentate (sulfur) GSH, and weak interligand interactions. Calculations of competitivity of this complex for Zn(II) binding at pH 7.4 indicate that it is likely to be formed in vivo under conditions of GSH depletion. Otherwise, GSH alone emerges as a likely Zn(II) carrier.