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.     

Composite Julia sets generated by infinite polynomial arrays

A definition of a generalized filled-in Julia set generated by an infinite array of proper polynomial mappings in  is introduced. It is shown that such Julia sets depend analytically on the defining polynomial mappings.     

Design of Hyperbolic Billiards

We formulate a general framework for the construction of hyperbolic billiards. Spherical symmetry is exploited for a simple treatment of billiards with spherical caps and soft billiards in higher dimensions. Other examples include the Papenbrock stadium. Reproduction of the entire article for non-commercial purposes is permitted without charge.     

Two 1-substituted 4-nitro­imidazoles

Crystalline 4-nitro-1-phenyl­imidazole, C₉H₇N₃O₂, (I), and 4′-­nitro-1-phenyl-4,1′-bii­imidazole, C₁₂H₉N₅O₂, (II), contain C—H⃛O and C—H⃛N hydrogen bonds, connecting the mol­ecules into infinite chains. The aromatic fragments in both compounds are nearly planar. The dihedral angles between the benzene and imidazole rings are 26.78 (5)° in (I) and 29.36 (8)° in (II).