On a Unique Ergodicity of Some Markov Processes

It is proved that the sufficient condition for the uniqueness of an invariant measure for Markov processes with the strong asymptotic Feller property formulated by Hairer and Mattingly (Ann Math 164(3):993–1032, 2006) entails the existence of at most one invariant measure for e-processes as well. Some application to time-homogeneous Markov processes associated with a nonlinear heat equation driven by an impulsive noise is also given.     

Approximation,solution operators and quantale-valued metrics

A generalized solution operator is a mapping abstractly describing a computational problem and its approximate solutions. It assigns a set of \(\varepsilon \)-approximations of a solution to the problem instance f and accuracy of approximation \(\varepsilon \). In this paper we study generalized solution operators for which the accuracy of approximation is described by elements of a complete lattice equipped with a compatible monoid structure, namely, a quantale. We provide examples of computational problems for which the accuracy of approximation of a solution is measured by such objects. We show that the sets of \(\varepsilon \)-approximations are, roughly, closed balls with radii \(\varepsilon \) with respect to a certain family of quantale-valued generalized metrics induced by a generalized solution operator.     

Finitely convergent deterministic and stochastic iterative methods for solving convex feasibility problems

We propose finitely convergent methods for solving convex feasibility problems defined over a possibly infinite pool of constraints. Following other works in this area, we assume that the interior of the solution set is nonempty and that certain overrelaxation parameters form a divergent series. We combine our methods with a very general class of deterministic control sequences where, roughly speaking, we require that sooner or later we encounter a violated constraint if one exists. This requirement is satisfied, in particular, by the cyclic, repetitive and remotest set controls. Moreover, it is almost surely satisfied for random controls.

     

SIMS accurate determination of matrix composition of topological crystalline insulator material Pb1 − xSnxSe

Substitutional alloy Pb_1 − xSn_xSe is a new class of electronic materials called topological crystalline insulators, which at the temperature range from 0 K to 300 K exhibit topological state at compositions in the range 0.18 < x < 0.40 (in the rock-salt structure). In this report, we present a secondary ion mass spectrometry (SIMS) analysis technique to provide accurate Pb and Sn composition based on the measurement of PbCs⁺ and SnCs⁺ cluster ions intensities. Studies of Pb_1 − xSn_xSe bulk samples with various values of x show that x/(1 − x) is linear in relation to the intensity ratio of PbCs⁺/SnCs⁺ over the range from x = 0.15 to x = 0.41. This technique allows us to obtain an accurate Sn content for multilayered heterostructures, quantum wells containing Pb_1 − xSn_xSe with different x values for each layer.     

Configurational and conformational preferences in stereoselective acylations of <Emphasis Type="Italic">N</Emphasis>-methyl-1,3-diaminopropane with acyl chlorides

Evidence for a stereoinduction profile of the reaction of N-methyl-1,3-diaminopropane with acyl chlorides has been provided. A possibility to engage in intramolecular CH₂⋯HN and Cl⋯H-N interactions and the proton migration process to the methylamino group leads to the E secondary amides carrying the N⋯H⁺⋯N or N-H⋯N bridges, that show unusual spectroscopic images. Empirical relations between the Δδ _C chemical shift differences, the polarizability of the CO(S) groups and hydrogen bonding strength have been found. Both ¹H-¹⁵N-GHSQC and GHMBC experiments provide insight into the nature of hydrogen bonding and confirm the cyclic array of atoms.     

Similarities and differences in the electron ionization-induced fragmentation of structurally related N-alkoxymethyl lactams and sultams

Unimolecular fragmentation patterns of the molecular ions of selected lactams and sultams bearing alkoxymethyl group at the nitrogen atom were studied. The main common fragmentation reaction observed for all compounds studied in this work is the elimination of an aldehyde molecule. This reaction is considered to proceed via two different mechanisms. For lactams, hydrogen rearrangement within an alkoxymethyl group is observed, which leads to the appropriate N-methyl derivatives. For sultams, transfer of the methyl group to the nitrogen and oxygen atoms, proceeding through an ion-neutral complex, dominates. Another important fragmentation channel characteristic exclusively for lactams is the loss of an alkyl radical. This process takes place within the N-alkoxymethyl moiety, yielding the appropriate protonated ion of N-formyllactams. This process is accompanied by relatively high kinetic energy release.     

Electronic structure and vibrational spectra of cis-diammine(orotato)platinum(II), a potential cisplatin analogue: DFT and experimental study

Orotic acid (vitamin B₁₃) is a key intermediate in biosynthesis of the pyrimidine nucleotides in living organisms, moreover, it may serve as the biological carrier for some metal ions. cis-Diammine(orotato)platinum(II), cis-[Pt(C₅H₂N₂O₄)(NH₃)₂] can be considered as a new potential cisplatin analogue. The FT-Raman and FT-IR spectra of the title complex are reported, for the first time. The molecular structure, vibrational frequencies, and the theoretical infrared and Raman intensities have been calculated by the density functional mPW1PW91 method. The detailed vibrational assignment has been made on the basis of the calculated potential energy distribution. The theoretically predicted IR and Raman spectra show very good agreement with experiment. Natural bond orbital (NBO) analyses were performed for cisplatin, carboplatin and the title complex. The results provided new data on the nature of platinum–ligand bonding in these compounds. Strong intramolecular hydrogen bond between the orotate ligand and the coordinated ammonia group stabilizes the structure of the platinum(II) complex. Thus, it is suggested that the orotate ligand in the title complex is more inert to the substitution reactions than the chloride ligands in cisplatin.