Complex potentials: bound states, quantum dynamics and wave operators

Schr\"odinger operator on half-line with complex potential and the corresponding evolution are studied within perturbation theoretic approach. The total number of eigenvalues and spectral singularities is effectively evaluated. Wave operators are constructed and a criterion is established for the similarity of perturbed and free propagators.Comment: 9 page

Spectral multiplicity for powers of weakly mixing automorphisms

We study the behavior of maximal multiplicities $mm (R^n)$ for the powers of a weakly mixing automorphism $R$. For some special infinite set $A$ we show the existence of a weakly mixing rank-one automorphism $R$ such that $mm (R^n)=n$ and $mm(R^{n+1}) =1$ for all $n\in A$. Moreover, the cardinality $cardm(R^n)$ of the set of spectral multiplicities for $R^n$ is not bounded. We have $cardm(R^{n+1})=1$ and $cardm(R^n)=2^{m(n)}$, $m(n)\to\infty$, $n\in A$. We also construct another weakly mixing automorphism $R$ with the following properties: $mm(R^{n}) =n$ for $n=1,2,3,..., 2009, 2010$ but $mm(T^{2011}) =1$, all powers $(R^{n})$ have homogeneous spectrum, and the set of limit points of the sequence $\{\frac{mm (R^n)}{n} : n\in \N \}$ is infinite

HIERARCHICAL ONTOLOGY OF THE BASIC CONCEPTS OF HARDWARE, INFORMATION AND MANAGEMENT SUPPORT FOR THE CONDITION OF A CARDIAC SURGICAL SUTURE

The proposed topic includes the development of classification systems and structuring of the basic concepts associated with cardiac surgical sutures to ensure the expected process of information management and quality care for patients with cardiovascular diseases

MHD alpha^2-dynamo, Squire equation and PT-symmetric interpolation between square well and harmonic oscillator

It is shown that the alpha^2-dynamo of Magnetohydrodynamics, the hydrodynamic Squire equation as well as an interpolation model of PT-symmetric Quantum Mechanics are closely related as spectral problems in Krein spaces. For the alpha^2-dynamo and the PT-symmetric model the strong similarities are demonstrated with the help of a 2x2 operator matrix representation, whereas the Squire equation is re-interpreted as a rescaled and Wick-rotated PT-symmetric problem. Based on recent results on the Squire equation the spectrum of the PT-symmetric interpolation model is analyzed in detail and the Herbst limit is described as spectral singularity.Comment: 21 pages, LaTeX2e, 10 figures, minor improvements, references added, to appear in J. Math. Phy

Синтез азометинов на основе производных 4-аминобензолсульфамида

Synthesis of (£)-azomethines, derivatives of 4-aminobenzenesulfonamide (Streptocidum), by condensation of substituted vanillin-like benzaldehydes with streptocidum in methanol, has been described.Представлен синтез функционально замещенных ароматических (Е)-азометинов - производных 4-аминобензол-сульфамида (стрептоцида), полученных конденсацией замещенных бензальдегидов ванилинового ряда и стрептоцида в среде метанола с выходом 70-82%

Group measure space decomposition of II_1 factors and W*-superrigidity

We prove a "unique crossed product decomposition" result for group measure space II_1 factors arising from arbitrary free ergodic probability measure preserving (p.m.p.) actions of groups \Gamma in a fairly large family G, which contains all free products of a Kazhdan group and a non-trivial group, as well as certain amalgamated free products over an amenable subgroup. We deduce that if T_n denotes the group of upper triangular matrices in PSL(n,Z), then any free, mixing p.m.p. action of the amalgamated free product of PSL(n,Z) with itself over T_n, is W*-superrigid, i.e. any isomorphism between L^\infty(X) \rtimes \Gamma and an arbitrary group measure space factor L^\infty(Y) \rtimes \Lambda, comes from a conjugacy of the actions. We also prove that for many groups \Gamma in the family G, the Bernoulli actions of \Gamma are W*-superrigid.Comment: Final version. Some extra details have been added to improve the expositio

СИНТЕЗ (E,E)-АЗОМЕТИНОКСИМОВ НА ОСНОВЕ ОКСИМА 4-АМИНОАЦЕТОФЕНОНА

4-Aminoacetophenone oxime is convenient and accessible reagent for chemical modification of substituted aromatic aldehydes to produce ligands for complexation with transition metals. By the reaction of 4-aminoacetophenone oxime with aldehydes vanillyl series by boiling in absolute methanol in the presence of catalytic amounts of glacial acetic acid, (E,E)-azomethyneoximes with 70–85 % yields were synthesized. By the reaction of 4-aminoacetophenone oxime with 9-phenanthrene carboxaldehyde, ferrocene carboxaldehyde, 5-phenylisoxazole-3-carboxaldehyde and 5-(p-tolyl)isoxazole- 3-carboxaldehyde, corresponding (E,E)-azomethineoximes with 77–84 % yield were obtained. By acylation of the (E)-1-{4-(E)-benzo[d][1,3]dioxol-5-ylmethyleneaminophenyl}ethan-1-one oxime in a solution of dry diethyl ester in the presence of triethylamine, corresponding ester was synthesized with 84 % yield. By quantum chemical calculations using DFT method using level B3LYP1 / MIDI using the theory GAMESS software package and a MIDI basic set, we defined the most thermodynamically stable isomers of the synthesized compounds. In the process of calculations a full optimization of all geometric parameters to achieve a minimum total energy (E,E)-, (E,Z)-, (Z,E)- and (Z,Z)-azomethineoximes was carried out.Оксим 4-аминоацетофенона является удобным и доступным реагентом для химической модификации замещенных ароматических альдегидов с целью получения лигандов для комплексообразования с переходными металлами. Взаимодействием оксима 4-аминоацетофенона с альдегидами ванилинового ряда, в среде кипящего абсолютного метанола в присутствии каталитических количеств ледяной уксусной кислоты были синтезированы (E,E)-азометины с выходами 70–85 %. Взаимодействием 4-аминоацетофенона с 9-фенантренкарбальдегидом, ферроценкарбальдегидом, 5-фенилизоксазол-3-карбальдегидом и 5-(п-толил)изоксазол-3-карбальдегидом были получены соответствующие (E,E)-азометиноксимы c выходом 77–84 %. Ацилированием оксима (E)-1-{4-(E)-бензо[d][1,3]диоксол-5-илметиленаминофенил}этан-1-она хлорангидридом 4,5-дихлоризотиазол-3-карбоновой кислоты в растворе сухого диэтилового эфира в присутствии триэтиламина был синтезирован соответствующий сложный эфир с вы- ходом 84 %. Путем квантово-химических расчетов с использованием метода DFT с применением уровня теории B3LYP1/MIDI, программного пакета GAMESS и базисного набора MIDI установлены наиболее термодинамически устойчивые изомеры ряда синтезированных соединений. При расчетах проводили оптимизацию всех геометрических параметров до достижения минимумов полных электронных энергий (E,E)-, (E,Z)-(Z,E)- и (Z,Z)-азометиноксимов