Abnormal reactions of 2‐methoxy‐4,9‐dimethyl‐1‐nitroacridine with selenous acid and selenium(IV) oxide. Synthesis of 1H‐selenopheno[2,3,4‐k,l]acridine‐1‐one: A new seleno‐containing ring system

Unusual course of the reaction was revealed on the oxidation of functionally substituted acridine containing the activated methyl groups by well‐known oxidants, such as selenous acid and selenium(IV) oxide. Treatment of 2‐methoxy‐4,9‐dimethyl‐1‐nitroacridine ( 5 ) with an excess of H₂SeO₃ in boiling ethanol gave a mixture of the normal reaction products, 2‐methoxy‐4‐methyl‐1‐nitro‐9‐formylacridine ( 11 ) (isolated yield 29%) and 2‐methoxy‐4‐methyl‐1‐nitroacridine‐9‐carboxylic acid ( 12 ) (36%), together with an abnormal product, 3‐methoxy‐5‐methyl‐1H‐selenopheno[2,3,4‐k,l]acridine‐1‐one ( 13 ) (21%), which is the first example of a new seleno‐containing ring system. With the use of SeO₂ the yield of selenolactone 13 was much lower. J. Heterocyclic Chem., 2011.     

Ab initio calculations of surface electronic states in indium oxide

A slab approach in the framework of ab initio calculations was applied to study surface electronic states in In₂O₃ crystal. Density functional theory (DFT) calculations were carried out employing the WIEN 2k code and using the full potential method with Augmented Plane Waves + local orbitals (APW+lo) formalism. Total and partial DOS (Density of States) were calculated for In and O atoms in two upper (110) surface layers. Comparison of total and partial DOS allowed determining a contribution of electronic states of different In and O surface atoms into formation of surface electronic spectra and corresponding chemical bonds. A dominant ionic character of chemical bonds in In₂O₃ is found. Calculations were performed for three slab models with different geometry parameters. It was shown that an optimal ratio between the whole vertical size of a supercell and the vertical size of atomic cluster has to be chosen. The size of vacuum region in the slab model influences significantly on the reliability of calculated characteristics of the surface electronic structure. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Photochemistry of dithiocarbamate Cu(II) complex in CCl4

Laser pulse photolysis was used to study the nature and reactions of intermediates in the photochemistry of the flat dithiocarbamate complex Cu(Et(2)dtc)(2) in CCl(4). A nanosecond laser pulse (355 nm) is shown to induce intermediate absorption bands of bivalent copper complex whose coordination sphere contains a dithiocarbamate radical Et(2)dtc(?) and a chloride ion at the axial position ([(Et(2)dtc)Cu(Et(2)dtc(?))Cl(a)]). At room temperature during some microseconds after the laser pulse, this intermediate interacts with the initial complex to form presumably a dimer [Cu(2)(Et(2)dtc)(3)(Et(2)dtc(?))Cl]. The latter vanishes in the second-order reaction. Analysis of kinetic and spectral features gives the arguments for the formation of a cluster [Cu(2)(Et(2)dtc)(3)Cl-tds-Cu(2)(Et(2)dtc)(3)Cl], which produces a new absorption band at 345 nm. The cluster decomposes in ～5 ms into final products, a binuclear complex [Cu(2)(Et(2)dtc)(3)Cl] and tetraethylthiuramdisulfide (Et(4)tds).     

The inverse spectral problem for a Stieltjes eight-shaped string

We consider a spectral problem generated by the Stieltjes string equation on a metric figure-of-eight graph and the corresponding inverse problem which is stated as follows. Values of the point masses located on one of the loops and the lengths of subintervals on it are given together with the spectrum of the spectral problem on the whole graph, the total length of the second loop and the length of the first subinterval on it, and a certain constant. Values of the masses and the lengths of subintervals on the second loop are to be found. Conditions sufficient for such a problem to be solvable are given in the implicit form. An algorithm for recovering the masses and the subintervals on the second loop is proposed.     

Convex topological algebras via linear vector fields and Cuntz algebras

A realization by linear vector fields is constructed for any Lie algebra which admits a biorthogonal system and for its any suitable representation. The embedding into Lie algebras of linear vector fields is in analogue to the classical Jordan—Schwinger map. A number of examples of such Lie algebras of linear vector fields is computed. In particular, we obtain examples of the twisted Heisenberg-Virasoro Lie algebra and the Schrödinger-Virasoro Lie algebras among others. More generally, we construct an embedding of an arbitrary locally convex topological algebra into the Cuntz algebra.     

Influence of the formation of hot excitons on the quantum efficiency of short-wavelength photoelectric conversion in III–V semiconductors

A new excitonic mechanism for decreasing the quantum efficiency of the photoelectric conversion process in surface-barrier structures is considered. This mechanism involves the formation of hot excitons which have a large ionization energy and are not subject to the influence of the barrier electric field. The spectral dependence of the hot photocarrier losses is derived in an explicit form from experimental data on the basis of a previously proposed model and is analyzed. This dependence has two segments with abrupt increases, which are caused by the formation of excitons in the L and X valleys of the semiconductor. Fiz. Tverd. Tela (St. Petersburg) 40, 944–945 (May 1998)     

Difference schrödinger operators with linear and exponential discrete spectra

Using the factorization method, we construct finite-difference Schrödinger operators (Jacobi matrices) whose discrete spectra are composed from independent arithmetic, or geometric series. Such systems originate from the periodic, orq-periodic closure of a chain of corresponding Darboux transformations. The Charlier, Krawtchouk, Meixner orthogonal polynomials, theirq-analogs, and some other classical polynomials appear as the simplest examples forN = 1 andN = 2 (N is the period of closure). A natural generalization involves discrete versions of the Painlevé transcendents.On leave of absence from the Institute for Nuclear Research, Russian Academy of Sciences, Moscow, Russia.     

On the Friedrichs extension of some block operator matrices

We give a matrix representation for the resolvent of the Friedrichs extension of some semibounded 2×2 operator matrices and study their essential spectrum.