Koplienko Spectral Shift Function on the Unit Circle

The note shows that, for every pair of contractions, a trace formula of Koplienko holds with a summable spectral shift function, see Theorem 1 below. This answers a question by F. Gesztesy, A. Pushnitski, B. Simon (see Zh Mat Fiz Anal Geom 4(1):63–107, 202, 2008, Open Question 11.2).     

Influence of Dopant Incomplete Ionization on the Capacitance of a Reverse-Biased 4H-SiC p+−i−n+ Diode

Technical Physics - The transient process in an RC circuit with a reverse-biased 4H-SiC p+−i−n+ diode serving as a capacitor has been numerically simulated using the SILVACO TCAD...     

On one problem of electrophysics with discontinuous nonlinearity

We consider a conductor heating problem in the following setting: a constant voltage and a constant temperature are maintained on the conductor surface, and the electric conductivity of the material experiences jumps when passing through certain temperatures. Earlier-obtained results for problems with a spectral parameter for equations of elliptic type with discontinuous nonlinearities are applied to this problem of electrophysics. We weaken the conditions imposed on the set of points of discontinuity of the nonlinearity (the electric conductivity of the conductor) occurring in the equation.     

Amplification of wind waves in reservoirs of finite depth

A method for predicting the generation and amplification of waves from the zone of generation to large fetches, where infragravity waves occur in water of finite depth, is developed from a physical model of interaction between a horizontal air flow and a water surface caused by periodic formation of vortices in the viscous air layer. The model describes the origination of multiple frequencies, and the displacement of wave energy to low-frequency region over a fetch.     

Synthesis Based on Electrophilic Selenium Reagents and Acetylenes

Reactions of dicyanodiselenide, selenenyl chlorides and bromides with acetylenes and some further transformations of obtained products have been studied.     

Regioselective heterocyclization of mixed phosphonium-iodonium ylides with acetylenes involving dimethyl acetylenedicarboxylate

Russian Chemical Bulletin - A new approach to the synthesis of λ5-phosphinolines was developed consisting in the reaction of mixed phosphonium-iodonium ylides with acetylenes in the presence...     

A Regioselective Synthesis of Novel Functionalized Organochalcogen Compounds by Chalcogenocyclofunctionalization Reactions Based on Chalcogen Halides and Natural Products

The regioselective synthesis of novel functionalized condensed organochalcogen compounds by chalcogenocyclofunctionalization reactions based on chalcogen halides and the natural products thymol and carvacrol has been developed. The reactions of selenium dibromide with allyl thymol and allyl carvacrol proceeded in methylene chloride at room temperature in the presence of NaHCO₃ affording bis[(7-isopropyl-4-methyl-2,3-dihydro-1-benzofuran-2-yl)methyl] and bis[(4-isopropyl-7-methyl-2,3-dihydro-1-benzofuran-2-yl)methyl] selenides in 90–92% yield. Similar sulfides were obtained in 70–72% yields by the reaction of sulfur dichloride in chloroform under reflux. Trihalotellanes containing the same organic moieties were synthesized from allyl thymol, allyl carvacrol and tellurium tetrachloride or tetrabromide in quantitative yields. Corresponding functionalized ditellurides were prepared in 91–92% yields by the reduction of the trichlorotellanes with sodium metabisulfite in two-phase solvent system. The comparison of reactivity of sulfur, selenium and tellurium halides in chalcogenocyclofunctionalization and distinguishing features of each reaction were discussed.     

High-frequency ultrasonic studies of the structural phase transition in an La<Subscript>0.875</Subscript>Sr<Subscript>0.125</Subscript>MnO<Subscript>3</Subscript> single crystal

The specific features of a phase transition from a disordered orbital state to an ordered orbital state in an La_0.875Sr_0.125MnO₃ single crystal are investigated using acoustic methods at a frequency f = 500 MHz. The phase transition is accompanied by a distortion of MnO₆ octahedra due to the cooperative Jahn-Teller effect and is a first-order phase transition, as judged from the sharp change observed in the damping of acoustic pulses, the acoustic wave velocity, and the temperature hysteresis. It is revealed that the parameters of the acoustic waves change significantly throughout the temperature range of existence of the cooperatively distorted structure. In an external magnetic field, the structural phase transition is shifted toward lower temperatures.