Finding any given 2‐factor in sparse pseudorandom graphs efficiently

Given an $n$‐vertex pseudorandom graph $G$ and an $n$‐vertex graph $H$ with maximum degree at most two, we wish to find a copy of $H$ in $G$, that is, an embedding $\phi :V\left(H\right)\to V\left(G\right)$ so that $\phi \left(u\right)\phi \left(v\right)\in E\left(G\right)$ for all $uv\in E\left(H\right)$. Particular instances of this problem include finding a triangle‐factor and finding a Hamilton cycle in $G$. Here, we provide a deterministic polynomial time algorithm that finds a given $H$ in any suitably pseudorandom graph $G$. The pseudorandom graphs we consider are $\left(p,\lambda \right)$‐bijumbled graphs of minimum degree which is a constant proportion of the average degree, that is, $\mathrm{\Omega }\left(pn\right)$. A $\left(p,\lambda \right)$‐bijumbled graph is characterised through the discrepancy property: $|e\left(A,B\right)?p|A||B||<\lambda \sqrt{|A||B|}$ for any two sets of vertices $A$ and $B$. Our condition $\lambda =O(p^{2}n/\log n)$ on bijumbledness is within a log factor from being tight and provides a positive answer to a recent question of Nenadov. We combine novel variants of the absorption‐reservoir method, a powerful tool from extremal graph theory and random graphs. Our approach builds on our previous work, incorporating the work of Nenadov, together with additional ideas and simplifications.     

Raman Scattering Enhancement Based on High-Pressure High-Temperature Diamonds†

Journal of Russian Laser Research - We discuss the use of high-pressure high-temperature (HPHT) diamonds for the determination of trace amounts of various Raman active substances. The amount of the...     

Effect of plasma treatment of the dielectric on electroforming of a thin-film MIM system

It was found that when a thin dielectric film is exposed to the plasma of a low-voltage gas discharge, channels with elevated conductivity form in the film and these channels significantly facilitate the subsequent electroforming of the MIM system. It is concluded from the experimental data that even in the case of metallic electrodes highly conducting channels are formed in the dielectric by electronic processes occurring under the conditions of a strong electric field and not by diffusion of the electrode material.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 94–98, October, 1991.     

Resonance phenomena of π-mode forming in multi-element gratings

An analysis of resonances of scattering from multi-element grating formed by a finite number of resonant elements is presented. It has been shown that gratings with three and more elements on its period can support the π-mode. The π-mode of a grating is characterized by the existence of the regions in the vicinity of the grating and along its period where the electromagnetic field has opposite phases. The existence and excitation of the π-mode in finite gratings with resonant cells formed by several scatterers having open cavities have been studied. The particular case of the grating with cells formed by three identical slotted cylinders has been considered in detail. An application of gratings which support the π-mode in electron-vacuum oscillators of millimeter waves for efficient deceleration of electrons and extracting energy from electron beam is discussed.     

On the origin of 1.5 μm luminescence in porous silicon coated with sol–gel derived erbium-doped Fe2O3 films

Sol–gel derived Fe₂O₃ films containing about 10 wt% of Er₂O₃ were deposited on porous silicon by dipping or by a spin-on technique followed by thermal processing at 1073 K for 15 min. The samples were characterized by means of PL, SEM and X-ray diffraction analyses. They exhibit strong room-temperature luminescence at 1.5 μm related to erbium in the sol–gel derived host. The luminescence intensity increases by a factor of 1000 when the samples are cooled from 300 to 4.2 K. After complete removal of the erbium-doped film by etching and partial etching the porous silicon, the erbium-related luminescence disappears. Following this, luminescence at 1.5 μm originating from optically active dislocations (“D-lines”) in porous silicon was detected. The influence of the conditions of synthesis on luminescence at 1.5 μm is discussed.     

Application of Horner–Emmons Olefination to the Crown-Ether Derivatives

An effective synthetic approach to the preparation of a new crown-ether vinylogs involving the Horner–Emmons olefination of carbonyl precursors with the use of C₂- and C₅-phosphonates was proposed. The effects of the conjugation chain length and the nature of the terminal polar functions in the phosphonate reagent on the yield and process stereoselectivity were discussed.     

Oxidation of bridging groups by carboxylate coordinated ligands in palladium clusters

Thermolysis of tetranuclear palladium clusters Pd₄(-Q)₄ Pd₄(-Q)₄(-O₂CR)₄ (Q=CPh₂ or CO;R=Me, CMe₃, Ph, CH₂Cl or CF₃) has been found to involve innersphere oxidation of carbene or carbonyl ligands during which an oxygen atom transfer occurs from the carboxylate group to the carbene or carbonyl ligand. The thermolysis of the carbonyl clusters gives rise to the products of CO₂ insertion into the C–H bond of benzene or toluene used as solvents forming benzoic acid from benzene and a mixture of phenylacetic and toluic acids from toluene. The reaction of [Pd(OAc)₂(PPh₃)]₂ with HCO₂H includes the transfer of an O atom from formate ligand to the P atom and cleavage of the P-Ph bond accompanied by transfer of the Ph group from PPh₃ ligand to the palladium atom. The structure of the complex formed, [Pd(-O₂PPh₂)(C₆H₅)(PPh₃)]₂, has been resolved by X-ray analysis.     

Structural, textural, and electronic properties of a nanosized mesoporous ZnxTi1-xO2-) solid solution prepared by a supercritical drying route

Mesoporous nanosized TiO2 and Zn(x)Ti(1-x)O(2-x) solid solution having a Zn content below 10 mol % with a particles size between 13 and 17 nm are prepared by a template-free sol-gel method followed by high-temperature supercritical drying in 2-propanol. The structural, textural, and electronic properties of the obtained nanomaterials are methodically investigated by using XRD, SEM, TEM, ED, HREM, EDX, ICP-OES, N(2) adsorption-desorption, Raman spectroscopy, and diffuse reflectance UV-vis spectroscopy. It is shown that the proposed synthesis technique leads to the formation of a Zn(x)Ti(1-x)O(2-x) solid solution based on the anatase crystal structure rather than a two-phase sample. High-resolution electron microscopy and electron diffraction indicate that the distribution of zinc atoms over the anatase structure does not lead to a considerable deformation of the crystal structure.