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...     

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.     

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.     

Synthesis, structure, and X-band (9.5 GHz) EPR characterization of the new series of pH-sensitive spin probes: N,N-disubstituted 4-amino-2,2,5,5-tetramethyl-3-imidazoline 1-oxyls

[reaction: see text] An approach to the synthesis of new imidazoline nitroxides bearing an N',N'-disubstituted amidine group is reported. The approach is based on the alkylation of diamagnetic 4-R-amino-1,2,2,5,5-pentamethyl-3-imidazolines with bromoacetic acid ethyl ester; the products of alkylation are further oxidized to the corresponding nitroxides. The approach allows a variety of functional groups to be introduced into the nitroxide molecule structure. Alkylation with bromoacetic acid ethyl ester was found to proceed with high regioselectivity and afford the products of exo-alkylation. The regiochemical assignment is made on the basis of 13C NMR spectra and confirmed by X-ray diffraction study. All of the nitroxides synthesized here were shown to have pH-dependent EPR spectra with pKa ranging from 3.5 to 6.2. For nitroxides 13 bearing the carboxylic group remote to the nitroxide moiety, the changes in isotropic magnetic parameters of EPR spectra due to reversible deprotonation of the carboxylic group were found to be small. For these nitroxides, we demonstrate an alternative approach for pKa determination that is based on measuring the peak-to-peak line width of the EPR spectrum in the presence of the paramagnetic broadening agent potassium ferricyanide. The partition coefficients of nitroxides in octanol/H2O and octanol/phosphate buffer solution mixtures were measured to reveal a range of their lipophilicities.     

Ethylenediaminetetraacetato-monoperoxo complexes of vanadium(V)

Summary The monoperoxo complexes, M₂[VO(HEDTA)(O₂)]· 4H₂O, where M is K⁺ or NH ₄ ⁺ and H₄EDTA is ethylene-diaminetetraacetic acid, were prepared and characterized by Raman and i.r. spectra in the solid state and in aqueous solution. The single crystal X-ray study revealed a pentagonal bipyramidal anion structure with a tetradentate HEDTA(3—) ligand. The decomposition of complexes in aqueous solution to blue vanadium(IV) complexes as end products proceeds via a nonperoxo complex of vanadium.