On the representation of functions by Dirichlet double series

We consider the problem of representing regular functions of two complex variables by Dirichlet double series with complex exponents.Translated from Matematicheski Zametki, Vol. 7, No. 1, pp. 53–61, January, 1970.     

Structural phase states and properties of the layer surfaced on low-carbon steel with Fe‒C‒Cr‒Nb‒W powder-core wire followed by electron-beam processing

Structural phase states and tribological properties of the coating surfaced onto Hardox 450 martensite low-carbon steel with powder wire Fe?C?Cr?Nb?W and modified by subsequent electron-beam processing are studied by methods of modern physical material science. It is shown that irradiation of ~5 thick surfaced layer with high intensity pulsed electron beams results in the formation of ~20 μm thick surface layer with the master phases of α-Fe and NbC, Fe₃C and M₆C(Fe₃W₃C) carbides. The main difference of the surface layer modified with electron-beam processing from the unmodified volume of the surfacing is the morphology and dimensions of the second phase inclusions. In the modified layer of the surfacing the inclusions have smaller dimensions and are located in the form of interlayers along the grain boundaries. In unmodified surfacing the particles of the faceted shape located chaotically in the grain volume are the basic morphological type of the inclusions. It is noted that the small value of crystal lattice Nb parameter observed in the experiment may be caused by the high level of vacant interstitial sites having the smaller size in comparison with the occupied interstitial sites. It is established that wear resistance of the surfaced layer after electron-beam processing increases more than 70-fold relative to wear resistance of Hardox 450 steel and friction coefficient decreases significantly (~3-fold).     

Influence of contact potential difference and electric potential on the microhardness of metals

The effect of the electric potential on the microhardness of aluminum, zirconium, and ferrosilicon was studied experimentally. The effect of the proper electric potential applied to a sample is compared with the effect of the potential induced by the contact potential difference upon contact with metals with a different electron work function. These two types of electrical action are revealed to be qualitatively equivalent to each other. It is established that these effects can markedly (up to 15%) change the microhardness of the metals.     

N‐Methylbenzoazacrown ethers with the nitrogen atom conjugated with the benzene ring: the improved synthesis and the reasons for the high stability of complexes with metal and ammonium cations

An improved method for the synthesis of formyl derivatives of N‐methylbenzoazacrown ethers is proposed. They are prepared in up to 68% yields over fewer steps and with a much shorter time required for the last step. The stability constants of complexes formed by N‐methylbenzoazacrown ethers and their structural analogs with alkali metal, alkaline‐earth metal and ammonium cations were determined by ¹H NMR titration in CD₃CN. High stability of complexes of N‐methyl derivatives of benzoazacrown ethers is demonstrated, comparable with or even exceeding the stability of benzocrown‐ether complexes and markedly exceeding the stability of complexes of phenylazacrown ethers with the same macrocycle size. The structures of azacrown ethers and their complexes with Ba(ClO₄)₂ were studied by X‐ray diffraction. A high degree of pre‐organization of N‐methylbenzoazacrown ethers toward the formation of complexes with metal and ammonium cations was noted, which is due to the clear‐cut pyramidal geometry of the nitrogen atom and the orientation of the lone electron pairs (LEPs) of most heteroatoms towards the centre of the macroheterocycle. Copyright © 2009 John Wiley & Sons, Ltd.     

Stereospecific [2+2] autophotocycloaddition in the dimeric complex of 18-crown-6 ether styryl dye bearing N-(3-ammoniopropyl) substituent

New 18-crown-6 ether styryl dye of the 4-pyridine series bearing N-(3-ammoniopropyl) substituent has been synthesized. In MeCN, the dye forms a stable dimeric complex of the syn-head-to-tail type due to the complexation of the ammonium group of one molecule with the crown ether fragment of another. In the dimeric complex, the ethylene bonds of the molecules are close in space and antiparallel, which promotes an efficient stereospecific [2+2] autophotocycloaddition to yield the only rctt-isomer of 1,2,3,4-tetrasubstituted cyclobutane. The cyclobutane derivative structure was confirmed by NMR spectroscopy and X-ray diffraction.     

Electron paramagnetic resonance of three-spin nitroxide-copper(II)-nitroxide clusters coupled by a strong exchange interaction

The complex of Cu(2+) hexafluoroacetylacetonate with two pyrazol-substituted nitronyl nitroxides represents an unusual exchange-coupled three-spin system. The antiferromagnetic exchange coupling, which already atT < 150 K is larger than the thermal energy kT, induces the transition from a total spin state S = (3)/(2) to a state S = (1)/(2) and produces static spin polarization. Anomalous electron paramagnetic resonance (EPR) spectra of an S = (1)/(2) state were detected experimentally and described theoretically. The effective g factor of the three-spin system is smaller than 2, despite the fact that all the individual components have g > 2. The observed signals with g < 2 are highly informative and can be employed for determination of the sign and value of the exchange interaction in three-spin nitroxide-copper-nitroxide clusters.     

Causes of Ultrasound Doppler Twinkling Artifact

Ultrasound Doppler twinkling artifact is analyzed. It usually appears as a frequent color alteration in the region of hyperechoic objects. Its noiselike spectrum can also be seen in spectral Doppler mode. Physicians use twinkling artifact as a clinical sign for kidney-stone and soft-tissue calculi detection. The advantageous peculiarity of this study is that the experiments were conducted utilizing raw signals obtained from a custom ultrasonic machine and a specially developed phantom. The phantom contained specimens with known qualities, allowing for reproducible and predictable results. The experiments revealed evidence for two physical causes of twinkling artifact, which were associated with two unique Doppler signals. The research laid the foundation for the new reflected-signal model introduced and used throughout this paper.     

Photophysical properties of aqueous solutions of a styryl dye in the presence of cucurbit[<Emphasis Type="Italic">n</Emphasis>]uril (<Emphasis Type="Italic">n</Emphasis> = 5, 6, 8)

Photophysical properties of aqueous solutions of the styryl dye 4-[(E)-2-(3,4-dimethoxyphenyl)-1-ethylpyridinium] perchlorate (1) in the presence of cucurbit[n]urils (CB[n]; n = 5, 6, 8) have been studied by fluorescent spectroscopy methods. The fluorescence intensity of a 10^–6 mol L^–1 solution of 1 increases by a factor of 12.6 upon the formation of 1 : 1 inclusion complexes with CB[6] or 1.3 in complexes with CB[8]. Upon the formation of inclusion complexes, the average lifetime of the electronically excited state of 1 increases to about 1 ns for both CB[6] and CB[8]. On the basis of fluorescence anisotropy measurements, the rotational relaxation times were estimated to be 408, 314, and 183 ps for the complexes with CB[6], CB[8], and for unbound 1, respectively. Using the fluorescence titration method developed for the case of poorly soluble cavitands, the binding constant of 1 with CB[6] was determined to be 1.1 × 10⁵ L mol^–1. The addition of CB[5] does not lead to changes in the photophysical properties of a solution of 1, indicating the absence of complexes between CB[5] and 1. It has been found on the basis of the experimental data that the fluorescence rate constant of 1 decreases about twice in the complex with CB[8], but doubles in the complex with CB[6].     

Structure and Properties of SnO2–In2O3–Ag–N Coatings Formed by a Complex Method on Copper

Russian Physics Journal - The aim of this work is to analyze the structure and properties of a coating of the SnO2–In2O3–Ag–N composition formed on copper by a complex method...