Weighted Hardy inequalities

For bounded Lipschitz domains D in it is known that if 1<p<∞, then for all β[0,β₀), where β₀=p−1>0, there is a constant c<∞ with

for all . We show that if D is merely assumed to be a bounded domain in that satisfies a Whitney cube-counting condition with exponent λ and has plump complement, then the same inequality holds with β₀ now taken to be . Further, we extend the known results (see [H. Brezis, M. Marcus, Hardy's inequalities revisited, Dedicated to Ennio De Giorgi, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 25 (1997–1998) 217–237; M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, A. Laptev, A geometrical version of Hardy's inequality, J. Funct. Anal. 189 (2002) 537–548; J. Tidblom, A geometrical version of Hardy's inequality for W^1,p(Ω), Proc. Amer. Math. Soc. 132 (2004) 2265–2271]) concerning the improved Hardy inequality

c=c(n,p), by showing that the class of domains for which the inequality holds is larger than that of all bounded convex domains.     

Influence of the charge of surface states on the characteristics of mis transistors made of p-type indium antimonide

An experimental investigation was made of metal-insulator-semiconductor transistors with thick insulator and long channel and made of single-crystal p-type InSb (78° K). An empirical relation was obtained for the output drain conductance in the case of carrier degeneracy in the n-type channel. The parameters of the InSb surface after etching were determined.Translated from Izvestiya Uchebnykh Zavedenii, Fizika, No. 4, pp. 84–88, April, 1980.     

Effect of operating parameters on noise emission from individual road vehicles

A noise survey has been undertaken on over 1000 vehicles operating on public roads. By the use of a remote device, vehicle velocity and acceleration have been measured and related to the instantaneous sound pressure level emission from the vehicle. The relationship is expressed in terms of A-weighted sound pressure level as a function of both velocity and acceleration. Octave band sound pressure levels are also expressed as functions of these variables. Light and heavy vehicle groups are considered separately.     

Electrostatic potential of a point charge lattice having lamina geometry

The Coulomb potential energy of a lattice of point charges having infinite extension in two dimensions only is evaluated using an Ewald-like transformation. An exponential rather than a Gaüssian charge spreading function is used. The derived expansion is rapidly convergent.     

Identification of cracks in welded joints of complex structures

The problem of the influence of a crack in a welded joint on the dynamic behaviour of a structural member is discussed in this work. Analytical and experimental investigation gave the relation between the change in natural frequency of vibration of a cantilever beam and the crack depth that appears at the built-in edge which is clamped by way of a weld. Measurement of the change of the natural frequency of the beam thus can give information for crack appearance and furthermore make possible the estimation of its depth. The results have been used to determine the behaviour of beams with different boundary conditions and can be extended to formed structures with complicated geometries.     

Mixed valence polyiodides from tetraphenyldithiapyranylidene: Crystalline structure and optical properties

Two conducting polyiodide salts have been obtained by direct oxidation of the donor DIPSØ₄ by iodine. These salts are characterized by X-ray diffraction, Raman and optical spectroscopy. The nature of iodine species is determined and the degree of charge transfer is evaluated.     

Measurement of the proton NMR field shift in aqueous solutions containing Cu2+, Cr3+, Fe3+ and Mn2+ ions

There are presented measurements of the NMR field shifts for aqueous protons in aqueous solutions containing paramagnetic inorganic compounds of Cu²⁺, Cr³⁺, Fe³⁺ and Mn²⁺ ions. The measurements have been performed on samples in the form of transversally magnetized long cylinders using both the internal and external NMR standards. The experimentally determined shifts are related to the NMR field position of protons in pure water. The results for demagnetizing shifts are compared with the data which were computed from the magnetic susceptibility values (measured by magnetostatic method), the chemical shifts are compared with the results of other authors. Results of measurements indicate a small chemical shift of internal standards in some solutions.     

Thermal lensing of laser beams in optically transmitting materials

Detailed numerical computations of thermal lensing in optically transmitting materials are carried out. The time evolution of the transmitted beam intensity, revealing defocusing and degradation effects, is displayed for a variety of materials, under a variety of geometrical configurations and operating conditions. While the degradation is monotonic with increasing time or incident power for materials with small induced birefringence, it may display an oscillatory character when birefringence effects are large. From the intensity degradation, criteria are formulated for rating optical performance of materials under transient and steady-state conditions. Ratings are obtained for a variety of transmitting materials at 10.6 μm. As a class, ionic materials are found to substantially outperform semiconductors and glasses at 10.6 μm.     

Luminescence of Mn ions in ordered and disordered LiAl5O8

The phosphorescence and excitation spectra of Mn ions in the ordered and disordered phases of LiAl₅O₈ have been measured. In both phases Mn²⁺ ions substitute for Al³⁺ ions in two different tetrahedral sites of the LiAl₅O₈ lattice. In both sites in the ordered phase, sharp zero-phonon transitions have been observed in the low temperature phosphorescence and excitation spectra - these transitions were considerably broadened in the disordered phase due to crystal field inhomogeneity in that phase. The deviation from neutrality caused by the Mn²⁺ ions in the ordered phase is largely compensated by Mn⁴⁺ ions occupying octahedral Al³⁺ sites. On disordering, a large proportion of Mn⁴⁺ is reduced to Mn²⁺, while the remainder takes up a site with a higher proportion of Li⁺ ions as next nearest neighbours. This leads to an increase in the ionicity of the Mn⁴⁺ site in the disordered phase and hence to a larger value of the Racah parameter B.     

The out-of-plane vibrational modes of chlorobenzene in its ground and first singlet excited states

The study of 2699 Å electronic band system of chlorobenzene has been extended to extract out all the six b₁ and three a₂ modes in both the ground state (^eA₁) and the electronically excited first singlet state (^eB₂). The procedure of the extraction of these modes on the basis of observed sequences, cross-sequences, and overtones has especially been elaborated. Strong Fermi interaction has been observed between the vibrational level ν′_6b and combination level ν′_16a + ν′_16b in ^eB₂ state. The uniqueness of the assignments of the modes has been critically discussed.