The Problem of the Pointwise Fourier Inversion for Piecewise Smooth Functions of Several Variables

We study the pointwise convergence problem for the inverse Fourier transform of piecewise smooth functions, i.e., whether S_rD f (\bx) ? f (\bx)S_{\rho D} f (\bx) \to f (\bx) as r? ￥\rho \to \infty . r? ￥\rho \to \infty . Here for \bx,\bxi ? \Rn\bx,\bxi \in \Rn S_rDf(\bmx)=\dsf1(2p)^n/2\intli_rD [^(f)](\bxi) e^{\dst iá\bmx,\bxi?} d\bxi . S_{\rho D}f(\bm{x})=\dsf1{(2\pi)^{n/2}}\intli_{\rho D} \widehat{f}(\bxi) e^{\dst i\langle\bm{x},\bxi\rangle} d\bxi~. is the partial sum operator using a convex and open set DD containing the origin, and rD={ r\bxi:\bxi ? D }\rho D=\left\{ \rho \bxi:\bxi\in D \right\}.     

Electrical and Spectral Properties of Complexes of Pyridine N-Oxide Derivatives with Iron Trichloride

Complexes (1 : 2) of iron trichloride with N-oxides of pyridine, picolines, and 2,6-lutidine were studied by optical spectroscopy, dielectrometry, and conductometry. In solid complexes, three crystalline phases are in equilibrium; the nuclei of each of these phases can be detected in the oily state. The enthalpies of the coordination bonds are different in different phases. One of the phases of the 3-picoline N-oxide complex shows a strong orientation disorder; disappearance of the short-range order causes weakening of the coordination bonds by 1.6 kcal. The thermal motion of free base molecules in two phases of the 2,6-lutidine N-oxide complex is gaslike. In the solid phase of this complex, there is a strong distribution of the relaxation frequencies; the mean relaxation frequency is close to 220 Hz. Upon irradiation of the complexes with solar or UV light, specific coloration centers can form. Weak alternating electric fields initiate in some compounds reversible chemical reactions. The intermolecular and charge equilibria in the compounds are very labile; the energy of generation of the low-temperature electrical conductivity in them is close to 0.9 eV.     

InclusiveK *+(890),K *+(1430) and\bar K^{ * - } (890) production inK + p interactions at 32 GeV/c

We present final results on inclusive production ofK ^*+(890),K ^*+(1430) andK ^*?(890) in \(\bar K^ + p\) interactions at 32 GeV/c, based on a statistics of ～27 events/μb. Total cross sections,p _T -andx-dependence of inclusive distributions are compared with experiments at other energies and with the Lund fragmentation model. Spin density matrix elements of theK ^*+(890) are also discussed. The results suggest that “recombination” of both initial state valence quarks \(\bar s\) andu of theK ⁺ intoK ^*+(890), responsible in the Lund model for ～45% of theK ^*+(890) cross section, is strongly suppressed.     

Inclusive production of non-strange resonances inK − p interactions at 32 GeV/c

New data on the inclusive production of the non-strange resonances ?⁰(770), ω(783), ?(1020) andf(1270) inK ^? p interactions at 32 GeV/c are presented. The inclusive production cross sections are equal to (4.32±0.72) mb, (3.7±1.4) mb, (0.65±0.10) mb and (0.91±0.35) mb respectively. Estimates of the topological cross sections are also obtained. The invariant and non-invariantx-distributions for the vector mesons ?⁰ and ? indicate the prevalence of forward resonance production in the c.m. system. For the tensorf-meson the rapidity andx-distributions are presented. Thet′-distributions for ?⁰, ?, andf have exponential slopes of 0.6±0.1 GeV^?2, 1.2±0.2 GeV^?2, and 0.8±0.5 GeV^?2 respectively. The exponential slope ofp _T ² -distribution of thef-meson is equal to (2.3±0.5) GeV^?2.     

The acoustic field excited by flexural vibrations of an elastic plate with a circular inclusion

The acoustic field excited by flexural vibrations of a thin elastic plate and the perturbations of this field caused by a homogeneous circular inclusion with other elastic properties are considered. Because the density of air widely differs from that of a metal, this problem can be solved with fair accuracy in two steps: first, by considering the vibrations of the plate in a free space, and, then, by calculating the acoustic field excited by the field of plate’s vertical deflections. The main results of this work are the asymptotic expressions for the far acoustic field excited by each of the Fourier components F _m (r)cosmφ of the flexural wave scattered by the inclusion.     

Scatter of a plane elastic wave by a rough crack edge

The aim of this paper is to investigate the effect of roughness of the crack edge on the reliability of ultrasonic NDE (nondestructive evaluation). The rough crack face has been modeled by earlier authors as a mosaic of large triangular facets and the effect of this roughness has been simulated using the Kirchhoff approximation. We now augment this model by the rough crack edge that is a polygonal line. We then model the scattered field using the Isakovich approach, originally developed for modeling scatter from rough surfaces, also with the help of the Kirchhoff approximation.     

Optical properties of teflon at high temperatures

Journal of Applied Mechanics and Technical Physics - When considering thermal decomposition of thermoplastics by a-thermal flux, the case wherein radiation is the dominant heat-transfer mechanism...