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Problem of focusing and the asymptotics of the spectral function of the Laplace-Beltrami operator. I
The connection between the asymptotics of the spectral function and the formal shortwave expansion of the solution of the problem of the asymptotics of the Green function near a geodesically concave boundary of a two-dimensional surface is considered in the paper. 相似文献
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B. M. Levitan 《Mathematische Nachrichten》1995,176(1):179-198
We offer a new proof of a special Tauberian theorem for Fourier type integrals. This Tauberian theorem was already considered by us in the papers [1] and [2]. The idea of our initial proof was simple, but the details were complicated because we used Bochner's definition of generalized Fourier transform for functions of polynomial growth. In the present paper we work with L. Schwartz's generalization. This leads to significant simplification. The paper consists of six sections. In Section 1 we establish an integral representation of functions of polynomial growth (subjected to some Tauberian conditions), in Section 2 we prove our main Tauberian theorems (Theorems 2.1 and 2.2.), using the integral representation of Section 1, in Section 3 we study the asymptotic behavior of M. Riesz's means of functions of polynomial growth, in Sections 4 and 5 we apply our Tauberian theorems to the problem of equiconvergence of eigenfunction expansions of Sturm-Liouville equations and expansion in ordinary Fourier integrals, and in Section 6 we compare our general equiconvergence theorems of Sections 4 and 5 with the well known theorems on eigenfunction expansions in classical orthogonal polynomials. In some sense this paper is a re-made survey of our results obtained during the period 1953-58. Another proof of our Tauberian theorem and some generalization can be found in the papers [3] and [4]. 相似文献
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Self-injection length in La0.7Ca0.3MnO3-YBa2Cu3O7-δ ferromagnet-superconductor multilayer thin films
We have carried out extensive studies on the self-injection problem in barrierless heterojunctions between La0.7Ca0.3MnO3 (LCMO) and YBa2Cu3O7-δ (YBCO) thin films. The heterojunctions were formed in situ by sequentially growing LCMO and YBCO films on 〈100〉 LaAlO3 (LAO) substrate using a pulsed laser deposition (PLD) system. YBCO micro-bridges with 64 μm width were patterned both on
the LAO (control) and LCMO side of the substrate. Critical current, I
c, was measured at 77 K on both the control side as well as the LCMO side for different YBCO film thickness. It was observed
that while the control side showed a J
c of ∼ 2 × 106 A/cm2, the LCMO side showed about half the value for the same thickness (1800 ?). The difference in J
c indicates that a certain thickness of YBCO has become ‘effectively’ normal due to self-injection. From the measurement of
J
c at two different thicknesses (1800 ? and 1500 ?) of YBCO films both on the LAO as well as the LCMO side, the value of self-injection
length (at 77 K) was estimated to be ∼ 900 ?. To the authors’ best knowledge, this is the first time that self-injection length
has been quantified. A control experiment carried out with LaNiO3 deposited by PLD on YBCO did not show any evidence of self-injection. 相似文献
7.
Yu. S. Levitan I. P. Nazarenko I. G. Panevin 《Journal of Applied Mechanics and Technical Physics》1975,16(2):270-275
The results of calculations of the temperature profiles and volt-ampere characteristics of a long cylindrical argon arc in a longitudinal uniform magnetic field are presented. The calculation was made for the following parameters: pressure p =0.1–10.0 atm; temperatures T = 1000-20,000°K; magnetic field induction B =0-10 T; diameter of cylindrical channel d = 1.0 cm. It is shown that for strongly radiating arcs (p1.0 atm) the temperature profiles become more inflated with an increase in the magnetic field, while for weakly radiating arcs (p 0.1 atm) the appearance of loops in the volt-ampere characteristics is typical for certain conditions (14,000T20,000°K, B1.0 T), indicating the impossibility of arcing under these conditions.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 147–153, March–April, 1975. 相似文献
8.
Study of magnetoresistance and conductance of bicrystal grain boundary in La0.67Ba0.33MnO3 thin film
La0.67Ba0.33MnO3 (LBMO) thin film is deposited on a 36.7°C SrTiO3 bicrystal substrate using laser ablation technique. A microbridge is created across bicrystal grain boundary and its characteristics
are compared with a microbridge on the LBMO film having no grain boundary. Presence of grain boundary exhibits substantial
magnetoresistance ratio (MRR) in the low field and low temperature region. Bicrystal grain boundary contribution in MRR disappears
at temperature T>175 K. At low temperature, I-V characteristic of the microbridge across bicrystal grain boundary is nonlinear. Analysis of temperature dependence of dynamic
conductance-voltage characteristics of the bicrystal grain boundary indicates that at low temperatures (T<175 K) carrier transport across the grain boundary in LBMO film is dominated by inelastic tunneling via pairs of manganese
atoms and tunneling through disordered oxides. At higher temperatures (T>175 K), magnetic scattering process is dominating. Decrease of bicrystal grain boundary contribution in magnetoresistance
with the increase in temperature is due to enhanced spin-flip scattering process. 相似文献
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Molar extinction coefficients of some carbohydrates viz. l-arabinose (C5H10O5), d-glucose (C6H12O6), d-mannose (C6H12O6), d-galactose (C6H12O6), d(-) fructose (C6H12O6) and maltose (C12H24O12) in aqueous solutions have been determined at 81, 356, 511, 662, 1173 and 1332 keV by gamma ray transmission method in a
narrow beam good geometry set-up. These coefficients have been found to depend upon the photon energy following a 4-parameter
polynomial. These extinction coefficients for different sugars having the same molecular formula have same values varying
within experimental uncertainty. Within concentration ranges studied, Beer-Lambert law is obeyed very well. 相似文献