The bitangential inverse spectral problem for canonical systems

The theory of the direct and bitangential inverse input impedance problem is used to solve the direct and bitangential inverse spectral problem. The analysis of the direct spectral problem uses and extends a number of results that appear in the literature. Special attention is paid to the class of canonical integral systems with matrizants that are strongly regular J-inner matrix valued functions in the sense introduced in [7]. The bitangential inverse spectral problem is solved in this class. In our considerations, the data for this inverse problem is a given nondecreasing p×p matrix valued function σ(μ) on and a normalized monotonic continuous chain of pairs , of entire inner p×p matrix valued functions. Each such chain defines a class of canonical integral systems in which we find a solution of the inverse problem for the given spectral function σ(μ). A detailed comparison of our investigations of inverse problems with those of Sakhnovich is presented.     

Transmission problems and spectral theory for singular integral operators on Lipschitz domains

We prove the well-posedness of the transmission problem for the Laplacian across a Lipschitz interface, with optimal non-tangential maximal function estimates, for data in Lebesgue and Hardy spaces on the boundary. As a corollary, we show that the spectral radius of the (adjoint) harmonic double layer potential K∗ in is less than , whenever is a bounded convex domain and 1<p?2.     

Large time behavior of the heat kernel

In this paper we study the large time behavior of the (minimal) heat kernel k_P^M(x,y,t) of a general time-independent parabolic operator Lu=u_t+P(x,∂_x)u which is defined on a noncompact manifold M. More precisely, we prove that

     

Polynomial sequences of bounded operators

The basic results of spectral theory are obtained using the sequence of powers of a bounded linear operator T,T²,…,Tⁿ,…. In this paper, we replace the powers Tⁿ by certain polynomials p_n(T), and make use of special properties of the polynomial sequence to derive some new results concerning operators. For example, using an arbitrary polynomial sequence , we obtain “binomial” spectral radii and semidistances, which reduce, in the case of the sequence of powers, to the usual spectral radius and semidistance.     

Ideals of operators and the metric approximation property

We prove that a Banach space X has the metric approximation property if and only if , the space of all finite rank operators, is an ideal in , the space of all bounded operators, for every Banach space Y. Moreover, X has the shrinking metric approximation property if and only if is an ideal in for every Banach space Y.Similar results are obtained for u-ideals and the corresponding unconditional metric approximation properties.     

Electrical characterization of strontium tartrate single crystals

The a.c. and d.c. conductivity of SrC₄H₄O₆·3H₂O are measured and are found to lie between usual conductivities of semiconductor and insulator. Temperature dependence of d.c. conductivity shows intrinsic conduction, which is confirmed by the slope of versus data. Due to application of thermal energy, noticeable conductivity peaks imply liberation of water molecules during dehydration and the formation of strontium oxalate. The conductivity plot has a nature similar to the intrinsic-to-extrinsic transition found in normal semiconductors. There occurs Efros hopping conduction in our samples.     

一种稳定的自由空间量子密钥分配实验系统

基于量子密钥分配的基本原理,采用B92方案,以单光子作为信息载体,使用极化编码,搭建了一个简单易行的实验装置,实现了自由空间传输的量子密钥分配,平均每脉冲光子数为0．1,粗码率12．7kbits／s,误码率4％左右。     

Comparative study of spectroscopic properties of Er^3＋／Yb^3＋-codoped tellurite glass and fibres under 980nm excitation＊

A tellurite fibre of TeO_{2}－ZnO－La_{2}O_{3}－Li_{2}O glass codoped with 20000 ppm ytterbium and 5000 ppm erbium was fabricated by the suction casting and rod-in-tube technologies. The absorption spectrum of Er^{3+}/Yb^{3+} -codoped bulk glass has been measured. From the Judd－Ofelt intensity parameters, the spontaneous emission probability and radiative lifetime τ_{rad} of Er^{3+}:{}^{4}I_{13/2}→{}^{4}I_{15/2} transition for the bulk glass have been calculated. The emission fluorescence spectra and lifetimes around 1.5μm, and subsequent upconversion fluorescence in the range of 500－700nm were measured in fibres and compared with those in bulk glass. The changes in amplified spontaneous emission with fibre length and pumping power was also measured. It was found that the emission spectrum from erbium in fibres is almost twice as broad as the corresponding spectrum in bulk glass when pumped at 980nm.