Free electron laser induced two-photon photoconductivity in Hg1-xCdxTe

The Beijing free electron laser ( BFEL) has been employed for the first time to study the nonlinear photoconductivity characteristics of the typical infrared photoelectronic material Hg_1-xCd_xTe Taking advantage of the high photon flux density of BFEL, we have investigated the photoconductivity characteristics in Hg^1-xCd_x Te induced by two-photon absorption by means of the photoconductivity technique, observed the photoconductivity signals saturation, and studied the two-photon photoconductivity characteristics on different bias voltages across the sample.     

M?ssbauer study on Sn-doped (Lal1-x,Srx)2Cu1-x,Snx,O4 superconductors under a new concept

¹¹⁹Sn M?ssbauer research is carried out on (La_1-xSr_x),Cu_1-xSn_xO₄(x = 0.075 and 0.110) superconductors which are designed under a new concept. The M?ssbauer spectra results show that Sn occupies Cu position in Sn⁴⁺ state, and there is no Sn²⁺ ion occupying La position. The local lattice deformation near Sn⁴⁺ site is small, but displays an increasing tendency with Sn doping. For La₂CuO₄ matrix, the simultaneous dopings of Sr/Sn induce holes and electrons on CuO₂ layer in a new mechanism which influences superconductivity. Under a new mechanism of extra oxygen, the extra oxygen effect of Sn-doping on superconductivity is discussed     

Mössbauer study on Sn-doped (Lal1-x,Srx)2Cu1-x,Snx,O4 superconductors under a new concept

¹¹⁹Sn Mössbauer research is carried out on (La_1-xSr_x),Cu_1-xSn_xO₄(x = 0.075 and 0.110) superconductors which are designed under a new concept. The Mössbauer spectra results show that Sn occupies Cu position in Sn⁴⁺ state, and there is no Sn²⁺ ion occupying La position. The local lattice deformation near Sn⁴⁺ site is small, but displays an increasing tendency with Sn doping. For La₂CuO₄ matrix, the simultaneous dopings of Sr/Sn induce holes and electrons on CuO₂ layer in a new mechanism which influences superconductivity. Under a new mechanism of extra oxygen, the extra oxygen effect of Sn-doping on superconductivity is discussed     

行列式detVn-(x1,...,xn)的准确值及其应用

本文给出行列式Ｖ_n^-(x₁,...,x_n)的准确值，它是通常的Ｖａｎｄｅｒｍｏｄｅ行列式计算公式的推广，以及它在理论上的一些重要应用．     

Phonon spectroscopy and transport properties of Y1-x Nd x Sr2Cu2.7Mo0.3O7-δ

The Raman and infrared spectra, resistivity as well as thermoelectric power of Y_1-xNd_xSr₂Cu_2.7Mo_0.3 O₇ δ(.x =0, 0.1. 0.2. 0.5, 0.8 and 1.0) are studied carefully. It was found that the structure characteristics of RSr₂Cu_2.7Mo_0.3O₇ δ cuprates are different from those of RBa₂Cu₃0₇ δ. The variations of the microstructure in Y_1-x Nd_xSr₂Cu_2.7Mo_0.3O₇ δ with Nd-doping affect the carrier distribution. so as a result the superconductivity changes. Furthermore, it is pointed out that the microstructure variations with the large rare earth ionic substitution cause the widely existing rare earth ionic size effect in HTSC. Project supported by the National Natural Science Foundation of China and the National Center for R & D Superconductivity.     

When isf(x1, x2, ..., xn) =u1(x1) +u2(x2) + ... +un(xn)?

We discuss subsetsS of ℝⁿ such that every real valued functionf onS is of the formf(x₁, x₂, ..., x_n) =u ₁(x₁) +u ₂(x₂) +...+u _n(x_n), and the related concepts and situations in analysis.     

A maximum principle in Rn + 1

In this paper we establish maximum principles of the Cauchy problem for hyperbolic equations in $\text{R}$³ and $\text{R}$^{n + 1}(n ? 2). Our maximum principles generalize the results of Weinberger [5], and Sather [3, 4] for a class of equations such that the coefficients can be allowed to depend upon t, as well, in {x₁, x₂, t}-space and {x₁, x₂,…, x_n, t}-space. Throughout this paper, the influence of the work of Douglis [1] is apparent. See [2].     

On extremal point distributions in the Euclidean plane

We ask for the maximum σ _n ^γ of Σ _i,j=1 ⁿ ‖x _i-x _j‖^γ, where x ₁,χ,x _n are points in the Euclidean plane R ² with ‖x_i-x_j‖ ≦1 for all 1≦ i,j ≦ n and where ‖.‖^γ denotes the γ-th power of the Euclidean norm, γ ≧ 1. (For γ =1 this question was stated by L. Fejes Tóth in [1].) We calculate the exact value of σ _n ^γ for all γ γ 1,0758χ and give the distributions which attain the maximum σ _n ^γ . Moreover we prove upper bounds for σ _n ^γ for all γ ≧ 1 and calculate the exact value of σ ₄ ^γ for all γ ≧ 1. This revised version was published online in June 2006 with corrections to the Cover Date.     

Influence of Fe3+ on perovskite oxides: La2/3Ca1/3Mn1-x Fe x O3

The structure and magnetoresistance properties in sintered samples of La_2/3Ca_1/3Mn_1-x Fe _x O₃(0≤x≤0.84) are studied by using Mössbauer spectroscopy, XRD and magnetic measurement. There are antiferromagnetic interactions between Fe and its nearest neighbors (Fe, Mn) when 0 <x ≤0.67, which are important factors influencing the double-exchange between Mn³⁺ and Mn⁴⁺, Curie temperature, magnetic moment and GMR. It is suggested that the Mn³⁺ (Fe³⁺) /Mn⁴⁺ system also consists of magnetic clusters with different sizes.     

A noncommutative analogue of |D(Xk|=|kXk−1|

The paper concerns alternating powers of a Hilbert space. Let ∧^k be defined by ∧^k(A)(x₁∧?∧x_k)=Ax₁∧?∧Ax_k. It is proved that the norm of the linear map D∧^k(A) depends only upon |A| and is assumed at the identity.     

Generalized cartan type k lie algebras in characteristic 0

The Lie algebra of Cartan type K which occurs as a subalgebra of the Lie algebra of derivations of the polynomial algebra F[x₀, x₁,…, x_n,x_n?1,…,x_?n], where F is a field of characteristic 0, was generalized by the first author to a class which included a subalgebra of the derivations of the Laurent polynomials F[x₀,x₁,…, x_n,x_?1,…,x_?n,X₀ ^?1x₁ ^-1,…,x_n ^?1,…,x_?1 ^?1…,x_?n ^?1]A further generalization of these algebras is the main topic of this paper. We show when these algebras are simple, determine all possible     

On Some Problems of P. Turán Concerning Lm Extremal Polynomials and Quadrature Formulas

The L_m extremal polynomials in an explicit form with respect to the weights (1−x)^−1/2 (1+x)^(m−1)/2 and (1−x)^(m−1)/2 (1+x)^−1/2 for even m are given. Also, an explicit representation for the Cotes numbers of the corresponding Turán quadrature formulas and their asymptotic behavior is provided.     

Convergence of Modified Lagrange Interpolation toLp-Functions Based on the Zeros of Orthonormal Polynomials with Freud Weights

We consider the “Freud weight”W²_Q(x)=exp(−Q(x)). let 1<p<∞, and letL*_n(f) be a modified Lagrange interpolation polynomial to a measurable functionf∈{f; ess sup_x∈ |f(x)| W_Q(x)(1+|x|)^α<∞},α>0. Then we have lim_n→∞ ∫^∞_−∞ [|f(x)−L*_n(f; x)| W_Q(x)(1+|x|)^−Δ]^p dx=0, whereΔis a constant depending onpandα.     

Effect of A-site cation substitution on magnetic transition temperature of (LaCa) MnO3

The ferromagnetic transition temperatures have been measured on two bathes of perovskite manganese oxides such as (La_1-x R _x )_2/3Ca_1/3MnO₃(R=Ce, Pr, Nd, etc.) and La_2/3(Ca_1-y Cd _y )_1/3MnO₃. It is found that the (La_1-x R _x )_2/3Ca_1/3MnO₃ samples have obviously different Curie temperatureT _C although their (r_A) (the average A-site cation radius) are almost identical, and theT _C in the system of (La_1-x R _x )_2/3Ca_1/3MnO₃(R=Ce, Pr, Nd, etc.) and La_2/3(Ca_1-y Cd _y )_1/3MnO₃. It is found that the (La_1-x R _x )_2/3Ca_1/3MnO₃ compounds increases with increasingy although (r_A) decreases slightly. It is suggested that the Curie temperature should be influenced by the average local A-site magnetic moment in the ferromagnetic perovskite manganite system. Project supported by the National Natural Science Foundation of China (Grant No. 19504012) and the Chinese Academy of Sciences.     

On the completeness of the system of function {e sin λnx}n = 1

In this paper, the biorthogonal system corresponding to the system {e^−αnx sin nx}_{n = 1}^∞ is represented in an appropriate form so that it is possible to obtain sufficiently good estimates of its norm. Then, by the stability of a completeness property we prove that the system of functions {e^−αλ_nx sin λ_nx}_{n = 1}^∞ is complete.     

The diophantine equation x3 + 3y3 = 2n

It is proved that the equation of the title has a finite number of integral solutions (x, y, n) and necessary conditions are given for (x, y, n) in order that it can be a solution (Theorem 2). It is also proved that for a given odd x₀ there is at most one integral solution (y, n), n ≥ 3, to x₀³ + 3y³ = 2ⁿ and for a given odd y₀ there is at most one integral solution (x, n), n ≥ 3, to x³ + 3y₀³ = 2ⁿ.     

Counting cycles and finite dimensional L norms

We obtain sharp bounds for the number of n-cycles in a finite graph as a function of the number of edges, and prove that the complete graph is optimal in more ways than could be imagined. We prove sharp estimates on both ∑_i=1ⁿx_i^k and ∑_i=1ⁿ|x_i|^k, subject to the constraints that ∑_i=1ⁿx_i²=C and ∑_i=1ⁿx_i=0.     

Notes on the nuclearity of random subalgebras of O2{\mathcal {O}_2}

There exists a separable exact C*-algebra A which contains all separable exact C*-algebras as subalgebras, and for each norm-dense measure μ on A and independent μ-distributed random elements x ₁, x ₂, ... we have lim_{n ? ￥}\mathbb P(C^*(x₁,?,x_n) is nuclear)=0{\rm {lim}}_{n \rightarrow \infty}\mathbb {P}(C^*(x_1,\ldots,x_n) \mbox{ is nuclear})=0. Further, there exists a norm-dense non-atomic probability measure μ on the Cuntz algebra O₂{\mathcal {O}_2} such that for an independent sequence x ₁, x ₂, ... of μ-distributed random elements x _i we have lim inf_{n ? ￥}\mathbb P(C^*(x₁,?,x_n) is nuclear)=0{\rm {lim\, inf}}_{n \rightarrow \infty}\mathbb {P}(C^*(x_1,\ldots,x_n) \mbox{ is nuclear})=0. We introduce the notion of the stochastic rank for a unital C*-algebra and prove that the stochastic rank of C([0, 1] ^d ) is d.     

Stopping rules forx n/n and related problems

The following results illustrate the problems with which this note deals. Letx _n (n=1, 2, ...) be non-negative, independent, identically distributed random variables, letβ>1 andEx ₁ ^β <∞. Then there exists a stopping ruleτ withP{τ<∞}=1, which maximizesE x _t/t among all stopping rulest. Moreover, the same rule maximizesE max (x ₁, ...,x _t)/t andE max (x ₁,..,x _τ)/τ=Ex _τ/τ Research supported in part by Grant GP-5705 of the National Science Foundation, USA.     

Representations for the first associated q-classical orthogonal polynomials

Let {p_k(x; q)} be any system of the q-classical orthogonal polynomials, and let be the corresponding weight function, satisfying the q-difference equation D_q(σ)=τ, where σ and τ are polynomials of degree at most 2 and exactly 1, respectively. Further, let {p_k⁽¹⁾(x;q)} be associated polynomials of the polynomials {p_k(x; q)}. Explicit forms of the coefficients b_n,k and c_n,k in the expansions

are given in terms of basic hypergeometric functions. Here _k(x) equals x^k if σ⁺(0)=0, or (x;q)_k if σ⁺(1)=0, where σ⁺(x)σ(x)+(q−1)xτ(x). The most important representatives of those two classes are the families of little q-Jacobi and big q-Jacobi polynomials, respectively.Writing the second-order nonhomogeneous q-difference equation satisfied by p_n−1⁽¹⁾(x;q) in a special form, recurrence relations (in k) for b_n,k and c_n,k are obtained in terms of σ and τ.