Remarks on stochastic non-linear birth and death models

The first part of this paper is an attempt to formulate and motivate additional work on the important problem of obtaining global bounds applicable to the controlled truncation of the paper relates specifically to the linear birth, quadratic death model. Asymptotic results are given for the first finite difference ΔT_m where T_m is the exactly known mean time to extinction starting from state m (m= 0,1,…). These results are in terms of the environmental carrying capacity n^* taken to be large. For m near zero ΔT_me^n*/(n^*)²; whereas, for m near n^*ΔT_m ≈ (π/2)^1/2/(n^*)^3/2. This indicates the vastly different time scales in those two regions of state space - with considerably slower action near extinction than near n^*.     

Effect of unidirectional solidification rate on Jc for current lead

The dependence of transport J_c value on the traveling rate and the nominal composition was investigated by taking different nominal compositions of YBa₂Cu₃O_6+x (Y123) + n mol% Y₂BaCuO₅ (Y211) (n = 10, 20, 30, 40 and 50) with addition of 0.5 wt% of Pt on samples processed by different unidirectional solidification rates, namely 1, 3 and 5 mm/h. The highest J_c was found in the sample with 30% Y211 addition by the higher traveling rate adjusted to prevent the formation of polycrystals. In this φ 1.56 × 60 mm sample the values of transport I_c and J_c were 1370 A and 71 700 A/cm², respectively, which were obtained by the conventional DC four-probe method with criterion of 1 μV/cm at 77 K and self-field.     

Ge-Sb-Se硫系玻璃的折射率和热光系数

Ge-Sb-Se硫系玻璃被认为是极佳的红外传输材料和有潜力的非线性光学材料.在光学设计中,玻璃的线性折射率(n)及其热光系数(ζ)是关键技术参数.以预测和调控Ge-Sb-Se玻璃的n和ζ为目的,考察了玻璃的n,ζ,密度(d)和体积膨胀系数(β)与化学参数dSe和拓扑网络结构参数r的内在联系.研究发现,玻璃的n随d的增加而增大;ζ随β的增大而近似线性减小;β随dSe的减小或r的增大而减小;当Ge含量固定时, d随dSe的减小或r的增大而增大,当Sb含量固定时, d在dSe=0时具有最小值.基于实测d和n,拟合获得了Ge, Sb和Se元素在2—12μm波段的摩尔折射度(R_i),分别为R_(Ge)=10.16—10.50 cm~3/mol,RSb=16.71—17.08 cm~3/mol和RSe=11.15—11.21 cm~3/mol,根据d和R_i计算得到的n与实测值的偏差小于1%.基于实测ζ和β,拟合得到了Ge, Sb和Se元素在2—12μm波段的摩尔折射度温度系数(φ_i),分别为φ_(Ge)=21.1—22.6 ppm/K,φ_(Sb)=7.2—8.4 ppm/K和φ_(Se)=90.2—94.2 ppm/K,根据β和φ_i计算得到的ζ与实测值的偏差小于6 ppm/K.     

1/f-type fluctuation of electron transmission in one-dimensional disordered systems

A universal feature of 1/f-type fluctuation is numerically observed in the system-size n dependence of the transmission amplitude t_n in various one-dimensional disordered systems. The power spectrum P(f) of the transmission coefficient T(n)=|t_n|² exhibits the power law of 1/f², irrespective to the type of disorder of the system whether it is of short-range or of long-range correlation. That of the phase θ_t(n) of t_n also does the universal power law of 1/f^1.4.     

应用分子子图指数估计与预测烷烃核磁共振碳谱位移和

系统地研究了核磁共振碳谱(¹³C NMR)与化学位移规律及其定量构谱关系(QSSR).本文研究了一组多元素分子子图指数矢量(VMSG),并发现它与烷烃化学位移和(CCSA)有很好线性相关性.采用多元线性回归(MVLR)进行准确估计与预测,结果良好.     

应用分子子图指数估计与预测烷烃核磁共振碳谱位移和

系统地研究了核磁共振碳谱(¹³C NMR)与化学位移规律及其定量构谱关系(QSSR).本文研究了一组多元素分子子图指数矢量(VMSG),并发现它与烷烃化学位移和(CCSA)有很好线性相关性.采用多元线性回归(MVLR)进行准确估计与预测,结果良好.     

Dielectric and ferroelectric properties of the mixed crystals system (CH3NH3)5Bi2(1 − x)Sb2xCl11

Dielectric and pyroelectric properties of the mixed crystals system, (CH₃NH₃)₅Bi_{2(1 − x)}Sb_2xCl₁₁ (0 < x < 0.25) were systematically investigated. Temperature dependencies of ′_c in the vicinity of ferro-paraelectric phase transition were measured for the mixed crystals with x = 0.05, 0.07, 0.11, 0.13 and 0.25 in the frequency region 1 kHz–1 MHz. The substitution of bismuth atoms by antimony drastically reduces the magnitude of ′_c and shifts the ferro-paraelectric phase transition towards higher temperatures. The dielectric dispersion of the complex electric permittivity, _c^*, in x = 0.05 crystals was studied in the frequency range from 30 to 1000 MHz. Around 321 K phase transition, two dielectric relaxators are postulated; a low-frequency one in the megahertz region showing a critical slowing down and a high-frequency one in the gigahertz region.     

Magnetic properties of the Bi1.95Sr2.05−xLaxCuOy (Bi-2201) superconducting phase

We have investigated the reversible mixed-state magnetization M of three lanthanum substituted Bi_1.95Sr_2.05−xLa_xCuO_y (Bi-2201) ceramic samples having different critical temperatures T_c ranging from 20.0 to 35.5 K. As for the Bi₂Sr₂CaCu₂O_8+δ (Bi-2212) phase, we found that anisotropy of Bi-2201 is large. A manifestation of this anisotropy is the field independent magnetization M^* observed at a temperature T^*. In the framework of the London model, and including thermal fluctuations of vortices, we found for the temperature dependence of the penetration depth λ_ab(T) = λ_ab(0)[1 − (T/T_c0)ⁿ]^−1/2, with n 1.7 and λ_ab (T = 0) 4000 Å. The estimated upper critical fields μ₀H_c2,c are of the order of 10 T. We observe a peculiar negative slope M/T at low temperature and sufficiently high external magnetic field. This feature seems to be a characteristic of the Bi-2201 phase. However, we do not know whether it is associated with the superconducting mixed-state. A small amount of magnetic impurities could also be responsible for this behavior. Finally, the behavior of the reversible magnetization of the Bi-2201 samples investigated, which are situated at the optimal and in the overdoped region, did not indicate any unusual temperature dependence for the upper critical field H_c2,c.     

Dilatometry of the high-temperature proton conductor Ba3Ca1.18Nb1.82O9 − δ

Firstly, the production of solid bulk specimens of the proton conductor Ba₃Ca_1.18Nb_1.82O_{9 − gd} (BCN18) of known water content up to [H^.] = n_H/n_Ba = 0.16 is described. Secondly, measuring the length change of such samples versus water content [H^.] demonstrated that the sample lengths increased linearly with a slope of (Δl/l)/[H^.] = (2.13 ±0.07) × 10⁻². Thirdly, the density of bulk samples was found to decrease linearly with water content [H^.]. This decrease was in good agreement with the above values derived from the length change. Fourthly, high temperature dilatometry showed that samples reach the thermodynamic solubility values in water vapor atmospheres only at temperatures above 700 °C. Two time scales were observed for the time-dependence of the elongation upon exposure to water vapor. A fast process occurred within minutes above 700 °C, a slow one took several hours. The fast one was identified as the chemical diffusion of the diffusion pair H^. and V_o^. which is required for the water uptake and loss of BCN18. The chemical diffusivity of water is described by the parameters D₀ = (0.022 ± 0.002) cm²/s and ΔH* = (0.79 ± 0.05) eV.     

Minimal renormalization without ε-expansion: Three-loop amplitude functions of the 0(n) symmetric Φ theory in three dimensions below Tc

We present an analytic three-loop calculation for thermodynamic quantities of the O(n) symmetric Φ⁴ theory below T_c within the minimal subtraction scheme at fixed dimension d = 3. Goldstone singularities arising at an intermediate stage in the calculation of O(n) symmetric quantities cancel among themselves leaving a finite result in the limit of zero external field. From the free energy we calculate the three-loop terms of the amplitude functions ƒ_Φ, F₊ and F₋ of the order parameter and the specific heat above and below Tc, respectively, without using the e = 4-d expansion. A Borel resummation for the case n = 2 yields resummed amplitude functions f_Φ and F₋ that are slightly larger than the one-loop results. Accurate knowledge of these functions is needed for testing the renormalization-group prediction of critical-point universality along the λ₋line of superfluid ⁴He. Combining the three-loop result for F₋ with a recent five-loop calculation of the additive renormalization constant of the specific heat yields excellent agreement between the calculated and measured universal amplitude ratio A⁺/A^- of the specific heat of ⁴He. In addition we use our result for f_Φ to calculate the universal combination Rc of the amplitudes of the order parameter, the susceptibility and the specific heat for n = 2 and n = 3. Our Borel-resummed three-loop result for R_c is significantly more accurate than the previous result obtained from the ε-expansion up to O(ε².     

(K3N)n(n=1,…,5)团簇结构与性质的密度泛函理论研究

利用密度泛函理论B3LYP方法,在6-311G*水平上对碱金属氮化物(K₃N)_n(n=1,…,5)团簇各种可能构型进行几何结构优化,预测各团簇的最稳定结构,并对其成键特性、电荷分布、振动特性及稳定性进行分析研究.结果表明,随着n的增大,(K₃N)_n(n=1,…,5)团簇的最稳定结构逐渐由平面结构向空间立体结构转变,(K₃N)₄、(K₃N)₅团簇为类似晶体的层状结构;团簇中N原子的配位数以5、6较多见;团簇中N原子的平均自然电荷为-1.608e,K原子的平均自然电荷为+0.550e,K-N键为较强的离子键;(K₃N)₄团簇有相对较高的动力学稳定性.     

Spin-polarized tunneling in nanostructured La2/3Sr1/3MnO3

We present magnetic and transport properties of nanocrystalline La_2/3Sr_1/3MnO₃ powders prepared by a gel-combustion method using citric acid as the fuel. The coercive magnetic field H_c is significantly different to the field H_c^* for which the magnetoresistance (MR) is maximum. The MR at low fields (LFMR) exhibits a power-law dependence with magnetization, MR∝Mⁿ, with n=2.5–3.3 for temperatures ranging from 5 to 200 K. The results are discussed in terms of a distribution of particle size in our sample.     

The oxidation of fullerene [C70] with various oxidants by ultrasonication

The reaction of C₇₀ by ultrasonication with various oxidants such as 3-chloroperoxy benzoic acid (Fluka 99%), 4-methyl morpholine N-oxide (Aldrich 97%), chromium (VI) oxide (Aldrich 99.9%), and oxone^® monopersulfate compound, at room temperature causes the oxidation of fullerene [C₇₀(O)_n] (n=1–2 or n=1). The FAB-MS, UV–visible, FT-IR spectra, and HPLC analysis confirmed that products of fullerene oxidation are [C₇₀(O)_n] (n=1–2 or n=1).     

Projective and affine connections on S and integrable systems

It is known that the Korteweg–de Vries (KdV) equation is a geodesic flow of an L² metric on the Bott–Virasoro group. This can also be interpreted as a flow on the space of projective connections on S¹. The space of differential operators Δ⁽ⁿ⁾=∂ⁿ+u₂∂ⁿ⁻²++u_n form the space of extended or generalized projective connections. If a projective connection is factorizable Δ⁽ⁿ⁾=(∂−((n+1)/2−1)p₁)(∂+(n−1)/2p_n) with respect to quasi primary fields p_i’s, then these fields satisfy ∑_i=1ⁿ((n+1)/2−i)p_i=0. In this paper we discuss the factorization of projective connection in terms of affine connections. It is shown that the Burgers equation and derivative non-linear Schrödinger (DNLS) equation or the Kaup–Newell equation is the Euler–Arnold flow on the space of affine connections.     

Generalized Einstein manifolds

A Finslerian manifold is called a generalized Einstein manifold (GEM) if the Ricci directional curvature R(u,u) is independent of the direction. Let F⁰(M, g_t) be a deformation of a compact n-dimensional Finslerian manifold preserving the volume of the unitary fibre bundle W(M). We prove that the critical points g₀ F⁰(g_t) of the integral I(g_t) on W(M) of the Finslerian scalar curvature (and certain functions of the scalar curvature) define a GEM. We give an estimate of the eigenvalues of Laplacian Δ defined on W(M) operating on the functions coming from the base when (M, g) is of minima fibration with a constant scalar curvature H admitting a conformal infinitesimal deformation (CID). We obtain λ ≥ H/(n − 1) (Δf = λf). If M is simply connected and λ = H/(n − 1), then (M, g) is Riemannian and is isometric to an n-sphere. We first calculate, in the general case, the formula of the second variationals of the integral I (g_t) for G = g₀, then for a CID we show that for certain Finslerian manifolds, I″(g₀) > 0. Applications to the gravitation and electromagnetism in general relativity are given. We prove that the spaces characterizing Einstein-Maxwell equations are GEMs.     

Probability of a ductile fracture

The present paper studies ductile fracture by a random fractal and calculates the fracture probability q of a ductile fracture. The fracture probability q is sensitive to the number n (microvoid size) and the probability p of forming microvoids. There are two critical probabilities p_c1 and p_c2. When pp_c2 = 1-1/n², the fracture probability q is 100%, the ductile fracture occurs with probability 1; when p_c2 > p>p_c1, there is a positive probability q (1>q>0), the fracture probability q increases with increasing probability p and/or decreasing number n; when p<p_c1, the fracture probability q is zero (in fact less than 0.00001), the fracture does not occur. The critical probabilities p_c1 and p_c2 increase with increasing n. When 1-1/n²>p>1-1/n, though a ductile fracture does not occur, there is at least a macrovoid which passes through the transverse plane of the specimen.     

Structural study and magnetoresistance effect of epitaxial La0.67Sr0.33MnO3–δ and Pr0.7Ca0.3MnO3−δ multilayer films

La_0.67Sr_0.33MnO_3−δ (LSMO) and Pr_0.7Ca_0.3MnO_3−δ (PCMO) multilayer epitaxial films, which were fabricated with different LSMO and PCMO layer thickness on LaAlO₃ single crystal substrates of (0 0 1) orientation by a direct current magnetron sputtering technique, were studied further, after the structure, magnetoresistance effect and magnetic properties of LSMO/PCMO/LSMO (LPL) trilayer epitaxial films were systemically studied. The superlattice structures of multilayer films were observed according to the diffraction peaks of X-ray diffraction patterns at small angles. The metal–insulator transition temperature (T_P) and peak resistivity (ρ_max) obviously changed when we altered the thickness of PCMO middle layer and the intra-field related with the thickness of those layers and their interaction. Considering the effect of the distribution of electrical field and current, and the interaction among the layers of LSMO and PCMO, an effective fact n* was introduced to replace n (the number of layer). All the calculated values of ρ (the resistivity of multilayer films) accorded with the experimental values.     

Flux creep and flux flow for thallium ceramics in a pulsed magnetic field

The resistive properties of Tl-ceramics with T_c|=0=114 K were investigated in a pulsed magnetic field (B) up to 30 T and in the temperature range of 4.2 K<T<140 K. It was shown that the character of the field dependence of the resistance differs qualitatively in high-and low-temperature regions. At low (T80K) temperatures the dynamic magnetoresistance arising in the sample is analogous to that observed earlier in LaSrCuO [1] and YBaCuO [2] ceramics. This magnetoresistance is defined by the magnetic field variation rate and leads to the appearance of a minimum at the maximum of the magnetic field pulse, i.e. at . In the region of high temperatures (80 K T<T_c) or magnetic fields (at T60K) the sample resistance rises monotonically with B increase, and dynamic resistance is not observed. In this temperature range the existence of a scaling relation is shown (here B^* and T^* meet the condition k=(B^*, T^*)/ _n(T^*)=const) for the ceramics resistance (B,T), which can be represented as . An estimate for the upper critical field B_c2(0)B_o=1030±40 T is obtained.     

关于动态位错场张量势的规范变换

本文引入并论证了描述动态位错场的张量势(A与B)的规范交换问题,而且证明这种变换可采取这样的形式:B′=B+▽F, A′=A-ρ?/(?t)▽G,x′=x-ρ?/(?t)F,其中x_i=e_iklA_kl。至于F与G,则为带有很大任意性的时空坐标的矢量函数,但它们要满足以下关系式:F=▽×G,▽²F-1/G_t²-(?²/?t²)F=0.进 关键词：     

Entropy of planar random surfaces on the lattice

We study planar random surfaces on a hypercubic lattice in two and three dimensions by Monte Carlo techniques. Our data are consistent with the formula n₀(A;C) A^b₀A, where n₀(A;C) is the number of planar random surfaces with area A and boundary C. We find b₀ = −1.4 ± 0.2, = 5.31 ± 0.03 (for d = 2) and b₀ = −1.5 ± 0.2, = 7.13 ± 0.05 (for d = 3). The values of b₀ disagree with those obtained from the Polyakov string model.