Three Octacyanometallate‐Based LnIII–MV (Ln = La,Ce; M = Mo,W) Bimetallic Assemblies with a One‐Dimensional Rope‐Ladder Chain Structure

Three octacyanometallate‐based hetero‐bimetallic complexes, [Ln(H₂O)₄(CH₃CN)₂][M(CN)₈] · CH₃CN [Ln = La, M = Mo( 1 ), W( 2 ); Ln = Ce, M = W( 3 )], were synthesized and characterized structurally. Single‐crystal X‐ray analysis reveals that 1 – 3 are isomorphous and consist of infinite one‐dimensional (1D) 3,3 rope‐ladder chains, in which the 12‐membered puckered square Ln₂M₂(CN)₄ is the basic building unit. The 1D chains are further linked through interchain hydrogen bonds, resulting in a three‐dimensional (3D) supramolecular network.     

An asymptotic relationship for ruin probabilities under heavy-tailed claims

The famous Embrechts-Goldie-Veraverbeke formula shows that, in the classical Cramér-Lundberg risk model, the ruin probabilities satisfy \(R(x, \infty ) \sim \rho ^{ - 1} \bar F_e (x)\) if the claim sizes are heavy-tailed, where F_e denotes the equilibrium distribution of the common d.f. F of the i.i.d. claims, ? is the safety loading coefficient of the model and the limit process is for x → ∞. In this paper we obtain a related local asymptotic relationship for the ruin probabilities. In doing this we establish two lemmas regarding the n-fold convolution of subexponential equilibrium distributions, which are of significance on their own right.     

A fluctuation theory for Markov chains

A fluctuation theory for Markov chains on an ordered countable state space is developed, using ladder processes. These are shown to be Markov renewal processes. Results are given for the joint distribution of the extremum (maximum or minimum) and the first time the extremum is achieved. Also a new classification of the states of a Markov chain is suggested. Two examples are given.     

On the number of -equivalent non-isomorphic models

We prove that if is consistent then is consistent with the following statement: There is for every a model of cardinality which is -equivalent to exactly non-isomorphic models of cardinality . In order to get this result we introduce ladder systems and colourings different from the ``standard' counterparts, and prove the following purely combinatorial result: For each prime number and positive integer it is consistent with that there is a ``good' ladder system having exactly pairwise nonequivalent colourings.

     

Raising and Lowering of Generalized Hulthén Potential from Supersymmetry Approaches

We obtain the exact bound states of the generalized of Hulthén potential with negative energy levels using an analytic approach. In order to obtain bound states, we use the associated Jacobi differential equation. Using the supersymmetry approach to quantum mechanics, we show that these bound states, via four pairs of first order differential operators, represent four types of ladder equations. Two types of these supersymmetric structures suggest derivation of algebric solutions for the bound states using two different approaches. PACS 21.60.Cs; 21.60.Fw; 21.60.-n; 03.65.Fd; 03.65.Ge; 03.65.-w     

关于软玻密子的结构

本文修改了Landshoff-Nachtmann的软玻密子(Pomeron P)场论模型.从强子组分夸克具有结构的观点出发,根据高能强作用软过程中的最大非微扰强作用反应假定,提出了有关软P新的结构图像.对撞强子中的一对组分夸克被分解为裸夸克和一系列非微扰胶子(和夸克对).与此相应,软P的结构是由胶子形成的一系列切割梯形图之和所代表.在系统能量s很大而动量转移|t|很小的多重雷吉(Regge)运动学区间,并在保留lns的领头阶近似下,计算了这组切割梯形图之和所对应的散射振幅和总截面.它们的表达式出现了对s的Regge型幂次因子,得出了软P轨迹的简洁表达式.简单说明了按本文提出的方案可以讨论那些相关的强作用过程.     

三能级Upper-ladder型系统中的

三能级Upper-ladder型系统中,在旋波、慢变振幅近似下,求解了考虑驱动场相位扩散后的系统密度矩阵运动方程,并给出了这个三能级梯型系统稳态线性解析解.利用对密度矩阵运动方程的稳态线性解析解的数值模拟结果,研究相位扩散对无反转激光增益、色散和粒子数差的影响;利用对密度矩阵运动方程的数值模拟结果,分析相位的扩散对无反...     

Synthesis, structural and magnetic properties of spin ladder compound Ca1−xCoxCu2O3

MCu₂O₃ (M=Ca and Co) system has two-leg spin ladder structure similar to that of the prototype SrCu₂O₃ system except that the rungs are buckled with an angle of 123° and 105° for CaCu₂O₃ and CoCu₂O₃ compounds, respectively. We have synthesized powder samples of (Ca_1−xCo_x)Cu₂O₃ (x=0.00-1.00) by the solid state reaction method and their structural and magnetic properties have been investigated. All the synthesized compounds crystallize in orthorhombic structure with space group Pmmn. Lattice parameters of (Ca_1−xCo_x)Cu₂O₃ decrease with the increase in Co content. DC magnetic susceptibility χ(T) results of the end products CaCu₂O₃ and CoCu₂O₃ show antiferromagnetic transition (T_N) at 27 and 215 K, respectively. Co doping into (Ca_1−xCo_x)Cu₂O₃ enhances its T_N systematically with increasing Co concentration. The χ(T) of CoCu₂O₃ shows a broad transition with the peak temperature around 215 K and it was found to be field independent up to 90 kOe. The ambiguity concerning the transition was ruled out by recording the temperature dependent X-ray diffraction pattern on CoCu₂O₃ system, which indicated that there is no structural transition in the investigated temperature range of 115-300 K. Further, specific heat measurement on CoCu₂O₃ confirms the magnetic phase transition by the appearance of a sharp peak at 215 K.     

Nuclear Spin–Lattice Relaxation of Single Crystal Sr14Cu24O41

Nuclear spin–lattice relaxation rate T ₁ ⁻¹ has been measured for the ladder sites of two single crystals Sr₁₄Cu₂₄O₄₁ (Sr14-A,B) by ⁶³Cu NMR/NQR. The hole localization around 100 K appears as a peak in the T variation of T ₁ ⁻¹(NQR). On the other hand, it is suppressed in the T ₁ ⁻¹ (NMR) data under the magnetic field H ∼ 11 T, and a new peak appears around 20 K. T ₁ ⁻¹(NMR) around the peak is more enlarged for Sr14-B than for Sr14-A. Hence, holes on the ladders of Sr14-B tend to be more localized. This is considered to be an origin for the occurrence of the magnetic order in Sr14-B under H ∼ 11 T.