Partition Lattice q-Analogs Related to q-Stirling Numbers

We construct a family of partially ordered sets (posets) that are q-analogs of the set partition lattice. They are different from the q-analogs proposed by Dowling [5]. One of the important features of these posets is that their Whitney numbers of the first and second kind are just the q-Stirling numbers of the first and second kind, respectively. One member of this family [4] can be constructed using an interpretation of Milne [9] for S[n, k] as sequences of lines in a vector space over the Galois field F _q. Another member is constructed so as to mirror the partial order in the subspace lattice.     

SOLVABILITY OF FORWARD-BACKWARD SDES AND THE NODAL SET OF HAMILTON-JACOBI-BELLMAN EQUATIONS

The solvability of a class of forward-backward stochastic differential equations (SDEs for short) over an arbitrarily prescribed time duration is studied. The authors design a stochastic relaxed control problem, with both drift and difftusion all being controlled, so that the solvability problem is converted to a problem of finding the nodal set of the viscosity solution to a certain Hamilton-Jacobi-Bellman equation. This method overcomes the fatal difficulty encountered in the traditional contraction mapping approach to the existence theorem of such SDEs.     

分段函数的分类及分离型分段函数与初等函数之间的关系

将分段函数划分为连结型分段函数 ,分离型分段函数和它们的组合形式三种类型 ,得到了分离型分段函数是初等函数的充分必要条件 ,完整地解决了分离型分段函数与初等函数之间的关系 ,并且给出了初等函数在其任一截取集上的限制函数 (截取函数 )仍然是初等函数的结果     

An Interval-Parameter Fuzzy Approach for Multiobjective Linear Programming Under Uncertainty

An interval-parameter fuzzy linear programming method (IFMOLP) is proposed in this study for multiple objective decision-making under uncertainty. As a hybrid of interval-parameter and fuzzy methodologies, the IFMOLP incorporates interval-parameter linear programming and fuzzy multiobjective programming approaches to form an integrated optimization system. The method inherits advantages of interval-parameter programming, and allows uncertainties and decision-makers’ aspirations to be effectively communicated into its programming processes and resulting solutions. Membership functions for both objectives and constraints are formulated to reflect uncertainties in different system components and their interrelationships. An interactive solution procedure has been developed based on solution approaches of the interval-parameter and fuzzy programming techniques, plus necessary measures for handling the multiobjective feature. A didactic example is provided in the paper to illustrate the detailed solution process. Possibilities of further improvements by seeking Pareto optimum and incorporating flexible preference within constraints are also discussed.     

一种计算量子拍讯号强度的新方法

本文运用密度矩阵方程推导了V型三能级系统的荧光量子拍讯号强度,并对其结果进行了分析和讨论。     

仿紧集上的拟—似变分不等式

借助于文（１）中的结论研究了仿紧集上的拟－似变分不等式，统一和发展了文（２－６）中的相应结果。     

A high spin isomer in 153Eu

A search for new isomers of nanosecond lifetimes were carried out in ¹⁵³Eu via the ¹⁵⁰Nd(⁷Li,xnγ) reaction. The single particle angular momentum alignment and dynamical moment of inertia estimated from the experimental data indicate a configuration change at rotational energy ħω∼ 0.30 MeV. A decrease of B(E2) values is also observed at the same frequency. An isomeric level is identified at an excitation energy of 3100 keV (J^π=35/2⁻) which corresponds to this frequency. The lifetime of the level is found to be 8.6 ± 1.3 nanosecond. Received: 22 April 1997 / Revised version: 26 September 1997     

Rotational bands in 181Ta

High-spin states in ¹⁸¹Ta have been studied via the ¹⁷⁶Yb(¹¹B,α2n) reaction at 52 MeV using the PEX array and at 57 MeV using the NORDBALL array, with α-particle detection. The previously known, K^π=(7/2)⁺ ground state band and K^π=(9/2)⁻ band have been extended to spins (29/2)⁺ and (31/2)⁻, respectively. Two new one-quasiparticle bands, the K^π=(5/2)⁺ band built on the known (5/2)⁺ isomer and a K^π=((1/2)⁻) band have been observed. Two other rotational bands with three-quasiparticle structure, K^π=(15/2)⁻ and ((19/2)⁺ with π(7/2)[404]ν²(1/2)[510](9/2)[624] and π(9/2)[514]ν²(1/2)[510](9/2)[624] configurations, respectively, have been newly observed. The half-life of the K^π=((19/2)⁺) bandhead which decays to the head of the (15/2)⁻ band has been measured to be 140(36) ns. However, transitions from the ((19/2)⁺) state to the (15/2)⁻ band have not been observed. Received: 26 August 1998     

Spectroscopy on very neutron-rich nuclei beyond N = 20

Recent studies on nuclear structure by using radioactive isotope beams available at the RIKEN projectile-fragment separator (RIPS) are introduced. Special emphasis is given to two selected experiments from recent programs that highlight studies on the magicity loss observed for very neutron-rich nuclei beyond N = 20 in the “island-of-inversion” region; the particle stability of ³¹F, and the low-lying excited states of ³⁴Mg. Received: 1 May 2001 / Accepted: 4 December 2001     

Evolution of shapes in 59Cu

High-spin states in ⁵⁹Cu were populated using the fusion-evaporation reaction ²⁸Si + ⁴⁰Ca at a beam energy of 122 MeV. The Gammasphere Ge-detector array in conjunction with the 4π charged-particle detector array Microball allowed for the detection of γ-rays in coincidence with evaporated light particles. The resulting extensive high-spin decay scheme of ⁵⁹Cu is presented, which comprises more than 320 γ-ray transitions connecting about 150 excited states. Their spins and parities have been assigned via directional correlations of γ-rays emitted from oriented states. Average quadrupole moments of rotational bands have been determined from the analysis of residual Doppler shifts. Shell model calculations in the fp shell are invoked to study some of the low-spin states, while the experimental characteristics of the rotational bands are analyzed in the configuration-dependent cranked Nilsson-Strutinsky (CNS) approach. Received: 15 February 2002 / Accepted: 23 April 2002