答YapH.P.和TeoS.K.问题

本文证得：如果Ｆ是Ｃｎ中的一条种路，则Ｇ中同时通过ｋ余弦ｅ１，ｅ２，．．．，ｅｋ而不通过Ｆ中的任一条边的圈最多只有一个且Ｇ中同时通过ｋ条弦ｅ１，ｅ２，．．．，ｅｋ的圈最多只有２个，进而由之给出了Ｍ（ｋ）的上界和ｍ（ｋ）的下界及ｍ（ｋ）＝（ｋ＋１）（ｋ＋２）／２成立的一个条件，否定地回答了ＹａｐＨ．Ｐ．和ＴｅｏＳ．Ｋ．１９８４年提出的一个问题。     

演化参数反演方法

给出了一类基于演化计算的演化参数反演方法,此类方法既可以给定参数的函数类,用遗传算法（Genetic Algorithms）来反演参数的最优估计值,也可以不指定函数类形式,用遗传程序设计（Genetic Programming）的方法反演出最优的函数模型,使参数反演实现客观化、自动化.由此建立反演系统后,在使用过程中可以根据最新获得的数据对模型中的物理参数作适时校准,一旦发现预报误差较大,就利用演化算法及时修正方程中的参数以改进预报.运用该方法于椭圆边值问题的物理参数反演的数值模拟,证实了此方法的有效性,为物理模型参数的反演提供了一种崭新的实用方法.     

格林函数变号时二阶离散周期边值问题正解的存在性

运用锥上的不动点指数理论,讨论了格林函数变号时的二阶离散周期边值问题■当λb(t)≡1时,该问题存在正解;当b:[1,n]_Z→R⁺时,该问题不存在正解,其中f∈C (R⁺,R⁺),k为满足■的常数,λ为参数■     

Algebraic Multigrid Preconditioning for Finite Element Solution of Inhomogeneous Elastic Inclusion Problems in Articular Cartilage

In studying biomechanical deformation in articular cartilage, the presence of cells (chondrocytes) necessitates the consideration of inhomogeneous elasticity problems in which cells are idealized as soft inclusions within a stiff extracellular matrix. An analytical solution of a soft inclusion problem is derived and used to evaluate iterative numerical solutions of the associated linear algebraic system based on discretization via the finite element method, and use of an iterative conjugate gradient method with algebraic multigrid preconditioning (AMG-PCG). Accuracy and efficiency of the AMG-PCG algorithm is compared to two other conjugate gradient algorithms with diagonal preconditioning (DS-PCG) or a modified incomplete LU decomposition (Euclid-PCG) based on comparison to the analytical solution. While all three algorithms are shown to be accurate, the AMG-PCG algorithm is demonstrated to provide significant savings in CPU time as the number of nodal unknowns is increased. In contrast to the other two algorithms, the AMG-PCG algorithm also exhibits little sensitivity of CPU time and number of iterations to variations in material properties that are known to significantly affect model variables. Results demonstrate the benefits of algebraic multigrid preconditioners for the iterative solution of assembled linear systems based on finite element modeling of soft elastic inclusion problems and may be particularly advantageous for large scale problems with many nodal unknowns.     

潜体在非均质流体中的平衡位置与平衡过程

以探空气球为例,讨论潜体在非均质流体中的平衡位置与平衡过程.     

关于态叠加原理的认同与争议

给出了不同学者关于量子力学态叠加原理的几种表述,分析比较了关于该原理的有关观点的争议,并对其中的原因进行了讨论。     

一维辐射系统吸收系数的反问题

辐射反问题是当前的研究热点之一。本文采用离散坐标法求解正问题,用共轭梯度法求解一维系统吸收系数的反问题。用正问题的计算结果加上误差作为反问题的求解条件。数值计算的结果表明,共轭梯度法可以比较好的反演辐射系统的吸收系数。在考虑散射时,反演效果比不考虑散射的反演效果好。     

Protective measurement and quantum reality

It is shown that from the expectation values of obervables, which can be measured for a single system using protective measurements, the linear structure, inner product, and observables in the Hilbert space can be reconstructed. A universal method of measuring the wave function of a single particle using its gravitational field is given. Protective measurement is generalized to the measurement of a degenerate state and to many particle systems. The question of whether the wave function is real is examined, and an argument of Einstein in favor of the ensemble interpretation of quantum theory is refuted.     

Laser produced plasma: A pumping source for cadmium photo-ionization laser

We report laser oscillations in Cd II on 4d ⁹5s ^{2 2} D _5/2 − 4d ¹⁰5p ² P _3/2 transition at 441.6 nm using laser produced tungsten plasma as a pumping source. Mach Zehnder interferometer is used to measure electron density. Design and working of the crossed heat pipe used in the studies is discussed.     

Flavour democracy calls for the fourth generation

It is argued with the help of an illustrative model, that the inter species hierarchy among the fermion masses and the quark mixing angles can be accommodated naturally in the standard model with (approximate) flavor democracy provided there are three exactly massless neutrinos and four families of sequential quark-leptons with all members of the fourth family having roughly equal masses. The special problem of light neutrino masses (if any) and possible solutions are also discussed.