拟常曲率空间的紧致极小子流形

通过揭示拟常曲率空间中紧致极小子流形Ｍ的内在量Ｋ、Ｑ和Ｒ之间的关系，给出拟常曲率空间紧致极小子流形是全测地子流形的几个充分条件．推广和包含了常曲率空间中Ｓ．Ｔ．Ｙａｕ的一个相应结果．     

A Simplified Convergence Proof for the Cone Partitioning Algorithm

We present a new convergence result for the cone partitioning algorithm with a pure -subdivision strategy, for the minimization of a quasiconcave function over a polytope. It is shown that the algorithm is finite when -optimal solution with > 0 are looked for, and that any cluster point of the points generated by the algorithm is an optimal solution in the case = 0. This result improves on the one given previously by the authors, its proof is simpler and relies more directly on a new class of hyperplanes and its associated simplicial lower bound.     

On extended versions of Dancs-Hegedüs-Medvegyev’s fixed-point theorem

In this article, we establish some fixed-point (known also as critical point, invariant point) theorems in quasi-metric spaces. Our results unify and further extend in some regards the fixed-point theorem proposed by Dancs, S.; Hegedüs, M.; Medvegyev, P. (A general ordering and fixed-point principle in complete metric space. Acta Sci. Math. 1983;46:381–388), the results given by Khanh, P.Q., Quy D.N. (A generalized distance and enhanced Ekeland?s variational principle for vector functions. Nonlinear Anal. 2010;73:2245–2259), the preorder principles established by Qiu, J.H. (A pre-order principle and set-valued Ekeland variational principle. J. Math. Anal. Appl. 2014;419:904–937) and the results obtained by Bao, T.Q., Mordukhovich, B.S., Soubeyran, A. (Fixed points and variational principles with applications to capability theory of wellbeing via variational rationality. Set-Valued Var. Anal. 2015;23:375–398). In addition, we provide examples to illustrate that the improvements of our results are significant.     

准二能级阈值泵浦光纤激光器的理论分析

 根据含损耗系数的稳态速率方程组,对掺准二能级稀土粒子光纤激光器的泵浦阈值进行了分析和完全解析求解。求得了泵浦阈值功率的显函数解析式,得到了泵浦光阈值功率随光纤位置变化的隐函数表达式,以及信号光功率和上能级粒子数随光纤位置变化的解析表达式。对所得的解进行了数值分析,并与已有的理论和实验结果进行了比较分析。结果表明：由于忽略了信号光和泵浦光损耗系数,不同近似条件下给出的泵浦阈值功率均比实验值低,但所导出的理论研究结果与已有实验结果的差异最小。     

基于四维表示的模糊数赋权排序及简便加减运算

引进模糊数的四维表示,并据此给出一种新的排序方法,简化了模糊数特别是e-型模糊数的加减运算。     

拟Z-代数domain

基于一般子集系统Z,引入拟Z-代数domain的概念,研究了拟Z-代数domain的一些映射性质,并讨论了拟Z-代数domain与拟Z-连续domain之间的关系及拟Z-代数domain的乘积。     

Analytical Solutions of the Schrödinger Equation with Power Potentials

Conditions for the existence of polynomial solutions of the Schrödinger equation with potentials which are linear combinations of powers of r ranging from ?2 to 2m, where m is a non‐negative integer, are derived and explicit expressions for the coefficients are given. Potentials with m = 0, 1, 2 are discussed in detail.     

Oscillating magnetocaloric effect in quantum nanoribbons

We investigate the oscillating magnetocaloric effect on a diamagnetic nanoribbon, using the model of a quasi-one-dimensional electron gas (Q1DEG) made with a parabolic confinement potential. We obtained analytical expressions for the thermodynamic potential and for the entropy change. The entropy change exhibits the same dependence on field and temperature observed for other diamagnetic systems. The period of the field-oscillating pattern is ~0.1 mT and the temperature of maximum entropy change is ~0.1 K with an applied field of the order of 1 T. An interesting feature of the results is the dependence of the oscillations with the strength of the confinement potential, as well as the possibility to provide a relationship among this last with nanoribbon width. In the limit of null confinement potential our expressions match those for the 2D diamagnetic system.     

ASYMPTOTIC NORMALITY OF QUASI MAXIMUM LIKELIHOOD ESTIMATE IN GENERALIZED LINEAR MODELS

For the Generalized Linear Model (GLM), under some conditions including that the specification of the expectation is correct, it is shown that the Quasi Maximum Likelihood Estimate (QMLE) of the parameter-vector is asymptotic normal. It is also shown that the asymptotic covariance matrix of the QMLE reaches its minimum (in the positive-definte sense) in case that the specification of the covariance matrix is correct.