Cochran's statistical theorem for outer inverses of matrices and matrix quadratic forms

We extend the matrix version of Cochran's statistical theorem to outer inverses of a matrix. As applications, we investigate the Wishartness and independence of matrix quadratic forms for Kronecker product covariance structures.     

ANTI FUZZY VECTOR SPACES（Ⅱ）

ＡＮＴＩＦＵＺＺＹＶＥＣＴＯＲＳＰＡＣＥＳ（Ⅱ）ＣｈｅｎＹｏｎｇｎｉａｎ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＸｉｎｊｉａｎｇＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，８３００５４，Ｘｉｎｊｉａｎｇ，Ｐ．Ｒ．Ｃｈｉｎａ）ＡＮＴＩＦＵＺＺＹＶＥＣＴ...     

AN ENCOMPASSING APPROACH TO MODELING FISHERY DYNAMICS: MODELING DYNAMIC NONLINEAR SYSTEMS

Uncertainty about the nature and significance of nonlinearities and the manner in which dynamics affect future realizations makes model specification the most difficult aspect of modeling dynamic systems. By interpreting several popular fishery models as subcases of a nesting dynamic Taylor series approximation, we isolate the specification differences between these models in a way that accounts for commonalities. On the argument that the differences due to alternative nonlinear forms are likely to be small compared to more mundane considerations such as delay difference and general dynamic lag specification, we propose an alternative model that uses the terms from the first order approximation common to all models combined with a data-based determination of the appropriate lags using the methods of state space time series analysis. Finally, the success of the alternative models is judged in an application to Pacific halibut data.     

我国空间物理学先驱桂质廷──纪念桂质廷教授100周年华诞

桂质廷（１８９５～１９６１），我国著名的地球物理学家．他是建国初期中国科学院地球物理组专门委员，第一个巡测了我国境内地磁常量的中国人．他最先和学生一道在国内进行了高空电离层的常规观测．他所创建的武汉大学游离层实验室，５０年来未曾间断电离层的观测研究．本文着重介绍他的生平简历、教学态度、学术成就和爱国主义思想．     

Momentum space distribution of electrons in an atom using hydrogenic wave functions

A formulation is developed to derive exact analytic expressions for electron-electron correlation and density of electrons in momentum space using hydrogenic wave functions. It is shown that for large atoms the expression for density of electrons has a simple form.     

On the Positivity of the Coefficients of a Certain Polynomial Defined by Two Positive Definite Matrices

It is shown that the polynomialp(t) = Tr[(A+tB)^m]has positive coefficients when m = 6 and A and B are any two 3-by-3 complex Hermitian positive definite matrices. This case is the first that is not covered by prior, general results. This problem arises from a conjecture raised by Bessis, Moussa, and Villani in connection with a long-standing problem in theoretical physics. The full conjecture, as shown recently by Lieb and Seiringer, is equivalent to p(t) having positive coefficients for any m and any two n-by-n positive definite matrices. We show that, generally, the question in the real case reduces to that of singular A and B, and this is a key part of our proof.     

Riemannian manifolds in noncommutative geometry

We present a definition of Riemannian manifold in noncommutative geometry. Using products of unbounded Kasparov modules, we show one can obtain such Riemannian manifolds from noncommutative spin^c${}^c$ manifolds; and conversely, in the presence of a spin^c${}^c$ structure. We also show how to obtain an analogue of Kasparov’s fundamental class for a Riemannian manifold, and the associated notion of Poincaré duality. Along the way we clarify the bimodule and first-order conditions for spectral triples.     

Observation of the exchange spring behavior in hard-soft-ferrite nanocomposite

Nanocomposite of hard (BaFe₁₂O₁₉) and soft ferrite (Ni_0.8Zn_0.2Fe₂O₄) are prepared by the mixing of the individual ferrite components at appropriate ratio and subsequent heat treatment. Initially the microstructure of the individual phases is controlled by suitable processing. We have observed the exchange spring behavior in the soft-hard ferrite composite for the first time by tailoring the particle size of the individual phases and by suitable thermal treatment of the composite. It is found that the exchange interaction dominates over the dipolar interaction for smaller particle sizes of the soft ferrite. The magnetization of the composite showed hysteresis loop that is characteristic of the exchange spring system. This gives experimental proof for some theoretical modeling as well as paves way for developing magnet with higher (BH)_max product based on ferrites.     

Subgroups of index 4 of the 2-dimensional space groups

There are 281 subgroups of index 4 for the 17 types of 2-dimension space groups: p1:7, p2:31, pm:19, pg:7, cm:11, p2mm:67, p2mg:23, p2gg:11, c2mm:31, p4:11, p4mm:31, p4gm:11, p3:4, p3m1:4, p31m:4, p6:4, p6mm:5. Every subgroup has been identified by its conventional cell disposition with respect to the conventional cell of the starting group. These subgroups may be arranged in 96 automorphism classes and 184 conjugation classes according to their starting groups.