逆（反）对策问题与“奇门遁甲”预测理论（术）

本文首先提出逆（反）对策这一新问题，给出了数学模型；探讨了“奇门遁甲”预测理论（术）中的数学问题；通过系统分析“专门遁甲”预测过程，可知它的预测过程隐含着一个特殊的逆（反）对策问题；最后指出逆（反）对策问题的广泛存在并给出案例分析．     

Riemannian Manifolds in Which Certain Curvature Operator Has Constant Eigenvalues along Each Circle

Riemannian manifolds for which a natural curvature operator has constant eigenvalues on circles are studied. A local classification in dimensions two and three is given. In the 3-dimensional case one gets all locally symmetric spaces and all Riemannian manifolds with the constant principal Ricci curvatures r ₁ = r ₂ = 0, r ₃= 0 , which are not locally homogeneous, in general.     

Assessing the Error Probability of the Model Selection Test

The asymptotic error probability of Linhart's model selection test isevaluated, and compared with the nominal significance level. We examine thecase where the expected discrepancies of the candidate models from the truemodel are asymptotically equal. The local alternatives method is employed inthe limiting operation of the asymptotic evaluation. Although the errorprobability under the null hypothesis is actually shown to be equal to orless than the level for most situations, intolerable violations of the errorcontrol are observed for nested models: It is often erroneously concludedthat the smaller model is significantly better than the larger model. Toprevent this violation, a modification of Linhart's test statistic isproposed. The effectiveness of the proposed test is confirmed throughtheoretical analysis and numerical simulations.     

自相似结构壳模型

为了扩展以简谐振子为基矢的常规壳模型（ＳＭ）计算到晕核，提出了自相似结构壳模型（ＳＳＭ）．通过对简谐振子动能项和势能项的重度规以及单粒子平均场模拟，可以得到ＳＳＭ中的单粒子轨道有态相关的圆频率，在ＳＳＭ中，晕核大的均方根半径、厚的中子皮以及Ｂｏｒｒｏｍｅａｎ晕核和的束缚态性质能够再现出来。     

一类新的插值结点

有界单连通区域Ｇ，其边界θＧ＝Г∈（１，α），α〉０。本计算节以广义Ｆａｂｅｒ多项式φｎ（ｚ）的零点为插值结点的Ｌａｇｒａｎｇｅ插值多项式的逼近性质，得到了它对Ａ（Ｇ↑－）中的函数的一致逼近阶和平均逼近阶的估计，并且得到了它对Ｅ＾ｐ（Ｇ）中函数的平均逼近阶的估计，还指出关于平均逼近阶的估计是不可改进的。     

广义分解定理与两个不等式

本文给出了Banach空间广义分解定理的一个初等证明,并利用它来证明两个对称不等式.这是首次在Banach空间获得这样的不等式.     

Comparative analysis of heterogeneous solid and soft materials by adsorption, NMR and thermally stimulated depolarisation current methods

Structural characterisation of such bio-objects as fibrinogen solution, yeast cells, wheat seeds and bone tissues has been done using two versions of cryoporometry based on the integral Gibbs-Thomson (IGT) equation for freezing point depression of pore liquids and the measurements by ¹H NMR spectroscopy (180-200 < T < 273 K) and the thermally stimulated depolarisation current (TSDC) method (90 < T < 273 K) of structured water. The IGT equation was solved using a self-consisting regularization procedure including the maximum entropy principle applied to the distribution function of pore size (PSD). Both methods give clear pictures of changes in the structural characteristics caused, e.g., by hydration and swelling of wheat seeds and yeast cells, coagulation and interaction of fibrinogen with solid nanoparticles in the aqueous media, and the human bone tissue disease.     

抓好数学建模竞赛 推动数学教学改革

本文通过近几年组织数学建模教学和指导学生参加竞赛的实践 ,探索抓好数学建模竞赛 ,促进数学教学改革 ,推动数学素质教育 ,提高人才培养质量的途径、措施和方法     

Little higgs models and T parity

Little Higgs models are an interesting extension of the Standard Model at the TeV scale. They provide a simple and attractive mechanism of electroweak symmetry breaking. We review one of the simplest models of this class, the Littlest Higgs model, and its extension with T parity. The model with T parity satisfies precision electroweak constraints without fine-tuning, contains an attractive dark matter candidate, and leads to interesting phenomenology at the Large Hadron Collider (LHC).     

The π-π-theorem for manifold pairs with boundaries

The surgery obstruction of a normal map to a simple Poincaré pair (X, Y) lies in the relative surgery obstruction group L _*(π ₁(Y) → π ₁(X)). A well-known result of Wall, the so-called π-π-theorem, states that in higher dimensions a normal map of a manifold with boundary to a simple Poincaré pair with π ₁(X) ? π ₁(Y) is normally bordant to a simple homotopy equivalence of pairs. In order to study normal maps to a manifold with a submanifold, Wall introduced the surgery obstruction groups LP _* for manifold pairs and splitting obstruction groups LS _*. In the present paper, we formulate and prove for manifold pairs with boundary results similar to the π-π-theorem. We give direct geometric proofs, which are based on the original statements of Wall’s results and apply obtained results to investigate surgery on filtered manifolds.