Cross -sections of star bodies and dual mixed volumes

In this paper, we establish an extension of Funk's section theorem. Our result has the following corollary: If is a star body in whose central -slices have the same volume (with appropriate dimension) as the central -slices of a centered body , then the dual quermassintegrals satisfy , for any , with equality if and only if . The case that is a centered body implies Funk's section theorem.

     

Cluster-Tilted Algebras of Type D n

Let H be a hereditary algebra of Dynkin type D _n over a field k and 𝒞 _H be the cluster category of H. Assume that n ≥ 5 and that T and T′ are tilting objects in 𝒞 _H . We prove that the cluster-tilted algebra Γ = End_{𝒞 H} (T)^op is isomorphic to Γ′ = End_{𝒞 H} (T′)^op if and only if T = τ ⁱ T′ or T = στ ^j T′ for some integers i and j, where τ is the Auslander–Reiten translation and σ is the automorphism of 𝒞 _H defined in Section 4.     

Harvesting of a phytoplankton–zooplankton model

Considering that some phytoplankton and zooplankton are harvested for food, a phytoplankton–zooplankton model with harvesting is proposed and investigated. First, stability conditions of equilibria and existence conditions of a Hopf-bifurcation are established. Our results indicate that over exploitation would result in the extinction of the population and an appropriate harvesting strategy should ensure the sustainability of the population which is in line with reality. Furthermore, the existence of bionomic equilibria and the optimal harvesting policy are discussed. The present value of revenues is maximized by using Pontryagin’s maximum principle subject to the state equations and the control constraints. We discussed the case of optimal equilibrium solution. It is found that the shadow prices remain constant over time in optimal equilibrium when they satisfy the transversality condition. It is established that the zero discounting leads to the maximization of economic revenue and that an infinite discount rate leads to complete dissipation of economic rent. Finally, some numerical simulations are given to illustrate our results.     

Existence of entire positive solutions for semilinear elliptic systems with gradient term

Under the Keller?COsserman condition on ${\Sigma_{j=1}^{2}f_{j}}$ , we show the existence of entire positive solutions for the semilinear elliptic system ${\Delta u_{1}+|\nabla u_{1}|=p_{1}(x)f_{1}(u_{1},u_{2}), \Delta u_{2}+|\nabla u_{2}|=p_{2}(x)f_{2}(u_{1},u_{2}),x \in \mathbb{R}^{N}}$ , where ${p_{j}(j=1, 2):\mathbb{R}^{N} \rightarrow [0,\infty)}$ are continuous functions.     

基于1–10GHz空地链路信号的雨强监测方法可行性研究

空地链路上的微波信号受降雨影响, 会产生功率衰减和去极化效应. 基于这些物理特性, 本文提出利用1–10 GHz空地链路信号的降雨干扰项获取雨强的方法, 并开展了相关理论研究. 根据空地链路信号与雨滴复杂的相互作用, 研究了空地链路信号频率为1–10 GHz时, 雨强 (rain rate, R) 对衰减 (attenuation, A) 和交叉极化分辨率 (cross-polarization discrimination, XPD)的影响, 分别建立了A-R和XPD-R关系模型. 通过数值模拟, 分别分析了利用上述两个关系模型估测雨强的可行性, 并系统研究了不同频率、极化方式和仰角条件下的适用性. 研究结果表明, 对于水平极化或圆极化, 且频率较高的空地链路信号, 利用A-R关系反演强降雨具有理论上的可行性; 对于不同频率和极化方式的信号, XPD-R关系模型都可以用于反演雨强, 并且对于1–50 mm·h^-1范围内的雨强, XPD较为敏感; 不同仰角条件下, A-R和XPD-R 模型都适用. 在4–10 GHz时, 本文的XPD-R模型和国际电信联盟ITU-R中XPD预测模型的结果非常接近. 所得出的结论对于下一步开展相关的验证实验, 拓展卫星系统的气象应用, 实时估测降雨强度, 实现全球降雨观测具有重要的参考价值. 关键词： 空地链路信号 雨强 衰减特性 交叉极化分辨率(XPD)     

Fredholm theory for pseudoholomorphic curves with brake symmetry

We study the pseudoholomorphic curves with brake symmetry in symplectization of a closed contact manifold. We introduce the pseudo-holomorphic curves with brake symmetry and the corresponding moduli space. Then we get the virtual dimension of the moduli space.     

Large Strain Tensile Deformation and Failure in Oriented Isotactic Polypropylene/Clay Nanocomposite: Role of Voiding and Molecular Orientation

Plane strain compression of isotactic polypropylene iPP)/clay nanocomposite in a channel die at 140 and 160°C, respectively, has been adopted to prepare oriented samples with well-controlled structure for comparative studies. Molecular orientation in the amorphous phase, independent of clay loadings, decreases with increasing preparation temperature, whereas crystallographic orientation is nearly the same for all oriented samples. Severer voiding and void coalescence during stretching, mostly induced by the crystals and inter-chain sliding in the amorphous phase, respectively, is suggested to be responsible for higher volume dilatation and lower failure strain in the oriented samples prepared at higher temperature (e.g., 160°C). Fracture toughness is well correlated with the molecular orientation and crystal-dependent voiding in the oriented samples with respect to preparation temperatures. Furthermore, debonding of clay in the iPP matrix, especially in the oriented samples prepared at 140°C, is another contributor to the enhanced toughness.     

Investigations on the g factors of the ground and excited states for Cu2+ ions in ZnO crystal

The g factors g _// and g _⊥ of the ground Γ₆(² T ₂) and excited Γ_4,5(² E), Γ₆(² E) states for trigonal Cu²⁺ centres in ZnO crystals are calculated from three theoretical methods, the complete diagonalization (of the energy matrix) method, the second-order perturbation method (PTM-I) and the simplified second-order perturbation method (PTM-II, this method was described in an earlier paper). These methods are based on the cluster approach in which the spin-orbit coupling parameters ζ, ζ′ and the orbital reduction factors k, k′ are calculated from a semi-empirical molecular orbital method. The crystal-field parameters used in the calculations are obtained from the superposition model and so the defect structure of Cu²⁺ centres in ZnO can be acquired. The calculated g factors from the three methods are in reasonable agreement with the experimental values and the defect structure of Cu²⁺ centres in ZnO is acquired. It appears that in some cases the approximate PTM can be applied in the studies of g factors of various states. The conditions that the PTM are ineffective are discussed.     

台湾地区高校基础物理教育见闻和一些感想

值台湾地区2015年物理学年会之际,应新竹清华大学邀请,作者一行4人于2015年1月27日至2015年2月5日赴新竹清华大学观摩物理学年会教育分会,并参观考察了台北东吴大学、新竹清华大学、新竹交通大学、高雄中山大学、台中中兴大学和桃园中央大学等校的物理系物理基础教育的情况.文章就10天来的所见所闻以及对有关问题的深入交流介绍给读者,并谈一下自己的感想,谨供同仁参考.     

OPCOT在Ru(0001)表面上的紫外光电子能谱研究

采用紫外光电子能谱,研究了新型有机发光材料八芳基环辛四烯(OPCOT)在金属Ru(0001)表面上的电子结构,以及它们之间的相互作用.位于费米能级以下43,69,93和114eV处的4个谱峰分别来自于OPCOT材料中苯环的πCC,σCC,σCH和σHH轨道,位于30eV处的谱峰反映了8个苯环聚合后具有π轨道特性的C—C键.OPCOT材料的价带顶位于费米能级以下25eV处,OPCOT材料在Ru(0001)表面上的功函数为395eV.150℃以下,OPCOT材料可以在Ru(0001)表面稳定存在.随温度的升高,OPCOT材料主要以脱附的形式减少 关键词： 八芳基环辛四烯 光电子能谱 价电子结构 脱附