Pure tetrahedral quadruple systems with index two

An oriented tetrahedron defined on four vertices is a set of four cyclic triples with the property that any ordered pair of vertices is contained in exactly one of the cyclic triples. A tetrahedral quadruple system of order $n$ with index $\lambda$, denoted by ${\text{TQS}}_{\lambda }\left(n\right)$, is a pair $\left(X,\mathrm{?}\right)$, where $X$ is an $n$‐set and $\mathrm{?}$ is a set of oriented tetrahedra (blocks) such that every cyclic triple on $X$ is contained in exactly $\lambda$ members of $\mathrm{?}$. A ${\text{TQS}}_{\lambda }\left(n\right)$ is pure if there do not exist two blocks with the same vertex set. When $\lambda =1$, the spectrum of a pure TQS $\left(n\right)$ has been completely determined by Ji. In this paper, we show that there exists a pure ${\text{TQS}}_2\left(n\right)$ if and only if $n\equiv 1,2\left(\mathrm{mod}3\right)$ and $n\ge 7$. A corollary is that a simple ${\text{QS}}_4\left(n\right)$ also exists if and only if $n\equiv 1,2\left(\mathrm{mod}3\right)$ and $n\ge 7$.     

Epidemiological models with quadratic equation for endemic equilibria—A bifurcation atlas

The existence and occurrence, especially by a backward bifurcation, of endemic equilibria is of utmost importance in determining the spread and persistence of a disease. In many epidemiological models, the equation for the endemic equilibria is quadratic, with the coefficients determined by the parameters of the model. Despite its apparent simplicity, such an equation can describe an amazing number of dynamical behaviors. In this paper, we shall provide a comprehensive survey of possible bifurcation patterns, deriving explicit conditions on the equation's parameters for the occurrence of each of them, and discuss illustrative examples.     

作业成本法数学模型的创新

随着企业产品价格竞争愈演愈烈，成本的合理分配、计算日显重要，但在间接费用的分摊上，传统成本会计对成本信息反映失真的局限性日益显露，会计理论界和实务界开始寻求一种新的准确的成本计算方法，作业成本法应运而生。本将由作业成本法基本原理推导出其数学模型，并将对其数学模型进一步改进，建立比较数学模型。使作业成本法向实际应用更进一步。     

Liquid-liquid phase equilibria of aqueous two-phase systems containing salts and polyethylene glycol

Liquid-liquid phase equilibria of the ternary systems: (a) polyethylene glycol - ammonium sulfate- water and (b) polyethylene glycol - sodium carbonate -water have been determined experimentally at 15°, 25°, 35° and 45°C and for two different molecular weights of the polymer (Avg. M.W. 1000 and 2000). Details of the glass cell and of the equilibration and analytical procedures used are described. Equilibrium data along with phase diagrams are presented. Finally the effect of temperature and of the molecular weight of the polymer are also discussed.     

Mathematical models of innovation diffusion with stage structure

Mathematical models with stage structures are proposed to describe the process of awareness, evaluation and decision-making. First, a system of ordinary differential equations is presented that incorporates the awareness stage and the decision-making stage. If the adoption rate is bilinear and imitations are dominant, we find a threshold above which innovation diffusion is successful. Further, if the adoption rate has a higher nonlinearity, it is shown that there exist bistable equilibria and a region such that an innovation diffusion is successful inside and is unsuccessful outside. Secondly, a model with a time delay is proposed that includes an evaluation stage of a product. It is proved that the system exhibits stability switches. The bifurcation direction of equilibria is also discussed.     

物质纯重力场部分的能量-动量张量研究

认为物质的质量(能量)存在形式可分为两部分，一部分是以纯物质形式存在的，另一部分是以纯重力场形式存在的.物质质量(能量)这两种形式各自对应着相应的能量 动量张量，物质总的能量-动量张量可表示为Tμν=T(Ⅰ)μν+T(Ⅱ)μν,这里，T(Ⅰ)μν，T（Ⅱ）μν分别代表物质纯物质部分和纯重力场部分的能量-动量张量.通过类比电磁理论，定义：ωμ≡-c2gμ0/g00,并引入一个反对称张量Dμν=ωμ/xν-ων/xμ，则物质纯重力场部分的能量-动量张量为T(Ⅱ)μν=(DμρDρν-gμνDαβDαβ/4 关键词： 能量-动量张量 纯重力场 重力场方程 标量重力势 矢量重力势     

氢氟烃/烷烃二元混合物的气液相平衡

整理了已公开发表的氢氟烃(HFC)/烷烃(HC)二元混合物气液相平衡实验数据,对实验数据进行了热力学一致性检验。采用PR方程加van der Waals混合规则描述该类混合物的气液相平衡性质,优化得到了11种混合物的二元交互作用系数,经比较表明采用优化结果能够高精度再现气液相平衡实验数据,比k_(ij)取0的计算结果有很大改善.     

On the origin of irreproducible behaviour of Na1−xLixNbO3 solid solutions

The irreproducibility of electrical properties of Na_0.88Li_0.12NbO₃ solid solution on thermal cycling reported by M.A.L. Nobre and S. Lanfredi is explained by gradual decomposition of the supersaturated solid solution below ca. 800 °C.     

Simple Entanglement Measure for Multipartite Pure States

A simple entanglement measure for multipartite pure states is formulated based on the partial entropy of a series of reduced density matrices. Use of the proposed new measure to distinguish disentangled, partially entangled, and maximally entangled multipartite pure states is illustrated.