Continuous and impulsive vaccination of SEIR epidemic models with saturation incidence rates

In this paper, two delayed SEIR epidemic models with continuous and impulsive vaccination and saturating incidence are investigated. The dynamical behaviors of the disease are analyzed. For continuous vaccination, we obtain a basic reproductive number _R1$R_1$ and prove that if _R1≤1$R_1\le 1$ then the disease-free equilibrium is globally attractive and if _R1>1$R_1>1$ then the disease is permanent by using the Lyapunov functional method. For impulsive vaccination, we obtain two thresholds R^∗$R^{\ast }$ and _R∗$R_{\ast }$ and prove that if R^∗<1$R^{\ast }<1$ then the disease-free periodic solution is globally attractive and if _R∗>1$R_{\ast }>1$ then the disease is permanent by using the comparison theorem of impulsive differential equation and the Lyapunov functional method. Lastly, we compared the effects of two vaccination strategies.     

On the surface area of the -star graph

We present an explicit formula for the surface area of the (n,k)-star graph, i.e., the number of nodes at a certain distance from the identity node in the graph, by identifying the unique cycle structures associated with the nodes in the graph, deriving a distance expression in terms of such structures between the identity node of the graph and any other node, and enumerating those cycle structures satisfying the distance restriction.The above surface area derivation process can also be applied to some of the other node symmetric interconnection structures defined on the symmetric group, when the aforementioned distance expression is available.     

Group path covering and distance two labeling of graphs

For a positive integer d, an L(d,1)-labeling f of a graph G is an assignment of integers to the vertices of G such that |f(u)−f(v)|?d if uv∈E(G), and |f(u)−f(v)|?1 if u and u are at distance two. The span of an L(d,1)-labeling f of a graph is the absolute difference between the maximum and minimum integers used by f. The L(d,1)-labeling number of G, denoted by λd,1(G), is the minimum span over all L(d,1)-labelings of G. An L^′(d,1)-labeling of a graph G is an L(d,1)-labeling of G which assigns different labels to different vertices. Denote by the L^′(d,1)-labeling number of G. Georges et al. [Discrete Math. 135 (1994) 103-111] established relationship between the L(2,1)-labeling number of a graph G and the path covering number of Gc, the complement of G. In this paper we first generalize the concept of the path covering of a graph to the t-group path covering. Then we establish the relationship between the L^′(d,1)-labeling number of a graph G and the (d−1)-group path covering number of Gc. Using this result, we prove that and for bipartite graphs G can be computed in polynomial time.     

Solving Third Order Differential Equations with Maximal Symmetry Group

The largest group of Lie symmetries that a third-order ordinary differential equation (ode) may allow has seven parameters. Equations sharing this property belong to a single equivalence class with a canonical representative v ^′′′(u)=0. Due to this simple canonical form, any equation belonging to this equivalence class may be identified in terms of certain constraints for its coefficients. Furthermore a set of equations for the transformation functions to canonical form may be set up for which large classes of solutions may be determined algorithmically. Based on these steps a solution algorithm is described for any equation with this symmetry type which resembles a similar scheme for second order equations with projective symmetry group. Received March 9, 2000; revised June 8, 2000     

On the Efficient Evaluation of Coalescence Integrals in Population Balance Models

The solution of population balance equations is a function f(t,r,x) describing a population density of particles of the property x at time t and space r. For instance, the additional independent variable x may denote the particle size. The describing partial differential equation contains additional sink and source terms involving integral operators. Since the coordinate x adds at least one further dimension to the spatial directions and time coordinate, an efficient numerical treatment of the integral terms is crucial. One of the more involved integral terms appearing in population balance models is the coalescence integral, which is of the form ∫ ₀ ^x κ(x–y, y) f(y) f(x–y)dy. In this paper, we describe an evaluation method of this integral which needs only operations, where n is the number of degrees of freedom with respect to the variable x. This cost can also be obtained in the case of a grid geometrically refined towards x=0.     

Systems programming for data communications on minicomputers

This paper examines some of the special considerations which apply to the development of such software for minicomputers. These are treated under the following general categories:

• loading and throughput
• the external interfaces of the system software
• the internal structure of the system software
• developing the software

.     

基于EPP-CAN接口卡的蓄电池组智能化成检测系统

针对蓄电池组充放电系统中单体电池数量较多，充放电时间较长，全部采集数据难于保存在微控制器中的实际情况，提出了一种EPP-CAN的智能接口解决方案，给出了硬件电路组成以及基于Delphi的软件实现方法。     

豫豆-25 11S球蛋白凝胶性的研究Ⅱ.加热时间和中性盐的影响

研究了加热时间和中性盐对豫豆 2511S球蛋白凝胶质构特性的影响.结果表明:随着加热时间的延长,凝胶的硬度、脆度、粘性增加,但30min后增加趋势不明显,豫豆 2511S球蛋白要形成成熟的、质构性能优良的凝胶,加热时间以大于30min为宜;NaCl对酸性凝胶与碱性凝胶的影响有很大的差异.     

PLC在三峡临时船闸人字门运行速度控制中的应用

本文描述了ＰＬＣ（可编程控制器）在液压泵控调速系统中的一个成功应用，提供了ＰＬＣ采用参数设置，高速计数、时钟中断、曲线控制等方法实现特殊的、复杂的工业过程控制的一些思路。     

多CPU微机数据并行处理系统的研究与实现

本文从计算机数据处理的实际需要出发，在对ＴＭＳ３２０Ｃ２５单片计算机和ＰＣ机处理数据进行研究的基础上，讨论了由两片ＴＭＳ３２０Ｃ２５构成的并行加速卡与ＰＣ机组成的硬件环境实现的有关问题。