The invariants of the binary nonic

We consider the algebra of invariants of binary forms of degree 9 with complex coefficients, find the 92 basic invariants, give an explicit system of parameters and show the existence of four more systems of parameters with different sets of degrees.     

On complete system of invariants for the binary form of degree 7

A minimal system of homogeneous generating elements of the algebra of invariants for the binary form of degree 7 is calculated.     

A complete minimal system of covariants for the binary form of degree 7

A minimal system of 147 homogeneous generators of the algebra of covariants for the binary form of degree 7 is calculated.     

基于二元决策图的集群计算系统性能分析

针对节点计算能力相同但故障分布不同的集群系统的性能分析问题,基于k-to-l-out-of-n结构对集群系统的性能进行建模,并提出了一种基于二元决策图（BDD）的分析方法。针对k-to-l-out-of-n结构的BDD模型生成问题,分析了BDD的结构特征并设计自顶向下生成算法,克服了传统的自底向上生成算法必须生成大量中间冗余节点的缺陷;然后利用生成的BDD模型高效地计算出系统处于一个特定性能级别的概率;最后通过实例说明了BDD方法能够有效分析节点具有不同故障分布的集群系统性能。     

On the complexity of binary samples

Consider a class of binary functions h: X→{ − 1, + 1} on an interval . Define the sample width of h on a finite subset (a sample) S ⊂ X as ω _S (h) =  min _x ∈ S |ω _h (x)| where ω _h (x) = h(x) max {a ≥ 0: h(z) = h(x), x − a ≤ z ≤ x + a}. Let be the space of all samples in X of cardinality ℓ and consider sets of wide samples, i.e., hypersets which are defined as Through an application of the Sauer-Shelah result on the density of sets an upper estimate is obtained on the growth function (or trace) of the class , β > 0, i.e., on the number of possible dichotomies obtained by intersecting all hypersets with a fixed collection of samples of cardinality m. The estimate is .      

非线性循环不变式的自动生成

提出了一个自动生成非线性循环不变式的算法。循环不变式可以表示成一个带参数的多项式的形式,根据断言的归纳特性,将循环不变式的生成问题转变成一个约束求解问题,这个约束求解问题的每个解对应于一个循环不变式,如果约束求解问题仅有零解,则说明不存在该参数多项式形式的循环不变式。该算法在Maple中得到了实现,并通过一些实例说明了该算法的有效性。     

Undulate phase boundaries on binary diagrams

Usually, an inflection point on a phase boundary is considered as an unambiguous indication that one of phases participating in the equilibrium is internally unstable, i.e. that it is prone to separation. Subsequently, it is habitually deemed that the inflection point may appear only if a thermodynamic model of this phase contains an excess term.

It is shown that in contrast to this belief, inflection points on a phase boundary may appear when a pure solid component or a stoichiometric binary phase is in equilibrium with the ideal binary solution, which is internally stable, indeed.     

基于RFID的二进制防碰撞算法的改进

本文从RFID(Radio Frequency Identification,无线射频识别技术)的关键技术之一射频标签序号防碰撞入手,先介绍了常用的二进制防碰撞算法,针对其在终端射频卡数量越多,UID(Ubiquitous Identifications,身份识别标签)位数越多,传送时间越长的缺点;提出了二进制防碰撞算法的改进算法,改进算法与传统算法相比,在标签位数逐渐增多的情况下,其查询次数增加速度明显减慢;最后通过仿真给以证实。     

The geometry and dynamics of binary trees

The modeling of a fully populated 3D tree able to regulate dynamically remains a relatively unexplored field. A non-dimensional representation of “autoregulation” coupled with an asymmetric binary tree algorithm has been developed. The tree has a defined topology as well as a spatial representation in 3D. An analysis using a simple linearization shows the systems dynamics when perturbed away from equilibrium. Results, based on previously published work by Karch and Schreiner are presented for a variety of parameters which provide different shapes of the tree and indicate a possible mechanism for “growing” the tree in specified directions. In addition the tree, through the use of local tagging has the ability to vary its size locally via a coupled set of conservation and reverting differential equations.