基于约束理论的订单履行系统设计与实现

现有对订单履行系统的研究存在2处不足：订单履行流程被分解为订单允诺和需求满足两方面,鲜有在同一系统框架下展开研究;订单履行实现涉及众多系统的信息,少有研究其体系架构。为解决上述问题,以按照约束理论构建的统一的订单履行流程为核心,以面向服务架构的Web服务集成技术为支撑,设计与实现了整合式的订单履行系统。该系统在某大型企业中获得成功的应用,验证了该流程及体系架构的可行性。     

On the number of higher order Delaunay triangulations

Higher order Delaunay triangulations are a generalization of the Delaunay triangulation that provides a class of well-shaped triangulations, over which extra criteria can be optimized. A triangulation is order-k Delaunay if the circumcircle of each triangle of the triangulation contains at most k points. In this paper we study lower and upper bounds on the number of higher order Delaunay triangulations, as well as their expected number for randomly distributed points. We show that arbitrarily large point sets can have a single higher order Delaunay triangulation, even for large orders, whereas for first order Delaunay triangulations, the maximum number is 2ⁿ⁻³. Next we show that uniformly distributed points have an expected number of at least 2^{ρ₁n(1+o(1))} first order Delaunay triangulations, where ρ₁ is an analytically defined constant (ρ₁≈0.525785), and for k>1, the expected number of order-k Delaunay triangulations (which are not order-i for any i<k) is at least 2^{ρ_kn(1+o(1))}, where ρ_k can be calculated numerically.     

Modelling concurrency with comtraces and generalized comtraces

Comtraces (combined traces) are extensions of Mazurkiewicz traces that can model the “not later than” relationship. In this paper, we first introduce the novel notion of generalized comtraces, extensions of comtraces that can additionally model the “non-simultaneously” relationship. Then we study some basic algebraic properties and canonical representations of comtraces and generalized comtraces. Finally we analyze the relationship between generalized comtraces and generalized stratified order structures. The major technical contribution of this paper is a proof showing that generalized comtraces can be represented by generalized stratified order structures.     

On the qualitative behaviors of solutions of third order nonlinear differential equations

We present some new results about oscillation and asymptotic behavior of solutions of third order nonlinear differential equations of the form

(r₂(t)(r₁(t)y^′)^′)^′+p(t)y^′+q(t)f(y(g(t)))=0.     

The Laplace transform in discrete fractional calculus

We develop properties of the Laplace Transform in a discrete, fractional calculus setting, giving a precise treatment to convergence along the way. The end goal is to apply the Laplace Transform Method to solve a fractional initial value problem.     

The short memory principle for solving Abel differential equation of fractional order

In this paper, the short memory principle (SMP) is applied for solving the Abel differential equation with fractional order. We evaluate the approximate solution at the end of required interval, and construct a suitable iteration scheme employing this end point as initial value. Numerical experiments show that our iteration method is simple and efficient, and that a proper length of memory could maintain the validity of the short memory principle.     

Efficient model checking for LTL with partial order snapshots

Certain behavioral properties of distributed systems are difficult to express in interleaving semantics, whereas they are naturally expressed in terms of partial orders of events or, equivalently, Mazurkiewicz traces. Two examples of such properties are serializability of a database and global snapshots of concurrent systems. Recently, a modest extension for LTL by an operator that expresses snapshots, has been proposed. It combines the ease of linear (interleaving) specification with this useful partial order concept. The new construct allows one to assert that a global snapshot appeared in the past, perhaps not in the observed execution sequence, but possibly in an equivalent one.     

A note on the stability of fractional order systems

In this paper, a new approach is suggested to investigate stability in a family of fractional order linear time invariant systems with order between 1 and 2. The proposed method relies on finding a linear ordinary system that possesses the same stability property as the fractional order system. In this way, instead of performing the stability analysis on the fractional order systems, the analysis is converted into the domain of ordinary systems which is well established and well understood. As a useful consequence, we have extended two general tests for robust stability check of ordinary systems to fractional order systems.