The (S−1,S) inventory model and its counterparts in queueing theory

We explore the relationship between the ($S?1,S$) inventory model and three well-known queueing models: the Erlang loss system, the machine-repair model and a two-node Jackson network. Exploiting this relationship allows us to obtain key performance measures of the ($S?1,S$) model, like the so-called virtual outdating time, the number of items on the shelf in steady state, the long-run rate of unsatisfied demands and the distribution of the empty shelf period.     

改进的粒子群算法在虚拟企业合作伙伴选择中的应用

根据虚拟企业合作伙伴选择的原则,给出了合作伙伴选择的多目标决策模型,用定量的方法对合作伙伴进行描述.同时,给出了改进的二进制粒子群优化算法,并对本文的多目标优化问题进行求解.通过仿真试验测试,证明该方法是可行性.     

Rigidity and flexibility of virtual polytopes

All 3-dimensional convex polytopes are known to be rigid. Still their Minkowski differences (virtual polytopes) can be flexible with any finite freedom degree. We derive some sufficient rigidity conditions for virtual polytopes and present some examples of flexible ones. For example, Bricard's first and second flexible octahedra can be supplied by the structure of a virtual polytope.     

On the Analysis of the Virtual Waiting Time in Open Queueing Networks

The model of an open queueing network in heavy traffic has been developed. These models are mathematical models of computer networks in heavy traffic. A limit theorem has been presented for the virtual waiting time of a customer in heavy traffic in open queueing networks. Finally, we present an application of the theorem—a reliability model from computer network practice.     

Computational Modeling of Organizations Comes of Age

As they are maturing—i.e., as they are becoming validated, calibrated and refined—computational emulation models of organizations are evolving into: powerful new kinds of organizational design tools for predicting and mitigating organizational risks; and flexible new kinds of organizational theorem-provers for validating extant organization theory and developing new theory. Over the past 50 years, computational modeling and simulation have had enormous impacts on the rate of advancement of knowledge in fields like physics, chemistry and, more recently, biology; and their subsequent application has enabled whole new areas of engineering practice. In the same way, as our young discipline comes of age, computational organizational models are beginning to impact behavioral, organizational and economic science, and management consulting practice. This paper attempts to draw parallels between computational modeling in natural sciences and computational modeling of organizations as a contributor to both social science and management practice.To illustrate the lifecycle of a computational organizational model that is now relatively mature, this paper traces the evolution of the Virtual Design Team (VDT) computational modeling and simulation research project at Stanford University from its origins in 1988 to the present. It lays out the steps in the process of validating VDT as a computational emulation model of organizations to the point that VDT began to influence management practice and, subsequently, to advance organizational science. We discuss alternate research trajectories that can be taken by computational and mathematical modelers who prefer the typical natural science validation trajectory—i.e., who attempt to impact organizational science first and, perhaps subsequently, to impact management practice.The paper concludes with a discussion of the current state-of-the-art of computational modeling of organizations and some thoughts about where, and how rapidly, the field is headed.     

Fluid and diffusion limits for transient sojourn times of processor sharing queues with time varying rates

We provide an approximate analysis of the transient sojourn time for a processor sharing queue with time varying arrival and service rates, where the load can vary over time, including periods of overload. Using the same asymptotic technique as uniform acceleration as demonstrated in [12] and [13], we obtain fluid and diffusion limits for the sojourn time of the M_t/M_t/1 processor-sharing queue. Our analysis is enabled by the introduction of a “virtual customer” which differs from the notion of a “tagged customer” in that the former has no effect on the processing time of the other customers in the system. Our analysis generalizes to non-exponential service and interarrival times, when the fluid and diffusion limits for the queueing process are known.     

On hyperbolic virtual polytopes and hyperbolic fans

Hyperbolic virtual polytopes arose originally as polytopal versions of counterexamples to the following A.D.Alexandrov’s uniqueness conjecture: Let K ⊂ ℝ³ be a smooth convex body. If for a constant C, at every point of ∂K, we have R ₁ ≤ C ≤ R ₂ then K is a ball. (R ₁ and R ₂ stand for the principal curvature radii of ∂K.) This paper gives a new (in comparison with the previous construction by Y.Martinez-Maure and by G.Panina) series of counterexamples to the conjecture. In particular, a hyperbolic virtual polytope (and therefore, a hyperbolic hérisson) with odd an number of horns is constructed. Moreover, various properties of hyperbolic virtual polytopes and their fans are discussed.     

On the Logical Status of the Virtual Work Law

The law of virtual work (VWL) is probably the first law in the history of mechanics; it is previous to the one on the lever, though not completely distinct from it. Here I will discuss the logical status of VWL, that is whether it is an autonomous principle or a theorem of some sort of mechanics. The problem is complicated by the fact that up to now no universally recognised expression has been accepted for it. From this article the problematical nature of VWL demonstrability is quite clear when the mechanics does not characterise completely the constraints. Italian schools in the XVIII century, even if we do not take Lagrange into consideration, had an important role, both in the development of VWL and in the discussion of its role.     

“线上线下-虚实结合”在有机化学实验教学中的应用探索——以正溴丁烷的制备实验为例

In response to the impact of the Covid-19 epidemic on organic chemistry laboratory teaching, this article analyzes and discusses the current limitation of traditional organic chemistry laboratory teaching. Taking the \"preparation of n-bromobutane\" as an example, a new \"online-offline and virtual-actual combination\" teaching mode with the combination of \"Tencent Meeting, MLabs, laboratory and WeChat group\" is introduced. The practice of the new mode of teaching includes the following steps: pre-class online guiding by teacher, student preview and practice based on the virtual simulation platform, students and teacher discussion and operation in laboratory, and post-classcomprehensive assessment and Q&A\", and good teaching effects have been received. It is significant in cultivating and improving the independent innovation and practical ability, and provides reference for the organic chemistry laboratory teaching reform and also lays a foundation for the construction of \"outstanding course\" of organic chemistry.