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.     

The General Solution of Ming Antu＇s Problem

In two centuries ago,Ming Autu discovered the famous Catalan numbers while he tried to expand the function sin(2px) as power series of sin(x) for the case p=1,2,3.Very recently,P.J.Larcombe shows that for any p,sin(2px) can always be expressed as an infinite power series of sin(x) involving precise combinations of Catalan numbers as part of all but the initial p terms and gave all expansions for the case p=4,5.The present paper presents the desired expansion for arbitrary integer p.     

Compact Einstein warped product spaces with nonpositive scalar curvature

We study Einstein warped product spaces. As a result, we prove the following: if is an Einstein warped product space with nonpositive scalar curvature and compact base, then is simply a Riemannian product space.

     

Liouville—Ttype Theorems for Conformal Gaussian Curvature Equations in R^2

In this paper,we derive an elementary identity for smooth solutions of the following equation:△u(x) K(x)e^2u(x)=0 in R^2 and use it to get some global properties of the solutions.     

Oscillatory Properties of Second Order Half-Linear Difference Equations

We study oscillatory properties of the second order half-linear difference equation

Factorization in finite-codimensional ideals of group algebras

Let G be a -compact, locally compact group and I be a closed2-sided ideal with finite codimension in L¹(G). It is shownthat there are a closed left ideal L having a right boundedapproximate identity and a closed right ideal R having a leftbounded approximate identity such that I = L + R. The proofuses ideas from the theory of boundaries of random walks ongroups. 2000 Mathematics Subject Classification: primary 43A20;secondary 42A85, 43A07, 46H10, 46H40, 60B11.     

Higher order symmetric spaces and the roots of the identity in a Lie group

Let denote the set of all -roots of the identity in a Lie group . We show that is always an embedded submanifold of , having the conjugacy classes of its elements as open submanifolds. These conjugacy classes are examples of -symmetric spaces and we show, more generally, that every -symmetric space of a Lie group is a covering manifold of an embedded submanifold of . We compute also the Hessian of the inclusions of and into , relative to the natural connection on the domain and to the symmetric connection on .

     

Powers of Euler's Product and Related Identities

Ramanujan's partition congruences can be proved by first showing that the coefficients in the expansions of (q; q) ^r satisfy certain divisibility properties when r = 4, 6 and 10. We show that much more is true. For these and other values of r, the coefficients in the expansions of (q; q) ^r satisfy arithmetic relations, and these arithmetic relations imply the divisibility properties referred to above. We also obtain arithmetic relations for the coefficients in the expansions of (q; q) ^r (q ^t; q ^t) ^s , for t = 2, 3, 4 and various values of r and s. Our proofs are explicit and elementary, and make use of the Macdonald identities of ranks 1 and 2 (which include the Jacobi triple product, quintuple product and Winquist's identities). The paper concludes with a list of conjectures.     

Birkhoff系统的时间积分定理

研究Birkhoff系统的时间积分定理.建立Birkhoff系统的时间积分等式，由此等式导出系统的类功率方程，Pfaff-Birkhoff积分变分原理以及Pfaff-Birkhoff-d′Alembert微分变分原理. 关键词： Birkhoff系统 时间积分等式 类功率方程 变分原理