An improved parallel hybrid bi-conjugate gradient method suitable for distributed parallel computing

An improved parallel hybrid bi-conjugate gradient method (IBiCGSTAB(2) method, in brief) for solving large sparse linear systems with nonsymmetric coefficient matrices is proposed for distributed parallel environments. The method reduces five global synchronization points to two by reconstructing the BiCGSTAB(2) method in [G.L.G. Sleijpen, H.A. van der Vorst, Hybrid bi-conjugate gradient methods for CFD problems, in: M. Hafez, K. Oshima (Eds.), Computational Fluid Dynamics Review 1995, John Wiley & Sons Ltd, Chichester, 1995, pp. 457–476] and the communication time required for the inner product can be efficiently overlapped with useful computation. The cost is only slightly increased computation time, which can be ignored, compared with the reduction of communication time. Performance and isoefficiency analysis shows that the IBiCGSTAB(2) method has better parallelism and scalability than the BiCGSTAB(2) method. Numerical experiments show that the scalability can be improved by a factor greater than 2.5 and the improvement in parallel communication performance approaches 60%.     

命题逻辑系统L*的有效集

针对命题逻辑系统L*,以及增加一元联结词△后的系统L*△,研究了该逻辑系统有效集的特征,进而以有效集为工具得到公式集F(S)的一类分划,即可将L*与L*△中的公式集F(S)分别分为16和20个等价类;最后给出了L*中对M P规则封闭的有效集的特征。     

Stability analysis of constrained inventory systems with transportation delay

Stability is a fundamental design property of inventory systems. However, the often exploited linearity assumptions in the current literature create a major gap between theory and practice. In this paper the stability of a constrained production and inventory system with a Forbidden Returns constraint (that is, a non-negative order rate) is studied via a piecewise linear model, an eigenvalue analysis and a simulation investigation. The APVIOBPCS (Automatic Pipeline, Variable Inventory and Order Based Production Control System) and EPVIOBPCS (Estimated Pipeline, Variable Inventory and Order Based Production Control System) replenishment policies are adopted. Surprisingly, all kinds of non-linear dynamical behaviours of systems can be observed in these simple models. Exact expressions of the asymptotic stability boundaries and Lyapunovian stability boundaries are derived when actual and perceived transportation lead-time is 1 and 2 periods long respectively. Asymptotically stable regions in the non-linear Forbidden Return systems are identical to the stable regions in its unconstrained counterpart. However, regions of bounded fluctuations that continue forever, including both periodicity and chaos, exist in the parametrical plane outside the asymptotically stable region. Simulation shows a complex and delicate structure in these regions. The results suggest that accurate lead-time information is essential to eliminate inventory drift and instability and that ordering policies have to be designed properly in accordance with the actual lead-time to avoid these fluctuations and divergence.     

Asymptotic behavior of a differential equation with distributed delays

In this paper, sufficient conditions are established for the asymptotical behavior of solutions of the delay differential equation

x^′(t)=F(t,xt)+G(t,xt)     

Oscillation of solutions of parabolic differential equations of neutral type

In this paper, we investigate a class of parabolic differential equations of neutral type, and obtain some sufficient conditions of the oscillation for such equations satisfying two kinds of boundary value conditions.     

MDD函数在单机总误工排序问题中的作用

本文把工件的修正工期（MDD：Modified Due Date）看成工件关于时间的函数，通过研究该函数在一定区间的性质建立了一个具有全局意义的定理，利用这个定理可以方便地导出有关单机总误工排序问题的一些重要结论．这些工作既能够很好地解释常用的MI）D规则的有效性，同时也说明MDD函数可以成为解决单机总误工排序问题的基本工具．     

THE EXPONENTIAL STABILIZATION FOR A SEMILINEAR WAVE EQUATION WITH LOCALLY DISTRIBUTED FEEDBACK

This paper considers the exponential decay of the solution to a damped semilinear wave equation with variable coefficients in the principal part by Riemannian multiplier method. A differential geometric condition that ensures the exponential decay is obtained.     

SYSTEM OF GENERALIZED VECTOR VARIATIONAL INEQUALITIES

1IntroductionA vector variational inequality(for short,VVI),as an important generalization of the clas-sical variational inequality,was first introduced and studied by Giannessi[6]in finite dimensionalEuclidean spaces.Later on,a VVI was studied and genera…     

Another complete invariant for Steiner triple systems of order 15

In this note, the 80 non‐isomorphic triple systems on 15 points are revisited from the viewpoint of the convex hull of the characteristic vectors of their blocks. The main observation is that the numbers, of facets of these 80 polyhedra are all different, thus producing a new proof of the non‐isomorphism of these triple systems. The space dimension of these polyhedra is also discussed. Finally, we observe the large number of facets of some of these polyhedra with few vertices, in relation with the upper bound problem for combinatorial polyhedra. © 2005 Wiley Periodicals, Inc. J Combin Designs.