The minimum volume of subspace trades

A subspace bitrade of type $T_q(t,k,v)$ is a pair $(T_0,T_1)$ of two disjoint nonempty collections of $k$-dimensional subspaces of a $v$-dimensional space $V$ over the finite field of order $q$ such that every $t$-dimensional subspace of $V$ is covered by the same number of subspaces from $T_0$ and $T_1$. In a previous paper, the minimum cardinality of a subspace $T_q(t,t+1,v)$ bitrade was established. We generalize that result by showing that for admissible $v$, $t$, and $k$, the minimum cardinality of a subspace $T_q(t,k,v)$ bitrade does not depend on $k$. An example of a minimum bitrade is represented using generator matrices in the reduced echelon form. For $t=1$, the uniqueness of a minimum bitrade is proved.     

On the number of SQSs,latin hypercubes and MDS codes

We establish that the logarithm of the number of latin d‐cubes of order n is and the logarithm of the number of sets of t ( is fixed) orthogonal latin squares of order n is . Similar estimations are obtained for systems of mutually strongly orthogonal latin d‐cubes. As a consequence, we construct a set of Steiner quadruple systems of order n such that the logarithm of its cardinality is as and .     

The spectrum of 1-rotational Steiner triple systems over a dicyclic group

The spectrum of values v for which a 1-rotational Steiner triple system of order v exists over a dicyclic group is determined.     

Configuration distribution and designs of codes in the Johnson scheme

The main goal of this article is to present several connections between perfect codes in the Johnson scheme and designs, and provide new tools for proving Delsarte conjecture that there are no nontrivial perfect Codes in the Johnson scheme. Three topics will be considered. The first is the configuration distribution which is akin to the weight distribution in the Hamming scheme. We prove that if there exists an e‐perfect code in the Johnson scheme then there is a formula which connects the number of vectors at distance i from any codeword in various codes isomorphic to . The second topic is the Steiner systems embedded in a perfect code. We prove a lower bound on the number of Steiner systems embedded in a perfect code. The last topic is the strength of a perfect code. We show two new methods for computing the strength of a perfect code and demonstrate them on 1‐perfect codes. We further discuss how to settle Delsarte conjecture. © 2006 Wiley Periodicals, Inc. J Combin Designs 15: 15–34, 2007     

The steiner tree packing problem in VLSI design

In this paper we describe several versions of the routing problem arising in VLSI design and indicate how the Steiner tree packing problem can be used to model these problems mathematically. We focus on switchbox routing problems and provide integer programming formulations for routing in the knock-knee and in the Manhattan model. We give a brief sketch of cutting plane algorithms that we developed and implemented for these two models. We report on computational experiments using standard test instances. Our codes are able to determine optimum solutions in most cases, and in particular, we can show that some of the instances have no feasible solution if Manhattan routing is used instead of knock-knee routing.     

The Generalized-Trend-Diffusion modeling algorithm for small data sets in the early stages of manufacturing systems

The statistical theories are not expected to generate significant conclusions, when applied to very small data sets. Knowledge derived from limited data gathered in the early stages is considered too fragile for long term production decisions. Unfortunately, this work is necessary in the competitive industry and business environments. Our previous researches have been aimed at learning from small data sets for scheduling flexible manufacturing systems, and this article will focus development of an incremental learning procedure for small sequential data sets. The main consideration concentrates on two properties of data: that the data size is very small and the data are time-dependent. For this reason, we propose an extended algorithm named the Generalized-Trend-Diffusion (GTD) method, based on fuzzy theories, developing a unique backward tracking process for exploring predictive information through the strategy of shadow data generation. The extra information extracted from the shadow data has proven useful in accelerating the learning task and dynamically correcting the derived knowledge in a concurrent fashion.     

GM(1,1)的改进及其在经济发展预测中的应用

针对传统GM(1,1)在模型参数绝对值较大时参数求解精度较差的问题,采用免疫进化算法对其参数求解方法进行改进,然后将改进后的GM(1,1)应用到四川省的经济发展指标预测,并和采用传统GM(1,1)所得的预测结果进行了对照.结果表明,采用免疫进化算法对GM(1,1)参数求解方法的改进是有效的,改进后的GM(1,1)对四川省的经济发展指标预测结果比传统GM(1,1)的预测结果有明显改进。     

Soliton solutions, Bäcklund transformation and Wronskian solutions for the extended (2+1)-dimensional Konopelchenko-Dubrovsky equations in fluid mechanics

This paper is to investigate the extended (2+1)-dimensional Konopelchenko-Dubrovsky equations, which can be applied to describing some phenomena in the stratified shear flow, the internal and shallow-water waves and plasmas. Bilinear-form equations are transformed from the original equations and N-soliton solutions are derived via symbolic computation. Bilinear-form Bäcklund transformation and single-soliton solution are obtained and illustrated. Wronskian solutions are constructed from the Bäcklund transformation and single-soliton solution.     

The poset structures admitting the extended binary Golay code to be a perfect code

Brualdi et al. [Codes with a poset metric, Discrete Math. 147 (1995) 57-72] introduced the concept of poset codes, and gave an example of poset structure which admits the extended binary Golay code to be a 4-error-correcting perfect P-code. In this paper we classify all of the poset structures which admit the extended binary Golay code to be a 4-error-correcting perfect P-code, and show that there are no posets which admit the extended binary Golay code to be a 5-error-correcting perfect P-code.     

The global dynamics of a model about HIV-1 infection in vivo

A four dimension ODE model is built to study the infection of human immunodeficiency virus (HIV) in vivo. We include in this model four components: the healthy T cells, the latent-infected T cells, the active-infected T cells and the HIV virus. Two types of HIV transmissions in vivo are also included in the model: the virus-to-cell transmission, and the cell-to-cell HIV transmission. There are two possible equilibriums: the healthy equilibrium, and the infected steady state. The basic reproduction number R ₀ is introduced. When R ₀ < 1, the healthy equilibrium is globally stable and when R ₀ > 1, the infected equilibrium exists and is globally stable. Through simulations, we find that, the cell-to-cell HIV transmission is very important for the final outcome of the HIV attacking. Some important clinical observations about the HIV infection situation in lymph node are also verified.      

The global Cauchy problem for the NLS and NLKG with small rough data

By using the unit-cube decomposition to the frequency spaces, we study the Cauchy problem for the nonlinear Schrödinger equation and the nonlinear Klein-Gordon equation. Some global well posedness results are obtained for the small Cauchy data in some modulation spaces .     

The Cumulative Idle Time in an ND/D/1 Queue

An ND/D/1 queueing model means that N independent periodic sources are served by a single server and the packets have the same size. These models have received close attention as general queueing models in telecommunications. Both discrete models, where it is only permitted to transmit packets at fixed time instances, and also continuous models, where the time of transmission is not restricted, can be applied in the modeling. This paper provides the exact distribution of the cumulative idle time duration in such queuing systems and also proposes accurate approximation formulae for large systems. The results of this paper are of practical significance because existing approximations of the distribution of the cumulative idle time can be replaced by the proposed formulae.AMS subject classification: 68M20, 60K25This revised version was published online in June 2005 with corrected coverdate     

The interdeparture-time distribution for each class in the ∑ i M i /G i /1 queue

A stationary queueing system is described in which a single server handles several competing Poisson arrival streams on a first-come first-served basis. Each class has its own generally distributed service time characteristics. The principal result is the Laplace-Stieltjes transform, for each class, of the interdeparture time distribution function. Examples are given and applications are discussed.     

l~p、B~p及内积空间中螺形映照的增长定理与掩盖定理

本文首先给出l~p空间中单位球上双全纯螺形映照的增长与1/4-定理。作为一个特例,给出B~P上相应结果。其次讨论一般复内积空间上螺形映照的增长及1/4-定理。并证明结论是不可改进的。     

TML中元的明聚点和ST-1分离性

在拓扑分子格（ＴＭＬ）中引进元的明聚点概念，并讨论了聚点的性质，研究了ＳＴ_-1分离性和ＴＭＬ的明导算子．     

The Remaining Service Time upon Reaching a High Level in M/G/1 Queues

The distribution of the remaining service time upon reaching some target level in an M/G/1 queue is of theoretical as well as practical interest. In general, this distribution depends on the initial level as well as on the target level, say, B. Two initial levels are of particular interest, namely, level 1 (i.e., upon arrival to an empty system) and level B–1 (i.e., upon departure at the target level).In this paper, we consider a busy cycle and show that the remaining service time distribution, upon reaching a high level B due to an arrival, converges to a limiting distribution for B. We determine this asymptotic distribution upon the first hit (i.e., starting with an arrival to an empty system) and upon subsequent hits (i.e., starting with a departure at the target) into a high target level B. The form of the limiting (asymptotic) distribution of the remaining service time depends on whether the system is stable or not. The asymptotic analysis in this paper also enables us to obtain good analytical approximations of interesting quantities associated with rare events, such as overflow probabilities.     

2‐(v,k,1) Designs Admitting a Primitive Rank 3 Automorphism Group of Affine Type: The Extraspecial and the Exceptional Classes

2‐(v,k,1) designs admitting a primitive rank 3 automorphism group , where G₀ belongs to the Extraspecial Class, or to the Exceptional Class of Liebeck's Theorem in [23], are classified.