On JB-Rings

A ring R is a QB-ring provided that aR bR=R with a,b∈R implies that there exists a y∈R such that a by∈R_q~(-1).It is said that a ring R is a JB-ring provided that R/J(R)is a QB-ring,where J(R)is the Jacobson radical of R.In this paper,various necessary and sufficient conditions,under which a ring is a JB-ring,are established.It is proved that JB-rings can be characterized by pseudo-similarity.Furthermore,the author proves that R is a JB-ring iff so is R/J(R)~2.     

OPTIMAL INSTAR PARASITIZATION IN A STAGE STRUCTURED HOST-PARASITOID MODEL

A stage structured host-parasitoid model is derived and the equilibria studied. It is shown under what conditions the parasitoid controls an exponentially growing host in the sense that a coexistence equilibrium exists. Furthermore, for host populations whose inherent growth rate is not too large it is proved that in order to minimize the adult host equilibrium level it is necessary that the parasitoids attack only one of the larval stages. It is also proved in this case that the minimum adult host equilibrium level is attained when the parasitoids attack that larval stage which also maximizes the expected number of emerging adult parasitoid per larva at equilibrium. Numerical simulations tentatively indicate that the first conclusion remains in general valid for the model. However, numerical studies also show that it is not true in general that the optimal strategy will maximize the number of emerging adult parasitoid per larva at equilibrium.     

A note on monotonically metacompact spaces

We show that any metacompact Moore space is monotonically metacompact and use that result to characterize monotone metacompactness in certain generalized ordered (GO) spaces. We show, for example, that a generalized ordered space with a σ-closed-discrete dense subset is metrizable if and only if it is monotonically (countably) metacompact, that a monotonically (countably) metacompact GO-space is hereditarily paracompact, and that a locally countably compact GO-space is metrizable if and only if it is monotonically (countably) metacompact. We give an example of a non-metrizable LOTS that is monotonically metacompact, thereby answering a question posed by S.G. Popvassilev. We also give consistent examples showing that if there is a Souslin line, then there is one Souslin line that is monotonically countable metacompact, and another Souslin line that is not monotonically countably metacompact.     

Multivariate process capability via Löwner ordering

Probability bounds can be derived for distributions whose covariance matrices are ordered with respect to Löwner partial ordering, a relation that is based on whether the difference between two matrices is positive definite. One example is Anderson’s Theorem. This paper develops a probability bound that follows from Anderson’s Theorem that is useful in the assessment of multivariate process capability. A statistical hypothesis test is also derived that allows one to test the null hypothesis that a given process is capable versus the alternative hypothesis that it is not capable on the basis of a sample of observed quality characteristic vectors from the process. It is argued that the proposed methodology is viable outside the multivariate normal model, where the p-value for the test can be computed using the bootstrap. The methods are demonstrated using example data, and the performance of the bootstrap approach is studied empirically using computer simulations.     

Generalising a characterisation of Hermitian curves

This article proves a characterisation of the classical unital that is a generalisation of a characterisation proved in 1982 by Lefèvre-Percsy. It is shown that if is a Buekenhout-Metz unital with respect to a line in such that a line of not through meets in a Baer subline, then is classical. An immediate corollary is that if is a unital in PG such that is Buekenhout-Metz with respect to two distinct lines, then is classical. Received 5 August 1999; revised 15 February 2000.     

Toeplitz算子在Dirichlet空间上的亚正规性

In this paper,we prove that the necessary and sufficient condition for a Toeplitz operator Tu on the Dirichlet space to be hyponormal is that the symbol u is constant for the case that the projection of u in the Dirichlet space is a polynomial and for the case that u is a class of special symbols,respectively.We also prove that a Toeplitz operator with harmonic polynomial symbol on the harmonic Dirichlet space is hyponormal if and only if its symbol is constant.     

Strong conjugation actions induced by flags of exact Borel subalgebras

Let A be a quasi-hereditary algebra with a strong exact Borel subalgebra. It is proved that for any standard semisimple subalgebra T there exists an exact Borel subalgebra B of A such that T is a maximal semisimple subalgebra of B. It is shown that the maximal length of flags of exact Borel subalgebras of A is the difference of the radium and the rank of Grothendic group of A plus 2. The number of conjugation-classes of exact Borel subalgebras is 1 if and only if A is basic; the number is 2 if and only if A is semisimple. For all other cases, this number is 0 or no less than 3. Furthermore, it is shown that all the exact Borel subalgebras are idempotent-conjugate to each other, that is, for any exact Borel subalgebras B and C of A, there exists an idempotent e of A, and an invertible element u of A, such that eBe = u^-1eCeu.     

Mathematical models of innovation diffusion with stage structure

Mathematical models with stage structures are proposed to describe the process of awareness, evaluation and decision-making. First, a system of ordinary differential equations is presented that incorporates the awareness stage and the decision-making stage. If the adoption rate is bilinear and imitations are dominant, we find a threshold above which innovation diffusion is successful. Further, if the adoption rate has a higher nonlinearity, it is shown that there exist bistable equilibria and a region such that an innovation diffusion is successful inside and is unsuccessful outside. Secondly, a model with a time delay is proposed that includes an evaluation stage of a product. It is proved that the system exhibits stability switches. The bifurcation direction of equilibria is also discussed.     

Implicitly restarted projection algorithm for solving optimization problems

An algorithm for solving the problem of minimizing a quadratic function subject to ellipsoidal constraints is introduced. This algorithm is based on the impHcitly restarted Lanczos method to construct a basis for the Krylov subspace in conjunction with a model trust region strategy to choose the step. The trial step is computed on the small dimensional subspace that lies inside the trust region.

One of the main advantages of this algorithm is the way that the Krylov subspace is terminated. We introduce a terminationcondition that allows the gradient to be decreased on that subspace.

A convergence theory for this algorithm is presented. It is shown that this algorithm is globally convergent and it shouldcope quite well with large scale minimization problems. This theory is sufficiently general that it holds for any algorithm that projects the problem on a lower dimensional subspace.     

关于连续区间映射的敏感依赖性

首先证明:若区间映射f是敏感依赖的,则f的拓扑熵ent(f)>0.然后通过引入一种扩张映射进一步证明了敏感依赖的区间映射的拓扑熵的下确界为0,即,上式中拓扑熵的下界0是最优的.最后通过实例展示稠混沌、Spatio-temporal混沌、Li-Yorke敏感及敏感性之间是几乎互不蕴含的.     

跳跃扩散过程的期权定价模型

假定股票价格的跳过程为计数过程,建立了股票价格服从跳扩散过程的行为模型.运用随机分析中的鞅方法,推导出了股票价格的跳过程为计数过程的欧式期权定价公式,推广了已有的结果.     

指数型一次Logistic迭代方程解的周期倍分岔现象

本文讨论了指数型一次Ｌｏｇｉｓｔｉｃ迭代方程解的周期倍分岔现象的存在性,给出了周期倍分合时的临界点参数应满足的方程,并证明了周期倍分岔的临界点参数序列的极限是存在的,进而证明了当参数越过这个极限时,指数型一次 Ｌｏｇｉｓｔｉｃ迭代方程存在混沌解．     

L-拓扑空间的局部Fuzzy紧性

定义了L-拓扑空间的局部Fuzzy紧性, 证明了这种局部Fuzzy紧性是L-好的推广, 是闭可遗传的, 在连续的、开的、满的L值Zadeh型函数下保持不变.     

ASYMPTOTIC NORMALITY OF QUASI MAXIMUM LIKELIHOOD ESTIMATE IN GENERALIZED LINEAR MODELS

For the Generalized Linear Model (GLM), under some conditions including that the specification of the expectation is correct, it is shown that the Quasi Maximum Likelihood Estimate (QMLE) of the parameter-vector is asymptotic normal. It is also shown that the asymptotic covariance matrix of the QMLE reaches its minimum (in the positive-definte sense) in case that the specification of the covariance matrix is correct.     

Equilibria in load balancing games

A Nash equilibrium （NE） in a multi-agent game is a strategy profile that is resilient to unilateral deviations. A strong Nash equilibrium （SE） is one that is stable against coordinated deviations of any coalition. We show that, in the load balancing games, NEs approximate SEs in the sense that the benefit of each member of any coalition from coordinated deviations is well limited. Furthermore, we show that an easily recognizable special subset of NEs exhibit even better approximation of SEs.     

Clean一般环的几个结果

证明了一般环I是Clean一般环当且仅当I上的形式幂级数一般环I[[x]]是Clean一般环;一般环I上的多项式环I[x]是Clean一般环当且仅当I是诣零的.引入了强Clean一般环的概念,它是强Clean环的推广.并证明了强π-正则的一般环是强Clean一般环.     

Neo-Mooreanism,contextualism, and the evidential basis of scepticism

Two of the main forms of anti-scepticism in the contemporary literature—namely, neo-Mooreanism and attributer contextualism—share a common claim, which is that we are, contra the sceptic, able to know the denials of sceptical hypotheses. This paper begins by surveying the relative merits of these views when it comes to dealing with the standard closure-based formulation of the sceptical problem that is focussed on the possession of knowledge. It is argued, however, that it is not enough to simply deal with this version of the sceptical challenge, since there is a more fundamental sceptical problem underlying the standard closure-based sceptical argument that can be expressed in terms of the evidential basis of our beliefs. Whilst it is argued that neo-Mooreanism has a slight edge over attributer contextualism when it comes to dealing with the closure-based formulation of the sceptical problem, it is claimed that this view is in an ever stronger dialectical position when it comes to the more pressing evidential formulation of the sceptical problem. It is shown that this is so even if one adapts the attributer contextualist thesis along the lines suggested by Michael Williams and Ram Neta so that it is explicitly designed to deal with the evidential variant of the sceptical problem.     

Semiring and Semimodule Issues in MV-Algebras

It is known that an atomic right LCM domain need not be a UFD but is a projectivity-UFD if it is also modular. This paper studies a slightly weaker and easier condition, the RAMP (acronym for the property in the title) , which also ensures that an atomic right LCM domain will be a projectivity-UFD. Among other things it is shown that in an atomic LCM domain, modularity is equivalent to the pair RAMP and LAMP (the left-right analog of RAMP). This result is then used to show that an atomic LCM domain with conjugation is modular. An example is given of an atomic LCM domain that has neither the RAMP nor the LAMP. All rings are not-necessarily commutative integral domains. Recall that an atomic ring is one in which every nonzero nonunit is a product of atoms (i.e. irreducibles) . A ring R is a right LCM domain if for any two elements a and b in R, aR ∩ bR is a principal right ideal. A right LCM domain need not be a left LCM domain [3] . If a ring has both properties it is called an LCM domain. It Is known (see Example 2 below) that, unlike the commutative case, an atomic right LCM domain need not be a UFD (unique factorization domain). In [1] it is shown that if the ring is also modular then it is a projectivity-UFD (definition of the latter recalled below)     

关于区间上的Lorenz映射

本文引进了变换ζ．首先，用比文［４］简捷的方法证明了Ｌｏｒｅｎｚ映射的Ｓａｒｋｏｖｓｋｉ定理并更正了文［４］中的一个错误，还得到了扩张的Ｌｏｒｅｎｚ映射中周期点的存在性与其扩张常数之间的关系．其次，证明了Ｌｏｒｅｎｚ映射与其在变换ζ的像具有相等的捏制行列式．此外，给出了广义的Ｌｏｒｅｎｚ映射的周期点的存在性适合Ｓａｒｋｏｖｓｋｉ序关系的一个充分条件