弱分离条件下的自共形迭代函数系统

开集条件是分形几何的一个重要概念,弱分离条件(WSC)在研究有重叠的迭代函数系统(IFS)中扮演着重要角色.本文考虑满足弱分离条件的自共形迭代函数系统,并给出确定其不变集的Hausdorff维数的一种方式.     

拓扑空间关于子基的紧致性

覆盖方法的应用在粗糙集理论研究中越来越受到重视,其中拓扑空间的子集关于子基的内部和闭包两个概念尤为重要.在由它们导入的关于子基的开集,闭集的基础上,给出了拓扑空间关于子基的紧致性概念,并研究它的性质,得到一般拓扑空间中紧致性的一种推广.     

云计算开源生态知识共享及风险治理的演化博弈研究

云计算开源生态正在逐步形成,促进知识共享、规避开源风险成为开源运营及开源治理的重要目标。本文基于演化博弈理论,构建了行业自律和政府监管两种治理机制下多方利益相关者(云计算企业、产业联盟以及政府)之间的演化博弈模型,分析了关键参数对各方策略及系统收益的影响。研究发现,在行业自律机制下,违约金和基金会补贴会促进知识共享合作,而产业联盟对于风险的存在则更为敏感。在政府监管机制下,罚款和政府补贴可以帮助参与者平衡风险并促进知识共享合作。研究结果可为云计算开源生态的可持续发展提供决策参考。     

GENERAL OPEN MAPPING THEOREMS FOR LINEAR TOPOLOGICAL SPACES

0IntroductionIntile1930's,thefirstoped1flappingtheoremforFr6clletspaceswasprovedbyS.B....htll].Sincethedtilevariousextellsiollsoftheopenmappingtheoremhaveapl)earedillsuccessiollforitsapplications(fordetails,see[4]).In1958,V.PtAkfoundoutthatoped1llappillgtheoremsareconllectedwithsolllecompleteness,alldheobtainedastrikillgextensiollofBallach'sclassicaltlleoreul,whichpoilltsoutthatcontinuouslillearmapsfi.olllB-colllpletespacesolltobarrelledspacesareoped['].1111965,T.Husaingaveaninlportalltope…     

The Study of Minimax Inequalities, Abstract Economics and Applications to Variational Inequalities and Nash Equilibria

In this survey, a new minimax inequality and one equivalent geometricform are proved. Next, a theorem concerning the existence of maximalelements for an LC-majorized correspondence is obtained.By the maximal element theorem, existence theorems of equilibrium point fora noncompact one-person game and for a noncompact qualitative game withLC-majorized correspondences are given. Using the lastresult and employing 'approximation approach', we prove theexistence of equilibria for abstract economies in which the constraintcorrespondence is lower (upper) semicontinuous instead of having lower(upper) open sections or open graphs in infinite-dimensional topologicalspaces. Then, as the applications, the existence theorems of solutions forthe quasi-variational inequalities and generalized quasi-variationalinequalities for noncompact cases are also proven. Finally, with theapplications of quasi-variational inequalities, the existence theorems ofNash equilibrium of constrained games with noncompact are given. Our resultsinclude many results in the literature as special cases.     

二维渗流中的最短开穿透

在二维边渗流模型中，设／ｒｎ／＝ｍｉｎ（／ｒ／：ｒ是正方形「０，ｎ」＾２的开穿透），这里／ｒ／表示ｒ的长度，本文证明了在上临界状态有ｌｉｍＥ／ｒｎ／／ｎ＝λ，在临界状态时，我们对Ｅ／ｎ／给出了上界，并对一个ｒｎｒｎ给出了Ｅ／ｒｎ／的下界。     

Water Impingement on a Vertical Wall due to Discontinuity Decay Above a Drop

The paper reports experimental data on the height of water impingement on a vertical wall during wave reflection due to discontinuity decay above an even bottom and a bottom drop. It is shown that for a bore type wave with a roller in its head, propagating over finitedepth water, the impingement height is proportional to the initial difference in freesurface level. In the case of a dry bottom in the tail water, this is also true for other types of waves formed during discontinuity decay.     

Factorization in generalized power series

The field of generalized power series with real coefficients and exponents in an ordered abelian divisible group is a classical tool in the study of real closed fields. We prove the existence of irreducible elements in the ring consisting of the generalized power series with non-positive exponents. The following candidate for such an irreducible series was given by Conway (1976): . Gonshor (1986) studied the question of the existence of irreducible elements and obtained necessary conditions for a series to be irreducible. We show that Conway's series is indeed irreducible. Our results are based on a new kind of valuation taking ordinal numbers as values. If we can give the following test for irreducibility based only on the order type of the support of the series: if the order type is either or of the form and the series is not divisible by any monomial, then it is irreducible. To handle the general case we use a suggestion of
M.-H. Mourgues, based on an idea of Gonshor, which allows us to reduce to the special case . In the final part of the paper we study the irreducibility of series with finite support.

     

On the structures of generating iterated function systems of Cantor sets

A generating IFS of a Cantor set F is an IFS whose attractor is F. For a given Cantor set such as the middle-3rd Cantor set we consider the set of its generating IFSs. We examine the existence of a minimal generating IFS, i.e. every other generating IFS of F is an iterating of that IFS. We also study the structures of the semi-group of homogeneous generating IFSs of a Cantor set F in under the open set condition (OSC). If dim_HF<1 we prove that all generating IFSs of the set must have logarithmically commensurable contraction factors. From this Logarithmic Commensurability Theorem we derive a structure theorem for the semi-group of generating IFSs of F under the OSC. We also examine the impact of geometry on the structures of the semi-groups. Several examples will be given to illustrate the difficulty of the problem we study.