A supplement to ‘A note on invariant measure semigroups’

A unified definition of measure semigroup is given and it is shown how the types of invariance for the measure are formulated and what effect they have on the embeddability of an Abelian semigroup in a group. The online version of the original article can be found under doi:.     

Smooth格和强Smooth格

引入了强smooth格的概念,讨论了smooth格与强smooth格的一些基本性质,证明了强smooth格可用保任意交和Scott闭集之并的映射嵌入到某方体[0,1]X之中.     

Fuzzifying闭包系统的研究

在Fuzzifying(模糊化)数学的框架下,建立了Fuzzifying闭包系统和Birkhoff型Fuzzifying闭包算子的概念; 引入了Fuzzifying闭包空间范畴和Fuzzifying闭包系统空间范畴,并从范畴论的角度证明Birkhoff型Fuzzifying闭包算子与Fuzzifying闭包系统是协调的.最后文中还得到Fuzzifying闭包空间范畴和Fuzzifying闭包系统空间范畴可以嵌入到Birkhoff型L-闭包空间范畴这一重要结果.     

虚拟数据中心的功率有效嵌入算法(英文)

针对虚拟化技术中,数据中心能源消耗问题,本文研究功率有效的虚拟数据中心嵌入算法.该算法由功率感知嵌入算法、准入策略算法和碎片整理算法三部分组成.在树形网络拓扑结构中,提出功率感知的嵌入算法,得到虚拟数据中心的最低功耗嵌入方式;在动态虚拟网络业务环境中,一般嵌入算法会造成功率波动,通过业务接入策略减少功率波动;随着业务动态地进入和离开,物理网络中出现计算资源碎片,提出碎片整理算法,通过虚拟机迁移的方法,提高服务器的利用率.仿真和评估证明:随着时间的推移,算法能减少功率开支并有效降低功率波动.     

基于高光谱散射图像技术的UVE-LLE苹果粉质化分类

利用高光谱散射图像技术研究了苹果的粉质化无损检测.提出了一种无信息变量消除法和局部线性嵌入相结合的苹果粉质化分类的新方法.经无信息变量消除法筛选后的波段降为全谱的23.5%.将波段选择后的原始图像数据用局部线性嵌入降维作为偏最小二乘判别分析的输入变量并建模.无信息变量消除法与局部线性嵌入相结合算法和局部线性嵌入降维方法得到的粉质化分类测试准确度分别是79.0%和79.0%|无信息变量消除法与平均反射法相结合和平均反射法特征提取得到的是77.4%和75.8%.结果表明,无信息变量消除法与局部线性嵌入想结合的方法可以大大地降低高光谱散射图像的数据量,同时保证了分类准确度,为在线检测、分类和高光谱数据的存储提供了一种实时、有效的方法.     

Embedding Structures

 For any quasiordered set (`quoset') or topological space S, the set Sub S of all nonempty subquosets or subspaces is quasiordered by embeddability. Given any cardinal number n, denote by p _n and q _n the smallest size of spaces S such that each poset, respectively, quoset with n points is embeddable in Sub S. For finite n, we prove the inequalities n + 1 ≤p _n ≤q _n ≤p _n + l(n) + l(l(n)), where l(n) = min{k∈ℕ∣n≤2 ^k }. For the smallest size b _n of spaces S so that Sub S contains a principal filter isomorphic to the power set ?(n), we show n + l(n) − 1 ≤b _n ≤n + l(n) + l(l(n))+2. Since p _n ≤b _n , we thus improve recent results of McCluskey and McMaster who obtained p _n ≤n ². For infinite n, we obtain the equation b _n = p _n = q _n = n. Received: April 19, 1999 Final version received: February 21, 2000     

Embedding Spacetime via a Geodesically Equivalent Metric of Euclidean Signature

Starting from the equations of motion in a 1 + 1 static, diagonal, Lorentzian spacetime, such as the Schwarzschild radial line element, I find another metric, but with Euclidean signature, which produces the same geodesics x(t). This geodesically equivalent, or dual, metric can be embedded in ordinary Euclidean space. On the embedded surface freely falling particles move on the shortest path. Thus one can visualize how acceleration in a gravitational field is explained by particles moving freely in a curved spacetime. Freedom in the dual metric allows us to display, with substantial curvature, even the weak gravity of our earth. This may provide a nice pedagogical tool for elementary lectures on general relativity. I also study extensions of the dual metric scheme to higher dimensions.     

Embedding complete trees into the hypercube

We consider embeddings of the complete t-ary trees of depth k (denotation T^k,t) as subgraphs into the hypercube of minimum dimension n. This n, denoted by dim(T^k,t), is known if max{k,t}2. First, we study the next open cases t=3 and k=3. We improve the known upper bound dim(T^k,3)2k+1 up to lim_k→∞dim(T^k,3)/k5/3 and show lim_t→∞dim(T^3,t)/t=227/120. As a co-result, we present an exact formula for the dimension of arbitrary trees of depth 2, as a function of their vertex degrees. These results and new techniques provide an improvement of the known upper bound for dim(T^k,t) for arbitrary k and t.     

ABELIAN 3-FOLDS IN PRODUCTS OF PROJECTIVE SPACES

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