On additive and multiplicative Hilbert cubes

Given subset E of natural numbers FS(E) is defined as the collection of all sums of elements of finite subsets of E and any translation of FS(E) is said to be Hilbert cube. We can define the multiplicative analog of Hilbert cube as well. E.G. Strauss proved that for every ε>0 there exists a sequence with density >1−ε which does not contain an infinite Hilbert cube. On the other hand, Nathanson showed that any set of density 1 contains an infinite Hilbert cube. In the present note we estimate the density of Hilbert cubes which can be found avoiding sufficiently sparse (in particular, zero density) sequences. As a consequence we derive a result in which we ensure a dense additive Hilbert cube which avoids a multiplicative one.     

Media theory: Representations and examples

In this paper we develop a representational approach to media theory. We construct representations of media by well-graded families of sets and partial cubes and establish the uniqueness of these representations. Two particular examples of media are also described in detail.     

Decomposition of complete graphs into 5‐cubes

Necessary conditions for the complete graph on n vertices to have a decomposition into 5‐cubes are that 5 divides n ? 1 and 80 divides n(n ? 1)/2. These are known to be sufficient when n is odd. We prove them also sufficient for n even, thus completing the spectrum problem for the 5‐cube and lending further weight to a long‐standing conjecture of Kotzig. © 2005 Wiley Periodicals, Inc. J Combin Designs 14: 159–166, 2006     

窗扫型成像光谱仪数据处理及误差校正研究

窗扫型傅里叶变换成像光谱仪具有高光通量和无动镜等特点,同时也增加了数据处理的难度,需要对采集的原始干涉图进行重组。通过对其数据处理流程特点的分析,设计了一种归一化算法,对由干涉图重组时产生的误差进行了校正,并对在数据采集过程中干涉图的中心暗纹位置的采样误差进行了二次曲线拟合校正。整个数据处理过程实现了从干涉数据立方体到光谱数据立方体的变换。从理论分析和实验结果的比较中验证了误差校正方法的有效性。     

倾斜封闭立方腔内多块孤立平板自然对流换热的实验研究

本文研究了平板的相互位置、腔体倾角及Rα数对倾斜封闭立方腔内多块孤立平板自然对流换热的影响．实验查明：在一定Rα数下存在着一个使每块板换热强度相当的间距；平均换热特性对位置很不敏感；平板的换热强度比相同Rα数下的大空间自然对流更弱，且随倾角增加，Nu数随Rα数增加的增长幅度逐渐减慢．     

A classification of regular embeddings of hypercubes Q_(2m) with m odd

In this paper we give a classification of the orientable regular embeddings of Q_n for n=2m with m odd.Actually we prove that the known examples given by Kwon are the only regular maps of Q_n when n=2m (m odd).     

Some sample path properties of a random walk on the cube

Some properties of the set of vertices not visited by a random walk on the cube are considered. The asymptotic distribution of the first timeQ this set is empty is derived. The distribution of the number of vertices not visited is found for times nearEQ. Next the first time all unvisited vertices are at least some distanced apart is explored. Finally the expected time taken by the path to come within a distanced of all points is calculated. These results are compared to similar results for random allocations.     

M－连续格到Hilbert方体的嵌入

本文主要讨论Ｍ－连续格到Ｈｉｌｂｅｒｔ方体的嵌入问题．我们建立了Ｍ－连续格的次直积表示理论，推广并统一了Ｒａｎｅｙ，Ｂｒｕｎｓ，Ｌａｗｓｏｎ，Ｂａｎｄｅｌｔ和Ｅｒｎｅ等人的相应工作．Ｒｅｎａｙ与Ｂｒｕｎｓ的经典方法是建立在对相应的弱辅助关系的极大完备链作深入分析之上的，富于技巧性，且有局限性．与之相比，本文所使用的方体则相当朴素而自然，但却能处理更为广泛的情形．     

Some remarks on generalized roundness

By using the links between generalized roundness, negative type inequalities and equivariant Hilbert space compressions, we obtain that the generalized roundness of the usual Cayley graph of finitely generated free groups and free abelian groups of rank  ≥ 2 equals 1. This answers a question of J-F. Lafont and S. Prassidis.