A generalization of a curious congruence on harmonic sums

Zhao established a curious harmonic congruence for prime :

In this note the authors extend it to the following congruence for any prime and positive integer :

Other improvements on congruences of harmonic sums are also obtained.

     

Distributions of Random Partitions and Their Applications

Assume that a random sample of size m is selected from a population containing a countable number of classes (subpopulations) of elements (individuals). A partition of the set of sample elements into (unordered) subsets, with each subset containing the elements that belong to same class, induces a random partition of the sample size m, with part sizes {Z ₁,Z ₂,...,Z _N } being positive integer-valued random variables. Alternatively, if N _j is the number of different classes that are represented in the sample by j elements, for j=1,2,...,m, then (N ₁,N ₂,...,N _m ) represents the same random partition. The joint and the marginal distributions of (N ₁,N ₂,...,N _m ), as well as the distribution of are of particular interest in statistical inference. From the inference point of view, it is desirable that all the information about the population is contained in (N ₁,N ₂,...,N _m ). This requires that no physical, genetical or other kind of significance is attached to the actual labels of the population classes. In the present paper, combinatorial, probabilistic and compound sampling models are reviewed. Also, sampling models with population classes of random weights (proportions), and in particular the Ewens and Pitman sampling models, on which many publications are devoted, are extensively presented.      

Congruences for generalized Frobenius partitions with 4 colors

We present some congruences involving the functions c?₄(n) and which denote, respectively, the number of generalized Frobenius partitions of n with 4 colors and 4-order generalized Frobenius partitions of n with 4 colors.     

对n-colour有序分拆的一些注记(英文)

本文研究了A.K.Agawarl在文献[1]中给出的n-colour有序分拆的组合性质.利用反例说明其中一个性质的不完全性,并纠正了此性质.此外,还给出了n-colour有序分拆组合性质的两个双射.     

Ensemble clustering in the belief functions framework

In this paper, belief functions, defined on the lattice of intervals partitions of a set of objects, are investigated as a suitable framework for combining multiple clusterings. We first show how to represent clustering results as masses of evidence allocated to sets of partitions. Then a consensus belief function is obtained using a suitable combination rule. Tools for synthesizing the results are also proposed. The approach is illustrated using synthetic and real data sets.     

The cluster deletion problem for cographs

The min-edge clique partition problem asks to find a partition of the vertices of a graph into a set of cliques with the fewest edges between cliques. This is a known NP-complete problem and has been studied extensively in the scope of fixed-parameter tractability (FPT) where it is commonly known as the Cluster Deletion problem. Many of the recently-developed FPT algorithms rely on being able to solve Cluster Deletion in polynomial time on restricted graph structures.     

中国不同光气候分区地面日光光谱的观测与分析

我国地域辽阔,各地光气候有很大区别,为了扩大和提高太阳能与天然光的利用范围及利用效率,采用一种便携式的光谱扫描仪,对我国不同光气候分区的7个代表性城市(昆明、西宁、北京、深圳、南京、南昌和重庆)一天中不同太阳高度角对应时刻的地面直射日光光谱在380～780 nm可见光谱段进行了跟踪观测,分析了不同光气候分区城市一天中不同太阳高度角对应时刻的日光光谱变化规律,比较了不同光气候分区城市的日光光谱曲线,总结了日光光谱辐射强度的影响因素。分析表明：不同光气候分区城市一天中不同太阳高度角对应时刻的日光光谱辐射强度不同,但日光光谱功率的分布和走向基本一致,总体呈先上升后下降的趋势,最大峰值出现在475 nm附近,380～475 nm之间光谱功率分布曲线出现陡升,475～700 nm之间曲线有下降趋势但基本平稳,＞700 nm曲线出现了反复的较大起伏;不同光气候分区城市的日光光谱功率分布曲线的分布和走向也基本一致,没有明显的与不同光气候分区直接相关的日光光谱功率分布差异性规律;日光光谱辐射强度与太阳高度角和日面状况密切相关。     

On the Validations of the Asymptotic Matching Conjectures

In this paper we review the asymptotic matching conjectures for r-regular bipartite graphs, and their connections in estimating the monomer-dimer entropies in d-dimensional integer lattice and Bethe lattices. We prove new rigorous upper and lower bounds for the monomer-dimer entropies, which support these conjectures. We describe a general construction of infinite families of r-regular tori graphs and give algorithms for computing the monomer-dimer entropy of density p, for any p∈[0,1], for these graphs. Finally we use tori graphs to test the asymptotic matching conjectures for certain infinite r-regular bipartite graphs.