Distance unimodular equivalence of graphs

Let G be a connected graph and D(G) be its distance matrix. In this article, the Smith normal forms of the integer matrices D(G) are determined for trees, wheels, cycles, complements of cycles and are reduced for complete multipartite graphs.     

Maximizing the distance between center,centroid and characteristic set of a tree

Consider a tree P_n-g,g , n≥ 2, 1≤ g≤ n-1 on n vertices which is obtained from a path on [1,2,?…?,n-g] vertices by adding g pendant vertices to the pendant vertex n-g. We prove that over all trees on n?≥?5 vertices, the distance between center and characteristic set, centroid and characteristic set, and center and centroid is maximized by trees of the form P_n-g,g , 2?≤?g?≤?n-3. For n≥ 5, we also supply the precise location of the characteristic set of the tree P_n-g,g , 2?≤?g?≤?n-3.     

On the Ratio Between 2-Domination and Total Outer-Independent Domination Numbers of Trees

A 2-dominating set of a graph G is a set D of vertices of G such that every vertex of V(G)\D has at least two neighbors in D.A total outer-independent dominating set of a graph G is a set D of vertices of G such that every vertex of G has a neighbor in D,and the set V(G)\D is independent.The 2-domination(total outer-independent domination,respectively)number of a graph G is the minimum cardinality of a 2-dominating(total outer-independent dominating,respectively)set of G.We investigate the ratio between2-domination and total outer-independent domination numbers of trees.     

Low power multipliers based on new hybrid full adders

Five hybrid full adder designs are proposed for low power parallel multipliers. The new adders allow NAND gates to generate most of the multiplier partial product bits instead of AND gates, thereby lowering the power consumption and the total number of needed transistors. For an 8×8 implementation, the ALL-NAND array multiplier achieves 15.7% and 7.8% reduction in power consumption and transistor count at the cost of a 6.9% increase in time delay compared to standard array multiplier. The ALL-NAND tree multiplier exhibits lower power consumption and transistor count by 12.5% and 7.3%, respectively, with a 4.4% longer time delay, compared to conventional tree multiplier.     

Mobile Multimodality: A Theoretical Approach to Facilitate Virtual Device Environments

The classical strategy of multimodal interactions is to simultaneously utilise several modalities offered on a ‘single’ device. However, practical restrictions appear, especially in mobile communications, due to the limitations of device’s interfaces and the continuously changing communication conditions. Taking multimodality out of this single-device scenario, this paper introduces a theoretical framework for dynamic Multi User Interfaces-Device Binding (MID-B). MID-B facilitates dynamic adaptation and customisation of physically distributed devices (and their user interfaces) into one ‘virtual’ multimodal environment, thus introducing ambient awareness into user interfaces. In MID-B, one device assumes the role of a “controller” which detects and binds the interfaces and modalities available on devices in the vicinity. After discovery, it binds these modalities to deliver the actual mobile service.

Free vibration of polar orthotropic circular plates with elastic growth stresses and drying stresses

This study was performed to analyze effect of transverse growth stresses and drying stresses on natural frequencies of transverse free vibration of thin tree disk with free boundary condition. Using Rayleigh-Ritz method and finite element method, explicit closed form expression was derived for homogeneous orthotropic circular plates with internal stresses, which enables to predict both the effects of growth stresses, drying stresses, and combined growth and drying stresses on the natural frequency changes. This model can be used for predicting growth stresses from known natural frequencies. The same approach can also be undertaken to validate models visco-elastic drying stresses.     

基于分类回归树的个人信用客观评分指标体系(英文)

本文提出了一种客观的个人信用指标体系.首先利用分类回归树量化每个指标对信用状况的影响程度,并以此量化值为每个指标设置不同的评分权重;然后通过定义风险度量值来确定指标中各个取值的评分,进而建立了新的评估指标体系.通过选取现实样本数据对指标体系做了实证分析,分析结果表明,新建的指标体系能很好地对借款人进行风险评价.     

Maximizing and minimizing the number of generalized colorings of trees

We classify the trees on $n$ vertices with the maximum and the minimum number of certain generalized colorings, including conflict-free, odd, non-monochromatic, star, and star rainbow vertex colorings. We also extend a result of Cutler and Radcliffe on the maximum and minimum number of existence homomorphisms from a tree to a completely looped graph on $q$ vertices.     

一款教育类移动应用程序“爱猜元素”的开发

北京大学化学国家级实验教学示范中心开发了一款名为"爱猜元素"的教育类移动应用程序。它是以元素周期表为框架,"猜谜游戏"为逻辑主线,围绕元素知识及相关原理而设计的科普资源平台。本文主要介绍了该化学教育类app的设计理念、产品特点及其应用场景。     

The intersection of all maximum stable sets of a tree and its pendant vertices

A stable set in a graph G is a set of mutually non-adjacent vertices, α(G) is the size of a maximum stable set of G, and is the intersection of all its maximum stable sets. It is known that if G is a connected graph of order n≥2 with 2α(G)>n, then , [V.E. Levit, E. Mandrescu, Combinatorial properties of the family of maximum stable sets of a graph, Discrete Applied Mathematics 117 (2002) 149-161; E. Boros, M.C. Golumbic, V.E. Levit, On the number of vertices belonging to all maximum stable sets of a graph, Discrete Applied Mathematics 124 (2002) 17-25]. When we restrict ourselves to the class of trees, we add some structural properties to this statement. Our main finding is the theorem claiming that if T is a tree of order n≥2, with 2α(T)>n, then at least two pendant vertices an even distance apart belong to .