具有3-部极小公平划分的树

对图进行公平划分是认识图的结构有效途径,通过讨论具有3-部公平划分的树的结构,刻画出了所有具有3-部极小公平划分的树类。

k-正则可图序列的公平划分问题

设π=(d_1,d_2,…,d_n)是非负整数序列,π_1,π_2是将π的所有元素划分为两部分后的两个子序列.如果-1≤|π_1|-|π_2|≤1,则称π_1,π_2是π的一个平衡二部划分,其中|π_i|(i=1,2)表示π_i中的元素数目.设k和n是两个正整数,π=(k^n)是k-正则可图序列.本文确定了ψ_(max)(π)的值和ψ_(min)(π)的值.

(k,k-1)-双正则可图序列的公平划分

设π= (d1,d2,…,dn)是非负整数序列,π1,π2是将π的所有元素划分为两部分后的两个子序列。如果-1≤|π1|-| π2|≤1,则称π1 π2 是π的一个平衡二部划分,其中|πi|(i=1,2)表示 πi中的元素数目。设k和m是两个正整数,π= (km,(k-1)m)是双正则可图序列。本文确定了 Ψmax(π)的值和Ψmin(π)的值。。

超图与图公平划分的l-元组

令S为一个图或超图的某顶点子集,则e(S)表示该图中端点全部在S内的边数。 Fan和Hou(2017)证明了每个最大度为△的m阶图G都存在一个k部划分(V1, V2,..., Vk),使得对于任意1≤i<j≤k,都成立e(Vi∪Vj)≤min{4/k^2m+4△/k,m/k-1}+o(m^7/8)。令H表示最大度为△的m阶r-一致超图,本文证明H存在一个k部划分(V1,V2...,Vk),对于任意1≤i<j≤k,满足e(Vi∪Vj)≤r-1/k-1m+o(m);也证明当△=o(m)时,HH存在一个k部划分(V1,V2...,Vk),使得对于任意l∈[k-1]和每个l元组(Vj1,...,Vj1),有e(Vj1∪…∪Vj1)≤l^r/k^rm+o(m)。

Energy efficient resource allocation for D2D multicast communications

The resource allocation for device-to-device(D2D)multicast communications is investigated.To achieve fair energy efficiency(EE)among different multicast groups,the max-min fairness criterion is used as the optimization criterion and the EE of D2D multicast groups are taken as the optimization objective function.The aim is to maximize the minimum EE for different D2D multicast groups under the constraints of the maximum transmit power and minimum transmit rate,which is modeled as a non-convex and mixed-integer fractional programming problem.Here,suboptimal resource allocation algorithms are proposed to solve this problem.First,channel assignment scheme is performed to assign channel to D2D multicast groups.Second,for a given channel assignment,iterative power allocation schemes with and without loss of cellular users’rate are completed,respectively.Simulation results corroborate the convergence performance of the proposed algorithms.In addition,compared with the traditional throughput maximization algorithm,the proposed algorithms can improve the energy efficiency of the system and the fairness achieved among different multicast groups.

New Program Projects Selection for TV Companies

Selecting new program projects plays an important role for TV companies. Balanced scorecard （BSC） which links financial and non-financial, tangible and intangible, inward and outward factors can provide an integrated viewpoint for decision makers to select optimal new program projects. This study combines BSC with analytic hierarchy process （AHP） to help Taiwan Residents TV company managers make better decisions in new program projects selection. Moreover, the practical application of the proposed approach is generic and also suitable to be exploited for Taiwan Residents TV companies.

恰有三个主特征值的树

设λ是图G的一个特征值,如果存在属于λ的一个特征向量X=(x1,x2,…,xn)T,使得∑nk=1xk≠0,则称λ是图G的主特征值。通过讨论图的主特征值数与公平划分之间的联系,给出某些具有三个主特征值的树类及其主特征值的计算方法。