几类有趣图的奇优美性和奇强协调性

对于简单图G=〈V,E〉,如果存在一个映射f:V(G)→{0,1,2,…,2|E|-1}满足:1)对任意的u,v∈V,若u≠v,则f(u)≠f(v);2)max{f(v)|v∈V}=2|E|-1;3)对任意的e_1,e_2∈E,若e_1≠e_2,则g(e_1)≠g(e_2),此处g(e)=|f(u)+f(v)|,e=uv;4)|g(e)|e∈E}={1,3,5,…,2|E|-1},则称G为奇优美图,f称为G的奇优美标号.设G=〈V,E〉是一个无向简单图.如果存在一个映射f:V(G)→{0,1,2,…,2|E|-1},满足:1)f是单射;2)■uv∈E(G),令f(uv)=f(u)+f(v),有{f(uv)|uv∈E(G)}={1,3,5,…,2|E|-1},则称G是奇强协调图,f称为G的.奇强协调标号或奇强协调值.给出了链图、升降梯等几类有趣图的奇优美标号和奇强协调标号.     

关于图P_n~3优美性的研究

在n个顶点的路Pn上,当且仅当两点的距离为3时增加一条边,所得的图称为P3n,本文给出了图P3n(n≥4)的优美标号,从而证明了P3n都是优美图.     

Cycle-magic graphs

A simple graph G=(V,E) admits a cycle-covering if every edge in E belongs at least to one subgraph of G isomorphic to a given cycle C. Then the graph G is C-magic if there exists a total labelling f:V∪E→{1,2,…,|V|+|E|} such that, for every subgraph H^′=(V^′,E^′) of G isomorphic to C, ∑_v∈V^′f(v)+∑_e∈E^′f(e) is constant. When f(V)={1,…,|V|}, then G is said to be C-supermagic.We study the cyclic-magic and cyclic-supermagic behavior of several classes of connected graphs. We give several families of C_r-magic graphs for each r?3. The results rely on a technique of partitioning sets of integers with special properties.     

The Harmonious Dissipative Operators and the Completely Square Conservative Difference Scheme in an Explicit Way

In this paper, a new definition on harmonious dissipative operators is given and some important properties of theirs are shown. Especially, the relationship between a harmonious dissipative operator and the completely square conservative difference scheme in an explicit way is revealed. Kinds of 2-order, 3-order and 4-order harmonious dissipative operators are constructed by using the traditional Runge-Kutta method and a species of general m-order harmonious dissipative operators is established in the linear case. In addition, an efficiency parameter to appraise the time benefits of a harmonious dissipative operator is defined in this paper. It is testified in numerical tests that the harmonious dissipative operators are indeed able to improve the time-efficiency and computational effect of the completely square conservative difference scheme in an explicit way.     

关于奇强协调图的一些结果

对于一个(p,q)-图G,如果存在一个单射f:V(G)→{0,1,…,2q-1},使得边标号集合{f(uv)|uv∈E(G)}={1,3,5,…,2q-1},其中边标号为f(uv)=f(u)+f(v),那么称G是奇强协调图,并称f是G的一个奇强协调标号.通过研究若干奇强协调图,得出一些奇强协调图的性质.     

On Cyclic Decompositions of Complete Graphs into Tripartite Graphs

We introduce two new labelings for tripartite graphs and show that if a graph G with n edges admits either of these labelings, then there exists a cyclic G‐decomposition of for every positive integer x. We also show that if G is the union of two vertext‐disjoint cycles of odd length, other than , then G admits one of these labelings.     

Advances in theoretical models of network science

In this review article, we will summarize the main advances in network science investigated by the CIAE Group of Complex Network in this field. Several theoretical models of network science were proposed and their topological and dynamical properties are reviewed and compared with the other models. Our models mainly include a harmonious unifying hybrid preferential model, a large unifying hybrid network model, a quantum interference network, a hexagonal nanowire network, and a small-world network with the same degree. The models above reveal some new phenomena and findings, which are useful for deeply understanding and investigating complex networks and their applications.      

QSAR modeling based on the bias/variance compromise: a harmonious

Modeling quantitative structure–activity relationships (QSAR) is considered with an emphasis on prediction. An abundance of methods are available to develop such models. Using a harmonious approach that balances the bias and variance of predictions, the best calibration models are identified relative to the bias and variance criteria used. Criteria utilized to determine the adequacy of models are the root mean square error of calibration (RMSEC) and validation (RMSEV), respective R ² values, and the norm of the regression vector. QSAR data from the literature are used to demonstrate concepts. For these data sets and criteria used, it is suggested that models obtained by ridge regression (RR) are more harmonious and parsimonious than models obtained by partial least squares (PLS) and principal component regression (PCR) when the data is mean-centered. The most harmonious RR models have the best bias/variance tradeoff reflected by the smallest RMSEC, RMSEV, and regression vector norms and the largest calibration and validation R ² values. The most parsimonious RR models have the smallest effective rank.     

干摩擦引起自激振动现象研究

对干摩擦引起自激振动现象进行分析,得到了其解析表达式,对振动过程进行了详细的分析,画出了振动曲线和相图,说明这就是弦弓乐器发出优美声乐的物理原因.     

Colorings at minimum cost

We define by min_c∑_{u,v}∈E(G)|c(u)−c(v)| the min-costMC(G) of a graph G, where the minimum is taken over all proper colorings c. The min-cost-chromatic numberχ_M(G) is then defined to be the (smallest) number of colors k for which there exists a proper k-coloring c attaining MC(G). We give constructions of graphs G where χ(G) is arbitrarily smaller than χ_M(G). On the other hand, we prove that for every 3-regular graph G^′, χ_M(G^′)≤4 and for every 4-regular line graph G^″, χ_M(G^″)≤5. Moreover, we show that the decision problem whether χ_M(G)=k is -hard for k≥3.