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Full Friendly Index Sets of Cartesian Products of Two Cycles

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Acta Mathematica Sinica,English Series 2010年第7期26卷 1233-1244页

作者： wai chee SHIU Department of Mathermatics Hong Kong Baptist University

Let G =（V, E） be a connected simple graph. A labeling f ： V → Z2 induces an edge labeling f＊： E → Z2 defined by f＊（xy） = f（x）＋f（y） for each xy ∈ E. For i ∈ Z2, let vf（i） = ｜f^-1（i）｜ and ef（i... 详细信息

Let G =（V, E） be a connected simple graph. A labeling f ： V → Z2 induces an edge labeling f＊： E → Z2 defined by f＊（xy） = f（x）＋f（y） for each xy ∈ E. For i ∈ Z2, let vf（i） = ｜f^-1（i）｜ and ef（i） = ｜f＊^-1（i）｜. A labeling f is called friendly if ｜vf（1） - vf（0）｜ ≤ 1. For a friendly labeling f of a graph G, we define the friendly index of G under f by if（G） = e（1） - el（0）. The set [if（G）｜ f is a friendly labeling of G} is called the full friendly index set of G, denoted by FFI（G）. In this paper, we will determine the full friendly index set of every Cartesian product of two cycles.

关键词： vertex labeling friendly labeling friendly index set Cartesian product of two cycles

Super-edge-graceful Labelings of Some Cubic Graphs

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Acta Mathematica Sinica,English Series 2006年第6期22卷 1621-1628页

作者： wai Chee SHIU Department of Mathematics Hong Kong Baptist University

The notion of super-edge-graceful graphs was introduced by Mitchem and Simoson in ***, few examples except trees are known. In this paper, we exhibit two classes of infinitely many cubic graphs which are super-edge-gr... 详细信息

关键词： super-edge-graceful cubic graph permutation cubic graph permutation Petersen graph,permutation ladder graph

A perturbation-incremental scheme for studying Hopf bifurcation in delayed differential systems

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Science China(Technological Sciences) 2009年第3期52卷 698-708页

作者： CHUNG Kwok wai Department of Mathematics City University of Hong Kong Kowloon

A new method, called perturbation-incremental scheme (PIS), is presented to investigate the periodic solution derived from Hopf bifurcation due to time delay in a system of first-order delayed differential equations. The method is summarized as three steps, namely linear analysis at critical value, perturba- tion and increment for continuation. The PIS can bypass and avoid the tedious calculation of the center manifold reduction (CMR) and normal form. Meanwhile, the PIS not only inherits the advantages of the method of multiple scales (MMS) but also overcomes the disadvantages of the incremental harmonic balance (IHB) method. Three delayed systems are used as illustrative examples to demonstrate the validity of the present method. The periodic solution derived from the delay-induced Hopf bifurcation is obtained in a closed form by the PIS procedure. The validity of the results is shown by their consis- tency with the numerical simulation. Furthermore, an approximate solution can be calculated in any required accuracy.

关键词： delayed differential equation perturbation-incremental scheme Hopf bifurcation synchronization center manifold

Graphs Whose Critical Groups Have Larger Rank

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Acta Mathematica Sinica,English Series 2011年第9期27卷 1663-1670页

作者： Yao Ping HOU wai Chee SHIU wai Hong CHAN Departement of Mathematics Hu'nan Normal University Changsha 410081 P. R. China Department of Mathematics Hong Kong Baptist University Kowloon Tong Hong Kong P. R. China

The critical group C（G） of a graph G is a refinement of the number of spanning trees of the graph and is closely connected with the Laplacian matrix. Let r（G） be the minimum number of generators （i.e., the rank） of the group C（G） and β（G） be the number of independent cycles of G. In this paper, some forbidden induced subgraphs axe given for r（G） = n - 3 and all graphs with r（G） = j3（G） = n - 3 are characterized

关键词： Critical group of a graph Laplacian matrix Smith normal form

SMA molecular line survey towards the massive star-forming region G10.6-0.4in W31complex

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Research in Astronomy and Astrophysics 2018年第11期18卷 29-42页

作者： wai-Ho Wong Tao An Key Laboratory of Radio Astronomy Shanghai Astronomical ObservatoryChinese Academy of SciencesShanghai 200030China University of Chinese Academy of Sciences Beijing 100049China

Line surveys of complex molecules with millimeter and sub-millimeter telescopes are important for probing the physical and chemical environments of massive star forming regions(MSFRs).We present a molecular line survey with the Submillimeter Array(SMA) in the frequency ranges of 220.3–222.3 GHz and 230.3–232.3 GHz toward G10.6-0.4, the brightest star forming core in the W31 complex. Ninety-nine transitions from 22 molecular species and their isotopologues are identified. The moment 0 images of typical molecules show a compact core which is concentrated at the continuum peak position. Based on the local thermodynamic equilibrium assumption, the molecular line data are modeled. The rotational temperatures of those molecular species range from 96 to 178 K and their column densities range from 2.0×1014to 3.7×1017cm-2. The observational data suggest that all complex molecules are located in a warm environment. Chemical environments of the molecules are discussed. We compared molecular abundances and gas temperatures in G10.6-0.4 with those in other MSFRs, and found that gas temperatures and fractional abundances of specific molecules in G10.6-0.4 are similar to the typical MSFR W51 North, suggesting that there are similar physical and chemical environments in these two MSFRs.

关键词： stars: formation ISM: abundances ISM: individual objects: G10.6-0.4 ISM: molecules radio lines: ISM

Molecular mechanisms regulating expression and function of transcription regulator “inhibitor of differentiation 3”

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Acta Pharmacologica Sinica 2005年第12期26卷 1409-1420页

作者： Robert wai-sui LIM 65212 USA Department of Medical Pharmacology and Physiology University of Missouri-Columbia

The transcription factor antagonist inhibitor of differentiation 3(Id3)has beenimplicated in many diverse developmental,physiological and *** expression and function is subjected to many levels of *** review summarizes the current understanding of these mecha-nisms and describes how they might be related to the diverse functions that havebeen attributed to the Id3 *** understanding of these mechanismsshould provide insights towards the development of therapeutic approaches tovarious diseases,including cancer and atherogenesis.

关键词： gene expression regulation inhibitor of differentiation 3 protein transcription factors neoplasm

Distance signless Laplacian spectrum of a graph

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Frontiers of Mathematics in China 2022年第4期17卷 653-672页

作者： Huicai JIA wai Chee SHIU College of Science Henan University of EngineeringZhengzhou451191China Department of Mathematics The Chinese University of Hong KongHong KongChina

Let G be a simple connected graph with n *** transmission Tv of a vertex v is defined to be the sum of the distances from v to all other vertices in G,that is,T_(v)=Σ_(u)∈Vd_(uv),where duv denotes the distance between u and *** T_(1),…,T_(n)be the transmission sequence of *** D=(dij)_(n×n)be the distance matrix of G,and T be the transmission diagonal matrix diag(T_(1),…,T_(n)).The matrix Q(G)=T+D is called the distance signless Laplacian of *** this paper,we provide the distance signless Laplacian spectrum of complete k-partite graph,and give some sharp lower and upper bounds on the distance signless Laplacian spectral radius q(G).

关键词： Distance signless Laplacian spectral radius bound

Radiometric normalization of overlapping LiDAR intensity data for reduction of striping noise

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International Journal of Digital Earth 2016年第7期9卷 649-661页

作者： wai Yeung Ahmed Shaker Department of Civil Engineering Ryerson UniversityTorontoOntarioCanada

Airborne LiDAR data are usually collected with partially overlapping strips in order to serve a seamless and fine resolution mapping *** of the factors limiting the use of intensity data is the presence of striping noise found in the overlapping *** recent researches have proposed physical and empirical approaches for intensity data correction,the effect of striping noise has not yet been *** paper presents a radiometric normalization technique to normalize the intensity data from one data strip to another one with partial *** normalization technique is built based on a second-order polynomial function fitted on the joint histogram plot,which is generated with a set of pairwise closest data points identified within the overlapping *** proposed method was tested with two individual LiDAR datasets collected by Teledyne Optech’s Gemini(1064 nm)and Orion(1550 nm)*** experimental results showed that radiometric correction and normalization can significantly reduce the striping noise found in the overlapping LiDAR intensity data and improve its capability in land cover *** coefficient of variation of five selected land cover features was reduced by 19–65%,where a 9–18%accuracy improvement was achieved in different classification *** the proven capability of the proposed method,both radiometric correction and normalization should be applied as a pre-processing step before performing any surface classification and object recognition.

关键词： LiDAR intensity striping noise radiometric correction radiometric normalization joint histogram land cover classification

On the adjacent vertex-distinguishing acyclic edge coloring of some graphs

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Applied Mathematics(A Journal of Chinese Universities) 2011年第4期26卷 439-452页

作者： SHIU wai Chee CHAN wai Hong ZHANG Zhong-fu BIAN Liang （Corresponding author） Department of Mathematics Hong Kong Baptist University 224 Waterloo Road Kowloon Tong Hong Kong. Department of Mathematics Hong Kong Baptist University 224 Waterloo Road Kowloon Tong Hong Kong. Institute of Applied Mathematics Lanzhou Jiaotong University Lanzhou 730070 China.

A proper edge coloring of a graph G is called adjacent vertex-distinguishing acyclic edge coloring if there is no 2-colored cycle in G and the coloring set of edges incident with u is not equal to the coloring set of edges incident with v, where uv∈ E（G）. The adjacent vertex distinguishing acyclic edge chromatic number of G, denoted by X＇Aa（G）, is the minimal number of colors in an adjacent vertex distinguishing acyclic edge coloring of G. If a graph G has an adjacent vertex distinguishing acyclic edge coloring, then G is called adjacent vertex distinguishing acyclic. In this paper, we obtain adjacent vertex-distinguishing acyclic edge coloring of some graphs and put forward some conjectures.

关键词： Adjacent strong edge coloring adjacent vertex-distinguishing acyclic edge coloring.