乘积图的Fractional控制

Let G =(V,E) be a simple graph.For any real function g :V-→ R and a subset S V,we write g(S) =∑v∈Sg(v).A function f :V-→ [0,1] is said to be a fractional dominating function(F DF) of G if f(N [v]) ≥ 1 holds for every vertex v ∈ V(G).The fractional domination number γf(G) of G is defined as γf(G) = min{f(V)|f is an F DF of G }.The fractional total dominating function f is defined just as the fractional dominating function,the difference being that f(N(v)) ≥ 1 instead of f(N [v]) ≥ 1.The fractional total domination number γ0f(G) of G is analogous.In this note we give the exact values ofγf(Cm × Pn) and γ0f(Cm × Pn) for all integers m ≥ 3 and n ≥ 2.     

Sequential paired covariance for improved visualization of mass spectrometry imaging datasets

Untargeted analyses in mass spectrometry imaging produce hundreds of ion images representing spatial distributions of biomolecules in biological tissues. Due to the large diversity of ions detected in untargeted analyses, normalization standards are often difficult to implement to account for pixel-to-pixel variability in imaging studies. Many normalization strategies exist to account for this variability, but they largely do not improve image quality. In this study, we present a new approach for improving image quality and visualization of tissue features by application of sequential paired covariance (SPC). This approach was demonstrated using previously published tissue datasets such as rat brain and human prostate with different biomolecules like metabolites and N-linked glycans. Data transformation by SPC improved ion images resulting in increased smoothing of biological features compared with commonly used normalization approaches.     

On Domination Number of 4-Regular Graphs

Let G be a simple graph. A subset S V is a dominating set of G, if for any vertex v V – S there exists a vertex u S such that uv E(G). The domination number, denoted by (G), is the minimum cardinality of a dominating set. In this paper we prove that if G is a 4-regular graph with order n, then (G) ⁴/₁₁ n     

Acid-catalyzed transformation of rubrene to indenonaphthacene and its paired interacting orbital (PIO) analysis

Treatment of rubrene (5,6,11,12-tetraphenylnaphthacene) with trifluoroacetic acid in dichloromethane gives 4b,9,10-triphenyl-4b,9-dihydroindeno[1,2,3-fg]naphthacene (1) as the sole isolable product. Paired interacting orbital (PIO) analysis indicates that the reaction is initiated by preferential attack of H⁺ at C(11) position of rubrene.     

Transfer Matrix Spectrum and Bound States for Lattice Classical Ferromagnetic Spin Systems at High Temperature

We obtain new properties of general d-dimensional lattice ferromagnetic spin systems with nearest neighbor interactions in the high-temperature region (1). Each model is characterized by a single-site a priori spin distribution, taken to be even. We state our results in terms of the parameter =s ⁴–3s ²², where s ^k denotes the kth moment of the a priori distribution. Associated with the model is a lattice quantum field theory which is known to contain particles. We show that for >0, small, there exists a bound state with mass below the two-particle threshold. The existence of the bound state has implications for the decay of correlations, i.e., the 4-point functions decay at a slower rate than twice that of the 2-point function. These results are obtained using a lattice version of the Bethe–Salpeter equation. The existence results generalize to N-component models with rotationally invariant a priori spin distributions.     

STUDIES ON THE MESOZOIC MARGINAL ARC SYSTEM OF THE SOUTHEAST COAST AND TAIWAN IN CHINA

The southeast coastal Zhejiang, Fujian, Guangdong provinces and Taiwan in China comprised an important area in ancient Asia where the Yenshanian continental margin magmatic arc well developed in the late Mesozoic time. It is believed that the oceanic trench and subduction zone are situated on the east side of the Central Range in Taiwan. It seems unlikely that the so-called Hercynian-Indosinian ancient island arc folded system would have occurred in this region.     

Constructive characterizations of （γp, γ）- and （γp, γpr）-trees

Let G =(V,E) be a graph without isolated vertices.A set S  V is a domination set of G if every vertex in V -S is adjacent to a vertex in S,that is N[S] = V .The domination number of G,denoted by γ(G),is the minimum cardinality of a domination set of G.A set S  V is a paired-domination set of G if S is a domination set of G and the induced subgraph G[S]has a perfect matching.The paired-domination number,denoted by γpr(G),is defined to be the minimum cardinality of a paired-domination set S in G.A subset S  V is a power domination set of G if all vertices of V can be observed recursively by the following rules:(i) all vertices in N[S] are observed initially,and(ii) if an observed vertex u has all neighbors observed except one neighbor v,then v is observed(by u).The power domination number,denoted by γp(G),is the minimum cardinality of a power domination set of G.In this paper,the constructive characterizations for trees with γp = γ and γpr = γp are provided respectively.