Kronecker乘积图的超连通性(英文)

设G1和G2是两个连通图,则G1和G2的Kronecker积G1×G2定义如下:V(G1×G2)=V(G1)×V(G2),E(G1×G2)={(u1,v1)(u2,v2):u1u2∈E(G1),v1v2∈E(G2)}.我们证明了G×Kn(n≥4)超连通图当且仅当κ(G)n>δ(G)(n 1),其中G是任意的连通图,Kn是n阶完全图.进一步我们证明了对任意阶至少为3的连通图G,如果κ(G)=δ(G),则G×Kn(n≥3)超连通图.这个结果加强了郭利涛等人的结果.     

A fluorescence toolbox: A review of investigation of electrophoretic separations,process, and interfaces

This review focuses on fluorescence spectroscopy techniques for the investigation of electrophoretic separations. Fluorescence has been used as a sensitive detector for capillary, gel, and microchip electrophoresis for decades. However, advanced fluorescence methods can be used to study transport, interfacial phenomena, intermolecular and affinity interactions, and other processes that occur during separation. This so‐called spectroscopic toolkit can be implemented to understand fundamental behavior in electrophoresis and electrokinetic chromatography. Techniques such as fluorescence recovery after photobleaching, fluorescence correlation spectroscopy, and fluorescence anisotropy are discussed in relation to electrophoretic separations. Newer methods such as super‐resolution microscope are also introduced.     

Reduction of nitroarenes,azoarenes and hydrazine derivatives by an organic super electron donor

Reduction of nitrobenzene by excess organic electron donor, 12, affords diphenylhydrazine in a reaction where azobenzene oxide and azobenzene are likely intermediates. No cleavage of the N-N σ-bond is seen under photoactivation conditions, whereas traces are seen under thermal activation. Hydrazone derivatives were prepared to explore the cleavage of N-N σ-bonds; the results show that a low-lying LUMO assists the transition state for accepting an electron, and the stabilisation that the potential fragments from N-N bond cleavage afford to the fragments is important in determining whether cleavage is observed.     

Synthesis,Single Crystal Growth and Crystal Structure of Ta7Cu10Ga34 – a 8 × 4 × 2 Super Structure of CsCl

Single crystals of Ta₇Cu₁₀Ga₃₄ were grown from the elements in a Cu/Ga melt. Ta₇Cu₁₀Ga₃₄ represents the first ternary compound of the system Ta/Cu/Ga. The crystal structure (Cmmm, oC102, Z = 2, a = 23.803(1), b = 12.2087(4), c = 5.7487(2) Å, 1291 refl. 78 parameters, R₁ = 0.037, wR₂ = 0.070). The crystal structure is characterized by rods of pentagonal prisms MGa₁₀, which are alternatingly occupied by Ta and Cu. Four of these rods are connected to columns running in direction (001). These columns are linked by cubic units TaGa₈, CuGa₈, and GaGa₈. According to the characteristic structural elements and the size of the unit cell Ta₇Cu₁₀Ga₃₄ represents a 8 × 4 × 2 super structure of CsCl or bcc. With respect to the underlying CsCl structure the formula can be written as [Ta₇Cu₁₀Ga₂□₁₃]Ga₃₂, i.e. a cubic primitive packing of 32 Ga atoms with Ta, Cu, and Ga in cubic voids and 13 vacancies. The pentagonal‐prismatic coordination of Ta and Cu can formally be obtained from the cubic primitive packing of Ga atoms by a 45° rotation of a part of the Ga₈ cubes. There is a close similarity to the binary compounds Ta₈Ga₄₁ and Ta_2–xGa_5+x. The first one is also related to a CsCl‐like structure, the latter one contains rods of pentagonal prisms, which form the same columns. There are also relations to the ternaries V₂Cu₃Ga₈ and V₁₁Cu₉Ga₄₆, whose cubic structures are more or less complex variants of CsCl.     

SOME CENTRAL LIMIT THEOREMS FOR SUPER BROWNIAN MOTION

1IntroductionLimittheoremsconstituteanimportantpartofthebranchingprocesstheory.Itisalwaysinterestingtofindconditionsunderwhichanon-degeneratelimitlawexists.SinceGaltonWatsonprocessesareunstable,peoplehavederivedlimittheoremsforthemthroughdevicessucllasmodifyingfactors,conditioning,immigration,etc.AunifiedtreatmentofthelimittheoryofGallon--WatsonprocessesisgiveninAthreyaandNey(1972).Someoftheabovementionedtechniqueshavealsobeenusedinthemeasure-valuedsettingtogetlimittheoremsforDawson-Watana…     

SOME CENTRAL LIMIT THEOREMS FOR SUPER BROWNIAN MOTION

The author proves a central limit theorem for the critical super Brownian motion, which leads to a Gaussian random field. In the transient case the limitingfield is the same as that obtained by Dawson (1977). In the recurrent case it is aspatially uniform field. The author also give a central limit theorem for the weightedoccupation time of the super Brownian motion with underlying dimension numberd 3, completing the results of Iscoe (1986).     

关于超有效点的注记

本文首先给出了赋范空间中Ｂｏｒｗｅｉｎ超有效点定义的二个与范数无关的等价形式,从而得出推广超有效点到局部凸空间的二个途径,并通过例子说明其中之一是不恰当的．我们还给出了超有效点集连通的二个结果．最后,我们指出文［１］引入的严有效点就是Ｈｅｎｉｇ有效点,其主要定理（［１］定理７）是［２］中定理３．３的特例     

超Ornstein-Uhlenbeck过程的占位时过程的绝对连续性

证明了分支特征为ψ（z)=z^2,底过程为d≤3的暂留Ornstein-Uhlenbeck（O．U．）过程的超过程Xt的占位时过程Y（t)=∫^t0Xsds关于Lebesgue测度绝对连续,且其密度过程Y（t,x)关于t≥0,x∈R^d联合连续。     

超临界水的分子动力学模拟

采用分子动力学(MD)模拟的方法对超临界条件下水的结构及扩散性质进行了研究.模拟结果表明超临界条件下水分子之间的氢键作用明显减弱,分子极性大大降低.扩散性质与常温下相比,其大小约上升了两个数量级.