Triades et familles de courbes gauches

Sans résumé Received: 3 April 1998 / in final form: 16 December 1998     

The non-bipartite integral graphs with spectral radius three

In this paper, we classify the connected non-bipartite integral graphs with spectral radius three.     

Geometry and spectrum of rapidly branching graphs

We study graphs whose vertex degree tends to infinity and which are, therefore, called rapidly branching. We prove spectral estimates, discreteness of spectrum, first order eigenvalue and Weyl asymptotics solely in terms of the vertex degree growth. The underlying techniques are estimates on the isoperimetric constant. Furthermore, we give lower volume growth bounds and we provide a new criterion for stochastic incompleteness.     

A note on a global invertibility of mappings on Rn

We provide sufficient conditions for a mapping f : Rⁿ → Rⁿ to be a global di?eomorphism in case f need not be continuously di?erentiable. Instead it is assumed to be strictly (Hadamard-like) and Fréchet di?erentiable. We use classical local invertibility conditions together with the non-smooth critical point theory.     

Eigenvalues of the k‐th power of a graph

The k‐th power of a graph G, denoted by 500183:mana201500183-math-0002" class="section_image" src="https://wol-prod-cdn.literatumonline.com/cms/attachment/e55bfe99-6125-4a44-a094-ed6ad998b2a6/mana201500183-math-0002.png">, is a graph with the same set of vertices as G such that two vertices are adjacent in 500183:mana201500183-math-0003" class="section_image" src="https://wol-prod-cdn.literatumonline.com/cms/attachment/cf19f968-eb5b-45a3-bdd6-3467388f74f0/mana201500183-math-0003.png"> if and only if their distance in G is at most k. In this paper, we give the bounds on the spectral radius of 500183:mana201500183-math-0004" class="section_image" src="https://wol-prod-cdn.literatumonline.com/cms/attachment/42f09283-da07-497a-8623-5970d769f4ec/mana201500183-math-0004.png"> and 500183:mana201500183-math-0005" class="section_image" src="https://wol-prod-cdn.literatumonline.com/cms/attachment/52bbfbac-cde1-47ce-98aa-626afb1e9898/mana201500183-math-0005.png">. The Nordhaus–Gaddum‐type inequality for the spectral radius of the graph 500183:mana201500183-math-0006" class="section_image" src="https://wol-prod-cdn.literatumonline.com/cms/attachment/afb97c4f-7c69-4eb0-9726-b630ea1be77f/mana201500183-math-0006.png"> is also presented. Moreover, we obtain an upper bound on the energy of the second power of graphs.     

Globally generated vector bundles on the Segre threefold with Picard number two

We classify globally generated vector bundles on 500077:mana201500077-math-0001" class="section_image" src="https://wol-prod-cdn.literatumonline.com/cms/attachment/be209db2-b66d-4789-b365-07cee0039dc0/mana201500077-math-0001.png"> with small first Chern class, i.e. 500077:mana201500077-math-0002" class="section_image" src="https://wol-prod-cdn.literatumonline.com/cms/attachment/06edd667-4e23-41e4-bf3c-50dd1ee030fb/mana201500077-math-0002.png">, 500077:mana201500077-math-0003" class="section_image" src="https://wol-prod-cdn.literatumonline.com/cms/attachment/283b4a16-0ff1-4ff1-a0e6-f19714ae04b1/mana201500077-math-0003.png">. Our main method is to investigate the associated smooth curves to globally generated vector bundles via the Hartshorne–Serre correspondence.     

NaBH4/DOWEX(R)50WX4: A Convenient Reducing System for Fast and Efficient Reduction of Carbonyl Compounds to Their Corresponding Alcohols

The reduction of a variety of carbonyl compounds was efficiently carried out with NaBH₄/DOWEX(R)50WX4 system. The reactions were performed to give the corresponding alcohols derivatives in perfect yields in THF at room temperature. Reduction of acyloins and a‐diketones by this reducing system produced efficiently the corresponding vicinal diols. Also, the reduction of aldehydes over ketones has been accomplished successfully by this system. Regioselectivity of this system was also investigated with exclusive 1,2‐reduction of conjugated carbonyl compounds to their corresponding allylic alcohols in high to excellent yields.     

Cu50Ni50合金快速凝固的分子动力学模拟

采用分子动力学模拟的方法研究了Cu₅₀Ni₅₀合金在不同冷却速度下的凝固过程,利用均方位移、径向分布函数和结构可视化等方法分析其微观结构.并对凝固模型进行拉伸模拟,通过应力应变曲线和直观结构变化分析其性能.研究表明：冷却速度对Cu₅₀Ni₅₀合金凝固形成的结构有较大影响,随着冷却速度的升高,凝固形成的结构中晶体含量减少,在较低的冷却速度下,如冷却1×10¹²K/s时,Cu₅₀Ni₅₀合金凝固形成晶体结构;在较高的冷却速度下,如1×10¹⁴K/s时,Cu₅₀Ni₅₀合金凝固形成非晶体结构,且非晶Cu₅₀Ni₅₀合金的抗拉性能要优于晶体Cu₅₀Ni₅₀合金.