Finding Δ(Σ) for a surface σ of characteristic χ(Σ) = −5

For each surface Σ, we define Δ(Σ) = max{Δ(G)|Gis a class two graph of maximum degree Δ(G) that can be embedded in Σ}. Hence, Vizing's Planar Graph Conjecture can be restated as Δ(Σ) = 5 if Σ is a plane. In this paper, we show that Δ(Σ) = 9 if Σ is a surface of characteristic χ(Σ) = ?5. © 2010 Wiley Periodicals, Inc. J Graph Theory 68:148‐168, 2011     

Low sets without subsets of higher many‐one degree

Given a reducibility ?_r, we say that an infinite set A is r‐introimmune if A is not r‐reducible to any of its subsets B with |A\B| = ∞. We consider the many‐one reducibility ?_m and we prove the existence of a low₁ m‐introimmune set in Π⁰₁ and the existence of a low₁ bi‐m‐introimmune set.     

A simple recipe for sophisticated cocktails: organocatalytic one-pot reactions--concept, nomenclature, and future perspectives

Asymmetric organocatalysis has been successfully incorporated in many multistep one-pot sequences to provide simple access to structurally complex target molecules in a highly stereoselective fashion. The key feature behind this success is the ability of organocatalyzed reactions to proceed efficiently in the presence of large amounts of spectator reagents. Additionally, owing to their organic nature and substoichiometric presence, organocatalysts are also expected to become innocent bystanders in subsequent transformations. In this Minireview, an easy-to-use classification and nomenclatural system that is capable of systematically and informatively describing each one-pot reaction is introduced, and selected important contributions within the field of organocatalytic one-pot reactions are reviewed according to this new system. Finally, future developments and perspectives in the field are discussed.     

一元多项式学习中易犯的几个错误

结合一元多项式中的一些重要概念,如多项式的最大公因式、多项式的重根及不可约多项式等,分析一元多项式学习中易犯的错误,并强调运用定理时要注意其适用的条件和前提．     

${[\ell_p]}_{e.r}$ Euler-Riesz Difference Sequence Spaces

Başar and Braha [1], introduced the sequence spaces $\breve{\ell}_\infty$, $\breve{c}$ and $\breve{c}_0$ of Euler-Cesáro bounded, convergent and null difference sequences and studied their some properties. Then, in [2], we introduced the sequence spaces ${[\ell_\infty]}_{e.r}, {[c]}_{e.r}$ and ${[c_0]}_{e.r}$ of Euler-Riesz bounded, convergent and null difference sequences by using the composition of the Euler mean $E_1$ and Riesz mean $R_q$ with backward difference operator $\Delta$. The main purpose of this study is to introduce the sequence space ${[\ell_p]}_{e.r}$ of Euler-Riesz $p-$absolutely convergent series, where $1 \leq p <\infty$, difference sequences by using the composition of the Euler mean $E_1$ and Riesz mean $R_q$ with backward difference operator $\Delta$. Furthermore, the inclusion $\ell_p\subset{[\ell_p]}_{e.r}$ hold, the basis of the sequence space ${[\ell_p]}_{e.r}$ is constructed and $\alpha-$, $\beta-$ and $\gamma-$duals of the space are determined. Finally, the classes of matrix transformations from the ${[\ell_p]}_{e.r}$ Euler-Riesz difference sequence space to the spaces $\ell_\infty, c$ and $c_0$ are characterized. We devote the final section of the paper to examine some geometric properties of the space ${[\ell_p]}_{e.r}$.     

求0-1型整数规划的一种新方法

本文给出求 0 -1型整数规划的一种新方法 ,该方法利用对所有目标函数值排序的方法 ,求出最优解 .该方法简单易行且计算量较小     

Knots with unknotting number one and Heegaard Floer homology

We use Heegaard Floer homology to give obstructions to unknotting a knot with a single crossing change. These restrictions are particularly useful in the case where the knot in question is alternating. As an example, we use them to classify all knots with crossing number less than or equal to nine and unknotting number equal to one. We also classify alternating knots with 10 crossings and unknotting number equal to one.     

双杂质一维原子链中的晶格振动

对于含有两个杂质的一维单原子链的振动方程求解,得到晶格振动频率的解.分析了振动频率和杂质质量以及两杂质间距离的关系.