关于形式三角矩阵环

本文研究形式三角矩阵环 R 的若干新性质,讨论 R-模的伪投射性,给出了形式三角矩阵环 R 是 V-环或半 V-环的充要条件．同时,给出了 R 是 PS-环的条件．     

关于Diophantine方程(20n)x+(21n)y=(29n)z

设a,b,c是满足条件a2+ b2=c2的两两互素的正整数.Jesmanowicz于1956年猜想对于任意给定的正整数n,方程(an)x+(bn)y=(cn)z仅有解(x,y,z)=(2,2,2).本文证明了方程(20n)x+(21n)y=(29n)z有唯一解(x,y,z)=(2,2,2).     

倾斜RnA-模及其导出的挠理论

本文通过函子Ｔ＝－ＡＲｎＡ讨论了倾斜Ａ 模与倾斜ＲｎＡ 模的重要联系，推广了［１］的主要结果；讨论了倾斜ＲｎＡ 模ＴＸ与倾斜Ａ 模导出的挠理论在相同性和分裂性等方面的关系．     

Triangulated Structures Induced by Triangle Functors

Given a triangle functor F : A → B, the authors introduce the half image hIm F,which is an additive category closely related to F. If F is full or faithful, then hIm F admits a natural triangulated structure. However, in general, one can not expect that hIm F has a natural triangulated structure. The aim of this paper is to prove that hIm F admits a natural triangulated structure if and only if F satisfies the condition(SM). If this is the case, hIm F is triangle-equivalent to the Verdier quotient A/Ker F.     

对偶扩张代数的分裂挠理论与Generic模

设A是一个有限维代数,R是A的对偶扩张代数.MA是一个A-模.给定一个倾斜R-模M（?）AR,我们知道MA一定是一个倾斜A-模 设（TM（?）AR,FM（?）AR）与（TM,FM）是分别由M（?）AR和MR导出的挠理论.本文讨论挠理论的分裂性以及GenericA-模与GenericR-模之间的关系.     

Von neumaivn regularity of sf-rings

A ring R is called left (right) SF-ring if all simple left (right) R-modules are flat. It is proved that R is Von Neumann regular if R is a right SF-ring whoe maximal essential right ideals are ideals. This gives the positive answer to a qestion proposed by R. Yue Chi MIng in 1985, and a counterexample is given to settle the follwoing question in the negative: If R is an ERT ring which is one-sided V-ring, is R a left and right V-ring? Some other conditions are given for a SF-ring to be regular.     

Hydrothermal Syntheses of CuO,CuO/Cu2O,Cu2O,Cu2O/Cu and Cu Microcrystals Using Ionic Liquids

In this paper, CuO, CuO/Cu₂O, Cu₂O, Cu₂O/Cu and Cu microcrystals were synthesized via a hydrothermal method by mixing Cu(NO₃)₂·3H₂O and NaOH together in the presence of an ionic liquid 1-butyl-3-methylimidazolium tetrafluoroborate([BMIM]BF₄) or 1-butyl-3-methylimidazolium chloride([BMIM]Cl). The structures and the morphologies of the obtained products were characterized by means of X-ray diffractometer(XRD), field-emission scanning electron microscopy/energy-dispersive spectroscopy(FESEM/EDS), transmission electron microscopy/selected area electron diffraction(TEM/SAED) and Raman spectroscopy. The result of XRD indicates that Cu₂O and Cu microcrystals are cubic phase and the Raman spectra confirm the presence of carbon. The results of FESEM and TEM images show Cu₂O microcrystals as rule cubes of 2 μm in length and Cu particles of 5 μm in diameter. According to the difference between crystal structures, bi-component and single component products were synthesized by adjusting the reaction conditions. A possible formation mechanism of Cu₂O and Cu was proposed in[BMIM]BF₄.     

边坡岩体浅层破坏的热应力效应研究

温度变化是影响边坡岩体风化并导致浅层破坏的一个重要因素。边坡岩体内的温度变化比较复杂, 且随地面温度的变化呈周期性的变化。温度的变化导致热应力的生成, 温度变化的周期性致使热应力具有交变性。在这种交变应力作用下, 边坡浅部岩体的破坏表现出疲劳特征。本文分析了边坡岩体中的温度场和热应力的分布特征以及边坡岩体疲劳破坏的机理及判据。     

Poisson structures on basic cycles

The Poisson structures on a basic cycle are determined completely via quiver techniques. As a consequence, all Poisson structures on basic cycles are inner.     

Derived equivalence of algebras

The derived equivalence and stable equivalence of algebrasR _A ^m and R _B ^m are studied. It is proved, using the tilting complex, thatR _A ^m andR _B ^m are derived-equivalent whenever algebrasA andB are derived-equivalent.