On artin algebras with almost all indecomposable modules of projective or injective dimension at most one

Let A be an artin algebra over a commutative artin ring R and ind A the category of indecomposable finitely generated right A-modules. Denote to be the full subcategory of ind A formed by the modules X whose all predecessors in ind A have projective dimension at most one, and by the full subcategory of ind A formed by the modules X whose all successors in ind A have injective dimension at most one. Recently, two classes of artin algebras A with co-finite in ind A, quasi-tilted algebras and generalized double tilted algebras, have been extensively investigated. The aim of the paper is to show that these two classes of algebras exhaust the class of all artin algebras A for which is co-finite in ind A, and derive some consequences. Dedicated to Stanislaw Balcerzyk on the occation of his 70th birthday     

Precovers

Let be an abstract class (closed under isomorpic copies) of left R-modules. In the first part of the paper some sufficient conditions under which is a precover class are given. The next section studies the -precovers which are -covers. In the final part the results obtained are applied to the hereditary torsion theories on the category on left R-modules. Especially, several sufficient conditions for the existence of -torsionfree and -torsionfree -injective covers are presented.     

On the Existence of Relative Injective Covers

Let be a hereditary torsion theory for the category -mod of unital left -modules over an associative ring with an identity element. The purpose of this note is to prove that if the associated Gabriel filter consists of finitely presented left ideals, then every module has a -injective cover and if contains a cofinal subset of finitely presented left ideals, then every module has a -torsionfree -injective cover. The methods used working with pure submodules contained in ``large" submodules also allow to unify the proofs of some previously known results.     

Nonlinear Rossby Waves and Their Interactions (Ⅰ) ——Collision of Envelope Solitary Rossby Waves

By using the multiple-scale perturbation method a set of equations which describes two interacting nonlinear Rossby waves in the barotropic atmosphere is derived. The equations are used to study the collision of two envelope solitary Rossby waves. It is found that for a range of parameters, the collision interactions are envelope soliton-like in that the properties of the two envelope solitary waves change very little. For other parameters, new "inelastic" effects are observed, including speed changes, fission of envelope solitary waves and energy dispersion. It is also found that despite of the complexity of the interacting process, the energy of each wave is conserved.     

Reconstructing Reliable Powder Patterns from Spikelets (Q)CPMG NMR Spectra: Simplification of UWNMR Crystallography Analysis

Spikelets NMR spectra are very popular as they enable the shortening of experimental time and give the possibility to obtain required NMR parameters for nuclei with ultrawide NMR patterns. Unfortunately, these resulted ssNMR spectra cannot be fitted directly in common software. For this reason, we developed UWNMRSpectralShape (USS) software which transforms spikelets NMR patterns into single continuous lines. Subsequently, these reconstructed spectral envelopes of the (Q)CPMG spikelets patterns can be loaded into common NMR software and automatically fitted, independently of experimental settings. This allows the quadrupole and chemical shift parameters to be accurately determined. Moreover, it makes fitting of spikelets NMR spectra exact, fast and straightforward.     

Bounded three-dimensional Fano varieties of integer index

The cube of the anticanonical class of a three-dimensional Fano variety with canonical singularities and integer Fano index is effectively bounded. Translated fromMatematicheskie Zametki, Vol. 66, No. 3, pp. 445–451, September, 1999.     

A Generalization of Auslander's Last Theorem

Before his death, Auslander announced that every finitely generated module over a local Gorenstein ring has a minimal Cohen–Macaulay approximation. Yoshimo extended Auslander's result to local Cohen–Macaulay rings admitting a dualizing module.Over a local Gorenstein ring the finitely generated maximal Cohen–Macaulay modules are the finitely generated Gorenstein projective modules so in fact Auslander's theorem says finitely generated modules over such rings have Gorenstein projective covers. We extend Auslander's theorem by proving that over a local Cohen–Macaulay ring admitting a dualizing module all finitely generated modules of finite G-dimension (in Auslander's sense) have a Gorenstein projective cover. Since all finitely generated modules over a Gorenstein ring have finite G-dimension, we recover Auslander's theorem when R is Gorenstein.     

单向恒定侧压下混凝土动态抗压特性试验研究

利用大连理工大学自行研制、改造的大型液压伺服混凝土静动三轴试验系统对立方体试件进行一向恒定侧压的动态压缩试验。完成了四个侧向恒定压力等级的试验,应变速率变化范围为10-5~10-2 s-1。探讨了不同应变速率以及不同恒定侧压条件下混凝土强度与变形的变化规律。以试验数据为基础,在八面体应力空间中建立了适用于单向恒定侧压条件下混凝土双轴动态破坏的强度公式,为大坝、海上采油平台等大型混凝土结构的抗震安全分析提供了参考。     

Relative purity over noetherian rings

In this note we are going to show that if M is a left module over a left noetherian ring R of the infinite cardinality λ ≥ |R|, then its injective hull E(M) is of the same size. Further, if M is an injective module with |M| ≥ (2^λ)⁺ and K ≤ M is its submodule such that |M/K| ≤ λ, then K contains an injective submodule L with |M/L| ≤ 2^λ. These results are applied to modules which are torsionfree with respect to a given hereditary torsion theory and generalize the results obtained by different methods in author’s previous papers: [A note on pure subgroups, Contributions to General Algebra 12. Proceedings of the Vienna Conference, June 3–6, 1999, Verlag Johannes Heyn, Klagenfurt, 2000, pp. 105–107], [Pure subgroups, Math. Bohem. 126 (2001), 649–652]. This research has been partially supported by the Grant Agency of the Charles University, grant #GAUK 301-10/203115/B-MAT/MFF and also by the institutional grant MSM 113 200 007.