Endomorphism Algebras of Supportτ-Tilting Modules

Let A be a finite dimensional k-algebra and T be a supportτ-tilting right A-module.In this note,we give lower and upper bounds for the global dimension of the endomorphism algebra End_(A)(T)under some mild conditions.Finally,we give some examples to illustrate that both the upper and lower bounds can be reached.

量子群主Tilting模的形式特征标

设p≥ 2 (h- 1) ,λ∈X+ 是p2 室中的正则支配权 .证明了主UΨ 模MΨ(λ0 +Pλ1)的形式特征标公式 ;描述了MΨ(λ0 +pλ1)的合成因子的分布状态 .对于A2 型量子群 ,给出了p2 室一般位置室中UΨ 模范畴主UΨ 模MΨ(λ0 +Pλ1)合成因子的分解模式 .

Wakamatsu tilting模的性质

设Λ为Artin代数,对给定的Wakamatsu tilting模,Wakamatsu tilting cotorsionpair以及相关类的性质。

光伏安装方位和倾角对榆林市发电特性影响的实验研究

为了使光伏组件产生更多电量,合理的方位和倾角设置极为重要。对安装在榆林地区变电站的光伏组件进行344 d的实验研究,获得不同方位以及不同倾角对该地区光伏发电特性的影响,探究年度发电量最大时的最佳方位和最优倾角。光伏组件安装方向分别为正东、正南和正西方向,且正东、正西方向有4个不同的倾斜角度(30°、35°、40°和90°),正南方向光伏板倾斜角度为25°、30°、35°、40°、45°、50°、55°、60°和90°。分别测量电流、电压、功率和太阳辐射强度,分析倾角和方位角对年发电特性的影响。结果显示:在不同方位相同倾角的情况下,正南方向的发电量最大。光伏矩阵朝南安装时,不考虑遮挡情况下,倾角为40°时的发电量最大。考虑到实际安装情况,光伏矩阵朝西和朝东安装时,90°角安装的发电量较低,为最大发电量的50%左右。如果受楼宇实际安装情况限制只能正东或正西90°安装时,建议正东安装。光伏组件全年工作中,受太阳辐射和环境温度双重影响,朝南安装时冬季发电量大,夏季发电量小,东西方向安装时春季发电量大,冬季发电量小。

A Construction of Characteristic Tilting Modules

Associated with each finite directed quiver Q is a quasi-hereditary algebra. the so-called twisted double of the path algebra kQ. Characteristic tilting modules over this class of quasi-hereditary algebras are constructed. Their endonorphism algebras are explicitly described. It turns out that this class of quasi-hereditary algebras is closed under taking the Ringel dual.

Comparisons of recollements and tilting modules

The purpose of this paper is to provide the TTF-theories and investigate the comparisons of recollements(one-sided recollements) both induced by the BB-tilting modules.

On the character of certain tilting modules

Let G be a semisimple group over an algebraically closed field of characteristic p > 0. We give a(partly conjectural) closed formula for the character of many indecomposable tilting rational G-modules assuming that p is large.

AN EFFECTIVE CRITERION FOR UNIQUENESS OF THE TILTING MODULE

Throughout this note, we assume that k is an algebraically closed field and A is a basic connected finite-dimensional algebra over k (associative, with identity). All modules over an algebra A are finitely generated left A-modules. We usually denote, up to isomorphism, by {P_A(a)|a∈I} the set of all indecomposable projective modules, by {E_A(a)|a∈I} the set of all indecomposable injective modules, and by {S_A(a)|a∈I} the set of all simple modules,

SEPARATING TILTING MODULES

Let A be a basic, connected and finite-dimensional algebra over an algebraically closed field k. A tilting module A^T is called separating if the torsion theory (F(A^T), G(A^T)) induced by A^T is splitting in A-mod, i. e. any indecomposable module A^M belongs either to F(A^T) or to G(A^T). In this note we prove the following main result by using the representation theory of representation-infinite hereditary algebra.

ENDOMORPHISM ALGEBRAS OF PREPROJECTIVE PARTIAL TILTING MODULES

Let be a connected finite quiver without oriented cycle, A=k（?） the corresponding path algebra with k being an algebraically closed field, AT a preprojective tilting module. B=EndAT. Then B is called a tame （resp. wild）concealed algebra provided is an Euclidean （resp. wild ） graph. The following result is important in the representation theory of tame concealed algebras （see [1,4.9]）: if A is tame concealed, T= T0⊕ T1 a tilting module with T0 nonzero preprojective and T1 regular, then EndAT0 is tame concealed. The main purpose of this note is to generalize it to the 'wild' case. For this we generally consider the endomorphism algebra of preprojective partial tilting modules over a concealed algebra. For the notations the readers can refer to Ref.[1].

G-stable support τ-tilting modules

Motivated by T-tilting theory developed by T. Adachi, O. Iyama, I. Reiten, for a finite-dimensional algebra A with action by a finite group G, we introduce the notion of G-stable support τ-tilting modules. Then we establish bijections among G-stable support τ-tilting modules over ∧, G-stable two-term silting complexes in the homotopy category of bounded complexes of finitely generated projective ∧-modules, and G-stable functorially finite torsion classes in the category of finitely generated left ∧-modules. In the case when ∧ is the endomorphism of a G-stable cluster-tilting object T over a Horn-finite 2-Calabi- Yau triangulated category L with a G-action, these are also in bijection with G-stable cluster-tilting objects in L. Moreover, we investigate the relationship between stable support τ-tilitng modules over ∧ and the skew group algebra ∧G.

Tensor products of tilting modules

We consider whether the tilting properties of a tilting A-module T and a tilting B-module T′ can convey to their tensor product T T′. The main result is that T T′ turns out to be an （n ＋ m）-tilting A B-module, where T is an m-tilting A-module and T′ is an n-tilting B-module.

Tilting modules over path algebras of Dynkin type and complete slice modules

Let T be a tilting A-module over a path algebra of Dynkin type.We prove that if the indecomposable direct summands of T are in the differentτ-orbits of the AR-quiver of A,then T is a complete slice module.

Graded and Nongraded Properties of Partial Tilting Modules and Tilting Modules

This paper gives the relationships among partial tilting objects （tilting objects） of categories of graded left A-modules of type G, left A-modules, left Ae-modules and A#-modules, and then proves that for graded partial tilting modules, there exist the Bongartz complements in the category of graded A-modules.

Tilting Bimodules from Tilting Pairs

Tilting pair was introduced by Miyashita in 2001 as a generalization of tilting module. In this paper, we construct a tilting left Endh（C）-right Endh（T）-bimodule for a given tilting pairs （C,T） in modh, where A is an Artin algebra.

Study on Seasonal Adjustment of Solar PV Tilt Angle around the North of 45th Parallel

The tilt angle of the small scale existing solar power plants is 60 degree and it is 45 degree for the megawatts(MW)class solar power plant in Mongolia.However,the PV module which is installed with 45 degree accumulates lots of snow during the winter.Currently,all solar PV systems installed in Mongolia are fixed the direction and tilt angles.According to the previous research result,the tilt angle of those systems was not suitable for using especially in the winter.The PV module which is installed with 60 degree does not accumulates snow even during the autumn and spring.According to the National Aeronautics and Space Administration(NASA)solar radiation database,solar irradiance for equator facing is largest at 32-degree tilted angle during the summer,47-degree during the spring and autumn,at 62-degree during the winter.The results of this paper show,the tilt angle of the PV module should be adjusted at least twice a year.For instance,the tilt angle will be adjusted at the 32-degree from 15th March to 24th August,at the 62-degree from 25th August to 15th March.In this case,the annual total energy output will be increased up to 30%than present production.

关于半对偶模的n-倾斜模及其刻画

设R为交换 Noether 环,给出关于半对偶R-模W的n-倾斜模的定义.利用同调代数的方法,讨论n-倾斜模(未必有限生成)与n-W-倾斜模之间的关系,研究n-W-倾斜模的若干性质和等价刻画.结果表明,T是n-W-倾斜模当且仅当 Hom R(W,T)是n-倾斜模;T是n-倾斜模当且仅当W R T是n-W-倾斜模.

无人机倾斜摄影在滑坡区域监测中的应用研究

为了提高滑坡区域监测能力,采用无人机倾斜摄影技术实现滑坡区域监测,同时采用特征点提取和匹配特征点的方法对滑坡监测区域数据信息特征进行监测。通过影像分析和变换,以提取所需特征的方法,提高数据信息应用和监测能力。将不同的硬件结构划分为电源模块和处理器、模拟/数字(A/D)转换模块、脉冲宽度调制(PWM)驱动模块、电平转换模块。通过这四个模块的配合,能够实现远程摄影相关工作。试验结果表明,该研究所运用的方法监测误差更小,最低达到4%以下。试验结果验证了方法的稳定性。

Generic modules for tilted algebras

IN the theory of infinite abelian groups, the concepts of torsion-free groups and divisible groups are well known. We know that there exists, up to isomorphism, one and only one abelian group which is both torsion-free and divisible at the same time. This is the additive group Q of the rational numbers. Q plays an important role in the study of infinite-abelian groups. The theory of infinite-dirnensional modules over a finite-dimensional algebra runs similarly to the theory of infinite abelian groups but there are also some substantial differences.

前囊抛光对白内障术后视觉质量的影响

目的:评价前囊抛光对白内障超声乳化术后视觉质量的影响。方法:前瞻性随机对照研究。纳入2021-11/2022-06于应急总医院眼科行白内障超声乳化联合人工晶状体(IOL)植入术的年龄相关性白内障患者65例73眼,随机分为抛光组(30例35眼,术中行前后囊联合抛光)和对照组(35例38眼,术中仅行后囊抛光)。观察术后1wk,1、3、6mo最佳矫正视力,术后3、6mo测量前囊口面积,并使用Pentacam三维眼前节系统评估后囊膜混浊程度(P评分)、IOL倾斜度和偏心量,使用OPD-ScanⅢ光程差分析系统评估波前像差、点扩散函数(PSF)的斯特列尔比(SR)和调制传递函数(MTF)。结果:术后1wk,1、3、6mo,抛光组患者最佳矫正视力均优于对照组(P<0.05)。术后3、6mo,两组患者前囊口面积、后囊膜混浊程度(P评分)、IOL偏心量、PSF的SR值和MTF均无差异(P>0.05)。术后3mo,两组患者IOL倾斜度、波前像差均无差异(P>0.05),但术后6mo,抛光组IOL倾斜度小于对照组[(1.65±0.60)°vs(2.34±0.43)°,P<0.001)],波前像差也小于对照组(0.03±0.01μm vs 0.06±0.03μm,P<0.001)。结论:白内障超声乳化吸除术中行360°抛光前后囊膜能提高术后最佳矫正视力,且术后IOL倾斜度更低、波前像差更小,视觉质量更好。