L(V)是无限维中心代数的初等证明

研究域F上无限维线性空间V的任一子空间W的线性变换在V上的扩张,用初等方法可证明V的线性变换代数L(V)是无限维的中心代数.在一定意义上推广了域F上的n级矩阵代数是中心代数这一结果.

第十五 讲倒数性质与应用

倒数在初中教材中占有一定的地位。没有它,除法不能用它的逆运算乘法来表示。如果我们很好地应用“倒数”,那么它在某些化简求值上,解某些特殊方程上,证明某些不等式上都会有特殊的转换作用。一、倒数的性质: [性质1] 若两个数互为倒数,则这两个数的乘积为1。 [性质2] 如果两个数互为倒数,那么这两个数的同次幂或者同次方根仍互为倒数。 [性质3] 如果两正数互为倒数,那么这两个正数的和不小于2。即a+1/a≥2(a】0)在高中还要继续学习和应用。

On the Centrosymmetric and Centroskewsymmetric Solutions to a Matrix Equation over a Central Algebra

Let Ω be a finite dimensional central algebra and chart Ω≠2 .The matrix equation AXB-CXD=E over Ω is considered.Necessary and sufficient conditions for the existence of centro(skew)symmetric solutions of the matrix equation are given.As a particular case ,the matrix equation X-AXB=C over Ω is also considered.

A special fermionic generalization of lineal gravity

The central extension of the (1+1)-dimensional Poincaré algebra by including fermionic charges which obey not supersymmetric algebra, but a special graded algebra containing in the right hand side a central element only is obtained. The corresponding theory being the fermionic extension of the lineal gravity is proposed. We considered the algebra of generators, the field transformations and found Lagrangian and equation of motion, then we derived the Casimir operator and obtained the con- stant black hole mass.

Evaluation of the HadISST1 and NSIDC 1850 onward sea ice datasets with a focus on the Barents-Kara seas

In recent years,long-term continuous sea-ice datasets have been developed,and they cover the periods before and after the satellite era.How these datasets differ from one another before the satellite era,and whether one is more reliable than the other,is important but unclear because the sea-ice record before 1979 is sparse and not continuous.In this letter,two sets of sea-ice datasets are evaluated:one is the HadISST1 dataset from the Hadley Centre,and the other is the SIBT1850(Gridded Monthly Sea Ice Extent and Concentration,from 1850 Onward)dataset from the National Snow and Ice Data Center(NSIDC).In view of its substantial importance for climate,the winter sea ice in the Barents and Kara seas(BKS)is of particular focus.A reconstructed BKS sea-ice extent(SIE)is developed using linear regression from the mean of observed surface air temperature at two adjacent islands,Novaya Zemlya and Franz Josef Land(proxy).One validation illustrates that the proxy is substantially coherent with the BKS sea-ice anomaly in the observations and the CMIP5(phase 5 of the Coupled Model Intercomparison Project)historical experiments.This result indicates that the proxy is reasonable.Therefore,the establishment of the reconstructed BKS SIE is also reasonable.The evaluation results based on the proxy suggest that the sea-ice concentration prior to the satellite era in the NSIDC dataset is more realistic and reliable than that in the Hadley Centre dataset,and thus is more appropriate for use.

Decreasing Trend in Summer Precipitation over the Western Sichuan Basin since the 1950s

Changing precipitation in the densely populated Sichuan basin may have a great impact on human life. This study analyzes the change in summer precipitation since 1951 over the western Sichuan basin, one of the regions of the heaviest rainfall in China, by using two datasets provided by the Chinese Meteorological Data Center. The results indicate that summer (from June to September) precipitation over the western Sichuan basin shows a significantly decreasing trend. The summer precipitation over this region has decreased by about 20% since the 1950s, with a rate of decrease of about 40 mm per decade.

Quantum Groups by Ore Extensions Associated withGroup Algebras

As a continuation of the work of Beattie on quantum groups constructed byOre extensions, in this paper, we characterize their centre and discuss the category ofquantum Yang-Baxter modules over them. In addition, we determine all finite dimen-sional irreducible representations over these quantum groups.

Systems of Matrix Equations over a Central Algebra

Let Ω be a finite dimensional central algebra with an involutorial anti-automorphism and chartΩ≠2.Two systems of matrix equations over Ω are consid-ered.Necessary and sufficient conditions for the existences of general solutions,andper(skew)selfconjugate solutions of the systems are given,respectively.

Cohen-Fischman-Westreich's Double Centralizer Theorem for Almost-Triangular Hopf Algebras

In this paper, the authors study the Cohen-Fischman-Westreich's double centralizer theorem for triangular Hopf algebras in the setting of almost-triangular Hopf algebras.

Central extensions of generalized orthosymplectic Lie superalgebras

We completely determine the universal central extension of the generalized orthosymplectic Lie superalgebra ospm 12n（R,-） that is coordinatized by an arbitrary unital associative superalgebra （R,-） with superinvolution. As a result, an identification between the second homology group of the Lie superalgebra ospm｜2n （R,-） and the first skew-dihedral homology group of the associative superalgebra （R,-） with superin-volution is created for positive integers m and n with （m, n）≠ （1, 1） and （m, n）≠（2, 1）. The second homology groups of the Lie superalgebras ospm1｜2（R,-） and ospm｜2n （R,-） are also characterized explicitly.