Two generalizations of the PRV conjecture

Let G be a complex connected reductive group. The PRV conjecture, which was proved independently by S. Kumar and O. Mathieu in 1989, gives explicit irreducible submodules of the tensor product of two irreducible G-modules. This paper has three aims. First, we simplify the proof of the PRV conjecture, then we generalize it to other branching problems. Finally, we find other irreducible components of the tensor product of two irreducible G-modules that appear for "the same reason" as the PRV ones

Embedding theorems on hyperelliptic varieties

In this paper, we investigate linear systems on hyperelliptic varieties. We prove analogues of well-known theorems on abelian varieties, like Lefschetz’s embedding theorem and higher k-jet embedding theorems. Syzygy or Np-properties are also deduced for appropriate powers of ample line bundles. This is a first result on linear series, on hyperelliptic varieties

Semistability of logarithmic cotangent bundle on some projective manifolds

In this article, we investigate the semistability of logarithmic de Rham sheaves on a smooth projective variety (X, D), under suitable conditions. This is related to existence of Kahler–Einstein metric on the open variety. We investigate this problem when the Picard number is one. Fix a normal crossing divisor D on X and consider the logarithmic de Rham sheaf ΩX (log D) on X. We prove semistability of this sheaf, when the log canonical sheaf KX + D is ample or trivial, or when −KX − D is ample, i.e., when X is a log Fano n-fold of dimension n ≤ 6. We also extend the semistability result for Kawamata coverings, and this gives examples whose Picard number can be greater than one

Total scattering descriptions of local and cooperative distortions in the oxide spinel (Mg,Cu)Cr2O4 with dilute Jahn-Teller ions

The normal spinel oxide MgCr2O4 is cubic at room temperature while the normal spinel CuCr2O4 is tetragonal as a consequence of the Jahn-Teller nature of Cu2+ on the tetrahedral sites. Despite different end-member structures, complete solid solutions of Mg_{1-x}Cu_xCr2O4 can be prepared that display a first-order structural transition with composition x = 0.43 at room temperature. Reverse Monte Carlo analysis of total neutron scattering on data acquired between 300 K and 15 K on samples with x = 0.10, 0.20, and 0.43 provides unbiased local and average structure descriptions of the samples, including an understanding of the transition from local Jahn-Teller distortions in the cubic phase to cooperative distortions that result in a tetragonal structure. Distributions of continuous symmetry measures help to understand and distinguish distorted and undistorted coordination around the tetrahedral site in the solid solutions. Magnetic exchange bias is observed in field-cooled hysteresis loops of samples with dilute Cu2+ concentration and in samples with tetragonal--cubic phase coexistence around 300 K.Comment: 10 pages, 14 figure

Distances in Geographically Distributed Team: A Review

Distributed team is a group of people collaborating together virtually from different locations, different time zones and are culturally diverse from each other. Such team have the characteristics of both virtual team and culturally diverse team and is termed as Geographically Distributed Team (GDT). Members of geographically distributed team (GDT) experiences different forms of distances while working together as team both in terms of objective distance based on physical location and subjective distance based on perception. Since the members are located in different continents and working at different time zones they heavily rely on computer mediated communication tools to collaborate.Being distant from each other members experiences a unique set of challenges compared to traditional collocated team which hinders collaboration. The most commonly highlighted issues are related to absence of social ties, distorted flow of information, misunderstanding, misperception and miscommunication. The inability to observe each other work and lack of spontaneous communication due to physical distance builds in perceptual distances among members. The cultural differences among the members being from different nationality, values, beliefs, work style and languages adds to the complexity of working together as a team. Several research studies have looked into both positive and negative effect of distances on team effectiveness. This paper examines the various forms of distances experienced by individuals working in a distributed teams, how it has been measured and the challenges posed by it in GDT