We investigate the properties of bounded operators which satisfy a certain spectral additivity condition, and use our results to study Lie and Jordan algebras of compact operators. We prove that these algebras have nontrivial invariant subspaces when their elements have sublinear or submultiplicative spectrum, and when they satisfy simple trace conditions. In certain cases we show that these co...

We characterize the initial terms under a diagonal term order of the supersymmetric Schur/Weyl module S(V V ) associated to a row-convex shape D. We show the biwords corresponding to the initial terms of S are closed under dual-Knuth equivalence and that the recording tableaux for these words are decomposable in the sense of [10]. We consider the natural action of bases of S in which the elemen...

We study the large scale geometry of the upper triangular subgroup of PSL2(Z[ 1 n ]), which arises naturally in a geometric context. We prove a quasi-isometry classification theorem and show that these groups are quasi-isometrically rigid with infinite dimensional quasi-isometry group. We generalize our results to a larger class of groups which are metabelian and are higher dimensional analogue...

Article history: Received 12 September 2015 Accepted 21 December 2015 Available online xxxx Submitted by R. Brualdi MSC: primary 05E15 secondary 15A21

In this paper, we investigate the recently defined notion of inverse along an element in the context of matrices over a ring. Precisely, we study the inverse of a matrix along a lower triangular matrix, under some conditions.

For the all-ones lower triangular matrices, the upper and lower bounds on rigidity are known to match [13]. In this short note, we apply these techniques to the allones extended lower triangular matrices, to obtain upper and lower bounds with a small gap between the two; we show that the rigidity is θ( 2 r ).

Guide vanes are a mechanical system used to direct flow in the desired direction. At lower operating conditions, implementing guide vane draft tube of hydro-turbine can decrease excess swirl and, thus, reduce pressure fluctuations. The present study discusses numerical methodology design an effective high head Francis model turbine. method is computationally efficient and saves computational ti...