Mahdi Hormozi

Symmetry classes of tensors associated with the semi-dihedral groups SD8n

We discuss the existence of an orthogonal basis consisting of decomposable vectors for all symmetry classes of tensors associated with semi-dihedral groups SD8n. In particular, a necessary and sufficient condition for the existence of such a basis associated with SD8n and degree two characters is given.

ORTHOGONAL BASES OF BRAUER SYMMETRY CLASSES OF TENSORS FOR GROUPS HAVING CYCLIC SUPPORT ON NON-LINEAR BRAUER CHARACTERS ∗

This paper provides some properties of Brauer symmetry classes of tensors. A dimension formula is derived for the orbital subspaces in the Brauer symmetry classes of tensors corresponding to the irreducible Brauer characters of the groups whose non-linear Brauer characters have support being a cyclic group. Using the derived formula, necessary and sufficient condition are investigated for the existence of an o-basis of dicyclic groups, semi-dihedral groups, and also those things are reinvestigated on dihedral groups. Some criteria for the non-vanishing elements in the Brauer symmetry classes of tensors associated to those groups are also included.

A note on a paper of Harris concerning the asymptotic approximation to the eigenvalues of -y'' + qy = λy, with boundary conditions of general form

AbstractIn this article, we derive an asymptotic approximation to the eigenvalues of the linear differential equation -y″(x)+q(x)y(x)=λy(x),x∈(a,b) with boundary conditions of general form, when q is a measurable function which has a singularity in (a, b) and which is integrable on subsets of (a, b) which exclude the singularity.Mathematics Subject Classification 2000: Primary, 41A05; 34B05; Secondary, 94A20.