In this paper, some zeros and non-zeros in the character tables of symmetric groups are displayed partition forms. particular, more self conjugate partitions beside odd permutations heavily investigated.

In this paper we prove that two Cartan subspaces of a semisimple symmetric pair (g, τ) are conjugate under G = Int(g) if and only if they are conjugate under (Gτ )0. Moreover we derive a double coset decomposition for G, which improves the results of Oshima and Matsuki.

We developed a fast numerical method for complex symmetric shifted linear systems, which is motivated by the quantum-mechanical (electronicstructure) theory in nanoscale materials. The method is named shifted Conjugate Orthogonal Conjugate Gradient (shifted COCG) method. The formulation is given and several numerical aspects are discussed.

We consider the problem of minimizing the energy of an inextensible elastic strut with length 1 subject to an imposed twist angle and force. In a standard calculus of variations approach, one first locates equilibria by solving the Euler–Lagrange ODE with boundary conditions at arclength values 0 and 1. Then one classifies each equilibrium by counting conjugate points, with local minima corresp...

Let M denote a complete simply connected Riemannian manifold with all sectional curvatures ≥ 1. The purpose of this paper is to prove that when M has conjugate radius at least π/2, its injectivity radius and conjugate radius coincide. Metric characterizations of compact rank one symmetric spaces are given as applications.

A novel C(3)-symmetric peptide conjugate bearing tryptophane zipper-forming peptides showed pH-responding self-assembly into nanospheres and nanofibers in water.