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.

Integer partitions which are simultaneously t–cores for distinct values of t have attracted significant interest in recent years. When s and t are relatively prime, Olsson and Stanton have determined the size of the maximal (s, t)-core κs,t. When k > 2, a conjecture of Amdeberhan on the maximal (2k − 1, 2k, 2k + 1)-core κ2k−1,2k,2k+1 has also recently been verified by numerous authors. In this ...

Let Z2 be the two-dimensional integer lattice. For an k≥1, a non-zero lattice point is k-free if greatest common divisor of its coordinates number. We consider proportions and twin points on path α-random walker in Z2. Using second-moment method tools from analytic number theory, we prove that these two are 1/ζ(2k) ∏p(1−2p−2k), respectively, where ζ Riemann zeta function infinite product takes ...

For a 6= 0 we define {E n } by ∑ k=0 ( n 2k ) a2kE n−2k = (1− a)n (n = 0,1,2, . . .), where [n/2] = n/2 or (n−1)/2 according as 2 | n or 2 n. In the paper we establish many congruences for E n modulo prime powers, and show that there is a set X and a map T : X → X such that (−1)nE 2n is the number of fixed points of T n. MSC: Primary 11B68, Secondary 11A07