Recently, many authors have focused on the question of symmetric positive solutions for ordinary differential equation boundary value problems, for example, see (Avery & Henderson, 2000; Çetin & Topal, 2012; Graef & Kong, 2008; Hamal & Yoruk, 2010; Jiang, Liu & Wu, 2013; Luo & Luo, 2010; Luo & Luo, 2012; Lin & Zhao, 2013; Tersenov, 2014) and the references therein. In (Avery & Henderson, 2003),...

The pseudo-angle characterizes the pseudo-conformal group G." Let S2m be a fixed 2m dimensional manifold contained in 2;2 so that m . n. LetP be an arbitrary point of S2m. Suppose that S2,1n is an arbitrary (2n 1) dimensional manifold in Z2., which contains P, and let the intersection of S2m and S2,-1 be an S2m-j. Thus S2m is not contained in S2,1. The pseudo-angle between any curve C, in S2m, ...

A Hermitian and an anti-Hermitian first-order intertwining operators are introduced and a class of η-weak-pseudo-Hermitian positiondependent mass (PDM) Hamiltonians are constructed. A corresponding reference-target η-weak-pseudo-Hermitian PDM – Hamiltonians’ map is suggested. Some η-weak-pseudo-Hermitian PT -symmetric Scarf II and periodic-type models are used as illustrative examples. Energy-l...

A brief proof of the existence of an equilibrium in incomplete markets is given for regular economies (Theorem 1) ; a robust example of such economies is provided . Theorem 2 establishes that the manifold fl of global pseudo-equilibria is a fiber bundle with the topological structure of a oneor two-fold covering space of G k . ", the space of k planes in R", where k is the number of assets in t...

In this paper, we investigate under what circumstances the Laplace–Beltrami operator on a pseudo-Riemannian manifold can be written as a sum of squares of vector fields, as is naturally the case in Euclidean space. We show that such an expression exists globally on one-dimensional manifolds and can be found at least locally on any analytic pseudo-Riemannian manifold of dimension greater than tw...

This paper addresses partly an open question raised in the Handbook of Mathematical economics about the orientability of the pseudo-equilibrium manifold in the basic two-period General Equilibrium with Incomplete markets (GEI) model. For a broad class of explicit asset structures, it is proved that the asset equilibrium space is an orientable manifold if S − J is even. This implies, under the s...

We give a loop group formulation for the problem of isometric immersions with flat normal bundle of a simply connected pseudo-Riemannian manifold M c,r, of dimension m, constant sectional curvature c 6= 0, and signature r, into the pseudo-Euclidean space R s , of signature s ≥ r. In fact these immersions are obtained canonically from the loop group maps corresponding to isometric immersions of ...