— We prove two new results about the Cauchy problem in the energy space for nonlinear Schrödinger equations on four-dimensional compact manifolds. The first one concerns global well-posedness for Hartree-type nonlinearities and includes approximations of cubic NLS on the sphere as a particular case. The second one provides, in the case of zonal data on the sphere, local well-posedness for quadr...

It is shown how solutions to the Tzitzéica equation can be used to construct a family of (pseudo) hyper-complex metrics in four dimensions.

It has been suggested that early experiences in families may be related to one's parenting as an adult. Conceptual models were tested that investigated how personality and marital relationships are linked to parenting within and between generations. Eighty mother-grandmother pairs completed questionnaires concerning personality, marital relationships, and parenting. Restrictive and nurturant pa...

Ferdinand Freudenstein (1926-2006) is widely acknowledged to be the father of modern kinematics of mechanisms and machines. His Ph. D. thesis in 1954 and subsequent research papers by him and his students have influenced academic and industrial research, teaching and practice related to the analysis and design of mechanisms and machines throughout the world. In this article, we revisit Freudens...

In this paper we solve the functional equation f ( αx+ (1− α)y ) + f ( βx+ (1− β)y ) = f ( γx+ (1− γ)y ) + f ( δx+ (1− δ)y ) which holds for all x, y ∈ I, where I ⊂ R is a non-void open interval, f : I → R is an unknown function and α, β, γ, δ ∈ (0, 1) are arbitrarily fixed.

We study the Schwinger-Dyson equation associated with a chirality-changing fermion 4-point function in a strongly-coupled U(1) gauge theory. After making appropriate simpliications, we solve the equation numerically via a relaxation method. Our analysis provides an estimate of the critical coupling and it gives some indication as to the general momentum dependence of the 4-point function.

In this paper, we determine all unitary solutions to the YangBaxter equation in dimension four. Quantum computation motivates this study. This set of solutions will assist in clarifying the relationship between quantum entanglement and topological entanglement. We present a variety of facts about the Yang-Baxter equation for the reader unfamiliar with the equation.

This paper studies the phi-four equation that arises in Quantum Mechanics. The topological 1-soliton solution or kink solution is obtained by the ansatz method. The bifurcation analysis is then subsequently carried out and several other solutions are retrieved from the analysis. These solutions include the solitary wave solutions, periodic waves and periodic singular waves. The constraint condi...