A surface in homogenous space Sol is said to be an invariant surface if it is invariant under some of the two 1-parameter groups of isometries of the ambient space whose fix point sets are totally geodesic surfaces. In this work we study invariant surfaces that satisfy a certain condition on their curvatures. We classify invariant surfaces with constant mean curvature and constant Gaussian curv...

In this note we prove that the space of linear anti-symplectic involutions is the homogenous space Gl(n,R)\Sp(n). This result is motivated by the study of symmetric periodic orbits in the restricted 3-body problem.

In this paper we consider a supervisory control scheme for non-homogenous multi-agent systems. Each agent is modeled through an independent strictly proper SISO state space model, and the supervisory controller, representing the information exchange among the agents, is implemented in turn via a linear state-space model. Controllability and observability of the overall system are characterized,...

BACKGROUND Homogeneous ventilation is important for prevention of ventilator-induced lung injury. Electrical impedance tomography (EIT) has been used to identify optimal PEEP by detection of homogenous ventilation in non-dependent and dependent lung regions. We aimed to compare the ability of volumetric capnography and EIT in detecting homogenous ventilation between these lung regions. METHOD...

In this paper we introduce projective geometry and one of its important theorems. We begin by defining projective space in terms of homogenous coordinates. Next, we define homgenous curves, and describe a few important properties they have. We then introduce Bezout’s Theorem, which asserts that the number of intersection points of two homogenous curves is less than or equal to the product of th...

In this article we study Sobolev metrics of order one on diffeomorphism groups on the real line. We prove that the space Diff1(R) equipped with the homogenous Sobolev metric of order one is a flat space in the sense of Riemannian geometry, as it is isometric to an open subset of a mapping space equipped with the flat L2-metric. Here Diff1(R) denotes the extension of the group of all either comp...