We prove results towards the equidistribution of certain families of periodic torus orbits on homogeneous spaces, with particular focus on the case of the diagonal torus acting on quotients of PGLn(R). After attaching to each periodic orbit an integral invariant (the discriminant) our results have the following flavour: certain standard conjectures about the distribution of such orbits hold up ...

Let T be a periodic time scale. The purpose of this paper is to use a modification of Krasnoselskii’s fixed point theorem due to T. A. Burton to show that the totally nonlinear dynamic equation with functional delay x△(t) =−a(t)x3(σ(t))+G ( t, x3(t), x3(t − r(t)) ) , t ∈ T, has a periodic solution. We invert this equation to construct a sum of a compact map and a large contraction, which is sui...

Spontaneous recanalization of atherothrombotic extracranial cerebral arteries is rare vis-à-vis recanalization of intracranial vessels. The time course is unknown. The question is the advisability and timing of surgery in a recanalized vessel. We describe a patient with spontaneous recanalization of a totally occluded left Internal Carotid Artery (ICA) who was monitored with periodic imaging an...

Typically, many of the modern buildings have concrete walls constructed from cinder block walls, that have periodic nature in their relative dielectric constant. This periodic nature excites higher-order Floquet harmonic modes at microwave frequencies, which leads to the propagation of scattered waves along with non-specular directions. Periodic structures exhibit different behaviors when illum...

We show that reversible holomorphic mappings of C2 have periodic points accumulating at an elliptic fixed point of general type. On the contrary, we also show the existence of holomorphic symplectic mappings that have no periodic points of certain periods in a sequence of deleted balls about an elliptic fixed point of general type. The radii of the balls are carefully chosen in terms of the per...

we prove that each normal automorphism of the $n$-periodic product of cyclic groups of odd order $rge1003$ is inner, whenever $r$ divides $n$.

Let R be a commutative noetherian local ring that is not Gorenstein. It is known that the category of totally reflexive modules over R is representation infinite, provided that it contains a non-free module. The main goal of this paper is to understand how complex the category of totally reflexive modules can be in this situation. Local rings (R, m) with m3 = 0 are commonly regarded as the stru...

Context. A flare-driven quasi-periodic extreme ultraviolet wave train totally reflected at a coronal hole boundary was well imaged on both temporal and spatial scales by AIA/SDO. Aims. We aim to investigate the driving mechanisms of demonstrate total reflection effect boundary. Methods. The speeds incident trains are studied. periodic correlation with related flare is probed. compare measured i...