For hybrid systems in which control consists of selection from a discrete finite set of modes, a somewhat unfamiliar formulation is needed for analysis of the possibility of closed loop (feedback) control. We are here concerned to examine the desiderata for such feedback from the viewpoint of descriptive modeling of implementation in a PDE context. A principal result is global existence, in an ...

BACKGROUND CONTEXT The X-STOP interspinous decompression device, as a treatment for neurogenic intermittent claudication (NIC) because of lumbar spinal stenosis (LSS), has been shown to be superior to nonoperative control treatment. Current Food and Drug Administration labeling limits X-STOP use to NIC patients with a maximum of 25° concomitant lumbar scoliosis. This value was arrived at arbitr...

In this note we show the somewhat surprising fact that proof of `if part' distinguished characterizations metric completeness due to Kirk, and Suzuki Takahashi, respectively, can be deduced in a straightforward manner from Hu's theorem space is complete if only any Banach contraction on bounded closed subsets thereof has fixed point. We also take advantage approach easily deduce characterizatio...

the main purpose of this paper is to introduce and study new classes of soft closed sets like soft regular generalized b-closed sets in soft topological spaces (brie y soft rgb-closed set) moreover, soft rg-closed, soft gpr-closed, soft gb-closed, soft gsp-closed, soft g-closed, soft gb-closed, and soft sgb-closed sets in soft topological spaces are introduced in this paper and we investigat...

Abstract In this paper, we introduce a topological method to produce new rough set models. This is based on the idea of “somewhat open sets” which one celebrated generalizations sets. We first generate some topologies from different types $$N_\rho $$ N ρ -neighborhoods....