The Geometry of the Gibbs-Appell Equations and Gauss' Principle of Least Constraint

We present a generalisation of the Gibbs-Appell equations which is valid for general Lagrangians. The general form of the Gibbs-Appell equations is shown to be valid in the case when constraints and external forces are present. In the case when the Lagrangian is the kinetic energy with respect to a Riemannian metric, the Gibbs function is shown to be related to the kinetic energy on the tangent bundle of the configuration manifold with respect to the Sasaki metric. We also make a connection with the Gibbs-Appell equations and Gauss' principle of least constraint in the general case

Boundedness of Maximal Operators of Schr\"odinger Type with Complex Time

Results of P. Sj\"olin and F. Soria on the Schr\"odinger maximal operator with complex-valued time are improved by determining up to the endpoint the sharp $s \geq 0$ for which boundedness from the Sobolev space $H^s(\mathbb{R})$ into $L^2(\mathbb{R})$ occurs. Bounds are established for not only the Schr\"odinger maximal operator, but further for a general class of maximal operators corresponding to solution operators for certain dispersive PDEs. As a consequence of additional bounds on these maximal operators from $H^s(\mathbb{R})$ into $L^2([-1, 1])$, sharp results on the pointwise almost everywhere convergence of the solutions of these PDEs to their initial data are determined.Comment: 12 pages. One further minor correction. To appear in the Revista Matem\'atica Iberoamerican

Multi-element spherical shell generation

A nozzle assembly in a multi-element spherical shell generation system includes first and second side-by-side spaced apart nozzles and a web portion extending between and connecting the nozzles. The first nozzle has an inner orifice adapted to discharge a first filler material and an outer annular orifice separated from and defined in concentric relation about the inner orifice and adapted to discharge a first shell material. The second nozzle has an inner orifice adapted to discharge a second filler material and an outer annular orifice separated from and defined in concentric relation about the inner orifice and adapted to discharge a second shell material. A multi-element spherical shell can be formed through employment of the nozzle assembly by merger with one another after discharge from the outer orifices of the nozzles of a pair of adjacent annular streams of liquid or molten shell wall material of different compositions and encapsulation by the mixed shell wall materials of a common encapsulated core fluids also simultaneously discharged by the inner orifices nozzles. On the other hand, the pair of encapsulating streams of shell wall material can be of the same materials which merge together and encapsulate core fluids of different compositions which will merge together after discharge from the nozzles

Adjustable steam producing flexible orifice independent of fluid pressure

A self-adjusting choke for a fluids nozzle includes a membrane constructed of a single piece of flexible or elastic material. This flexible material is shaped to fit into the outlet of a nozzle. The body of the membrane has at least two flow channels, from one face to the other, which directs two streams of water to cross at the opening of the nozzle or at some point beyond. The elasticity and thickness of the membrane is selected to match the range of expected pressures and fluid velocities. The choke may have more than two flow channels, as long as they are aligned adjacent to one another and directed towards each other at the exit face. In a three orifice embodiment, one is directed upward, one is directed downward, and the one in the middle is directed forward. In this embodiment all three fluid streams intersect at some point past the nozzle opening. Under increased pressure the membrane will deform causing the orifices to realign in a more forward direction, causing the streams to intersect at a smaller angle. This reduces the force with which the separate streams impact each other, still allowing the separate streams to unify into a single stable spiralling stream in spite of the increased pressure

Total immersion crystal growth

Crystals of wide band gap materials are produced by positioning a holder receiving a seed crystal at the interface between a body of molten wide band gap material and an overlying layer of temperature-controlled, encapsulating liquid. The temperature of the layer decreases from the crystallization temperature of the crystal at the interface with the melt to a substantially lower temperature at which formation of crystal defects does not occur, suitably a temperature of 200 to 600 C. After initiation of crystal growth, the leading edge of the crystal is pulled through the layer until the leading edge of the crystal enters the ambient gas headspace which may also be temperature controlled. The length of the column of liquid encapsulant may exceed the length of the crystal such that the leading edge and trailing edge of the crystal are both simultaneously with the column of the crystal. The crystal can be pulled vertically by means of a pulling-rotation assembly or horizontally by means of a low-angle withdrawal mechanism

Implementation and evaluation of a nurse-administered dysphagia screening tool to identify patient’s at high risk for post-extubation dysphagia

Purpose: Post-extubation dysphagia (PED) occurs in 3% to 62% of intensive care unit patients. Patients with moderate or severe PED are more likely to experience pneumonia, reintubation, or death. Early identification of post-extubation dysphagia is crucial so diet modifications, temporary feeding measures, and/or advanced swallow evaluations and therapies can be implemented. The purpose of this quality improvement project was to implement a nurse-administered dysphagia screening tool (NADST) for post-extubated patients in a 21-bed mixed medical intensive care unit (MICU) at a large academic medical center. Methods: Utilizing quality improvement methods, a modified dysphagia screening tool was trialed in a MICU for two months. Eight Super Users (RNs) were recruited and attended one of three train the trainer sessions taught by a Speech Language Pathologist. The Super Users trained the remaining unit nurses (RNs). A 5-minute video for the unit nurses was created to supplement the trainings. Pre- and post-intervention surveys were administered to measure changes in knowledge, beliefs, and practices around PED screening. Patient electronic health records were reviewed to identify all patients eligible for PED screening and screening dispositions. Results: Of the 59 eligible patients, 34 patients were screened utilizing the NADST. Nurses had a high level of knowledge but varying practices and comfort with dysphagia screening prior to the intervention. The intervention increased the comfort level and screening frequencies for PED. The NADST was found to be useful for improving nursing practice. Conclusions: Through the utilization of a Super User training model, this quality improvement project demonstrated that implementing a standardized PED screening tool does improve PED screening frequencies

The Looming Battle for Control of Multidistrict Litigation in Historical Perspective

2018 marks fifty years since the passage of the Multidistrict Litigation Act. But instead of thoughts of a golden-anniversary celebration, an old Rodney Dangerfield one-liner comes to mind: “[M]y last birthday cake looked like a prairie fire.” Indeed, after a long period of relative obscurity, multidistrict litigation (MDL) has become a subject of major controversy—and not only among scholars of procedure. For a long time, both within and beyond the rarified world of procedure scholars, MDL was perceived as the more technical, less extreme cousin of the class action, which attracted most of the controversy. My goal in this Article is to shed light on the reasons the Multidistrict Litigation Act was constructed as it was and suggest that those engaged in the current debate ask, after becoming informed by available data, whether those reasons have lost any of their currency. I also offer some tenuous predictions about the path forward, recognizing that the prediction business is a dangerous one in the current political climate. First, I review the history to explain why the MDL framework was built without Rules Committee involvement. Then, I fast-forward to the present day and discuss briefly the nascent proposals to either amend the MDL statute or provide for Federal Rules of Civil Procedure for MDL. Finally, I conclude by assessing the current debate and make some suggestions as this debate winds its way forward. In 1968, the small cadre of judges who developed and fought for the MDL statute won the battle for procedural power. Today, fifty years later, the MDL statute continues to operate as they imagined. However, with success comes scrutiny, and what had been settled is now once again up for debate