Initial data, basic geometric constructions, and the future null condition failure factor

Author(s):  
Gregory J. Galloway

Let S be a spacelike slice (defined formally in Section 2) in a space-time M. We will say that S is future causally complete in M if for each p ε J+(S) the closure in S of the set J-(p) ∩ S is compact. Define past causal completeness time-dually. Then S is causally complete if it is both future and past causally complete. A compact spacelike slice is necessarily causally complete, as is any Cauchy surface, but the concept of causal completeness is much broader than either of these two conditions. For example the slices t = const. ≠ 0 in the space-time obtained by removing the origin from Minkowski space are causally complete, although they are neither Cauchy nor compact. The slice t = 0 in the previous example and the hyperboloid in Minkowski space (where (t, x1, …, xn) are standard inertial coordinates) are examples of slices which are not causally complete. Physically speaking, an edgeless slice S is future causally complete if the information from S which reaches a point in the future of S comes from a finite nonsingular region in S. The Maximal Reissner-Nordstrom space-time is a well-known example in which this finiteness condition is not fulfilled by any of its asymptotically flat partial Cauchy surfaces. Indeed for any such partial Cauchy surface S, J-(p) ∩ S is non-compact for any p ε H+(S). However, as has been discussed in the literature (e.g. [17], p. 625 f), it is believed that the Cauchy horizon in this situation is unstable with respect to perturbations of the initial data on S.


2021 ◽  
Vol 108 (Supplement_6) ◽  
Author(s):  
T Sooriyamoorthy

Abstract Aim To compare the contents of the ENT SHO bag with the recommendations by ENT UK. To address any deficiencies in the bag and prevent it from recurring in the future. Method Over 5 consecutive days, the night SHO would compare the contents of the ENT bag with a checklist based on ENT UK guidelines. This was repeated post-intervention. Results The initial data collection showed that the bag was missing numerous items, ranging from tongue depressors to nasal catheters. It also contained bulky, unnecessary items such as Lahey forceps. The bag was replenished, unnecessary items removed, and a new checklist was introduced which the SHO had to complete every night shift. Any missing equipment was to be replaced at that time. PPE was added to the bag. The next round of data collection showed that the bag remained well stocked, with only minor equipment missing such as merocele packs and Sofradex drops. However, the bag contained alternatives such as Rapid Rhinos and Gentisone drops. Conclusions The introduction of a checklist has ensured that the SHO bag remains well stocked. This improves the efficiency of on-calls as the SHO no longer has to repeatedly travel between A&E and ENT stores. This is also beneficial when dealing with emergencies as all the equipment is readily accessible. The addition of PPE was prudent as ENT is a high-risk speciality in the COVID pandemic. Currently the checklist is completed weekly, in order to reduce the workload for the SHO – something to re-audit in the future.


Author(s):  
Karen L. Sanzo ◽  
Tancy Vandecar-Burdin ◽  
Tisha M. Paredes ◽  
Lisa Mayes ◽  
Brian Payne

In 2020, Old Dominion University was awarded a State Council for Higher Education for Virginia grant in order to re-imagine the future of experiential learning at the institution. This campus-wide effort is led by a taskforce to create a vision, framework, and plan for the future of experiential learning at Old Dominion University. The taskforce is composed of stakeholders that include students, faculty, administrators, and community and business partners. In this chapter, the authors report on process and progress, with particular attention to the first three phases of the design thinking process. In the empathy phase, they have engaged in design thinking sprints, hosted monthly taskforce meetings, engaged in an exhaustive review of current experiential learning activities, and deployed surveys of relevant stakeholders. During the defining phase, they analyzed initial data, synthesized their collective empathy work, and identified root issues to craft their “How might we” questions to inform the ideation work. In this chapter, they also share the results of the ideation phase.


1961 ◽  
Vol 13 ◽  
pp. 29-41
Author(s):  
Wm. Markowitz
Keyword(s):  

A symposium on the future of the International Latitude Service (I. L. S.) is to be held in Helsinki in July 1960. My report for the symposium consists of two parts. Part I, denoded (Mk I) was published [1] earlier in 1960 under the title “Latitude and Longitude, and the Secular Motion of the Pole”. Part II is the present paper, denoded (Mk II).


1978 ◽  
Vol 48 ◽  
pp. 387-388
Author(s):  
A. R. Klemola
Keyword(s):  

Second-epoch photographs have now been obtained for nearly 850 of the 1246 fields of the proper motion program with centers at declination -20° and northwards. For the sky at 0° and northward only 130 fields remain to be taken in the next year or two. The 270 southern fields with centers at -5° to -20° remain for the future.


Author(s):  
Godfrey C. Hoskins ◽  
Betty B. Hoskins

Metaphase chromosomes from human and mouse cells in vitro are isolated by micrurgy, fixed, and placed on grids for electron microscopy. Interpretations of electron micrographs by current methods indicate the following structural features.Chromosomal spindle fibrils about 200Å thick form fascicles about 600Å thick, wrapped by dense spiraling fibrils (DSF) less than 100Å thick as they near the kinomere. Such a fascicle joins the future daughter kinomere of each metaphase chromatid with those of adjacent non-homologous chromatids to either side. Thus, four fascicles (SF, 1-4) attach to each metaphase kinomere (K). It is thought that fascicles extend from the kinomere poleward, fray out to let chromosomal fibrils act as traction fibrils against polar fibrils, then regroup to join the adjacent kinomere.


Author(s):  
Nicholas J Severs

In his pioneering demonstration of the potential of freeze-etching in biological systems, Russell Steere assessed the future promise and limitations of the technique with remarkable foresight. Item 2 in his list of inherent difficulties as they then stood stated “The chemical nature of the objects seen in the replica cannot be determined”. This defined a major goal for practitioners of freeze-fracture which, for more than a decade, seemed unattainable. It was not until the introduction of the label-fracture-etch technique in the early 1970s that the mould was broken, and not until the following decade that the full scope of modern freeze-fracture cytochemistry took shape. The culmination of these developments in the 1990s now equips the researcher with a set of effective techniques for routine application in cell and membrane biology.Freeze-fracture cytochemical techniques are all designed to provide information on the chemical nature of structural components revealed by freeze-fracture, but differ in how this is achieved, in precisely what type of information is obtained, and in which types of specimen can be studied.


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