scholarly journals DISTINGUISHING PERFECT SET PROPERTIES IN SEPARABLE METRIZABLE SPACES

2016 ◽  
Vol 81 (1) ◽  
pp. 166-180
Author(s):  
ANDREA MEDINI

AbstractAll spaces are assumed to be separable and metrizable. Our main result is that the statement “For every space X, every closed subset of X has the perfect set property if and only if every analytic subset of X has the perfect set property” is equivalent to b > ω1 (hence, in particular, it is independent of ZFC). This, together with a theorem of Solecki and an example of Miller, will allow us to determine the status of the statement “For every space X, if every Γ subset of X has the perfect set property then every Γ′ subset of X has the perfect set property” as Γ, Γ′ range over all pointclasses of complexity at most analytic or coanalytic.Along the way, we define and investigate a property of independent interest. We will say that a subset W of 2ω has the Grinzing property if it is uncountable and for every uncountable Y ⊆ W there exists an uncountable collection consisting of uncountable subsets of Y with pairwise disjoint closures in 2ω. The following theorems hold.(1)There exists a subset of 2ω with the Grinzing property.(2)Assume MA + ¬CH. Then 2ω has the Grinzing property.(3)Assume CH. Then 2ω does not have the Grinzing property.The first result was obtained by Miller using a theorem of Todorčević, and is needed in the proof of our main result.

1937 ◽  
Vol 10 (4) ◽  
pp. 247-258 ◽  

1.The connection between the rate of maturity (number of days between birth and production of the first egg) and egg production of 938 White Leghorn pullets, hatched and reared on the Experimental farm of the Oliefabrieken Calvé-Delft was investigated. The pullets were of various strains and received widely differing treatment as regards feeding.2.There is a curvilinear correlation between rate of maturity and to talproduction and also between rate of maturity and winter production. It is, therefore, not correct to calculate with rectilinear correlations or regressions.3.The conditions, obtaining during the rearing, influence not only the rate of maturity, but also the connection between the rate of maturity and egg production.4.It is, therefore, impossible to state any generally acceptable rules concerning the way in which the existing connection can be used to raise the average production by the elimination of certain birds.5.Even when the pullets have been carefully culled either before or at the commencement of production, it is possible to raise the average production still further by eliminating those birds, which come into production last. A considerable number of bad producers are found among the birds with the slowest rate of maturity.6.No connection was found between rate of maturity and mortality.7.Neither was there any connection between rate of nlaturity and the average weight of the eggs produced after December.8.For the 514 birds which began production after 30th September, 1935, a rectilinear correlation of +0.66±0.02 was found between rate of maturity and the average weight of the first ten eggs produced. The regression-eo-efficient of this “inception egg-weight” to rate of maturity in +0.16±0.02.


2014 ◽  
Vol 20 (6) ◽  
pp. 380-389 ◽  
Author(s):  
Henry O'Connell ◽  
Sean P. Kennelly ◽  
Walter Cullen ◽  
David J. Meagher

SummaryProviding optimal healthcare for increasingly elderly hospital populations who have high rates of cognitive disorder is a great challenge. Using delirium as an example, we describe how improved management of acute cognitive problems through a multifaceted hospital-wide programme can promote cognitive-friendly hospital environments. A specific plan of action is described that spans interventions in day-to-day clinical care of individual patients all the way to wider organisational practices.Learning Objectives•Understand the concept of cognitive friendliness and how addressing the problem of delirium can contribute to this in our healthcare system.•Become more aware of specific aspects of a cognitive-friendly programme and how these can be implemented in practice.•Explore the key outstanding issues for research that can further enhance our awareness of cognitive-friendly practices.


1975 ◽  
Vol 4 (4) ◽  
pp. 689-695
Author(s):  
Justin Leiber

The notion of moral philosophy that has been dominant in Anglo-American philosophizing since G.E. Moore is peculiar. Reviewing traditional works such as Aristotle's Nicomachean Ethics, Hume's Treatise, Kant's Critique of Pure Reason, and Mill's Utilitarianism, one is tempted to call this new notion of moral philosophy a different subject; and if one does this, it is less peculiar. However, let us accept that this new sort of moral philosophy does belong to the previous tradition; granted this, I shall explain why I think it peculiar through considering the status of the judgement that Hitler was a bad man.Consider the sentential function ‘x is (was) a bad man’. ‘Hitler’ seems an obviously suitable substitution for ‘x, at least in the most important sense. That is, one wants to say that if it is not proper or true to say that ‘Hitler was a bad man’ or ‘Hitler was bad’, it fs never proper or true to issue a sentence of this form, restricting x to human beings. Hitler seems indeed, in this most important sense, to be a paradigm case. One wants to say: if Hitler was not a bad man, who could be?


PMLA ◽  
1939 ◽  
Vol 54 (4) ◽  
pp. 1007-1017
Author(s):  
S. B. Ewing

The late “Elizabethan” tragedy Andromana; or, The Merchant's Wife, probably written shortly after 1642 and first published in 1660, furnishes interesting evidence of the assimilation of certain material into the drama just as the Puritans were closing the London theatres. In its sources, in many of its ideas, in the way of presenting its problem, and in its mood, it reflects the influence of John Ford's studies of abnormal psychology, modelled on the case histories presented in Burton's Anatomy of Melancholy. The play allows a carefully documented study of this literary material and of the deepening interest in its dramatic presentation in that its story can be examined in three successive stages at three widely separated dates:In the generally acknowledged source, the Plangus story in Sidney's Arcadia (1590).In Beaumont and Fletcher's Cupid's Revenge (ca. 1611).In Andromana (after 1642).


1990 ◽  
Vol 138 ◽  
pp. 501-516
Author(s):  
Robert J. Rutten

I have found four models in the literature for doing conference summaries: 1.The Literal Summary.One summarizes all t h a t has been presented, preferably interspersed with comments as “of particular interest was…”.2.The Historical Perspective.One places all (or some) presentations within a historical background, preferably implying that science progresses smoothly in well-planned, orderly fashion.3.The Future Perspective.One points out the way to go, preferably in overly optimistic vein.4.The personal Impressions.One concedes lack of wisdom to forego balanced summarizing, prefering to discuss primarily one's own interests. Which model to choose here? Literal summarizing seems superfluous for the oral presentations. They are printed in the preceding pages, each is effectively a summary of work published elsewhere, and many have an author's summary already. It won't be useful to summarize them here once more, but some perspective may be worthwhile.


1959 ◽  
Vol 11 ◽  
pp. 353-369 ◽  
Author(s):  
Reinhold Baer

Supersoluble immersion of a normal subgroup K of a finite group G shall be defined by the following property:If σ is a homomorphism of G, and if the minimal normal subgroup J of Gσ is part of Kσ then J is cyclic (of order a prime).Our principal aim in the present investigation is the proof of the equivalence of the following three properties of the normal subgroup K of the finite group G:(i)K is supersolubly immersed in G.(ii)K/ϕK is supersolubly immersed in G/ϕK.(iii)If θ is the group of automorphisms induced in the p-subgroup U of K by elements in the normalizer of U in G, then θ' θp-1 is a p-subgroup of θ.Though most of our discussion is concerned with the proof of this theorem, some of our concepts and results are of independent interest.


1994 ◽  
Vol 144 ◽  
pp. 431-434
Author(s):  
M. Minarovjech ◽  
M. Rybanský

AbstractThis paper deals with a possibility to use the ground-based method of observation in order to solve basic problems connected with the solar corona research. Namely:1.heating of the solar corona2.course of the global cycle in the corona3.rotation of the solar corona and development of active regions.There is stressed a possibility of high-time resolution of the coronal line photometer at Lomnický Peak coronal station, and use of the latter to obtain crucial observations.


1994 ◽  
Vol 144 ◽  
pp. 279-282
Author(s):  
A. Antalová

AbstractThe occurrence of LDE-type flares in the last three cycles has been investigated. The Fourier analysis spectrum was calculated for the time series of the LDE-type flare occurrence during the 20-th, the 21-st and the rising part of the 22-nd cycle. LDE-type flares (Long Duration Events in SXR) are associated with the interplanetary protons (SEP and STIP as well), energized coronal archs and radio type IV emission. Generally, in all the cycles considered, LDE-type flares mainly originated during a 6-year interval of the respective cycle (2 years before and 4 years after the sunspot cycle maximum). The following significant periodicities were found:• in the 20-th cycle: 1.4, 2.1, 2.9, 4.0, 10.7 and 54.2 of month,• in the 21-st cycle: 1.2, 1.6, 2.8, 4.9, 7.8 and 44.5 of month,• in the 22-nd cycle, till March 1992: 1.4, 1.8, 2.4, 7.2, 8.7, 11.8 and 29.1 of month,• in all interval (1969-1992):a)the longer periodicities: 232.1, 121.1 (the dominant at 10.1 of year), 80.7, 61.9 and 25.6 of month,b)the shorter periodicities: 4.7, 5.0, 6.8, 7.9, 9.1, 15.8 and 20.4 of month.Fourier analysis of the LDE-type flare index (FI) yields significant peaks at 2.3 - 2.9 months and 4.2 - 4.9 months. These short periodicities correspond remarkably in the all three last solar cycles. The larger periodicities are different in respective cycles.


1977 ◽  
Vol 36 ◽  
pp. 69-74

The discussion was separated into 3 different topics according to the separation made by the reviewer between the different periods of waves observed in the sun :1) global modes (long period oscillations) with predominantly radial harmonic motion.2) modes with large coherent - wave systems but not necessarily global excitation (300 s oscillation).3) locally excited - short period waves.


1979 ◽  
Vol 44 ◽  
pp. 357-372
Author(s):  
Z. Švestka

The following subjects were discussed:(1)Filament activation(2)Post-flare loops.(3)Surges and sprays.(4)Coronal transients.(5)Disk vs. limb observations.(6)Solar cycle variations of prominence occurrence.(7)Active prominences patrol service.Of all these items, (1) and (2) were discussed in most detail and we also pay most attention to them in this report. Items (3) and (4) did not bring anything new when compared with the earlier invited presentations given by RUST and ZIRIN and therefore, we omit them.


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