The universal splitting property. II

1984 ◽  
Vol 49 (1) ◽  
pp. 137-150 ◽  
Author(s):  
M. Lerman ◽  
J. B. Remmel
Keyword(s):  
Turing Degree ◽  
Splitting Theorem ◽  
Splitting Property ◽  
Exhaustive Study

We say that a pair of r.e. sets B and C split an r.e. set A if B ∩ C = ∅ and B ∪ C = A. Friedberg [F] was the first to study the degrees of splittings of r.e. sets. He showed that every nonrecursive r.e. set A has a splitting into nonrecursive sets. Generalizations and strengthenings of Friedberg's result were obtained by Sacks [Sa2], Owings [O], and Morley and Soare [MS].The question which motivated both [LR] and this paper is the determination of possible degrees of splittings of A. It is easy to see that if B and C split A, then both B and C are Turing reducible to A (written B ≤TA and C ≤TA). The Sacks splitting theorem [Sa2] is a result in this direction, as are results by Lachlan and Ladner on mitotic and nonmitotic sets. Call an r.e. set A mitotic if there is a splitting B and C of A such that both B and C have the same Turing degree as A; A is nonmitotic otherwise. Lachlan [Lac] showed that nonmitotic sets exist, and Ladner [Lad1], [Lad2] carried out an exhaustive study of the degrees of mitotic sets.The Sacks splitting theorem [Sa2] shows that if A is r.e. and nonrecursive, then there are r.e. sets B and C splitting A such that B <TA and C <TA. Since B is r.e. and nonrecursive, we can now split B and continue in this manner to produce infinitely many r.e. degrees below the degree of A which are degrees of sets forming part of a splitting of A. We say that an r.e. set A has the universal splitting property (USP) if for any r.e. set D ≤T A, there is a splitting B and C of A such that B and D are Turing equivalent (written B ≡TD).

scholarly journals The Cognitive and Psychiatric Subacute Impairment in severe Covid-19.

2021 ◽  
Author(s):  
Pedro J. Serrano-Castro ◽  
Francisco J Garzón-Maldonado ◽  
Ignacio Casado-Naranjo ◽  
Angela Ollero-Ortiz ◽  
Adolfo Mínguez-Castellanos ◽  
...  
Keyword(s):  
Principal Component ◽  
Severe Infection ◽  
Cross Sectional Study ◽  
Inflammatory Factors ◽  
Information Processing Speed ◽  
Cross Sectional ◽  
Cognitive Domains ◽  
Neuropsychiatric Manifestations ◽  
Exhaustive Study

Abstract Background: Neurologic impairment persisting months after acute severe SARS-CoV-2 infection has been described because of several pathogenic mechanisms, including persistent systemic inflammation. The objective of this study is to analyze the selective involvement of the different cognitive domains, it impacts on quality of life and the possible existence of related biomarkers.Methods: Cross-sectional study of patients who survived severe infection with SARS-CoV-2 consecutively recruited from 13 neurology services in Spain between 90 and 120 days after hospital discharge. All patients underwent an exhaustive study of cognitive functions as well as plasma determination of pro-inflammatory factors (chemokines), and neurotrophic factors and light-chain neurofilaments. A Principal Component Analysis extracted the main independent characteristics of the syndrome.Results: 152 patients were recruited. The results of our study show a pattern of cognitive impairment with preferential involvement of episodic and working memory, executive functions, and attention and relatively less affectation of information processing speed, denomination, verbal fluency, and other cortical functions. In addition, psychiatric affectation such as anxiety and depression pictures are constant in our cohort. Several plasma chemokines concentrations were elevated compared with both, a non-SARS-Cov2 infected cohort of neurological outpatients or a control healthy general population, suggesting a pro-inflammatory chronic state derived of viral infection.Conclusion: The neurologic Subacute Impairment in severe Covid-19 consist in an amnesic and dysexecutive syndrome with neuropsychiatric manifestations. We do not know if the deficits detected can persist in the long term and, in this case, if this can trigger or accelerate the onset of neurodegenerative diseases.

Self-similar state of a weakly turbulent plasma

1980 ◽  
Vol 24 (3) ◽  
pp. 551-575 ◽  
Author(s):  
R. Balescu
Keyword(s):  
Electric Current ◽  
Turbulent Energy ◽  
Turbulent Plasma ◽  
Spectral Densities ◽  
Self Similar ◽  
Exhaustive Study ◽  
Detailed Determination

The models of Vekshtein, Ryutov & Sagdeev (VRS), describing a marginally stable turbulent plasma sustaining an electric current, are shown to be incomplete by their neglect of the equations determining the spectral densities of the driving modes. An exhaustive study of these models including a detailed determination of the frequencies, spectral densities and turbulent energy densities, shows that, strictly speaking, there exists no self-similar turbulent state (SSTS). However, an approximate SSTS can be constructed, based on the finding that the tail of the spectral densities behaves self-similarly.

scholarly journals Some density determinations

1923 ◽  
Vol 103 (722) ◽  
pp. 487-499 ◽  
Keyword(s):  
Carbon Tetrachloride ◽  
Specific Gravity ◽  
Physical Constant ◽  
Small Samples ◽  
General Character ◽  
Metallic Elements ◽  
Ethylene Dibromide ◽  
Density Measurements ◽  
Exhaustive Study

It was required to determine the densities of small quantities of metallic elements to an accuracy of about one part in 10,000, and this paper is an account of some of the work undertaken to reach that end. In the course of the work, the densities of the following substances have been determined :─ (1) Carbon tetrachloride. (2) Ethylene dibromide. (3) Cadmium. (4) Lead and isotopic lead from uranium ore. Kahlbaum who has made the most exhaustive study of the density of metals, states that the determination of specific gravity of metals is a delicate matter which can only be effected with success on large quantities of substance, and one cannot attribute to the result the general character of a physical constant for the metal; the determined value belongs exclusively to the sample on which the determination is carried out. These statements are in our opinion too sweeping ; but in this paper it is only intended to describe an improvement in density measurements which renders possible determinations with accuracy on comparatively small samples, and to give a few illustration of the effectiveness of the method.

Galactic orbits of stars

1966 ◽  
Vol 25 ◽  
pp. 93-97
Author(s):  
Richard Woolley
Keyword(s):  
Globular Cluster ◽  
Potential Field ◽  
High Velocity ◽  
Velocity Vector ◽  
Variable Stars ◽  
The Sun ◽  
Proper Motions ◽  
Rr Lyrae ◽  
The Galaxy

It is now possible to determine proper motions of high-velocity objects in such a way as to obtain with some accuracy the velocity vector relevant to the Sun. If a potential field of the Galaxy is assumed, one can compute an actual orbit. A determination of the velocity of the globular clusterωCentauri has recently been completed at Greenwich, and it is found that the orbit is strongly retrograde in the Galaxy. Similar calculations may be made, though with less certainty, in the case of RR Lyrae variable stars.

Distance to SN 1987A and the LMC

1999 ◽  
Vol 190 ◽  
pp. 549-554
Author(s):  
Nino Panagia
Keyword(s):  
Angular Size ◽  
Large Magellanic Cloud ◽  
Magellanic Cloud ◽  
Light Curves ◽  
Distance Modulus ◽  
Absolute Size ◽  
Sn 1987A

Using the new reductions of the IUE light curves by Sonneborn et al. (1997) and an extensive set of HST images of SN 1987A we have repeated and improved Panagia et al. (1991) analysis to obtain a better determination of the distance to the supernova. In this way we have derived an absolute size of the ringRabs= (6.23 ± 0.08) x 1017cm and an angular sizeR″ = 808 ± 17 mas, which give a distance to the supernovad(SN1987A) = 51.4 ± 1.2 kpc and a distance modulusm–M(SN1987A) = 18.55 ± 0.05. Allowing for a displacement of SN 1987A position relative to the LMC center, the distance to the barycenter of the Large Magellanic Cloud is also estimated to bed(LMC) = 52.0±1.3 kpc, which corresponds to a distance modulus ofm–M(LMC) = 18.58±0.05.

International determination of the total motion of the pole

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

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).

Time and Latitude in South Africa

1972 ◽  
Vol 1 ◽  
pp. 27-38
Author(s):  
J. Hers
Keyword(s):  
South Africa ◽  
Cape Town ◽  
Astronomical Observations ◽  
Royal Observatory ◽  
The Republic ◽  
Astronomical Determination ◽  
Limited Accuracy ◽  
Better Than

In South Africa the modern outlook towards time may be said to have started in 1948. Both the two major observatories, The Royal Observatory in Cape Town and the Union Observatory (now known as the Republic Observatory) in Johannesburg had, of course, been involved in the astronomical determination of time almost from their inception, and the Johannesburg Observatory has been responsible for the official time of South Africa since 1908. However the pendulum clocks then in use could not be relied on to provide an accuracy better than about 1/10 second, which was of the same order as that of the astronomical observations. It is doubtful if much use was made of even this limited accuracy outside the two observatories, and although there may – occasionally have been a demand for more accurate time, it was certainly not voiced.

Large-scale Motion of Solar Filaments

2000 ◽  
Vol 179 ◽  
pp. 205-208
Author(s):  
Pavel Ambrož ◽  
Alfred Schroll
Keyword(s):  
Magnetic Flux ◽  
Proper Motion ◽  
Time Scale ◽  
Large Scale ◽  
Accuracy Of Measurements ◽  
Solar Filaments ◽  
General Movement ◽  
Scale Motion ◽  
Velocity Scatter

AbstractPrecise measurements of heliographic position of solar filaments were used for determination of the proper motion of solar filaments on the time-scale of days. The filaments have a tendency to make a shaking or waving of the external structure and to make a general movement of whole filament body, coinciding with the transport of the magnetic flux in the photosphere. The velocity scatter of individual measured points is about one order higher than the accuracy of measurements.

Practical Realization of a Reference System for Earth Dynamics by Satellite Methods

1975 ◽  
Vol 26 ◽  
pp. 341-380 ◽  
Author(s):  
R. J. Anderle ◽  
M. C. Tanenbaum
Keyword(s):  
Reference Frame ◽  
Polar Motion ◽  
Pole Position ◽  
Control Points ◽  
Significant Information ◽  
Crustal Motion ◽  
Average Reference ◽  
Future Data ◽  
Existing Data

AbstractObservations of artificial earth satellites provide a means of establishing an.origin, orientation, scale and control points for a coordinate system. Neither existing data nor future data are likely to provide significant information on the .001 angle between the axis of angular momentum and axis of rotation. Existing data have provided data to about .01 accuracy on the pole position and to possibly a meter on the origin of the system and for control points. The longitude origin is essentially arbitrary. While these accuracies permit acquisition of useful data on tides and polar motion through dynamio analyses, they are inadequate for determination of crustal motion or significant improvement in polar motion. The limitations arise from gravity, drag and radiation forces on the satellites as well as from instrument errors. Improvements in laser equipment and the launch of the dense LAGEOS satellite in an orbit high enough to suppress significant gravity and drag errors will permit determination of crustal motion and more accurate, higher frequency, polar motion. However, the reference frame for the results is likely to be an average reference frame defined by the observing stations, resulting in significant corrections to be determined for effects of changes in station configuration and data losses.

Models of Thermodynamic Properties of Prominences

1979 ◽  
Vol 44 ◽  
pp. 349-355
Author(s):  
R.W. Milkey
Keyword(s):  
Thermodynamic Properties ◽  
Mass Transport ◽  
Emission Spectrum ◽  
Thermodynamic Parameters ◽  
Working Group ◽  
Physical Processes ◽  
Theoretical Concepts ◽  
Group 3 ◽  
Observational Techniques

The focus of discussion in Working Group 3 was on the Thermodynamic Properties as determined spectroscopically, including the observational techniques and the theoretical modeling of physical processes responsible for the emission spectrum. Recent advances in observational techniques and theoretical concepts make this discussion particularly timely. It is wise to remember that the determination of thermodynamic parameters is not an end in itself and that these are interesting chiefly for what they can tell us about the energetics and mass transport in prominences.

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