scholarly journals Baernstein’s star-function, maximum modulus points and a problem of Erdős

2021 ◽  
Vol 47 (1) ◽  
pp. 181-202
Author(s):  
Ivan I. Marchenko
Keyword(s):  
Meromorphic Function ◽  
Maximum Modulus ◽  
The Relationship

  The paper is devoted to the development of Baernstein's method of \(T^{*}\)-function. We consider the relationship between the number of separated maximum modulus points of a meromorphic function and the \(T^{*}\)-function. The results of Bergweiler, Bock, Edrei, Goldberg, Heins, Ostrovskii, Petrenko, Wiman are generalized. We also give examples showing that the obtained estimates are sharp.

scholarly journals Sunspot magnetic fields: a comparison between the CrAO and SDO/HMI data

2020 ◽  
Vol 1 (2) ◽  
pp. 1-5
Author(s):  
Regina Biktimirova ◽  
Valentina Abramenko
Keyword(s):  
Magnetic Field ◽  
Linear Regression ◽  
Linear Approximation ◽  
Pearson Correlation ◽  
Field Measurements ◽  
Maximum Modulus ◽  
Maximum Magnetic Field ◽  
Magnetic Field Measurements ◽  
The Relationship ◽  
The Magnetic Field

We performed a digitization of maximum magnetic field measurements in sunspots. The original data were acquired as drawings at the Crimean Astrophysical Observatory of the Russian Academy of Sciences (CrAO RAS). About 1000 sunspots observed in 2014 have been analyzed. The data were compared to the corresponding measurements from the SDO/HMI instrument (with both the line-of-sight magnetic field Bz(HMI) and the modulus of the magnetic field vector B(HMI)). For the same sunspot, the maximum modulus of the magnetic field derived at CrAO was compared to the corresponding value from HMI. The Crimean data and the space-based data (of both types) were found to be in direct proportion to each other. A linear approximation over the entire range of measurements (1–4) kilogauss (kG) shows a Pearson correlation coefficient of 0.71 (with the 95 % confidence boundaries of 0.68–0.74) and a slope of linear regression of 0.65±0.02 for both types of the space-based data. A linear approximation over the range of strong fields B(CrAO) > 1.8 kG gives a similar correlation, however the slope of linear regression is far closer to unity and constitutes 0.90 for the relationship (Bz(HMI) vs B(CrAO)) and 0.84 for the relationship (B(HMI) vs B(CrAO)). In the range of weak fields B(CrAO) < 1.8 kG, a non-linear deviation (exceeding) of the space-based data is observed. Non-linearity can be explained, in part, by a specific routine of the magnetic field measurements at CrAO, however further investigations are needed to explore sources of possible non-linearity in the HMI data. The Crimean measurements of the maximum magnetic field in sunspots are concluded to be in good agreement with the corresponding SDO/HMI measurements, and therefore they can be used for scientific purposes.

scholarly journals p,q-Growth of Meromorphic Functions and the Newton-Padé Approximant

2019 ◽  
Vol 2019 ◽  
pp. 1-6
Author(s):  
Mohammed Harfaoui ◽  
Loubna Lakhmaili ◽  
Abdellah Mourassil
Keyword(s):  
Meromorphic Function ◽  
Upper Bound ◽  
Meromorphic Functions ◽  
Padé Approximant ◽  
Supremum Norm ◽  
Pade Approximant ◽  
Degree Of Convergence ◽  
The Relationship ◽  
Best Rational Approximation ◽  
Convergence In Capacity

In this paper, we have considered the generalized growth (p,q-order and p,q-type) in terms of coefficient of the development pnn given in the (n, n)-th Newton-Padé approximant of meromorphic function. We use these results to study the relationship between the degree of convergence in capacity of interpolating functions and information on the degree of convergence of best rational approximation on a compact of ℂ (in the supremum norm). We will also show that the order of meromorphic functions puts an upper bound on the degree of convergence.

scholarly journals An Inequality of Meromorphic Vector Functions and Its Application

2011 ◽  
Vol 2011 ◽  
pp. 1-13
Author(s):  
Wu Zhaojun ◽  
Chen Yuxian
Keyword(s):  
Meromorphic Function ◽  
Characteristic Function ◽  
Meromorphic Functions ◽  
The Relationship ◽  
Vector Valued

Firstly, an inequality for vector-valued meromorphic functions is established which extend a corresponding inequality of Milloux for meromorphic scalar-valued function (1946). As an application, the relationship between the characteristic function of a vector-valued meromorphic functionfand its derivativef'is studied, results are obtained to extend some related results for meromorphic scalar-valued function of Weitsman (1969) and Singh and Gopalakrishna (1971).

Interstellar gas in the central region of the Galaxy

1967 ◽  
Vol 31 ◽  
pp. 239-251 ◽  
Author(s):  
F. J. Kerr
Keyword(s):  
Central Region ◽  
Galactic Plane ◽  
Neutral Hydrogen ◽  
Continuum Emission ◽  
Galactic Centre ◽  
Interstellar Gas ◽  
Hydrogen Recombination ◽  
The Galaxy ◽  
Centre Region ◽  
The Relationship

A review is given of information on the galactic-centre region obtained from recent observations of the 21-cm line from neutral hydrogen, the 18-cm group of OH lines, a hydrogen recombination line at 6 cm wavelength, and the continuum emission from ionized hydrogen.Both inward and outward motions are important in this region, in addition to rotation. Several types of observation indicate the presence of material in features inclined to the galactic plane. The relationship between the H and OH concentrations is not yet clear, but a rough picture of the central region can be proposed.

The relationship of the scleractinian corals to the rugose corals

Paleobiology ◽  
1980 ◽  
Vol 6 (02) ◽  
pp. 146-160 ◽  
Author(s):  
William A. Oliver
Keyword(s):  
Critical Points ◽  
Scleractinian Corals ◽  
Convincing Evidence ◽  
Early Triassic ◽  
Rugose Corals ◽  
History Of ◽  
The Subject ◽  
Relationship Of ◽  
The Relationship ◽  
Biologic Factors

The Mesozoic-Cenozoic coral Order Scleractinia has been suggested to have originated or evolved (1) by direct descent from the Paleozoic Order Rugosa or (2) by the development of a skeleton in members of one of the anemone groups that probably have existed throughout Phanerozoic time. In spite of much work on the subject, advocates of the direct descent hypothesis have failed to find convincing evidence of this relationship. Critical points are:(1) Rugosan septal insertion is serial; Scleractinian insertion is cyclic; no intermediate stages have been demonstrated. Apparent intermediates are Scleractinia having bilateral cyclic insertion or teratological Rugosa.(2) There is convincing evidence that the skeletons of many Rugosa were calcitic and none are known to be or to have been aragonitic. In contrast, the skeletons of all living Scleractinia are aragonitic and there is evidence that fossil Scleractinia were aragonitic also. The mineralogic difference is almost certainly due to intrinsic biologic factors.(3) No early Triassic corals of either group are known. This fact is not compelling (by itself) but is important in connection with points 1 and 2, because, given direct descent, both changes took place during this only stage in the history of the two groups in which there are no known corals.

Choosing a Markov blanket

2020 ◽  
Vol 43 ◽  
Author(s):  
Thomas Parr
Keyword(s):  
Markov Blanket ◽  
Target Article ◽  
The Relationship

Abstract This commentary focuses upon the relationship between two themes in the target article: the ways in which a Markov blanket may be defined and the role of precision and salience in mediating the interactions between what is internal and external to a system. These each rest upon the different perspectives we might take while “choosing” a Markov blanket.

Tinkering with cognitive gadgets: Cultural evolutionary psychology meets active inference

2019 ◽  
Vol 42 ◽  
Author(s):  
Paul Benjamin Badcock ◽  
Axel Constant ◽  
Maxwell James Désormeau Ramstead
Keyword(s):  
Evolutionary Psychology ◽  
Research Program ◽  
Active Inference ◽  
Innovative Research ◽  
Cognitive Faculties ◽  
Cultural Evolutionary ◽  
The Relationship

Abstract Cognitive Gadgets offers a new, convincing perspective on the origins of our distinctive cognitive faculties, coupled with a clear, innovative research program. Although we broadly endorse Heyes’ ideas, we raise some concerns about her characterisation of evolutionary psychology and the relationship between biology and culture, before discussing the potential fruits of examining cognitive gadgets through the lens of active inference.

Radiation Damage, Contrast and Statistics in High Resolution Biological Electron Microscopy

1970 ◽  
Vol 28 ◽  
pp. 260-261
Author(s):  
Robert M. Glaeser
Keyword(s):  
High Resolution ◽  
Particle Flux ◽  
Unit Area ◽  
Signal To Noise ◽  
Resolution Image ◽  
High Resolution Image ◽  
Pass Through ◽  
Counting Statistics ◽  
The Relationship ◽  
Picture Element

It is well known that a large flux of electrons must pass through a specimen in order to obtain a high resolution image while a smaller particle flux is satisfactory for a low resolution image. The minimum particle flux that is required depends upon the contrast in the image and the signal-to-noise (S/N) ratio at which the data are considered acceptable. For a given S/N associated with statistical fluxtuations, the relationship between contrast and “counting statistics” is s131_eqn1, where C = contrast; r2 is the area of a picture element corresponding to the resolution, r; N is the number of electrons incident per unit area of the specimen; f is the fraction of electrons that contribute to formation of the image, relative to the total number of electrons incident upon the object.

Skeletal elements of crinoid echinoderms: High-resolution structural and microanalytical results

1983 ◽  
Vol 41 ◽  
pp. 194-195
Author(s):  
D. F. Blake ◽  
L. F. Allard ◽  
D. R. Peacor
Keyword(s):  
High Resolution ◽  
Marine Invertebrates ◽  
Sea Urchins ◽  
Structural Features ◽  
Sea Stars ◽  
High Resolution Tem ◽  
Relationship Of ◽  
The Relationship ◽  
Insight Into

Echinodermata is a phylum of marine invertebrates which has been extant since Cambrian time (c.a. 500 m.y. before the present). Modern examples of echinoderms include sea urchins, sea stars, and sea lilies (crinoids). The endoskeletons of echinoderms are composed of plates or ossicles (Fig. 1) which are with few exceptions, porous, single crystals of high-magnesian calcite. Despite their single crystal nature, fracture surfaces do not exhibit the near-perfect {10.4} cleavage characteristic of inorganic calcite. This paradoxical mix of biogenic and inorganic features has prompted much recent work on echinoderm skeletal crystallography. Furthermore, fossil echinoderm hard parts comprise a volumetrically significant portion of some marine limestones sequences. The ultrastructural and microchemical characterization of modern skeletal material should lend insight into: 1). The nature of the biogenic processes involved, for example, the relationship of Mg heterogeneity to morphological and structural features in modern echinoderm material, and 2). The nature of the diagenetic changes undergone by their ancient, fossilized counterparts. In this study, high resolution TEM (HRTEM), high voltage TEM (HVTEM), and STEM microanalysis are used to characterize tha ultrastructural and microchemical composition of skeletal elements of the modern crinoid Neocrinus blakei.

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