scholarly journals On the Roots of the Modified Orbit Polynomial of a Graph

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 972
Author(s):  
Modjtaba Ghorbani ◽  
Matthias Dehmer
Keyword(s):  
Positive Root ◽  
Current Work ◽  
Positive Zero ◽  
Unique Positive Root ◽  
Definition Of

The definition of orbit polynomial is based on the size of orbits of a graph which is OG(x)=∑ix|Oi|, where O1,…,Ok are all orbits of graph G. It is a well-known fact that according to Descartes’ rule of signs, the new polynomial 1−OG(x) has a positive root in (0,1), which is unique and it is a relevant measure of the symmetry of a graph. In the current work, several bounds for the unique and positive zero of modified orbit polynomial 1−OG(x) are investigated. Besides, the relation between the unique positive root of OG in terms of the structure of G is presented.

Signalling over a Gaussian channel with feedback and autoregressive noise

1975 ◽  
Vol 12 (4) ◽  
pp. 713-723 ◽  
Author(s):  
J. Wolfowitz
Keyword(s):  
Regression Coefficient ◽  
Positive Root ◽  
Average Energy ◽  
Gaussian Channel ◽  
Straightforward Manner ◽  
First Order ◽  
Unique Positive Root ◽  
Equivalent Expression ◽  
Optimal Linear ◽  
General Regression

We study in detail the case of first-order regression, but our results can be extended to the general regression in a straightforward manner. An average energy constraint ((1.2) below) is imposed on each signal. In Section 2 we give an optimal linear signalling scheme (definition and proof in Section 4) for this channel. We conjecture that this scheme is optimal among all signalling schemes. Then the capacity C of the channel is (see Section 5) – log b, where b is the unique positive root (in x) of the equation x2 = (1 + g2(1 + |α|x)2)–1. Here a is the regression coefficient, and g2 is the ratio of the average energy per signal to the variance of the noise. An equivalent expression is C = ½log(1 + g2(1 + |α| b)2).

Hyperbolic Groups

2017 ◽  
Author(s):  
Moon Duchin
Keyword(s):  
Word Problem ◽  
Hyperbolic Group ◽  
Hyperbolic Spaces ◽  
Hyperbolic Groups ◽  
Positive Zero ◽  
Surface Groups ◽  
Research Projects ◽  
Intrinsic Geometry ◽  
Point Condition ◽  
Definition Of

This chapter deals with hyperbolic groups. It begins with an overview of curvature, a fundamental way of understanding the intrinsic geometry of manifolds, and its three regimes—positive, zero, and negative. In terms of surfaces, each regime corresponds to the sphere, the plane, and the saddle, respectively. The chapter proceeds by considering the definition of hyperbolicity in terms of triangles in trees, thin triangles, insize, the four-point condition, and invariance. It then looks at some examples of groups and spaces that are δ‎–hyperbolic and some obstructions to δ‎–hyperbolicity. It also explores surface groups and some qualitative geometric properties of hyperbolic spaces before concluding with an analysis of a property of hyperbolic groups that seems combinatorial: every hyperbolic group possesses an algorithm to solve the word problem. The discussion includes exercises and research projects.

Degrees of homogeneity of potential fields and structural indices of Euler deconvolution

Geophysics ◽  
2007 ◽  
Vol 72 (1) ◽  
pp. L1-L12 ◽  
Author(s):  
Petar Stavrev ◽  
Alan Reid
Keyword(s):  
Potential Field ◽  
Variable Density ◽  
Point Sources ◽  
Index Formula ◽  
Potential Fields ◽  
Positive Zero ◽  
Euler Deconvolution ◽  
Structural Index ◽  
Field Source ◽  
Definition Of

Homogeneity is a well-known property of the potential fields of simple point sources used in field inversion. We find that the analytical expressions of potential fields created by sources of complicated shape and constant or variable density or magnetization also show this property. This is true if all variables of length dimension are involved in the test of homogeneity. The coordinates of observation points and the source coordinates and sizes form an extended set of variables, in relation to which the field expression is homogeneous. In this case, the principal definition of homogeneity applied to a potential field can be treated as an operator of a space transform of similarity. The ratio between the transformed and original fields determines the value and sign of the degree of homogeneity [Formula: see text]. The latter may take on positive, zero, or negative values. The degree of homogeneity depends on the type of field and on the assumed physical parameter of the field source, and can be nonunique for a given field element. We analyze the potential field of one singular point as the simplest case of homogeneity. Thus, we deduce results for the structural index, [Formula: see text], in Euler deconvolution. The structural index can also be positive, zero, or negative, but it has a unique value. Analytical considerations, as well as numerical tests on the gravity contact model, confirm the proposed physical interpretation of [Formula: see text], and lead to an extended version of Euler’s differential equation for potential fields.

The Computer Implementation of an Algorithm for Solving Nonlinear Optimization Problems

2013 ◽  
Vol 427-429 ◽  
pp. 1845-1848
Author(s):  
Da Xin Zhu ◽  
Xiao Dong Wang
Keyword(s):  
Nonlinear Optimization ◽  
Order Of Convergence ◽  
Optimization Problems ◽  
Positive Root ◽  
General Point ◽  
Computer Implementation ◽  
Software Packages ◽  
Unique Positive Root ◽  
Practical Algorithm ◽  
Convergence Orders

In this work, we develop a simple yet practical algorithm for solving nonlinear optimization problems by finding a root of a real function with a good local convergence. The algorithm can be easily implemented in software packages for achieving desired convergence orders. For the general-point formula,the order of convergence rate of the presented algorithm is , the unique positive root of the equation .

scholarly journals Towards an event annotated corpus of Polish

2015 ◽  
pp. 253-267 ◽  
Author(s):  
Michał Marcińczuk ◽  
Marcin Oleksy ◽  
Tomasz Bernaś ◽  
Jan Kocoń ◽  
Michał Wolski
Keyword(s):  
Current Work ◽  
Annotation Task ◽  
University Of Technology ◽  
Polish Text ◽  
The Future ◽  
Polish Language ◽  
Event Annotation ◽  
Definition Of ◽  
Future Work

Towards an event annotated corpus of PolishThe paper presents a typology of events built on the basis of TimeML specification adapted to Polish language. Some changes were introduced to the definition of the event categories and a motivation for event categorization was formulated. The event annotation task is presented on two levels – ontology level (language independent) and text mentions (language dependant). The various types of event mentions in Polish text are discussed. A procedure for annotation of event mentions in Polish texts is presented and evaluated. In the evaluation a randomly selected set of documents from the Corpus of Wrocław University of Technology (called KPWr) was annotated by two linguists and the annotator agreement was calculated. The evaluation was done in two iterations. After the first evaluation we revised and improved the annotation procedure. The second evaluation showed a significant improvement of the agreement between annotators. The current work was focused on annotation and categorisation of event mentions in text. The future work will be focused on description of event with a set of attributes, arguments and relations.

Signalling over a Gaussian channel with feedback and autoregressive noise

1975 ◽  
Vol 12 (04) ◽  
pp. 713-723 ◽  
Author(s):  
J. Wolfowitz
Keyword(s):  
Regression Coefficient ◽  
Positive Root ◽  
Average Energy ◽  
Gaussian Channel ◽  
Straightforward Manner ◽  
First Order ◽  
Unique Positive Root ◽  
Equivalent Expression ◽  
Optimal Linear ◽  
General Regression

We study in detail the case of first-order regression, but our results can be extended to the general regression in a straightforward manner. An average energy constraint ((1.2) below) is imposed on each signal. In Section 2 we give an optimal linear signalling scheme (definition and proof in Section 4) for this channel. We conjecture that this scheme is optimal among all signalling schemes. Then the capacity C of the channel is (see Section 5) – log b, where b is the unique positive root (in x) of the equation x 2 = (1 + g 2(1 + |α|x)2)–1. Here a is the regression coefficient, and g 2 is the ratio of the average energy per signal to the variance of the noise. An equivalent expression is C = ½log(1 + g2(1 + |α| b)2).

Introductory paper

1966 ◽  
Vol 24 ◽  
pp. 3-5
Author(s):  
W. W. Morgan
Keyword(s):  
Line Intensity ◽  
Classification Scheme ◽  
Two Dimensional ◽  
Spectral Classification ◽  
Dimensional Array ◽  
Rr Lyrae ◽  
Metallic Line ◽  
Introductory Paper ◽  
Parameter Varying ◽  
Definition Of

1. The definition of “normal” stars in spectral classification changes with time; at the time of the publication of theYerkes Spectral Atlasthe term “normal” was applied to stars whose spectra could be fitted smoothly into a two-dimensional array. Thus, at that time, weak-lined spectra (RR Lyrae and HD 140283) would have been considered peculiar. At the present time we would tend to classify such spectra as “normal”—in a more complicated classification scheme which would have a parameter varying with metallic-line intensity within a specific spectral subdivision.

2.2. Working Group 2: Conceptual Definitions of Reference Coordinate Systems for Earth Dynamics

1975 ◽  
Vol 26 ◽  
pp. 21-26
Keyword(s):  
Coordinate System ◽  
Working Group ◽  
General Character ◽  
Coordinate Systems ◽  
Reference Coordinate System ◽  
Group 2 ◽  
Definition Of ◽  
Earth Dynamics

An ideal definition of a reference coordinate system should meet the following general requirements:1. It should be as conceptually simple as possible, so its philosophy is well understood by the users.2. It should imply as few physical assumptions as possible. Wherever they are necessary, such assumptions should be of a very general character and, in particular, they should not be dependent upon astronomical and geophysical detailed theories.3. It should suggest a materialization that is dynamically stable and is accessible to observations with the required accuracy.

Symbiotic Stars at Optical, Infrared and Radio Wavelengths

1979 ◽  
Vol 46 ◽  
pp. 125-149 ◽  
Author(s):  
David A. Allen
Keyword(s):  
Temperature Regime ◽  
Type Star ◽  
Stellar Systems ◽  
Symbiotic Stars ◽  
Lower Excitation ◽  
Definition Of ◽  
Original Type

No paper of this nature should begin without a definition of symbiotic stars. It was Paul Merrill who, borrowing on his botanical background, coined the termsymbioticto describe apparently single stellar systems which combine the TiO absorption of M giants (temperature regime ≲ 3500 K) with He II emission (temperature regime ≳ 100,000 K). He and Milton Humason had in 1932 first drawn attention to three such stars: AX Per, CI Cyg and RW Hya. At the conclusion of the Mount Wilson Ha emission survey nearly a dozen had been identified, and Z And had become their type star. The numbers slowly grew, as much because the definition widened to include lower-excitation specimens as because new examples of the original type were found. In 1970 Wackerling listed 30; this was the last compendium of symbiotic stars published.

Immunoferritin localization of intracellular antigens in positively stained frozen sections

1978 ◽  
Vol 36 (2) ◽  
pp. 168-169
Author(s):  
K. T. Tokuyasu
Keyword(s):  
Surface Tension ◽  
Water Surface ◽  
Thin Layers ◽  
The Other ◽  
Positive Staining ◽  
Frozen Sections ◽  
The Past ◽  
Ultrathin Frozen Sections ◽  
Definition Of

During the past investigations of immunoferritin localization of intracellular antigens in ultrathin frozen sections, we found that the degree of negative staining required to delineate u1trastructural details was often too dense for the recognition of ferritin particles. The quality of positive staining of ultrathin frozen sections, on the other hand, has generally been far inferior to that attainable in conventional plastic embedded sections, particularly in the definition of membranes. As we discussed before, a main cause of this difficulty seemed to be the vulnerability of frozen sections to the damaging effects of air-water surface tension at the time of drying of the sections.Indeed, we found that the quality of positive staining is greatly improved when positively stained frozen sections are protected against the effects of surface tension by embedding them in thin layers of mechanically stable materials at the time of drying (unpublished).

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