scholarly journals Minimum Variable Connectivity Index of Trees of a Fixed Order

2020 ◽  
Vol 2020 ◽  
pp. 1-4
Author(s):  
Shamaila Yousaf ◽  
Akhlaq Ahmad Bhatti ◽  
Akbar Ali
Keyword(s):  
Real Number ◽  
Topological Index ◽  
Nonnegative Real Number ◽  
Point Of View ◽  
Connectivity Index ◽  
Star Graph ◽  
Arbitrary Vertex ◽  
Mathematical Properties ◽  
Fixed Order ◽  
Definition Of

The connectivity index, introduced by the chemist Milan Randić in 1975, is one of the topological indices with many applications. In the first quarter of 1990s, Randić proposed the variable connectivity index by extending the definition of the connectivity index. The variable connectivity index for graph G is defined as ∑vw∈EGdv+γdw+γ−1/2, where γ is a nonnegative real number, EG is the edge set of G, and dt denotes the degree of an arbitrary vertex t in G. Soon after the innovation of the variable connectivity index, its various chemical applications have been reported in different papers. However, to the best of the authors’ knowledge, mathematical properties of the variable connectivity index, for γ>0, have not yet been discussed explicitly in any paper. The main purpose of the present paper is to fill this gap by studying this topological index in a mathematical point of view. More precisely, in this paper, we prove that the star graph has the minimum variable connectivity index among all trees of a fixed order n, where n≥4.

scholarly journals On the Minimum Variable Connectivity Index of Unicyclic Graphs with a Given Order

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Shamaila Yousaf ◽  
Akhlaq Ahmad Bhatti ◽  
Akbar Ali
Keyword(s):  
Real Number ◽  
Connectivity Index ◽  
Star Graph ◽  
Randić Index ◽  
Unicyclic Graphs ◽  
Randic Index ◽  
Degree Of A Vertex ◽  
Fixed Order ◽  
Negative Real Number

The variable connectivity index, introduced by the chemist Milan Randić in the first quarter of 1990s, for a graph G is defined as ∑vw∈EGdv+γdw+γ−1/2, where γ is a non-negative real number and dw is the degree of a vertex w in G. We call this index as the variable Randić index and denote it by Rvγ. In this paper, we show that the graph created from the star graph of order n by adding an edge has the minimum Rvγ value among all unicyclic graphs of a fixed order n, for every n≥4 and γ≥0.

scholarly journals New Definition of Atomic Bond Connectivity Index to Overcome Deficiency of Structure Sensitivity and Abruptness in Existing Definition

2019 ◽  
Vol 3 (4) ◽  
pp. 1-20 ◽  
Author(s):  
Abaid ur Rehman Virk ◽  
M. A. Rehman ◽  
Waqas Nazeer
Keyword(s):  
Topological Index ◽  
Molecular Graph ◽  
Structure Sensitivity ◽  
Connectivity Index ◽  
Smoothness Property ◽  
Silicon Carbides ◽  
Abc Index ◽  
Definition Of

Topological Index (TI) is a numerical value associated with the molecular graph of the compound. Smoothness property states that a TI is good if its Structure Sensitivity (SS) is as large as possible and its Abruptness (Abr) is small. In 2013, Gutman proved that Atomic Bond Connectivity (ABC) index has small SS and high Abr. In this paper, we defined reverse Atomic Bond Connectivity (ABC) index to overcome this problem. Moreover, we computed reverse ABC index for Silicon Carbides, Bismith Tri-Iodide and Dendrimers.

scholarly journals Choosing the exponent in the definition of the connectivity index

2001 ◽  
Vol 66 (9) ◽  
pp. 605-611 ◽  
Author(s):  
Ivan Gutman ◽  
Mirko Lepovic
Keyword(s):  
Carbon Atom ◽  
Topological Index ◽  
Organic Molecules ◽  
Molecular Graph ◽  
Chemical Properties ◽  
Connectivity Index ◽  
Physico Chemical ◽  
Definition Of ◽  
Molecular Branching ◽  
Suitable Measure

Let ?v denote the degree of the vertex v of a molecular graph G. Then the connectivity index of G is defined as C (?) = G (?,C) = ? (?u?v)?, where the summation goes over all pairs of adjacent vertices. The exponent ? is usually chosen to be equal to -1/2, but other options were considered as well, especially ?=-1. We show that whereas C(-1/2) is a suitable measure of branching of the carbon-atom skeleton of organic molecules, and thus applicable as a topological index for modeling physico-chemical properties of the respective compounds, this is not the case with C(-1). The value of ? is established, beyond which C(?) fails to correctly reflect molecular branching.

On the maximum general sum-connectivity index of trees with a fixed order and maximum degree

2020 ◽  
pp. 2150042
Author(s):  
Shahzad Ahmed
Keyword(s):  
Real Number ◽  
Maximum Degree ◽  
Connectivity Index ◽  
Nonzero Real Number ◽  
Fixed Order

The general sum-connectivity index of a graph [Formula: see text], denoted by [Formula: see text], is defined as [Formula: see text], where [Formula: see text] is the edge connecting the vertices [Formula: see text], [Formula: see text] denotes the degree of the vertex [Formula: see text], and [Formula: see text] is a nonzero real number. This paper is devoted to characterizing the graphs having the maximal [Formula: see text] value among all the trees with order [Formula: see text] and fixed maximum degree.

Understanding functional illiteracy from a policy, adult education, and cognition point of view: Towards a joint referent framework

2019 ◽  
Vol 30 (2) ◽  
pp. 109-122
Author(s):  
Aleksandar Bulajić ◽  
Miomir Despotović ◽  
Thomas Lachmann
Keyword(s):  
Adult Education ◽  
Operational Definition ◽  
Literacy Skills ◽  
Point Of View ◽  
Industrialized Countries ◽  
Functional Illiteracy ◽  
Scale Levels ◽  
Components Of Reading ◽  
The One ◽  
Definition Of

Abstract. The article discusses the emergence of a functional literacy construct and the rediscovery of illiteracy in industrialized countries during the second half of the 20th century. It offers a short explanation of how the construct evolved over time. In addition, it explores how functional (il)literacy is conceived differently by research discourses of cognitive and neural studies, on the one hand, and by prescriptive and normative international policy documents and adult education, on the other hand. Furthermore, it analyses how literacy skills surveys such as the Level One Study (leo.) or the PIAAC may help to bridge the gap between cognitive and more practical and educational approaches to literacy, the goal being to place the functional illiteracy (FI) construct within its existing scale levels. It also sheds more light on the way in which FI can be perceived in terms of different cognitive processes and underlying components of reading. By building on the previous work of other authors and previous definitions, the article brings together different views of FI and offers a perspective for a needed operational definition of the concept, which would be an appropriate reference point for future educational, political, and scientific utilization.

Dosimetry and optimization in digital radiography based on the contrast-detail resolution

2018 ◽  
Vol 6 (3) ◽  
Author(s):  
Wilson Otto Gomes Batista ◽  
Alexandre Gomes De Carvalho
Keyword(s):  
Image Quality ◽  
Inverse Image ◽  
Point Of View ◽  
Complete Analysis ◽  
Portable Devices ◽  
Evaluation Tool ◽  
Air Kerma ◽  
Direct Radiography ◽  
Definition Of ◽  
Entrance Surface Air Kerma

Contrast-detail (C-D) curves are useful in evaluating the radiographic image quality in a global way. The objective of the present study was to obtain the C-D curves and the inverse image quality figure. Both of these parameters were used as an evaluation tool for abdominal and chest imaging protocols. The C-D curves were obtained with the phantom CDRAD 2.0 in computerized radiography and the direct radiography systems (including portable devices). The protocols were 90 and 102 kV in the range of 2 to 20 mAs for the chest and 80 kV in the range of 10 to 80 mAs for the abdomen. The incident air kerma values were evaluated with a solid state sensor. The analysis of these C-D curves help to identify which technique would allow a lower value of the entrance surface air kerma, Ke, while maintaining the image quality from the point of view of C-D detectability. The results showed that the inverse image quality figure, IQFinv, varied little throughout the range of mAs, while the value of Ke varied linearly directly with the mAs values. Also, the complete analysis of the curves indicated that there was an increase in the definition of the details with increasing mAs. It can be concluded that, in the transition phase for the use of the new receptors, it is necessary to evaluate and adjust the practised protocols to ensure, at a minimum, the same levels of the image quality, taking into account the aspects of the radiation protection of the patient.

DIRECTIONS OF ASSOCIATIVE IDENTIFICATION OF PERSONAL NAMES

2019 ◽  
Vol 18 (28) ◽  
pp. 118-128
Author(s):  
Olena Karpenko ◽  
Tetiana Stoianova
Keyword(s):  
Proper Names ◽  
Mental Lexicon ◽  
Point Of View ◽  
Sound Symbolism ◽  
Personal Names ◽  
Communicative Process ◽  
Proper Name ◽  
Definition Of ◽  
Scientific Value ◽  
The Brain

The article is devoted to the study of personal names from a cognitive point of view. The study is based on the cognitive concept that speech actually exists not in the speech, not in linguistic writings and dictionaries, but in consciousness, in the mental lexicon, in the language of the brain. The conditions for identifying personal names can encompass not only the context, encyclopedias, and reference books, but also the sound form of the word. In the communicative process, during a free associative experiment, which included a name and a recipient’s mental lexicon. The recipient was assigned a task to quickly give some association to the name. The aggregate of a certain number of reactions of different recipients forms the associative field of a proper name. The associative experiment creates the best conditions for identifying the lexeme. The definition of a monosemantic personal name primarily includes the search of what it denotes, while during the process of identifying a polysemantic personal name recipients tend have different reactions. Scientific value is posed by the effect of the choice of letters for the name, sound symbolism, etc. The following belong to the generalized forms of identification: usage of a hyperonym; synonyms and periphrases or simple descriptions; associations denoting the whole (name stimulus) by reference to its part (associatives); cognitive structures such as “stimulus — association” and “whole (stimulus) — part (associative)”; lack of adjacency; mysterious associations. The topicality of the study is determined by its perspective to identify the directions of associative identification of proper names, which is one of the branches of cognitive onomastics. The purpose of the study is to identify, review, and highlight the directions of associative identification of proper names; the object of the research is the names in their entirety and variety; its subject is the existence of names in the mental lexicon, which determines the need for singling out the directions for the associative identification of the personal names.

DEFINITION OF THE PUBLIC SECURITY AND ORDERLINESS ENSURING MECHANISM IN UKRAINE

2018 ◽  
Vol 1 (11) ◽  
pp. 155-163
Author(s):  
Marina Aleksandrovna Kalievskaya
Keyword(s):  
Human Rights ◽  
Development Strategy ◽  
State Policy ◽  
The State ◽  
Point Of View ◽  
Public Security ◽  
National Priority ◽  
Institu Tions ◽  
Protection Of Human Rights ◽  
Definition Of

In this article, a model of the mechanism of ensuring public security and orderliness in accordance with the principles and tasks of the relevant institu- tions in public administration, taking into account resources, technologies, mea- sures for the state policy implementation in the spheres of ensuring the protection of human rights and freedoms, the interests of society and the state, combating crime, maintaining public security and order. It was found that ensuring public security and order in Ukraine is a mechanism for the implementation of national goals of state policy in the areas of ensuring the protection of human rights and freedoms, the interests of society and the state, combating crime, maintaining public security and order, by defining tasks according to certain principles. The idea is that if one considers the state policy in the spheres of ensuring the protec- tion of human rights and freedoms, the interests of society and the state, combat- ing crime, maintaining public security and order as a national priority (purpose, task), then the mechanism of ensuring public security and order in Ukraine needs coordination with the state development strategy. From the point of view of the implementation of the state policy in the areas of ensuring the protection of hu- man rights and freedoms, the interests of society and the state, combating crime, maintaining public security and order, the mechanism of ensuring public security and order in Ukraine can be considered as the main system providing intercon- nection such elements as institutions (implementing the specified state policy), resources (human resources, logistical, natural and so on, with the help of which it is possible to implement state policy), technologies (skills, knowledge, means and so on the implementation of state policy), measures (action plans), as well as external (internal) threats.

О вопросах фольклоризма в письменной литературе

2019 ◽  
pp. 31-33
Author(s):  
Суусар Искендерова
Keyword(s):  
Modern Science ◽  
Folk Songs ◽  
Point Of View ◽  
The Past ◽  
Scientific Term ◽  
Literature Culture ◽  
Definition Of ◽  
The Relationship

Аннотация: Исследование проблемы фольклоризма является наиболее актуальной в современной науке о фольклоре. На разных этапах развития художественной литературы для формирования индивидуального творчества писателя особенно значимым становятся фольклорные жанры, сюжетные мотивы и художественные средства. В статье рассматривается связь письменной литературы и фольклора, особенно точка зрения проблеме фольклоризма в прошлом и их анализ. Термин «фольклоризм» начал использоваться советскими исследователями учеными как научный термин еще в 1930-х гг. Термин «фольклоризм» используется в различных сферах культуры, а в этой статье мы будем рассматривать в литературе. Несмотря на то, что на протяжении многих лет этот вопрос изучается литературоведами, фольклористами, все -таки нет единого теоретического определения понятия. Ключевые слова: фольклор, фольклоризм, литература, культура, письменная литература, художественная литература, оседлый народ, пословицы и поговорки, фольклорные песни. Аннотация: Көркөм адабияттын өнүгүүсүнүн ар кайсы баскычтарында сүрөткердин жеке чыгармачылыгынын калыптанышы үчүн фольклордук жанрлар, сюжеттер, мотивдер жана көркөм каражаттар айрыкча мааниге ээ. Макалада жазма адабият менен фольклордук карым-катышы, айрыкча фольклоризм маселеси жөнүндө мурдагы көз караштарга кайрылып, аларга талдоо жүргүзүү менен бирге автор өз байкоолорунда келтирет. “Фольклоризм” деген илимий термин 1930-жылы баштап колдонула баштаган. “Фольклоризм” термини маданияттын түрдүү сфераларында кеңири колдо- нулат, бул жерде адабияттагы колдонулушун каралат. Макалада адабий материал менен фольклордук байланышын терең түшүнүү үчүн адабий фольклоризм маселесинин талаштуу жактары каралат. Түйүндүү сөздөр: фольклор, фольклоризм, адабият, маданият, жазма адабият, көркөм адабият, көчмөн калк, макал-лакап, фольклордук ырлар. Annotation: The study of the problem of folklore is the most relevant in the modern science of folklore. At various stages in the development of fiction, folklore genres, plot motifs, and artistic means become especially significant for the formation of the writer's individual creativity. The article examines the relationship between written literature and folklore, especially the point of view of the problem of folklorism in the past and their analysis. The term "folklorism" began to be used by Soviet scholars as a scientific term back in the 1930s. The term "folklorism" is used in various fields of culture, and in this article we will consider in the literature. Despite the fact that for many years this issue has been studied by literary scholars, folklorists, all the same there is no single theoretical definition of the concept. Keywords: folklore, folklorism, literature, culture, written literature, fiction, settled people, proverbs and sayings, folk songs.

On the Problems of Acts Qualification as Violations of Antimonopoly Legislation in Administrative and Judicial Practice

2020 ◽  
Vol 10 ◽  
pp. 62-69
Author(s):  
К. А. Pisenkо ◽  
Keyword(s):  
Russian Federation ◽  
Point Of View ◽  
Judicial Practice ◽  
Illegal Acts ◽  
The Russian Federation ◽  
Definition Of

The article is devoted to defining the main approaches to classifying acts as violations of аntimonopoly legislation. On administrative and judicial practice discusses current issues and problems of definition of illegal acts, both from the point of view of antimonopoly regulation, and the delineation of antimonopoly violations and violations of other mandatory requirements established by the legislation of the Russian Federation.

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