On the new Narayana polynomials, the Gauss Narayana numbers and their polynomials

2020 ◽  
pp. 2150100
Author(s):  
Engi̇n Özkan ◽  
Bahar Kuloğlu
Keyword(s):  
Hankel Transform ◽  
Pell Numbers ◽  
Pascal’S Triangle ◽  
Narayana Numbers ◽  
Definition Of ◽  
Pascal's Triangle ◽  
The Relationship ◽  
Derivatives Of

We give a new definition of Narayana polynomials and show that there is a relationship between the coefficient of the new Narayana polynomials and Pascal’s triangle. We define the Gauss Narayana numbers and their polynomials. Then we show that there is a relationship between the Gauss Narayana polynomials and the new Narayana polynomials. Also, we show that there is a relationship between the derivatives of the new Narayana polynomials and Pascal’s triangle. We also explain the relationship between the new Narayana polynomials and the known Pell numbers. Finally, we give the Hankel transform of the new Narayana polynomials.

Pascal's Prism

2012 ◽  
Vol 96 (536) ◽  
pp. 213-220
Author(s):  
Harlan J. Brothers
Keyword(s):  
Probability Theory ◽  
Fractal Geometry ◽  
Euclidean Geometry ◽  
Fibonacci Series ◽  
Pascal’S Triangle ◽  
Number Sequences ◽  
Definition Of ◽  
Image Position ◽  
Pascal's Triangle

Pascal's triangle is well known for its numerous connections to probability theory [1], combinatorics, Euclidean geometry, fractal geometry, and many number sequences including the Fibonacci series [2,3,4]. It also has a deep connection to the base of natural logarithms, e [5]. This link to e can be used as a springboard for generating a family of related triangles that together create a rich combinatoric object.2. From Pascal to LeibnizIn Brothers [5], the author shows that the growth of Pascal's triangle is related to the limit definition of e.Specifically, we define the sequence sn; as follows [6]:

scholarly journals Distance Fibonacci Polynomials by Graph Methods

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 2075
Author(s):  
Dominik Strzałka ◽  
Sławomir Wolski ◽  
Andrzej Włoch
Keyword(s):  
Initial Conditions ◽  
Symmetric Matrix ◽  
Fibonacci Polynomials ◽  
Pascal’S Triangle ◽  
Graph Interpretation ◽  
Symmetric Structure ◽  
Binomial Formula ◽  
Narayana Numbers ◽  
Pascal's Triangle

In this paper we introduce and study a new generalization of Fibonacci polynomials which generalize Fibonacci, Jacobsthal and Narayana numbers, simultaneously. We give a graph interpretation of these polynomials and we obtain a binomial formula for them. Moreover by modification of Pascal’s triangle, which has a symmetric structure, we obtain matrices generated by coefficients of generalized Fibonacci polynomials. As a consequence, the direct formula for generalized Fibonacci polynomials was given. In addition, we determine matrix generators for generalized Fibonacci polynomials, using the symmetric matrix of initial conditions.

Combinatorics Connections: Playoff Series and Pascal's Triangle

1992 ◽  
Vol 85 (7) ◽  
pp. 532-535
Author(s):  
Bonnie H. Litwiller ◽  
David R. Duncan
Keyword(s):  
Real World ◽  
School Mathematics ◽  
Discrete Mathematics ◽  
National Council ◽  
Major Theme ◽  
Evaluation Standards ◽  
Mathematical Ideas ◽  
Pascal’S Triangle ◽  
Pascal's Triangle ◽  
The Relationship

One major theme of the National Council of Teachers of Mathematic's Curriculum and Evaluation Standards far School Mathematics (1989) is the connection between mathematical ideas and their applications to real-world situations. We shall use concepts from discrete mathematics in describing the relationship between sports series and Pascal's triangle.

scholarly journals Entropic Explanation of Power Set

2021 ◽  
Vol 16 (4) ◽  
Author(s):  
Yutong Song ◽  
Yong Deng
Keyword(s):  
Probability Theory ◽  
Mass Function ◽  
Information Measure ◽  
Event Space ◽  
Pascal’S Triangle ◽  
Power Set ◽  
Finite Set ◽  
Pascal's Triangle ◽  
The Relationship ◽  
Deng Entropy

A power set of a set S is defined as the set of all subsets of S, including set S itself and empty set, denoted as P(S) or 2S. Given a finite set S with |S|=n hypothesis, one property of power set is that the amount of subsets of S is |P(S)| = 2n.  However, the physica meaning of power set needs exploration. To address this issue, a possible explanation of power set is proposed in this paper. A power set of n events can be seen as all possible k-combination, where k ranges from 0 to n. It means the power set extends the event space in probability theory into all possible combination of the single basic event. From the view of power set, all subsets or all combination of basic events, are created equal. These subsets are assigned with the mass function, whose uncertainty can be measured by Deng entropy. The relationship between combinatorial number, Pascal's triangle and power set is revealed by Deng entropy quantitively from the view of information measure. 

ADMINISTRATIVE AND LEGAL STATUS OF THE CAPITAL OF UKRAINE - THE HERO CITY OF KYIV AS A GUARANTEE OF THE RIGHTS OF CITIZENS OF UKRAINE AND THE TERRITORIAL COMMUNITY OF THE CITY

2017 ◽  
Author(s):  
Oleksii Chepov ◽  
Keyword(s):  
Legal Status ◽  
Modern World ◽  
Legal Regime ◽  
Legal Doctrine ◽  
City Councils ◽  
The Social ◽  
District Management ◽  
Definition Of ◽  
The Relationship ◽  
The City

The qualitative and clear definition of the legal regime of the capital of Ukraine, the hero city of Kyiv, is influenced by its legislative enshrinement, however, it should be noted that discussions are ongoing and one of the reasons for the unclear legal status of the capital is the ambiguity of current legislation in this area. Separation of the functions of the city of Kyiv, which are carried out to ensure the rights of citizens of Ukraine and the functions that guarantee the rights of the territorial community of the city of Kyiv. In the modern world, in legal doctrine and practice, the capital is understood as the capital of the country, which at the legislative level received this status and, accordingly, is the administrative and political center of the state, which houses the main state bodies and diplomatic missions of other states. It is the identification of the boundaries of the relationship between the competencies of state administrations and local self-government, in practice, often raises questions about their delimitation and ways of regulatory solution. Peculiarities of local self-government in Kyiv city districts are defined in the provisions of the Law on the Capital, which reveal the norms of the Constitution in these legal relations, according to which the issue of organizing district management in cities belongs to city councils. Likewise, it is unregulated by law to lose the particularity of the legal status of the territory of the city. It should be emphasized that the subject of administrative-legal relations is not a certain administrative-territorial entity, but the social group is designated - the territorial community of the city of Kiev, kiyani. Thus, the provisions on the city of Kyiv partially ignore the potential of the territorial community.

Compliance and Conflict of Value in Public Policy Implementation: Comparison between the New Order and the Reformation Era

2018 ◽  
Vol 2 (2) ◽  
pp. 99 ◽  
Author(s):  
Dwiyanto Indiahono ◽  
Erwan Purwanto ◽  
Agus Pramusinto
Keyword(s):  
Public Policy ◽  
Policy Implementation ◽  
Local Level ◽  
Group Discussion ◽  
New Order ◽  
The Reformation ◽  
Public Policy Implementation ◽  
Definition Of ◽  
Conflict Of Value ◽  
The Relationship

This research aims to examine differences in the relationship of bureaucratic and political officials during the New Order (Soeharto’s era) and the Reformation (post-Soeharto) era within the arena of public policy implementation. This is a matter of importance given that there is a change in relations between the two from integration in the New Order to bureaucratic impartiality in the Reformation Era. This study attempts to answer the question: How were the relations of bureaucratic and political officials in the implementation of local level public policy during the New Order and the Reformation Era? A qualitative research has been conducted in Tegal Municipality using the following data collection techniques: interview, focus group discussion, documentation, and observation. Tegal Municipality was selected as the study location because of the unique relationship shown between the mayor and the bureaucracy. Its uniqueness lies in the emergence of bureaucratic officials who dare to oppose political officials, based on their convictions that bureaucratic/public values should be maintained even if it means having to be in direct conflict with political officials. This research indicates that the relationship between bureaucratic and political officials in the arena of local level policy implementation during the New Order was characterized as being full of pressure and compliance, whereas during the Reformation Era bureaucrats have the audacity to hinder policy implementation. Such audacity to thwart policies is considered to have developed from a stance that aims to protect public budget and values in policies. The occurring conflict of values here demonstrates a dichotomy of political and bureaucratic officials that is different from the prevailing definition of politics-administration dichotomy introduced at the onset of Public Administration studies.

The Concept of Europeanization and Possibilities of its Application to the Analysis of Ukraine-EU Relations

2017 ◽  
pp. 149-160
Author(s):  
Natalia Popova
Keyword(s):  
European Integration ◽  
Theoretical Research ◽  
Member States ◽  
External Governance ◽  
Definition Of ◽  
The Relationship ◽  
Eu Studies ◽  
The Eu

The concept of Europeanization has become quite fashionable in EU studies in recent years. It is often used for the analysis of the relations between the EU and non-member states. The aim of the article is to examine the possibilities of its application in explaining the relationship between the EU and Ukraine. The structure of the article is as follows: firstly, the concept of Europeanization is defined considering such two disputable issues as distinguishing among concepts of Europeanization and European integration as well as Europeanization and EU-ization. Next, the evolution of the theoretical research of Europeanization and definition of this concept are analyzed. Two main mechanisms of Europeanization (conditionality and socialization) are examined. The author considers main approaches to the analysis of the "external" Europeanization emphasizing the concept of "external governance". Three groups of factors which influence the effectiveness of Europeanization are briefly analyzed. And finally, the peculiarities of application of the Europeanization concept to the Ukraine-EU relations are outlined. Keywords: EU, Ukraine, Europeanization, EU-ization, ‘external’ Europeanization, conditionality, socialization, concept of ‘external governance’

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.

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