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2020

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Articles 14281 - 14310 of 15207

Full-Text Articles in Physical Sciences and Mathematics

An Exploration Of Β -Hydroxy- Α -Diazo Carbonyls In Synthesis: Fragmentation, Vinyl Cation Formation And Conjugate Addition Reactions, Jian Fang Jan 2020

An Exploration Of Β -Hydroxy- Α -Diazo Carbonyls In Synthesis: Fragmentation, Vinyl Cation Formation And Conjugate Addition Reactions, Jian Fang

Graduate College Dissertations and Theses

β-hydroxy-α-diazo carbonyl compounds have been shown to display diverse reactivity profiles that can lead to a variety of useful products. This specific combination of functional groups can react in several mechanistically distinct ways depending on the presence or absences of other groups within the molecule. For example, -silyloxy-β-hydroxy-α-diazo carbonyls react with Lewis acids via fragmentation reactions to generate tethered aldehyde ynoate or ynone products. A portion of this thesis describes how this methodology was applied toward the synthesis of an important bioactive natural product: aspidospermidine. β-Hydroxy-α-diazo carbonyls are also convenient precursors to vinyl cations. The vinyl cation is generated by …

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Measurement Of Sound Velocity In Oil Wells Based On Fast Adaptive Median Filtering, Wei Zhou, Juan Liu, Liqun Gan Jan 2020

Measurement Of Sound Velocity In Oil Wells Based On Fast Adaptive Median Filtering, Wei Zhou, Juan Liu, Liqun Gan

Turkish Journal of Electrical Engineering and Computer Sciences

Measurement of sound velocity in oil wells has long been a challenging industrial issue due to the difficulty in obtaining clear oil pipe coupling waves in strong noise. In this paper, a novel sound velocity measurement method is developed for the dynamic liquid level of oil wells based on fast adaptive median filtering. First, to solve the noise interference problem in the reflected oil pipe coupling wave, a fast adaptive median filtering algorithm is proposed to obtain an accurate oil pipe coupling wave. Then a curve fitting method based on range discrete coefficient is developed to estimate the sound velocity …

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A High-Level And Adaptive Metaheuristic Selection Algorithm For Solving Highdimensional Bound-Constrained Continuous Optimization Problems, Osman Gökalp, Aybars Uğur Jan 2020

A High-Level And Adaptive Metaheuristic Selection Algorithm For Solving Highdimensional Bound-Constrained Continuous Optimization Problems, Osman Gökalp, Aybars Uğur

Turkish Journal of Electrical Engineering and Computer Sciences

Metaheuristic algorithms are used to find sufficiently good solutions for the optimization problems that are not solvable in a polynomial time. Although metaheuristics offer a general problem-solving framework and can be applied to various types of optimization problems, their performances depend heavily on the problem to be solved. Thus, hybrid metaheuristics are used to combine strong parts of different algorithms. In this study, a novel adaptive metaheuristic selection algorithm is proposed for solving bound-constrained continuous optimization problems. The developed method hybridizes artificial bee colony, differential evolution, and particle swarm optimization at a high level where each algorithm works independently from …

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Experimental And Predicted Xlpe Cable Insulation Properties Under Uvradiation, Abdallah Hedir, Ali Bechouche, Mustapha Moudoud, Madjid Teguar, Omar Lamrous, Sebastien Rondot Jan 2020

Experimental And Predicted Xlpe Cable Insulation Properties Under Uvradiation, Abdallah Hedir, Ali Bechouche, Mustapha Moudoud, Madjid Teguar, Omar Lamrous, Sebastien Rondot

Turkish Journal of Electrical Engineering and Computer Sciences

This paper deals with the behavior of the crosslinked polyethylene (XLPE) used as high-voltage power cable insulation under ultraviolet (UV) radiations. For this, XLPE samples have been irradiated for 240 h using low-pressure vapor fluorescent lamps. Electrical (surface and volume resistivities), mechanical (tensile strength, elongation at break and surface hardness) and physical (weight loss, water absorption, work of water adhesion and contact angle) tests have been first carried out. Experimental results show that the XLPE characteristics are affected by UV radiation. Indeed, a decline in surface resistivity, mechanical properties, and contact angle, and an increase in the water retention amount …

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A Novel Genome Analysis Method With The Entropy-Based Numerical Techniqueusing Pretrained Convolutional Neural Networks, Bi̇hter Daş, Suat Toraman, İbrahi̇m Türkoğlu Jan 2020

A Novel Genome Analysis Method With The Entropy-Based Numerical Techniqueusing Pretrained Convolutional Neural Networks, Bi̇hter Daş, Suat Toraman, İbrahi̇m Türkoğlu

Turkish Journal of Electrical Engineering and Computer Sciences

The identification of DNA sequences as exon and intron is a common problem in genome analysis. The methods used for feature extraction and mapping techniques for the digitization of sequences affect directly the solution of this problem. The existing mapping techniques are not enough to detect coding and noncoding regions in some genomes because the digital representation of each base in a DNA sequence with an integer does not fully reflect the structure of an original DNA sequence. In the entropy-based mapping technique, we could overcome this problem because the technique deepens distinction rates of exon regions, and better reflects …

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The Illegal Wildlife Trade: Through The Eyes Of A One-Year-Old Pangolin (Manis Javanica), Lelia Bridgeland-Stephens Jan 2020

The Illegal Wildlife Trade: Through The Eyes Of A One-Year-Old Pangolin (Manis Javanica), Lelia Bridgeland-Stephens

Animal Studies Journal

This paper explores the literature on the illegal wildlife trade (IWT) by following the journey of a single imagined Sunda pangolin (Manis javanica) through the entire trading process. Literature on IWT frequently refers to non-human animals in terms of collectives, species, or body parts, for example ‘tons of pangolin scales’, rather than as subjective individuals. In contrast, this paper centralizes the experiences of an individual pangolin by using a cross- disciplinary methodology, combining fact with a fictional narrative of subjective pangolin experience, in an empathetic and egomorphic process. The paper draws together known legislation, trade practices, and pangolin biology, structured …

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กรอบงานการควบคุมการเข้าถึงบนฐานบทบาทสำหรับตัวจัดการความมั่นคงไมโครเซอร์วิส, จิตติภัทร ผสมทรัพย์ Jan 2020

กรอบงานการควบคุมการเข้าถึงบนฐานบทบาทสำหรับตัวจัดการความมั่นคงไมโครเซอร์วิส, จิตติภัทร ผสมทรัพย์

Chulalongkorn University Theses and Dissertations (Chula ETD)

ปัจจุบัน แพลตฟอร์มไมโครเซอร์วิสได้รับความนิยมเพื่อเปลี่ยนผ่านไปสู่ระบบไม่รวมศูนย์ที่มีความเร็วและกินพื้นที่น้อย อย่างไรก็ตาม จำนวนบริการที่เพิ่มมากขึ้นส่งผลให้เกิดความท้าทายในการบำรุงรักษาความมั่นคงของการควบคุมการเข้าถึง พื้นผิวการโจมตีที่มากขึ้นสามารถนำมาซึ่งความเสี่ยงในด้านความมั่นคงปลอดภัยและความเป็นส่วนตัวเข้าสู่ข้อมูลที่สำคัญและละเอียดอ่อน ดังนั้น ในงานนี้จึงได้นำเสนอแนวทางห่วงโซ่ของโดเมนที่เชื่อถือได้เพื่อแก้ไขปัญหาดังกล่าว แบบจำลองที่ขยายเพิ่มจากโมเดลการควบคุมการเข้าถึงตามบทบาทได้ถูกพัฒนาขึ้นเพื่อจัดการกับภัยคุกคามจากการเข้าถึงข้อมูลสารสนเทศที่สำคัญโดยไม่ได้รับอนุญาต รวมทั้งจัดการการตรวจสอบตัวตนในทุกสภาพแวดล้อมในโซลูชันคอนเทนเนอร์แอปพลิเคชัน ตัวจัดการความมั่นคงได้ถูกออกแบบบนพื้นฐานแบบจำลองอาร์แบ็กเพื่อพิสูจน์ตัวตน อนุญาต และระบุการควบคุมการเข้าถึงของผู้ใช้ผ่านเอพีไอเกตเวย์ ระบบต้นแบบที่ผสานรวมกับเซิร์ฟเวอร์การตรวจสอบสิทธิ์ได้ถูกพัฒนาขึ้นเพื่อการศึกษาเชิงประจักษ์ ผลลัพธ์รายงานว่าแนวทางดังกล่าวช่วยให้เข้าถึงข้อมูลสารสนเทศได้เร็วขึ้นและยืดหยุ่นมากขึ้น นอกจากนี้ ยังช่วยปรับปรุงเวลาในการตอบสนองต่อเหตุการณ์ให้ดีขึ้น

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Geometric Properties Of Partial Sums Of Generalized Koebe Function, Erhan Deni̇z, Erkan Yalçin Jan 2020

Geometric Properties Of Partial Sums Of Generalized Koebe Function, Erhan Deni̇z, Erkan Yalçin

Turkish Journal of Mathematics

The aim of the present paper is to investigate the starlikeness, convexity, and close-to-convexity of some partial sums of the generalized Koebe function. Furthermore, we give some special results related with special cases of $c$ constant. The results, which are presented in this paper, would generalize those in related works of several earlier authors.

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Continuous Dependence Of Solutions For Damped Improved Boussinesq Equation, Sema Bayraktar, Şevket Gür Jan 2020

Continuous Dependence Of Solutions For Damped Improved Boussinesq Equation, Sema Bayraktar, Şevket Gür

Turkish Journal of Mathematics

In this paper, the initial-boundary value problem for a damped nonlinear improved Boussinesq equation is studied. A priori estimates for the solution of the equation are obtained in terms of initial data and coefficients of the problem. The continuous dependence of solutions on dispersive $(\delta)$ and $(r)$ and dissipative $(b)$ coefficients are established by multiplier method.

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Approximation By Matrix Transforms In Weighted Orlicz Spaces, Sadulla Jafarov Jan 2020

Approximation By Matrix Transforms In Weighted Orlicz Spaces, Sadulla Jafarov

Turkish Journal of Mathematics

In this work the approximation problems of the functions by matrix transforms in weighted Orlicz spaces with Muckenhoupt weights are studied.We obtain the degree of approximation of functions belonging to Lipschitz class $Lip(\alpha ,M,\omega )$ through matrix transforms $% T_{n}^{\left( A\right) }(x,f)$,$~$and Nörlund means $N_{n}\left(x,f\right) ~$of their trigonometric Fourier series.

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Prolongations Of Isometric Actions To Vector Bundles, Hülya Kadioğlu Jan 2020

Prolongations Of Isometric Actions To Vector Bundles, Hülya Kadioğlu

Turkish Journal of Mathematics

In this paper, we define an isometry on a total space of a vector bundle $\mathbb{E}$ by using a given isometry on the base manifold $\mathbb{M}$. For this definition, we assume that the total space of the bundle is equipped with a special metric which has been introduced in one of our previous papers. We prove that the set of these derived isometries on $\mathbb{E}$ form an imbedded Lie subgroup $\tilde{G}$ of the isometry group $I(E)$. Using this new subgroup, we construct two different principal bundle structures based one on $\mathbb{E}$ and the other on the orbit space $\mathbb{E}/\tilde{G}$.

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The Strong 3-Rainbow Index Of Edge-Amalgamation Of Some Graphs, Zata Yumni Awanis, Anm Salman, Suhadi Wido Saputro, Martin Baca, Andrea Semanicova-Fenovcikova Jan 2020

The Strong 3-Rainbow Index Of Edge-Amalgamation Of Some Graphs, Zata Yumni Awanis, Anm Salman, Suhadi Wido Saputro, Martin Baca, Andrea Semanicova-Fenovcikova

Turkish Journal of Mathematics

Let G be a nontrivial, connected, and edge-colored graph of order n≥? 3, where adjacent edges may be colored the same. Let k be an integer with 2 ≤? k ≤? n. A tree T in G is a rainbow tree if no two edges of T are colored the same. For S ? V (G), the Steiner distance d(S) of S is the minimum size of a tree in G containing S . An edge-coloring of G is called a strong k-rainbow coloring if for every set S of k vertices of G there exists a rainbow tree of …

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A New Method For Obtaining The Inconsistent Elements In A Decision Table Based On Dominance Principle, Yasemen Uçan, Ahmet Topal, Ni̇lgün Güler Bayazit Jan 2020

A New Method For Obtaining The Inconsistent Elements In A Decision Table Based On Dominance Principle, Yasemen Uçan, Ahmet Topal, Ni̇lgün Güler Bayazit

Turkish Journal of Mathematics

In this study,using only the dominance relation,we propose a set defining inconsistent elements in the decision table. Then, we show the accuracy of our proposition with an example. We also express the computational complexity comparisons of the proposed method with general method in terms of the number of set intersection operations and the real number comparison operations.

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The Bochner-Convolution Integral For Generalized Functional-Valued Functions Of Discrete-Time Normal Martingales, Chen Jinshu Jan 2020

The Bochner-Convolution Integral For Generalized Functional-Valued Functions Of Discrete-Time Normal Martingales, Chen Jinshu

Turkish Journal of Mathematics

Let $M$ be a discrete-time normal martingale satisfying some mild conditions, $\mathcal{S}(M)\subset L^2(M)\subset\mathcal{S}^*(M)$ be the Gel'fand triple constructed from the functionals of $M$. As is known, there is no usual multiplication in $\mathcal{S}^*(M)$ since its elements are continuous linear functionals on $\mathcal{S}(M)$. However, by using the Fock transform, one can introduce convolution in $\mathcal{S}^*(M)$, which suggests that one can try to introduce a type of integral of an $\mathcal{S}^*(M)$-valued function with respect to an $\mathcal{S}^*(M)$-valued measure in the sense of convolution. In this paper, we just define such type of an integral. First, we introduce a class of $\mathcal{S}^*(M)$-valued measures …

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Bertrand And Mannheim Curves Of Framed Curves In The 3-Dimensional Euclidean Space, Shun'ichi Honda, Masatomo Takahashi Jan 2020

Bertrand And Mannheim Curves Of Framed Curves In The 3-Dimensional Euclidean Space, Shun'ichi Honda, Masatomo Takahashi

Turkish Journal of Mathematics

A Bertrand curve is a space curve whose principal normal line is the same as the principal normal line of another curve. On the other hand, a Mannheim curve is a space curve whose principal normal line is the same as the binormal line of another curve. By definitions, another curve is a parallel curve with respect to the direction of the principal normal vector. Even if that is the regular case, the existence conditions of the Bertrand and Mannheim curves seem to be wrong in some previous research. Moreover, parallel curves may have singular points. As smooth curves with …

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Higher-Order Character Dedekind Sum, Mümün Can Jan 2020

Higher-Order Character Dedekind Sum, Mümün Can

Turkish Journal of Mathematics

In this paper, we are interested in higher-order character Dedekind sum% \[ \sum\limits_{v=0}^{ck-1}\chi_{1}\left( v\right) \mathcal{B}_{p,\chi_{2}% }\left( a\frac{v+z}{c}+x\right) \mathcal{B}_{q}\left( b\frac{v+z}% {ck}+y\right) ,\text{ }a,b,c\in\mathbb{N} \text{ and }x,y,z\in\mathbb{R}, \] where $\chi_{1}$ and $\chi_{2}$ are primitive characters of modulus $k,$ $\mathcal{B}_{p}\left( x\right) $ and $\mathcal{B}_{p,\chi_{2}}\left( x\right) $ are Bernoulli and generalized Bernoulli functions, respectively. We employ the Fourier series technique to demonstrate reciprocity formulas for this sum. Derived formulas are analogues of Mikolas' reciprocity formula. Moreover, we offer Petersson--Knopp type identities for this sum.

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Star Versions Of The Hurewicz Basis Covering Property And Strong Measure Zero Spaces, Manoj Bhardwaj, Alexander Osipov Jan 2020

Star Versions Of The Hurewicz Basis Covering Property And Strong Measure Zero Spaces, Manoj Bhardwaj, Alexander Osipov

Turkish Journal of Mathematics

In this paper,we introduced the star version of the Hurewicz basis covering property,studied by Babinkostova, Ko?cinac, and Scheepers in 2004. The authors obtained the relationship between star-selection principles and the star version of the Hurewicz basis covering property for metrizable spaces. We also consider the star version of Hurewicz measure zero spaces and characterized these new spaces by the star-selection principle related to star-Hurewicz spaces.

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Gradient Weyl-Ricci Soliton, Cornelia-Livia Bejan, Şemsi̇ Eken Meri̇ç, Erol Kiliç Jan 2020

Gradient Weyl-Ricci Soliton, Cornelia-Livia Bejan, Şemsi̇ Eken Meri̇ç, Erol Kiliç

Turkish Journal of Mathematics

The classical notion of gradient Ricci soliton is extended here to the gradient Weyl-Ricci soliton. A Weyl structureofthebasemanifold M is lifted to its tangent bundle TM, by using the Sasaki metric. We give some necessary and sufficient conditions such that the Weyl structure on TM to be a gradient Weyl-Ricci soliton.

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An Extragradient Algorithm For Split Generalized Equilibrium Problem And The Set Of Fixed Points Ofquasi-$\Phi $-Nonexpansive Mappings In Banach Spaces, Olawale Oyewole, Oluwatosin Mewomo, Lateef Jolaoso, Safeer Hussain Khan Jan 2020

An Extragradient Algorithm For Split Generalized Equilibrium Problem And The Set Of Fixed Points Ofquasi-$\Phi $-Nonexpansive Mappings In Banach Spaces, Olawale Oyewole, Oluwatosin Mewomo, Lateef Jolaoso, Safeer Hussain Khan

Turkish Journal of Mathematics

In this paper, we study the problem of finding a common solution to split generalized mixed equilibrium problem and fixed point problem for quasi-$% \phi $-nonexpansive mappings in 2-uniformly convex and uniformly smooth Banach space $E_1$ and a smooth, strictly convex, and reflexive Banach space $% E_2$. An iterative algorithm with Armijo linesearch rule for solving the problem is presented and its strong convergence theorem is established. The convergence result is obtained without using the hybrid method which is mostly used when strong convergence is desired. Finally, numerical experiments are presented to demonstrate the practicability, efficiency, and performance of our …

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Abstract Korovkin-Type Theorems In The Filter Setting With Respect To Relative Uniform Convergence, Antonio Boccuto, Kami̇l Demi̇rci̇, Sevda Yildiz Jan 2020

Abstract Korovkin-Type Theorems In The Filter Setting With Respect To Relative Uniform Convergence, Antonio Boccuto, Kami̇l Demi̇rci̇, Sevda Yildiz

Turkish Journal of Mathematics

We prove a Korovkin-type approximation theorem using abstract relative uniform filter convergence of a net of functions with respect to another fixed filter, a particular case of which is that of all neighborhoods of a point, belonging to the domain of the involved functions. We give some examples, in which we show that our results are strict generalizations of the classical ones.

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A Semi-Markovian Renewal Reward Process With $\Gamma(G)$ Distributed Demand, Asli Bektaş Kamişlik, Büşra Alakoç, Tülay Kesemen, Tahi̇r Khani̇yev Jan 2020

A Semi-Markovian Renewal Reward Process With $\Gamma(G)$ Distributed Demand, Asli Bektaş Kamişlik, Büşra Alakoç, Tülay Kesemen, Tahi̇r Khani̇yev

Turkish Journal of Mathematics

We consider a classical semi-Markovian stochastic model of type $(s,S)$ with Logistic distributed demand random variables. Logistic distribution is a member of special distribution class known as $\Gamma(g)$ that encounters in many real-life applications involving extreme value theory. The objective of this study is to observe some major characteristics of a stochastic process $X(t)$ which represents semi-Markovian renewal reward process of type $(s,S)$. We used new approximation results for renewal function that allow us to obtain three-term asymptotic expansion for ergodic distribution function and for $n^{th}$ order moments of ergodic distribution of the process $X(t)$.

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$T$-Soft Equality Relation, Tareq Alshami, Mohammed El-Shafei Jan 2020

$T$-Soft Equality Relation, Tareq Alshami, Mohammed El-Shafei

Turkish Journal of Mathematics

The desire of generalizing some set-theoretic properties to the soft set theory motivated many researchers to define various types of soft operators. For example, they redefined the complement of a soft set, and soft union and intersection between two soft sets in a way that satisfies De Morgan's laws. In this paper, we introduce and study the concepts of $T$-soft subset and $T$-soft equality relations. Then, we utilize them to define the concepts of $T$-soft union and $T$-soft intersection for arbitrary family of soft sets. By $T$-soft union, we successfully keep some classical properties via soft set theory. We conclude …

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An Analytical Investigatıon On Starlikeness And Convexity Properties For Hypergeometric Functions, İsmet Yildiz, Alaatti̇n Akyar Jan 2020

An Analytical Investigatıon On Starlikeness And Convexity Properties For Hypergeometric Functions, İsmet Yildiz, Alaatti̇n Akyar

Turkish Journal of Mathematics

In this study, we analytically investigate hypergeometric functions having some properties such as convexity and starlike. We fundamentally focus on obtaining desired conditions on the parameters \(a,b\), and $c$ in order that a hypergeometric function to be in various subclasses of starlike and convex functions of order \(\alpha=2^{-r}\) and order \(\alpha=2^{-r}\) type $\beta=2^{-1}$, with $r$ is a positive integer.

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Asymptotic Socle Behaviors For Cones Over Curves In Positive Characteristic, Jinjia Li Jan 2020

Asymptotic Socle Behaviors For Cones Over Curves In Positive Characteristic, Jinjia Li

Turkish Journal of Mathematics

This paper studies the distribution of socle degrees of $R/I^{[p^e]}$ when $e$ is large, for a homogeneous ideal $I$ in a two-dimensional standard-graded normal domain $R$ in positive characteristic $p$. We prove that the distribution is very much related to the asymptotic slopes of the syzygy bundle Syz$(I)$, which have been known to determine the Hilbert-Kunz multiplicity of $I$.

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Various Results For Series Expansions Of The Error Functions With The Complex Variable And Some Of Their Implications, Hüseyi̇n Irmak Jan 2020

Various Results For Series Expansions Of The Error Functions With The Complex Variable And Some Of Their Implications, Hüseyi̇n Irmak

Turkish Journal of Mathematics

This scientific investigation deals with introducing certain basic information relating to the error functions in z-plane, establishing extensive relations between various series expansions of the complex error functions and presenting a number of their implications.

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Some Higher-Order Identities For Generalized Bi-Periodic Horadam Sequences, Ho-Hon Leung, Eli̇f Tan Jan 2020

Some Higher-Order Identities For Generalized Bi-Periodic Horadam Sequences, Ho-Hon Leung, Eli̇f Tan

Turkish Journal of Mathematics

In this paper, we derive higher-order identities for the generalized bi-periodic Horadam sequences. Some of our results generalize the identities for the classical Fibonacci sequences and Horadam sequences obtained by Hoggatt, Horadam and Waddill. As an application, we derive some congruence properties satisfied by the generalized bi-periodic Horadam sequences.

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Lattice Ordered Semigroups And $\Gamma$-Hypersemigroups, Niovi Kehayopulu Jan 2020

Lattice Ordered Semigroups And $\Gamma$-Hypersemigroups, Niovi Kehayopulu

Turkish Journal of Mathematics

As we have already seen in Turkish Journal of Mathematics (2019) 43: 2592-2601 many results on hypersemigroups do not need any proof as they can be obtained from lattice ordered semigroups. The present paper goes a step further, to show that many results on $\Gamma$-hypersemigroups as well can be obtained from lattice ordered semigroups. It can be instructive to prove them directly, but even in that case the proofs go along the lines of lattice ordered semigroups (or $poe$-semigroups). In the investigation, we faced the problem to correct the definition of $\Gamma$-hypersemigroups given in the existing bibliography.

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On Certain Subclasses Of Starlike And Convex Functions Associated With Pascal Distribution Series, Bi̇lal Şeker, Sevtap Sümer Eker Jan 2020

On Certain Subclasses Of Starlike And Convex Functions Associated With Pascal Distribution Series, Bi̇lal Şeker, Sevtap Sümer Eker

Turkish Journal of Mathematics

In this article, we introduced a new power series whose coefficients are probabilities of the Pascal distribution. We investigated new approaches between the Pascal distribution series and some subclasses of normalized analytic functions. Also, we defined some mappings containing these functions the Alexander type integral operator. Moreover, we obtained sufficient conditions such that these mappings belong to some subclass of univalent functions.

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Commutator Subgroups Of Generalized Hecke And Extended Generalized Hecke Groups,Ii, Gülşah Doğrayici, Recep Şahi̇n Jan 2020

Commutator Subgroups Of Generalized Hecke And Extended Generalized Hecke Groups,Ii, Gülşah Doğrayici, Recep Şahi̇n

Turkish Journal of Mathematics

Let $p_{1},\ \cdots,\ p_{n}$ be integers where $n\geq 2$ and each $p_{i} \geq 2$. Let also $H(p_{1},\ \cdots,\ p_{n})$ be the generalized Hecke group associated to all $p_{i}\geq 2.$ In this paper, we study the commutator subgroups $H^{\prime}(p_{1},\ \cdots,\ p_{n})$ and $\overline{H}^{\prime }(p_{1},\ \cdots,\ p_{n})$ of the generalized Hecke group $H(p_{1},\ \cdots,\ p_{n})$ and the extended generalized Hecke group $\overline{H}% (p_{1},\ \cdots,\ p_{n})$. We give the generators and the signatures of $% H^{\prime}(p_{1},\ \cdots,\ p_{n})$ and $\overline{H}^{\prime}(p_{1},\ \cdots,\ p_{n})$.

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New Classes Of Catalan-Type Numbers And Polynomials With Their Applications Related To $P$-Adic Integrals And Computational Algorithms, İrem Küçükoğlu, Burçi̇n Şi̇mşek, Yilmaz Şi̇mşek Jan 2020

New Classes Of Catalan-Type Numbers And Polynomials With Their Applications Related To $P$-Adic Integrals And Computational Algorithms, İrem Küçükoğlu, Burçi̇n Şi̇mşek, Yilmaz Şi̇mşek

Turkish Journal of Mathematics

The aim of this paper is to construct generating functions for new classes of Catalan-type numbers and polynomials. Using these functions and their functional equations, we give various new identities and relations involving these numbers and polynomials, the Bernoulli numbers and polynomials, the Stirling numbers of the second kind, the Catalan numbers and other classes of special numbers, polynomials and functions. Some infinite series representations, including the Catalan-type numbers and combinatorial numbers, are investigated. Moreover, some recurrence relations and computational algorithms for these numbers and polynomials are provided. By implementing these algorithms in the Python programming language, we illustrate the …

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