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2022

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Articles 961 - 990 of 1375

Full-Text Articles in Mathematics

Cholera Transmission Dynamic Model With Environmental Impacts Of Plankton Reservoirs, Sweety Sarker Jan 2022

Cholera Transmission Dynamic Model With Environmental Impacts Of Plankton Reservoirs, Sweety Sarker

Electronic Theses and Dissertations, 2020-2023

Cholera is an acute disease that is a global threat to the world and can kill people within a few hours if left untreated. In the last 200 years, seven pandemics occurred, and, in some countries, it remains endemic. The World Health Organization (WHO) declared a global initiative to prevent cholera by 2030. Cholera dynamics are contributed by several environmental factors such as salinity level of water, water temperature, presence of plankton especially zooplankton such as cladocerans, rotifers, copepods, etc. Vibrio cholerae (V. cholerae) bacterium is the main reason behind the cholera disease and the growth of V. cholerae depends …

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Decoding Cyclic Codes Via Gröbner Bases, Eduardo Sosa Jan 2022

Decoding Cyclic Codes Via Gröbner Bases, Eduardo Sosa

Honors Theses

In this paper, we analyze the decoding of cyclic codes. First, we introduce linear and cyclic codes, standard decoding processes, and some standard theorems in coding theory. Then, we will introduce Gr¨obner Bases, and describe their connection to the decoding of cyclic codes. Finally, we go in-depth into how we decode cyclic codes using the key equation, and how a breakthrough by A. Brinton Cooper on decoding BCH codes using Gr¨obner Bases gave rise to the search for a polynomial-time algorithm that could someday decode any cyclic code. We discuss the different approaches taken toward developing such an algorithm and …

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Representation Theory And Its Applications In Physics, Jakub Bystrický Jan 2022

Representation Theory And Its Applications In Physics, Jakub Bystrický

Honors Theses

Representation theory is a branch of mathematics that allows us to represent elements of a group as elements of a general linear group of a chosen vector space by means of a homomorphism. The group elements are mapped to linear operators and we can study the group using linear algebra. This ability is especially useful in physics where much of the theories are captured by linear algebra structures. This thesis reviews key concepts in representation theory of both finite and infinite groups. In the case of finite groups we discuss equivalence, orthogonality, characters, and group algebras. We discuss the importance …

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Decomposing Manifolds In Low-Dimensions: From Heegaard Splittings To Trisections, Suixin "Cindy" Zhang Jan 2022

Decomposing Manifolds In Low-Dimensions: From Heegaard Splittings To Trisections, Suixin "Cindy" Zhang

Honors Theses

The decomposition of a topological space into smaller and simpler pieces is useful for understanding the space. In 1898, Poul Heegaard introduced the concept of a Heegaard splitting, which is a bisection of a 3-manifold. Heegaard diagrams, which describe Heegaard splittings combinatorially, have been recognized as a powerful tool for classifying 3-manifolds and producing important invariants of 3-manifolds. Handle decomposition, invented by Stephen Smale in 1962, describes how an n-manifold can be constructed by successively adding handles. In 2012, Gay and Kirby introduced trisections of 4-manifold, which are a four-dimensional analogues of Heegaard splittings in dimension three. Trisection diagrams give …

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Khovanov Homology & Uniqueness Of Surfaces In The 4-Ball, Isaac Sundberg Jan 2022

Khovanov Homology & Uniqueness Of Surfaces In The 4-Ball, Isaac Sundberg

Bryn Mawr College Dissertations and Theses

We use the functoriality of Khovanov homology to examine the smooth, boundary-preserving isotopy of surfaces embedded in the 4-ball. We exemplify an infinite family of prime knots that bound an arbitrarily-large number of smoothly-distinct slice disks by distinguishing the maps they induce on Khovanov homology. Similar techniques produce an infinite family of knots that each bound a pair of exotic surfaces of arbitrary genus.

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Hamiltonian Approach To Modelling Interfacial Internal Waves Over Variable Bottom, Rossen Ivanov, Calin Martin, Michail Todorov Jan 2022

Hamiltonian Approach To Modelling Interfacial Internal Waves Over Variable Bottom, Rossen Ivanov, Calin Martin, Michail Todorov

Articles

We study the effects of an uneven bottom on the internal wave propagation in the presence of stratification and underlying non-uniform currents. Thus, the presented models incorporate vorticity (wave–current interactions), geophysical effects (Coriolis force) and a variable bathymetry. An example of the physical situation described above is well illustrated by the equatorial internal waves in the presence of the Equatorial Undercurrent (EUC). We find that the interface (physically coinciding with the thermocline and the pycnocline) satisfies in the long wave approximation a KdV–mKdV type equation with variable coefficients. The soliton propagation over variable depth leads to effects such as soliton …

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Neuromatch Academy: A 3-Week, Online Summer School In Computational Neuroscience, Bernard Marius 'T Hart, Titipat Achakulvisut, Ayoade Adeyemi, Athena Akrami, Bradly Alicea, Alicia Alonso-Andres, Diego Alzate-Correa, Arash Ash, Jesus J. Ballesteros, Aishwarya Balwani, Eleanor Batty, Ulrik Beierholm, Ari S. Benjamin, Upinder Bhalla, Gunnar Blohm, Joachim C. H. Blohm, Kathryn Bonnen, Marco Brigham, Bingni W. Brunton, John Butler, Brandon Caie, N Alex Cayco Gajic, Sharbatanu Chatterjee, Spyridon Chavlis, Ruidong Chen, You Cheng, H. M. Chow, Raymond Chua, Yunwei Dai, Isaac David, Eric E. J. Dewitt, Julien Denis, Alish Dipani, Arianna Dorschel, Jan Drugowitsch, Kshitij Dwivedi, Sean Escola, Haoxue Fan, Roozbeh Farhoodi, Yicheng Fei, Pierre-Étienne Fiquet, Lorenzo Fontolan, Jeremy Forest, Yuki Fujishima, Byron V. Galbraith, Mario Galdamez, Richard Gao, Julijana Gjorgjieva, Alexander Gonzalez, Qinglong Gu, Yueqi Guo, Ziyi Guo, Pankaj K. Gupta, Busra Tugce Gurbuz, Caroline Haimerl, Jordan B. Harrod, Alexandre Hyafil, Martin Irani, Daniel Jacobson, Michelle Johnson, Ilenna Simone Jones, Gili Karni, Robert E. Kass, Hyosub Edward Kim, Andreas M. Kist, Randal Koene, Konrad Kording, Matthew R. Krause, Arvind Kumar, Norma K. Kühn, Ray Lc, Matthew L. Laporte, Junseok Lee, Songting Li, Sikun Lin, Yang Lin, Shuze Liu, Tony Liu, Jesse A. Livezey, Linlin Lu, Jakob H. Macke, Kelly Mahaffy, A. Lucas Martins, Nicolás Martorell, Manolo Martínez, Marcelo G. Mattar, Jorge Aurelio Menendez, Kenneth D. Miller, Patrick J. Mineault, Nosratullah Mohammadi, Yalda Mohsenzadeh, Elenor Morgenroth, Taha Morshedzadeh, Alice Claudia Mosberger, Madhuvanthi Muliya, Marieke Mur, John D. Murray, Yashas Nd, Richard Naud, Prakriti Nayak, Anushka Oak, Itzel Olivos Castillo, Seyedmehdi Orouji, Jorge Otero-Millan, Marius Pachitariu, Biraj Pandey, Renato Paredes, Jesse Parent, Il Memming Park, Megan A. K. Peters, Xaq Pitkow, Panayiota Poirazi, Haroon Popal, Sandhya Prabhakaran, Tian Qiu, Srinidhi Ragunathan, Raul Rodriguez-Cruces, David Rolnick, Ashish Kumar Sahoo, Saeed Salehinajafabadi, Cristina Savin, Shreya Saxena, Paul Schrater, Karen Schroeder, Alice C. Schwarze, Madineh Sedigh-Sarvestani, K. Yuvaraj Sekhar, Reza Shadmehr, Maryam M. Shanechi, Siddhant Sharma, Eric Shea-Brown, Krishna V. Shenoy, Carolina L. Shimabukuro, Sergey Shuvaev, Man Ching Alison Sin, Maurice Smith, Nicholas A. Steinmetz, Karolina Stosio, Elizabeth Straley, Gabrielle Strandquist, Carsen Stringer, Rimjhim Tomar, Ngoc Tran, Sofia Triantafillou, Lawrence Udeigwe, Davide Valeriani, Vincent Valton, Maryam Vaziri-Pashkam, Peter Vincent, Gal Vishne, Pascal Wallisch, Peiyuan Wang, Claire Ward, Michael Waskom, Kunlin Wei, Anqi Wu, Zhengwei Wu, Brad Wyble, Lei Zhang, Daniel Zysman, Federico D’Oleire Uquillas, Tara Van Viegen Jan 2022

Neuromatch Academy: A 3-Week, Online Summer School In Computational Neuroscience, Bernard Marius 'T Hart, Titipat Achakulvisut, Ayoade Adeyemi, Athena Akrami, Bradly Alicea, Alicia Alonso-Andres, Diego Alzate-Correa, Arash Ash, Jesus J. Ballesteros, Aishwarya Balwani, Eleanor Batty, Ulrik Beierholm, Ari S. Benjamin, Upinder Bhalla, Gunnar Blohm, Joachim C. H. Blohm, Kathryn Bonnen, Marco Brigham, Bingni W. Brunton, John Butler, Brandon Caie, N Alex Cayco Gajic, Sharbatanu Chatterjee, Spyridon Chavlis, Ruidong Chen, You Cheng, H. M. Chow, Raymond Chua, Yunwei Dai, Isaac David, Eric E. J. Dewitt, Julien Denis, Alish Dipani, Arianna Dorschel, Jan Drugowitsch, Kshitij Dwivedi, Sean Escola, Haoxue Fan, Roozbeh Farhoodi, Yicheng Fei, Pierre-Étienne Fiquet, Lorenzo Fontolan, Jeremy Forest, Yuki Fujishima, Byron V. Galbraith, Mario Galdamez, Richard Gao, Julijana Gjorgjieva, Alexander Gonzalez, Qinglong Gu, Yueqi Guo, Ziyi Guo, Pankaj K. Gupta, Busra Tugce Gurbuz, Caroline Haimerl, Jordan B. Harrod, Alexandre Hyafil, Martin Irani, Daniel Jacobson, Michelle Johnson, Ilenna Simone Jones, Gili Karni, Robert E. Kass, Hyosub Edward Kim, Andreas M. Kist, Randal Koene, Konrad Kording, Matthew R. Krause, Arvind Kumar, Norma K. Kühn, Ray Lc, Matthew L. Laporte, Junseok Lee, Songting Li, Sikun Lin, Yang Lin, Shuze Liu, Tony Liu, Jesse A. Livezey, Linlin Lu, Jakob H. Macke, Kelly Mahaffy, A. Lucas Martins, Nicolás Martorell, Manolo Martínez, Marcelo G. Mattar, Jorge Aurelio Menendez, Kenneth D. Miller, Patrick J. Mineault, Nosratullah Mohammadi, Yalda Mohsenzadeh, Elenor Morgenroth, Taha Morshedzadeh, Alice Claudia Mosberger, Madhuvanthi Muliya, Marieke Mur, John D. Murray, Yashas Nd, Richard Naud, Prakriti Nayak, Anushka Oak, Itzel Olivos Castillo, Seyedmehdi Orouji, Jorge Otero-Millan, Marius Pachitariu, Biraj Pandey, Renato Paredes, Jesse Parent, Il Memming Park, Megan A. K. Peters, Xaq Pitkow, Panayiota Poirazi, Haroon Popal, Sandhya Prabhakaran, Tian Qiu, Srinidhi Ragunathan, Raul Rodriguez-Cruces, David Rolnick, Ashish Kumar Sahoo, Saeed Salehinajafabadi, Cristina Savin, Shreya Saxena, Paul Schrater, Karen Schroeder, Alice C. Schwarze, Madineh Sedigh-Sarvestani, K. Yuvaraj Sekhar, Reza Shadmehr, Maryam M. Shanechi, Siddhant Sharma, Eric Shea-Brown, Krishna V. Shenoy, Carolina L. Shimabukuro, Sergey Shuvaev, Man Ching Alison Sin, Maurice Smith, Nicholas A. Steinmetz, Karolina Stosio, Elizabeth Straley, Gabrielle Strandquist, Carsen Stringer, Rimjhim Tomar, Ngoc Tran, Sofia Triantafillou, Lawrence Udeigwe, Davide Valeriani, Vincent Valton, Maryam Vaziri-Pashkam, Peter Vincent, Gal Vishne, Pascal Wallisch, Peiyuan Wang, Claire Ward, Michael Waskom, Kunlin Wei, Anqi Wu, Zhengwei Wu, Brad Wyble, Lei Zhang, Daniel Zysman, Federico D’Oleire Uquillas, Tara Van Viegen

Articles

No abstract provided.

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Various Operators In Relation To Fractional Order Calculus And Some Of Their Applications To Normalized Analytic Functions In The Open Unit Disk, Hüseyi̇n Irmak Jan 2022

Various Operators In Relation To Fractional Order Calculus And Some Of Their Applications To Normalized Analytic Functions In The Open Unit Disk, Hüseyi̇n Irmak

Turkish Journal of Mathematics

The main object of this scientific work is firstly to introduce various operators of fractional calculus (that is that fractional integral and fractional derivative(s)) in certain domains of the complex plane, then to determine certain results correlating with normalized analytic functions, which are analytic in certain domains in the complex plane, as a few applications of those operators, and also to present a number of extensive implications of them as special results.

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Wittgenstein On Miscalculation And The Foundations Of Mathematics, Samuel J. Wheeler Jan 2022

Wittgenstein On Miscalculation And The Foundations Of Mathematics, Samuel J. Wheeler

Philosophy Faculty Publications

In Remarks on the Foundations of Mathematics, Wittgenstein notes that he has 'not yet made the role of miscalculating clear' and that 'the role of the proposition: "I must have miscalculated"...is really the key to an understanding of the "foundations" of mathematics.' In this paper, I hope to get clear on how this is the case. First, I will explain Wittgenstein's understanding of a 'foundation' for mathematics. Then, by showing how the proposition 'I must have miscalculated' differentiates mathematics from the physical sciences, we will see how this proposition is the key to understanding the foundations of mathematics.

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Notes On The Quadraticity Of Linear Combinations Of A Cubic Matrix And A Quadratic Matrix That Commute, Tuğba Peti̇k, Hali̇m Özdemi̇r, Burak Tufan Gökmen Jan 2022

Notes On The Quadraticity Of Linear Combinations Of A Cubic Matrix And A Quadratic Matrix That Commute, Tuğba Peti̇k, Hali̇m Özdemi̇r, Burak Tufan Gökmen

Turkish Journal of Mathematics

Let $A_{1}$ and $A_{2}$ be an $\{\alpha_{1}, \beta_{1}, \gamma_{1}\}$-cubic matrix and an $\{\alpha_{2}, \beta_{2}\}$-quadratic matrix, respectively, with $\alpha_{1} \neq \beta_{1}$, $\beta_{1} \neq \gamma_{1}$, $\alpha_{1} \neq \gamma_{1}$ and $\alpha_{2}\neq \beta_{2}$. In this work, we characterize all situations in which the linear combination $A_{3}=a_{1}A_{1}+a_{2}A_{2}$ with the assumption $A_{1}A_{2}=A_{2}A_{1}$ is an $\{\alpha_{3}, \beta_{3}\}$-quadratic matrix, where $a_{1}$ and $a_{2}$ are unknown nonzero complex numbers.

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On Unbounded Order Continuous Operators, Bahri̇ Turan, Bi̇rol Altin, Hüma Gürkök Jan 2022

On Unbounded Order Continuous Operators, Bahri̇ Turan, Bi̇rol Altin, Hüma Gürkök

Turkish Journal of Mathematics

Let $U$ and $V$ be two Archimedean Riesz spaces. An operator $S:U\rightarrow V$ is said to be unbounded order continuous ($uo$-continuous), if $r_{\alpha }\overset{uo}{\rightarrow }0$ in $U$ implies $Sr_{\alpha }\overset{uo}{% \rightarrow }0$ in $V$. In this paper, we give some properties of the $uo$% -continuous dual $U_{uo}^{\sim }$ of $U$. We show that a nonzero linear functional $f$ on $U$ is $uo$-continuous if and only if $f$ is a linear combination of finitely many order continuous lattice homomorphisms. The result allows us to characterize the $uo$-continuous dual $U_{uo}^{\sim }.$ In general, by giving an example that the $uo$-continuous dual $U_{uo}^{\sim …

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Subsequence Characterization Of Statistical Boundedness, Leila Miller Van Wieren Jan 2022

Subsequence Characterization Of Statistical Boundedness, Leila Miller Van Wieren

Turkish Journal of Mathematics

In this paper, we present some relationships between statistical boundedness and statistical monotonicity of a given sequence and its subsequences. The results concerning statistical boundedness and monotonicity presented here are also closely related to earlier results regarding statistical convergence and are dealing with the Lebesgue measure and with the Baire category.

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On Some Fractional Operators Generated From Abel's Formula, Eki̇n Uğurlu Jan 2022

On Some Fractional Operators Generated From Abel's Formula, Eki̇n Uğurlu

Turkish Journal of Mathematics

This work aims to share some fractional integrals and derivatives containing three real parameters. The main tool to introduce such operators is the corresponding Abel's equation. Solvability conditions for the Abel's equations are shared. Semigroup properties for fractional integrals are introduced. Integration by parts rule is given. Moreover, mean value theorems and related results are shared. At the end of the paper, some directions for some fractional operators are given.

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K−Uniformly Multivalent Functions Involving Liu-Owa Q−Integral Operator, Asena Çeti̇nkaya Jan 2022

K−Uniformly Multivalent Functions Involving Liu-Owa Q−Integral Operator, Asena Çeti̇nkaya

Turkish Journal of Mathematics

In this paper, we introduce $q-$analogue of Liu-Owa integral operator and define a subclass of $k-$uniformly multivalent starlike functions of order $\gamma, (0\leq\gamma< p; p\in\mathbb{N})$ by using the Liu-Owa $q-$integral operator. We examine coefficient estimates, growth and distortion bounds for the functions belonging to the subclass of $k-$uniformly multivalent starlike functions of order $\gamma$. Moreover, we determine radii of $k-$uniformly starlikeness, convexity and close-to-convexity for the functions belonging to this subclass.

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Variational Geometry For Surfaces In Conformally Flat Space, Najma Mosadegh, Esmaiel Abedi Jan 2022

Variational Geometry For Surfaces In Conformally Flat Space, Najma Mosadegh, Esmaiel Abedi

Turkish Journal of Mathematics

In this paper, it is shown that a closed surface in 3-dimensional harmonic conformally flat space is minimal if the sign of the mean curvature does not change. Also, it is determined that the critical point of mean curvature functional of the surface is homeomorphic to the sphere.

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Hyperelastic Curves In $3-$Dimensional Lightlike Cone, Sümeyra Tuğçe Kağizman, Ahmet Yücesan Jan 2022

Hyperelastic Curves In $3-$Dimensional Lightlike Cone, Sümeyra Tuğçe Kağizman, Ahmet Yücesan

Turkish Journal of Mathematics

We study hyperelastic curves known as a generalization of elastic curves in $3-$dimensional lightlike cone which is a degenerate hypersurface in Minkowski $4-$space as critical points of the cone curvature energy functional constructed with the $r-$th power of the cone curvature depending on the given boundary conditions for the natural number $r \geq 2$. We derive the Euler-Lagrange equations for the critical points of this functional that is namely the hyperelastic curves and solve completely the Euler-Lagrange equations by quadratures. Then, we construct Killing vector fields along the hyperelastic curves. Lastly, we give explicitly the hyperelastic curves by integral according …

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Hyers-Ulam Stability Of A Certain Fredholm Integral Equation, Alberto Simões, Ponmana Selvan Jan 2022

Hyers-Ulam Stability Of A Certain Fredholm Integral Equation, Alberto Simões, Ponmana Selvan

Turkish Journal of Mathematics

In this paper, by using fixed point theorem we establish the Hyers-Ulam stability and Hyers-Ulam-Rassias stability of certain homogeneous Fredholm Integral equation of the second kind $$ \phi(x) = \lambda \int_{0}^{1}(1+x+t) \, \phi(t) \, dt $$ and the nonhomogeneous equation $$ \phi(x) = x + \lambda \int_{0}^{1}(1+x+t) \, \phi(t) \, dt $$ for all $x \in [0,1]$ and $0

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On Isolated Gaps In Numerical Semigroups, Harold J. Smith Jan 2022

On Isolated Gaps In Numerical Semigroups, Harold J. Smith

Turkish Journal of Mathematics

A numerical semigroup is said to be perfect if it does not contain any isolated gaps. In this paper, we will look at some basic properties of isolated gaps in numerical semigroups. In particular, we will see how they are related to elements of the Apery set. We will use these properties to find all of the isolated gaps in a numerical semigroup of embedding dimension two and demonstrate a simple method of generating some examples of perfect numerical semigroups of embedding dimension three.

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Geodesics Of Fiberwise Cigar Soliton Deformation Of The Sasaki Metric, Liana Lotarets Jan 2022

Geodesics Of Fiberwise Cigar Soliton Deformation Of The Sasaki Metric, Liana Lotarets

Turkish Journal of Mathematics

Ricci solitons arose in proof the Poincare conjecture by R. Hamilton and G. Perelman. The first example of a noncompact steady Ricci soliton on a plane was found by R. Hamilton. This two-dimensional manifold is conformally equivalent to the plane and it is called by R. Hamilton's cigar soliton. The cigar soliton metric can be considered as a fiber-wise conformal deformation of the Euclidean metric on a fiber of the tangent bundle. In the paper we propose a deformation of the classical Sasaki metric on the tangent bundle of an n-dimensional Riemannian manifold that induces the cigar soliton type metric …

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Examination Of Eigenvalues And Spectral Singularities Of A Discrete Dirac Operator With An Interaction Point, Şeri̇fenur Cebesoy Jan 2022

Examination Of Eigenvalues And Spectral Singularities Of A Discrete Dirac Operator With An Interaction Point, Şeri̇fenur Cebesoy

Turkish Journal of Mathematics

In this paper, the main content is the consideration of the concepts of eigenvalues and spectral singularities of an operator generated by a discrete Dirac system in $\ell_{2}(\mathbb{Z},\mathbb{C}^{2})$ with an interior interaction point. Defining a transfer matrix $ M $ enables us to present a relationship between the $ M_{22} $ component of this matrix and Jost functions of mentioned Dirac operator so that its eigenvalues and spectral properties can be studied. Finally, some special cases are examined where the impulsive condition possesses certain symmetries.

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To The Solution Of Integro-Differential Equations With Nonlocal Conditions, Kamil R. Aida-Zade, Vagif M. Abdullayev Jan 2022

To The Solution Of Integro-Differential Equations With Nonlocal Conditions, Kamil R. Aida-Zade, Vagif M. Abdullayev

Turkish Journal of Mathematics

We investigate linear integro-differential equations with ordinary derivatives. The kernels of the integrands depend only on the variable of integration, and the conditions involve the terms with the point and integral values of the unknown function. We drive necessary and sufficient conditions for the existence and uniqueness of the solution of the problem, which can be used both for analytical and numerical solutions. We present the results of solving an illustrative test problem.

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Upper And Lower Bounds Of The $A$-Berezin Number Of Operators, Mualla Bi̇rgül Huban Jan 2022

Upper And Lower Bounds Of The $A$-Berezin Number Of Operators, Mualla Bi̇rgül Huban

Turkish Journal of Mathematics

Let $A$ be a positive bounded linear operator acting on a complex Hilbert space $\mathcal{H}$. Any positive operator $A$ induces a semiinner product on $\mathcal{H}$ defined by $\left\langle x,y\right\rangle _{A}:=\left\langle Ax,y\right\rangle _{\mathcal{H}},$ $\forall x,y\in\mathcal{H}.$ For any $T\in\mathcal{B}\left( \mathcal{H}\left( \Omega\right) \right) $, its $A$-Berezin symbol $\widetilde{T}^{_{A}}$ is defined on $\Omega$ by $\widetilde{T}^{_{A}% }:=\left\langle T\widehat{K}_{\lambda},\widehat{K}_{\lambda}\right\rangle _{A},$ $\lambda\in\Omega,$where $\widehat{K}_{\lambda}$ is the normalized reproducing kernel of $\mathcal{H}$. In this paper, we introduce the notions $\left( A,r\right) $-adjoint of operators and $A$-Berezin number of operators on the reproducing kernel Hilbert space and prove some upper and lower bounds of the $A$-Berezin numbers of operators. In …

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New Extension Of Alexander And Libera Integral Operators, Hatun Özlem Güney, Shigeyoshi Owa Jan 2022

New Extension Of Alexander And Libera Integral Operators, Hatun Özlem Güney, Shigeyoshi Owa

Turkish Journal of Mathematics

Let $T$ be the class of analytic functions in the open unit disc $\mathbb{U}$ with $f(0)=0$ and $f'(0)=1.$ For $f(z)\in T,$ the Alexander integral operator $A_{-1}f(z),$ the Libera integral operator $L_{-1}f(z)$ and the Bernardi integral operator $B_{-1}f(z)$ were considered before. Using $A_{-1}f(z)$ and $L_{-1}f(z),$ a new integral operator $F_{\lambda}f(z)$ is considered. After discuss some properties of dominant for $F_{\lambda}f(z),$ another new integral operator $O_{-1}f(z)$ of $f(z)\in T$ is discussed. The object of the present paper is to discuss the dominant of new integral operators $F_{\lambda}f(z)$ and $O_{-1}f(z)$ concerning with some starlike functions and convex functions in $\mathbb{U}.$

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Classification Of Some Geometric Structures On 4-Dimensional Riemannian Lie Group, Esmaeil Peyghan, Davood Seifipour Jan 2022

Classification Of Some Geometric Structures On 4-Dimensional Riemannian Lie Group, Esmaeil Peyghan, Davood Seifipour

Turkish Journal of Mathematics

In this paper we study the spectral geometry of a $4$-dimensional Lie group. The main focus of this paper is to study the $2$-Stein and $2$-Osserman structures on a $4$-dimensional Riemannian Lie group. In this paper, we study the spectrum and trace of Jacobi operator and also we study the characteristic polynomial of generalized Jacobi operator on the non-abelian $4$-dimensional Lie group $G$, whenever $G$ is equipped with an orthonormal left invariant Riemannian metric $g$. The Lie algebra structures in dimension four have key role in this paper. It is known that in the classification of $4$-dimensional non-abelian Lie algebras …

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Multivariate Approximation In $\Varphi$-Variation For Nonlinear Integral Operators Via Summability Methods, İsmai̇l Aslan Jan 2022

Multivariate Approximation In $\Varphi$-Variation For Nonlinear Integral Operators Via Summability Methods, İsmai̇l Aslan

Turkish Journal of Mathematics

We consider convolution-type nonlinear integral operators endowed with Musielak-Orlicz $\varphi$-variation. Our aim is to get more powerful approximation results with the help of summability methods. In this study, we use $\varphi$-absolutely continuous functions for our convergence results. Moreover, we study the order of approximation using suitable Lipschitz class of continuous functions. A general characterization theorem for $\varphi $-absolutely continuous functions is also obtained. We also give some examples of kernels in order to verify our approximations. At the end, we indicate our approximations in figures together with some numerical computations.

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Sober Spaces, Mehmet Baran, Hassan Abughalwa Jan 2022

Sober Spaces, Mehmet Baran, Hassan Abughalwa

Turkish Journal of Mathematics

The goal of this paper is to introduce various forms of sober objects in a topological category and investigate the relationships among these various forms. Moreover, we characterize quasi-sober objects, $T_{0}$ objects and each of various forms of sober objects in some topological categories and give some invariance properties of them. Finally, we compare our results with some well-known results in the category of topological spaces.

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Finite Ordered $\Gamma$-Hypersemigroups Constructed By Ordered $\Gamma$-Semigroups, Niovi Kehayopulu Jan 2022

Finite Ordered $\Gamma$-Hypersemigroups Constructed By Ordered $\Gamma$-Semigroups, Niovi Kehayopulu

Turkish Journal of Mathematics

In the investigation of ordered $\Gamma$-hypersemigroups we often need counterexamples (of finite order) given by a table of multiplication and a figure that are impossible to make by hand and very difficult to write programs as well. So it is useful to have examples of ordered $\Gamma$-semigroups for which is much more easier to write programs and then from these examples to obtain corresponding examples of ordered $\Gamma$-hypersemigroups. In this respect we show that from every example of a regular, intra-regular, right (left) regular, right (left) quasi-regular, semisimple, right (left) simple, simple, strongly regular ordered $\Gamma$-semigroup given by a table …

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Commutativity Degree Of Crossed Modules, Zekeri̇ya Arvasi̇, Eli̇f Ilgaz Çağlayan, Alper Odabaş Jan 2022

Commutativity Degree Of Crossed Modules, Zekeri̇ya Arvasi̇, Eli̇f Ilgaz Çağlayan, Alper Odabaş

Turkish Journal of Mathematics

In this work, we define the notion of commutativity degree of crossed modules and find some bounds on commutativity degree for special types of crossed modules. Also, we give a function for finding commutativity degree of crossed modules in GAP and classify crossed modules by using this function.

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Infinitely Many Positive Solutions For An Iterative System Of Conformable Fractional Order Dynamic Boundary Value Problems On Time Scales, Mahammad Khuddush, Kapula Rajendra Prasad Jan 2022

Infinitely Many Positive Solutions For An Iterative System Of Conformable Fractional Order Dynamic Boundary Value Problems On Time Scales, Mahammad Khuddush, Kapula Rajendra Prasad

Turkish Journal of Mathematics

In this paper, we establish infinitely many positive solutions for the iterative system of conformable fractional order dynamic equations on time scales $$ \begin{aligned} &\mathcal{T}_α^{\Delta}\big[\mathcal{T}_β^{\Delta}\big(\vartheta_\mathtt{n}(t)\big)\big]=\varphi(t)\mathtt{f}_\mathtt{n}\left(\vartheta_{\mathtt{n}+1}(t)\right),~t\in(0,1)_\mathbb{T},~1

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Uniformly Convergent Finite Difference Method For Reaction-Diffusion Type Third Order Singularly Perturbed Delay Differential Equation, Rajendran Mahendran, Veerasamy Subburayan Jan 2022

Uniformly Convergent Finite Difference Method For Reaction-Diffusion Type Third Order Singularly Perturbed Delay Differential Equation, Rajendran Mahendran, Veerasamy Subburayan

Turkish Journal of Mathematics

A class of third order reaction-diffusion type singularly perturbed ordinary delay differential equations is considered in this article. A fitted finite difference method on Shishkin mesh is suggested to solve the problem. Moreover, we present a class of nonlinear problems. An error estimation is obtained based on the maximum norm and it is of almost first order convergence. Numerical results are given to support theoretical claims.

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