Langevin Delayed Equations With Prabhakar Derivatives Involving Two Generalized
Fractional Distinct Orders,
2024
TÜBİTAK
Langevin Delayed Equations With Prabhakar Derivatives Involving Two Generalized Fractional Distinct Orders, Mustafa Aydin
Turkish Journal of Mathematics
This paper is devoted to defining the delayed analogue of the Mittag-Leffler type function with three parameters and investigating a representation of a solution to Langevin delayed equations with Prabhakar derivatives involving two generalized fractional distinct orders, which are first introduced and investigated, by means of the Laplace integral transform. It is verified by showing the solution satisfies the introduced system. Special cases which are also novel are presented as examples. The findings are illustrated with the help of the RLC circuits.
Isometries Of Length 1 In Purely Loxodromic Free Kleinian Groups
And Trace Inequalities,
2024
TÜBİTAK
Isometries Of Length 1 In Purely Loxodromic Free Kleinian Groups And Trace Inequalities, İlker Savaş Yüce, Ahmet Nedi̇m Narman
Turkish Journal of Mathematics
In this paper, we prove a generalization of a discreteness criteria for a large class of subgroups of PSL2(C) . In particular, given a finitely generated purely loxodromic free Kleinian group Γ = ⟨ξ1, ξ2, . . . , ξn⟩ for n ≥ 2, we show that |trace2(ξi) − 4| + |trace(ξiξjξ −1 i ξ −1 j ) − 2| ≥ 2 sinh2 ( 1 4 log αn ) for some ξi and ξj for i ̸= j in Γ provided that certain conditions on the hyperbolic displacements given by ξi , ξj and their length 3 conjugates formed by …
On The Reconstruction Of An Integro-Differential Dirac Operator With Parameter-Dependent Nonlocal Integral Boundary Conditions From The Nodal Data, Baki Keskin, Yu Ping Wang
Turkish Journal of Mathematics
We consider the integro-differential Dirac operator with parameter-dependent nonlocal integral boundary conditions. We derive the asymptotic expressions for the eigenvalues and the zeros of eigenfunctions (nodal points or nodes) and develop a constructive procedure for solving the inverse nodal problem for this operator.
On The Oscillation And Asymptotic Behavior Of Solutions Of Third Order Nonlineardifferential Equations With Mixed Nonlinear Neutral Terms, Shaimaa Salem, Mohamed M. A. El-Sheikh, Ahmed Mohamed Hassan
Turkish Journal of Mathematics
This paper is concerned with the oscillation and asymptotic behavior of solutions of third-order nonlinear neutral differential equations with a middle term and mixed nonlinear neutral terms in the case of the canonical operator. We establish several oscillation criteria that guarantee that all solutions are oscillatory or converge to zero. The given results are obtained by applying the comparison method, the Riccati transformation and the integral averaging technique. The results improve significantly and extend existing ones in the literature. Finally, illustrative examples are given.
Modules Over Invertible 1-Cocycles,
2024
TÜBİTAK
Modules Over Invertible 1-Cocycles, José Manuel Fernández Vilaboa, Ramon Gonzalez Rodriguez, Brais Ramos Pérez, Ana Belén Rodríguez Raposo
Turkish Journal of Mathematics
In this paper, we introduce in a braided setting the notion of left module for an invertible 1-cocycle and we prove some categorical equivalences between categories of modules associated to an invertible 1-cocycle and categories of modules associated to Hopf braces.
Duality And Norm Completeness In The Classes Of Limitedly Lwc Anddunford–Pettis Lwc Operators,
2024
TÜBİTAK
Duality And Norm Completeness In The Classes Of Limitedly Lwc Anddunford–Pettis Lwc Operators, Ömer Şafak Alpay, Eduard Emelyanov, Svetlana Gorokhova
Turkish Journal of Mathematics
We study the duality and norm completeness in the new classes of limitedly L-weakly compact and Dunford–Pettis L-weakly compact operators from Banach spaces to Banach lattices.
Lightcone Framed Curves In The Lorentz-Minkowski 3-Space,
2024
TÜBİTAK
Lightcone Framed Curves In The Lorentz-Minkowski 3-Space, Liang Chen, Masatomo Takahashi
Turkish Journal of Mathematics
For a nonlightlike nondegenerate regular curve, we have the arc-length parameter and the Frenet-Serret type formula by using a moving frame like a regular space curve in the Euclidean space. If a point of the curve moves between spacelike and timelike regions, then there is a lightlike point. In this paper, we consider mixed types of not only regular curves but also curves with singular points. In order to consider mixed type of curves with singular points, we introduce a frame, so-called the lightcone frame, and lightcone framed curves. We investigate differential geometric properties of lightcone framed curves.
Timelike Surfaces With Parallel Normalized Mean Curvature Vector Field In The
Minkowski 4-Space,
2024
TÜBİTAK
Timelike Surfaces With Parallel Normalized Mean Curvature Vector Field In The Minkowski 4-Space, Victoria Bencheva, Velichka Milousheva
Turkish Journal of Mathematics
In the present paper, we study timelike surfaces with parallel normalized mean curvature vector field in the four-dimensional Minkowski space. We introduce special isotropic parameters on each such surface, which we call canonical parameters, and prove a fundamental existence and uniqueness theorem stating that each timelike surface with parallel normalized mean curvature vector field is determined up to a rigid motion in the Minkowski space by three geometric functions satisfying a system of three partial differential equations. In this way, we minimize the number of functions and the number of partial differential equations determining the surface, thus solving the Lund-Regge …
Fusion In Supersolvable Hall Subgroups,
2024
TÜBİTAK
Fusion In Supersolvable Hall Subgroups, Muhammet Yasi̇r Kizmaz
Turkish Journal of Mathematics
Let H be a supersolvable Hall π -subgroup of a finite group G. We prove that G has a normal π -complement if and only if H controls G-fusion in H.
An Extension Of The Definition On The Compositions Of The Singular Distributions,
2024
TÜBİTAK
An Extension Of The Definition On The Compositions Of The Singular Distributions, Emi̇n Özçağ
Turkish Journal of Mathematics
Gelfand and Shilov give the definition of the composition δ(g(x)) for an infinitely differentiable function g(x) having any number of simple roots. In the paper, we consider their definition for an infinitely differentiable function having any number of multiple roots by using the method of the discarding of unwanted infinite quantities from asymptotic expansions and give some examples. Further, we define the compositions δ(g+) and δ(g−) for a locally summable function g(x).
Existence Of Solutions By Coincidence Degree Theory For Hadamard Fractionaldifferential Equations At Resonance,
2024
Missouri University of Science and Technology
Existence Of Solutions By Coincidence Degree Theory For Hadamard Fractionaldifferential Equations At Resonance, Martin Bohner, Alexander Domoshnitsky, Seshadev Padhi, Satyam Narayan Srivastava
Turkish Journal of Mathematics
Using the coincidence degree theory of Mawhin and constructing appropriate operators, we investigate the existence of solutions to Hadamard fractional differential equations (FRDEs) at resonance { − (HDγu ) (t) = f(t, u(t)), t ∈ (1, e), u(1) = 0, u(e) = ∫ e 1 u(t)dA(t), where 1 < γ < 2, f : [1, e]×R2 → R satisfies Carathéodory conditions, ∫ e 1 u(t)dA(t) is the Riemann–Stieltjes integration, and (HDγu ) is the Hadamard fractional derivation of u of order γ . An example is included to illustrate our result.
Qualitative Results For A Generalized 2-Component Camassa-Holm System With
Weak Dissipation Term,
2024
Department of Mathematics, Dicle University, 21280, Diyarbakir, Turkey
Qualitative Results For A Generalized 2-Component Camassa-Holm System With Weak Dissipation Term, Nurhan Dündar
Turkish Journal of Mathematics
Our main aim in the current study is to examine the mathematical properties of a generalized 2-component Camassa-Holm system with a weakly dissipative term. Firstly, we acquire the theorem of well-posedness in locally for the generalized system with weak dissipation. Then, we demonstrate that this system can reveal the blow-up phenomenon. Finally, we acquire the theorem of global existence utilizing a method of the Lyapunov function.
Special Subdiagrams Of Young Diagrams And Numerical Semigroups,
2024
Batman University
Special Subdiagrams Of Young Diagrams And Numerical Semigroups, Meral Süer, Mehmet Yeşi̇l
Turkish Journal of Mathematics
In this study, Young diagrams and their corresponding numerical sets are considered, and a new notion called special subdiagrams is described. Characterizations of special subdiagrams and their corresponding numerical sets, as well as the conditions when they are numerical semigroups, are provided. Young diagrams of symmetric, almost symmetric and Arf numerical semigroups are also considered and properties of their special subdiagrams are given.
Strongly I-Bicritical Graphs,
2024
University of Victoria
Strongly I-Bicritical Graphs, Michelle Edwards, Gary Macgillivray, Shahla Nasserasr
Theory & Applications of Graphs
A graph $G$ is \emph{strongly $i$-bicritical} if it has independent domination number $i(G) \geq 3$, and $i(G - \{x, y\}) = i(G) - 2$ whenever $x$ and $y$ are two non-adjacent vertices of $G$. We describe five constructions of strongly $i$-bicritical graphs. For four of them, necessary and sufficient conditions for the graph produced by the construction to be strongly $i$-bicritical are given. The strongly $i$-bicritical graphs with independent domination number $i(G) = 3$ are characterized, and it is shown that the strongly $i$-bicritical graphs with independent domination number $i(G) \geq 5$ may be hard to characterize. It is shown …
A Characterization Of The Operator Entropy In Terms Of An Isometry Property Related To Trace Norms,
2024
Meijo University, Tenpaku, Nagoya 468- 8502, Japan
A Characterization Of The Operator Entropy In Terms Of An Isometry Property Related To Trace Norms, Ryo Inayoshi
Journal of Stochastic Analysis
No abstract provided.
Machine Learning Application Of Generalized Gaussian Radial Basis Function And Its Reproducing Kernel Theory,
2024
University of Texas at Tyler
Machine Learning Application Of Generalized Gaussian Radial Basis Function And Its Reproducing Kernel Theory, Himanshu Singh
Math Faculty Publications and Presentations
Gaussian Radial Basis Function Kernels are the most-often-employed kernel function in artificial intelligence for providing the optimal results in contrast to their respective counterparts. However, our understanding surrounding the utilization of the Generalized Gaussian Radial Basis Function across different machine learning algorithms, such as kernel regression, support vector machines, and pattern recognition via neural networks is incomplete. The results delivered by the Generalized Gaussian Radial Basis Function Kernel in the previously mentioned applications remarkably outperforms those of the Gaussian Radial Basis Function Kernel, the Sigmoid function, and the ReLU function in terms of accuracy and misclassification. This article provides a …
Thermal Performance Of Forced Convection Of Water- Nepcm Nanofluid Over A Semi-Cylinder Heat Source,
2024
Missouri University of Science and Technology
Thermal Performance Of Forced Convection Of Water- Nepcm Nanofluid Over A Semi-Cylinder Heat Source, Xiaoming Wang, Rassol H. Rasheed, Babak Keivani, Dheyaa J. Jasim, Abbas J. Sultan, Sajad Hamedi, Hamed Kazemi-Varnamkhasti, Soheil Salahshour, Davood Toghraie
Mathematics and Statistics Faculty Research & Creative Works
1) Background: Phase change materials (PCMs) have been used statically, which has caused the use of these materials to face challenges. Encapsulating PCMs and combining them with the base fluid can significantly solve the problem of using PCMs in BTM systems. In the present study, based on computational fluid dynamics, forced convection heat transfer of nano-encapsulated phase change materials (NEPCM) in a BTM system are simulated. The main aim of the present research is to reduce the temperature at the surface of the hot cylinder. 2) Methods: In this research, we simulated lithium battery thermal management systems in both steady …
Why Pavement Cracks Are Mostly Longitudinal, Sometimes Transversal, And Rarely Of Other Directions: A Geometric Explanation,
2024
Universidad de Piura in Peru (UDEP)
Why Pavement Cracks Are Mostly Longitudinal, Sometimes Transversal, And Rarely Of Other Directions: A Geometric Explanation, Edgar Daniel Rodriguez Velasquez, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In time, pavements deteriorate, and need maintenance. One of the most typical pavement faults are cracks. Empirically, the most frequent cracks are longitudinal, i.e., following the direction of the road; less frequent are transversal cracks, which are orthogonal to the direction of the road. Sometimes, there are cracks in different directions, but such cracks are much rarer. In this paper, we show that simple geometric analysis and fundamental physical ideas can explain these observed relative frequencies.
Why Linear And Sigmoid Last Layers Work Better In Classification,
2024
Óbuda University
Why Linear And Sigmoid Last Layers Work Better In Classification, Lehel Dénes-Fazakas, Lásló Szilágyi, Vladik Kreinovich
Departmental Technical Reports (CS)
Usually, when a deep neural network is used to classify objects, its last layer computes the softmax. Our empirical results show we can improve the classification results if instead, we have linear or sigmoid last layer. In this paper, we provide an explanation for this empirical phenomenon.
Why Two Fish Follow Each Other But Three Fish Form A School: A Symmetry-Based Explanation,
2024
Azerbaijan State University of Economics
Why Two Fish Follow Each Other But Three Fish Form A School: A Symmetry-Based Explanation, Shahnaz Shahbazova, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Recent experiments with fish has shown an unexpected strange behavior: when two fish of the same species are placed in an aquarium, they start following each other, while when three fish are placed there, they form (approximately) an equilateral triangle, and move in the direction (approximately) orthogonal to this triangle. In this paper, we use natural symmetries -- such as rotations, shifts, and permutation of fish -- to show that this observed behavior is actually optimal. This behavior is not just optimal with respect to one specific optimality criterion, it is optimal with respect to any optimality criterion -- as …
