Nonoscillatory Solutions Of Third-Order Nonlinear Dynamic Equations: Existence And Nonexistence,
2025
Missouri University of Science and Technology
Nonoscillatory Solutions Of Third-Order Nonlinear Dynamic Equations: Existence And Nonexistence, Özkan Öztürk, Elvan Akin, Nesli̇han Nesli̇ye Pelen
Turkish Journal of Mathematics
This paper investigates a third-order nonlinear dynamic equation on arbitrary time scales, a nonempty closed subset of the real numbers, unifying continuous and discrete analyses. We study the qualitative behavior of nonoscillatory solutions and their quasi-derivatives, focusing on their limiting behaviors. The existence of such solutions are established using improper integral criteria and Schauder’s and Knaster’s fixed point theorems. In addition, we establish the criteria for the nonexistence of nonoscillatory solutions. Furthermore, we prove the existence of Kneser-type solutions of the corresponding linear dynamic equation on isolated time scales, addressing an open problem in the literature. Several examples of theoretical …
Structural Stability For Damped Nonlinear Wave Equations,
2025
TÜBİTAK
Structural Stability For Damped Nonlinear Wave Equations, Sevda Isayeva, Varga Kalantarov
Turkish Journal of Mathematics
We study the problem of continuous dependence on parameters for solutions to initial-boundary value problems for nonlinear strongly damped wave equations. Specifically, we consider three classes of equations: a strongly damped wave equation with a nonlinear damping term; a strongly damped wave equation incorporating both a nonlinear damping term and a nonlinear source term; and a strongly damped wave equation with a nonlinear source term and a linear weak damping term. For each class, we establish structural stability results, showing that the solutions depend continuously on the relevant parameters.
The Action Of The Superposition Operator On Weighted Banach Sequence Spaces LP,Σ,
2025
TÜBİTAK
The Action Of The Superposition Operator On Weighted Banach Sequence Spaces LP,Σ, Nermin Okičić, Fehim Dedagić
Turkish Journal of Mathematics
We consider a nonlinear superposition operator on weighted Banach spaces lp,σ, where σ is the weighted function with the property that (∀n ∈ ℕ) σ(n) ≥ 1. We present the necessary and sufficient conditions for the action of the superposition operator from lp,σ to lq,τ, 1 ≤ p, q ≤ ∞, as well as the L-characteristic of the action of the considered operator.
The Geometry Of Semislant Submersions Whose Total Manifolds Are Locally Conformal Kähler Manifolds,
2025
TÜBİTAK
The Geometry Of Semislant Submersions Whose Total Manifolds Are Locally Conformal Kähler Manifolds, Çağrihan Çi̇men, Hakan Mete Taştan
Turkish Journal of Mathematics
We study semislant submersions whose total manifolds are locally conformal Kähler manifolds. We provide conditions for the total geodesicity and integrability of the distributions involved in the definition. Next, we establish a condition under which such a submersion is a Clairaut submersion. Finally, we obtain some optimal inequalities for a semislant submersion whose total manifold is Hopf space form.
The Generalization Of Rectifying Helices,
2025
Ahi Evran University
The Generalization Of Rectifying Helices, Bülent Altunkaya
Turkish Journal of Mathematics
This work establishes connections between different classes of arbitrary speed rectifying helices. We further analyze how the involute of a space curve can exhibit spherical helicity and how the evolute can inherit rectifying properties, thereby providing an alternative characterization of these helices. These relationships, along with their interplay with involutes and evolutes, are supported by illustrative examples that offer deeper insights into their geometric properties.
Room-Temperature Alignment-Free Magnetometry With Boron Vacancies In Hot-Pressed Hexagonal Boron Nitride,
2025
Nova Southeastern University
Room-Temperature Alignment-Free Magnetometry With Boron Vacancies In Hot-Pressed Hexagonal Boron Nitride, Raul Coto Cabrera
Mathematics Colloquium Series
Magnetic field sensing is essential for applications in communication, environmental monitoring, and biomedical diagnostics. Quantum magnetic field sensors based on solid-state spin defects, such as NV centers in diamond, typically require precise alignment between the external magnetic field and the defect’s spin quantization axis to achieve reliable and directional sensing. This alignment constraint imposes challenges for device integration, especially in scalable or fielddeployable applications. Here, we demonstrate room-temperature optically detected magnetic resonance (ODMR) from negatively charged boron vacancies (VB-) in commercially available hot-pressed polycrystalline hexagonal boron nitride (hBN). Owing to the random orientation of grains in the material, the system …
Solitary Waves For Power Degenerate Non Linear Schro ̈Dinger Equation And Fourth Order Wave Equation.,
2025
University of Alabama at Birmingham
Solitary Waves For Power Degenerate Non Linear Schro ̈Dinger Equation And Fourth Order Wave Equation., Vishnu Iyer
All ETDs from UAB
In this dissertation we prove the existence and stability of solitary waves for the power degenerate non linear Schr ̈odinger equation (2.1.1) and a fourth order wave equation (3.1.1). Construction of the waves are variational in nature. For the NLS we consider a semilinear Schr ̈odinger equation, driven by the power degenerate second order differential operator ∇ · (|x|2a∇), a ∈ (0, 1). We construct the solitary waves, in the sharp range of parameters, as minimizers of the Caffarelli- Kohn-Nirenberg’s inequality. Depending on the parameter a and the nonlinearity, we establish a number of properties, such as positivity, smoothness (away …
Calibrating A Holling-Tanner Model With Applications To S&P500 Forecasting,
2025
University of Alabama at Birmingham
Calibrating A Holling-Tanner Model With Applications To S&P500 Forecasting, Jonathon Knowles
All ETDs from UAB
The primary goal of this thesis is to improve upon existing dynamical system models in economics. Existing models utilizing Lotka-Volterra dynamics display a tendency to suffer from unrealistic forecasts dominated by exponential growth and decay. Additionally, current inverse methods are only applicable in differential equation systems with linear coefficients. In this body of work, we propose novel methods for handling these challenges.
Analytical And Numerical Approaches To Parameter Estimation In Damped Oscillatory Systems,
2025
University of Tennessee at Chattanooga
Analytical And Numerical Approaches To Parameter Estimation In Damped Oscillatory Systems, Gracie Crooks, F. Ayça Çetinkaya
CODEE Journal
We investigate the inverse problem of identifying damping and stiffness parameters in one-dimensional damped oscillatory systems governed by second-order differential equations. Focusing on mass–spring–damper models, we analyze the qualitative behavior of solutions across underdamped, critically damped, and overdamped regimes, and derive explicit conditions for parameter recovery based on time-domain observations such as equilibrium crossings and turnaround points. Two numerical estimation methods are developed and compared: a finite-difference least-squares approach based on central difference approximations, and a finite element formulation derived from a variational framework using piecewise linear basis functions. Computational experiments using synthetic data assess the accuracy, stability, and noise …
How Euler Could Have Done It: Euler And A Direct Proof For The Functional Equation For The Riemann Zeta-Function,
2025
Johannes Gutenberg Universitat, Mainz
How Euler Could Have Done It: Euler And A Direct Proof For The Functional Equation For The Riemann Zeta-Function, Alexander Aycock
Euleriana
We present a chain of argumentation for a direct proof of the functional equation for the Riemann ζ–function that Euler could have presented.
Euler’S Original Derivation Of Elastica Equation,
2025
Kanazawa University
Euler’S Original Derivation Of Elastica Equation, Shigeki Matsutani
Euleriana
Euler derived the differential equations of elastica by the variational method in 1744, but his original derivation has never been properly interpreted or explained in terms of modern mathematics. We elaborate Euler's original derivation of elastica and show that Euler used Noether's theorem concerning the translational symmetry of elastica, although Noether published her theorem in 1918. It is also shown that his equation is essentially the static modified KdV equation which is obtained by the isometric and isoenergy conditions, known as the Goldstein-Petrich scheme.
Early Theories On Fluid Resistance And Translation Of Euler’S “Dilucidationes De Resistentia Fluidorum”,
2025
Independent Researcher
Early Theories On Fluid Resistance And Translation Of Euler’S “Dilucidationes De Resistentia Fluidorum”, Sylvio R. Bistafa
Euleriana
In 1763, Euler published Dilucidationes de resistentia fluidorum (Explanations on the resistance of fluids), a memoir that challenges the fluid resistance theories proposed by Isaac Newton and d’Alembert. Euler's work explores the resistance experienced by solid bodies moving through fluids, critiquing both Newton's "common rule" and d’Alembert's paradox, which predicted zero resistance for non-viscous fluids. Euler's treatise is divided into two parts: the first focuses on the mathematical modeling of fluid flow patterns, while the second addresses the calculation of fluid resistance on surfaces. Despite significant advancements, Euler's work remains constrained by the limitations of non-viscous fluid assumptions, ultimately grappling …
Assistance For The Calculation Of Sines (Translation Of E246),
2025
Stanford University OHS
Assistance For The Calculation Of Sines (Translation Of E246), Julian Schennach
Euleriana
Paralleling his famous relation eiφ = cos(φ) + i sin(φ), Euler establishes the equality (cos φ + i sin φ)n = (cos nφ + i sin nφ). He uses it to comprehensively derive trigonometric identities that convert arbitrary powers of sines and cosines of an angle (and products thereof) into sums of sines and cosines of multiples of that angle. Some negative and fractional powers are shown to yield infinite series. Euler further describes a general method to evaluate various infinite series involving weighted trigonometric functions. These results foreshadow Fourier series. As Euler points out, the scope of …
On Amicable Numbers,
2025
Lancaster University
On Amicable Numbers, Jonathan David Evans
Euleriana
This is an English translation of Euler's 1750 paper "De numeris amicabilibus" (E152), the most substantial of his three works with this name. In it, he expounds at great length the ad hoc methods he has developed to search for pairs of amicable numbers, concluding with a list of around 60 new pairs.
A Reader's Guide To Daniel Bernoulli's "Recurrent Series",
2025
University of San Diego
A Reader's Guide To Daniel Bernoulli's "Recurrent Series", Stacy Langton
Euleriana
This is a commentary and reader’s guide to Daniel Bernoulli’s article “Observations concerning recurrent series”. It is intended to help the modern reader understand what Bernoulli is doing in that article.
Daniel Bernoulli's "Observations Concerning Recurrent Series",
2025
University of San Diego
Daniel Bernoulli's "Observations Concerning Recurrent Series", Stacy Langton
Euleriana
Daniel Bernoulli’s article "Observations concerning Recurrrent Series" is one of the gems of the mathematical literature. It describes a numerical method for solving polynomial equations. This method, now known as “Bernoulli’s method”, is still in use today. The basis of the method is the study of certain sequences of numbers that satisfy what we now call linear recurrence relations. Bernoulli’s article shows how to find solutions of these recurrence relations. A nice application is a now well-known formula for the Fibonacci numbers. Bernoulli also uses his theory of recurrence relations to give a proof of an early form of De …
Comprehensive Conversations,
2025
University of the Pacific
Comprehensive Conversations, Christopher Goff, Erik Tou
Euleriana
An introduction to the contents in Volume 5 (Issue 1) of Euleriana.
Generalized Transversality Conditions For Fuzzy Quantum-Symmetric Variational Problems Via Granular Approach,
2025
Missouri University of Science and Technology
Generalized Transversality Conditions For Fuzzy Quantum-Symmetric Variational Problems Via Granular Approach, Martin Bohner, Ewa Girejko, Agnieszka B. Malinowska, Linh Nguyen, Baruch Schneider, Tri Truong
Mathematics and Statistics Faculty Research & Creative Works
This paper investigates fuzzy q-symmetric variational problems with natural boundary conditions. Based on the relative distance measure fuzzy arithmetic and horizontal membership functions (HMFs), we propose novel concepts of differentiability and integrability for fuzzy functions on quantum geometric subsets of real numbers. Then, fundamental foundations of q-symmetric calculus of variations based on HMFs are provided. With the help of HMFs and granular q-symmetric differentiability, we derive necessary optimality conditions for fuzzy q-symmetric variational problems that depend on free endpoints. Moreover, sufficient conditions for minimizers of q-symmetric variational problems are obtained. Some numerical examples illustrating the proposed approach are presented.
Novel Statistical And Topological Data Analyses Of 2d Electronic Images,
2025
Missouri University of Science and Technology
Novel Statistical And Topological Data Analyses Of 2d Electronic Images, Robert L. Paige, Vic Patrangenaru
Mathematics and Statistics Faculty Research & Creative Works
In this paper, novel statistical and topological data analyses of 2D images are developed. One considers methodologies based on the Region Covariance Descriptor (RCD) and Topological Data Analysis (TDA) rooted in the simplicial as well as cubical persistent homologies. These methods provide statistical methods for data from populations of complex data objects that are elements of non-Euclidean spaces. The 2D image data considered consist of pictures of two leaves—A and B—from the same tree, twenty of each leaf, from different perspectives. The novel statistical procedures developed are used for correctly determining that leaf A images and leaf B images are …
Strong External Difference Families And Classification Of Α-Valuations,
2025
Michigan Technological University
Strong External Difference Families And Classification Of Α-Valuations, Donald L. Kreher, Maura B. Paterson, Douglas R. Stinson
Michigan Tech Publications
One method of constructing (Formula presented.) -SEDFs (i.e., strong external difference families) in (Formula presented.) makes use of (Formula presented.) -valuations of complete bipartite graphs (Formula presented.). We explore this approach and we provide a classification theorem which shows that all such (Formula presented.) -valuations can be constructed recursively via a sequence of “blow-up” operations. We also enumerate all (Formula presented.) -SEDFs in (Formula presented.) for (Formula presented.) and we show that all these SEDFs are equivalent to (Formula presented.) -valuations via affine transformations. Whether this holds for all (Formula presented.) as well is an interesting open problem. We also …
