Recurrence Of Locally Perturbed Random Walks With Long Jumps,
2026
The University of Texas Rio Grande Valley
Recurrence Of Locally Perturbed Random Walks With Long Jumps, Tamer Oraby, András Telcs
School of Mathematical & Statistical Sciences Faculty Publications
We study the effect of local perturbations on the recurrence of random walks with long jumps. Such walks serve as discrete models for infinite-horizon Lorentz processes, in which a particle can take arbitrarily long steps in specific directions. Motivated by a question of Sinai in the finite-horizon case and its extension by Szász to the infinite-horizon setting, we give recurrence and transience criteria for long-jump walks on Z2 and certain classes of graphs, and we prove that local perturbations in a bounded region do not change the recurrence property. Our proofs combine the Markov chain approach with the electrical network …
Compilation Of A Nationwide River Image Dataset For Identifying River Channels And River Rapids Via Deep Learning,
2026
Utah State University
Compilation Of A Nationwide River Image Dataset For Identifying River Channels And River Rapids Via Deep Learning, Nicholas Brimhall, Kelvyn K. Bladen, Thomas Kerby, Carl J. Legleiter, Cameron Swapp, Hannah Fluckiger, Julie Bahr, Makenna Roberts, Kaden Hart, Christina L. Stegman, Brennan L. Bean, Kevin R. Moon
Mathematics and Statistics Student Research and Class Projects
Remote sensing enables large-scale, image-based assessments of river dynamics, offering new opportunities for hydrological monitoring. We present a publicly available dataset consisting of 281,024 satellite and aerial images of U.S. rivers, constructed using an Application Programming Interface (API) and the U.S. Geological Survey’s National Hydrography Dataset. The dataset includes images, primary keys, and ancillary geospatial information. We use a manually labeled subset of the images to train models for detecting rapids, defined as areas where high velocity and turbulence lead to a wavy, rough, or even broken water surface visible in the imagery. To demonstrate the utility of this dataset, …
Projective Corepresentations And Cohomology Of Compact Quantum Groups,
2026
Indian Statistical Institute
Projective Corepresentations And Cohomology Of Compact Quantum Groups, Kiran Maity
Doctoral Theses
In this thesis, we briefly review various types of projective corepresentations of compact quantum groups and prove the existence of suitable envelopes for them. We also study the associated invariant (dual) 2-cohomology and calculate it in a few concrete examples
High Frobenius Pushforwards Generate The Bounded Derived Category,
2026
University of South Carolina
High Frobenius Pushforwards Generate The Bounded Derived Category, Matthew R. Ballard, Srikanth B. Iyengar, Pat Lank, Alapan Mukhopadhyay, Josh Pollitz
Faculty Publications
This work concerns generators for the bounded derived category of coherent sheaves over a noetherian scheme X of prime characteristic. The main result is that when the Frobenius map on X is finite, for any compact generator G of D(X) the Frobenius pushforward Fe*G generates the bounded derived category whenever pe is larger than the codepth of X, an invariant that is a measure of the singularity of X. The conclusion holds for all positive integers e when X is locally complete intersection. The question of when one can take G = …
Does Sequence Matter? Impact Of Redesigning Sequential Calculus Course On Students’ Learning Outcomes,
2026
Purdue University
Does Sequence Matter? Impact Of Redesigning Sequential Calculus Course On Students’ Learning Outcomes, Chantal Levesque-Bristol Dr., Wonki Lee Dr., Emily M. Bonem, Benjamin C. Wiles, Jennifer D. Moss, Wilella D. Burgess, Weiling Li
International Journal of Teaching and Learning in Higher Education
As colleges and universities increasingly transform their STEM courses through the adoption of more active, student-centered pedagogies, there is a growing need to understand the impact of these educational innovations on student outcomes. This study is conducted in the context of a university-wide faculty development and course redesign project, IMPACT (Instruction Matters, Purdue Academic Course Transformation). IMPACT supports faculty in implementing student-centered pedagogical practices and creating equitable and inclusive learning environments. This study focuses on a sequence of two introductory calculus courses (Calculus 1 and Calculus 2, hereafter CALC 1 and CALC 2) that were transformed as part of the …
Arbitrage-Free Pricing With Diffusion-Dependent Jumps,
2026
Dept of Math., Hofstra University, Hempstead, NY 11549, USA
Arbitrage-Free Pricing With Diffusion-Dependent Jumps, Hamza A. Virk, Yihren Wu, Majnu John
Journal of Stochastic Analysis
Standard jump-diffusion models assume independence between jumps and diffusion components. We develop a multi-type jump-diffusion model where jump occurrence and magnitude depend on contemporaneous diffusion movements. Unlike previous one-sided models that create arbitrage opportunities, our framework includes upward and downward jumps triggered by both large upward and large downward diffusion increments. We derive the explicit no-arbitrage condition linking the physical drift to model pa- rameters and market risk premia by constructing an Equivalent Martingale Measure using Girsanov’s theorem and a normalized Esscher transform. This condition provides a rigorous foundation for arbitrage-free pricing in models with diffusion-dependent jumps.
Rogue Peakon, Posedness And Blow-Up Phenomenon For An Integrable Camassa–Holm Type Equation,
2026
The University of Texas Rio Grande Valley
Rogue Peakon, Posedness And Blow-Up Phenomenon For An Integrable Camassa–Holm Type Equation, Mingxuan Zhu, Zhenteng Zeng, Zaihong Jiang, Baoqiang Xia, Zhijun Qiao
School of Mathematical & Statistical Sciences Faculty Publications
In this paper, we study an integrable Camassa–Holm (CH) type equation with quadratic nonlinearity. The CH type equation is shown integrable through a Lax pair, and particularly the equation is found to possess a new kind of peaked soliton (peakon) solution – called rogue peakon, that is given in a rational form with some logarithmic function, but not a regular traveling wave. We also provide multi-rogue peakon solutions. Furthermore, we discuss the local well-posedness of the solution in the Besov space 𝐵𝑠𝑝,𝑟 with 1 ≤ p, r ≤ ∞, 𝑠 >max{1+1/𝑝,3/2} or 𝐵3/22,1 , and then prove the ill-posedness …
Nonresonance For Problems Involving (P, Q)-Laplacian Equations With Nonlinear Perturbations,
2026
Swarthmore College
Nonresonance For Problems Involving (P, Q)-Laplacian Equations With Nonlinear Perturbations, E. Lopera, Nsoki Mavinga, D. Sánchez
Mathematics & Statistics Faculty Works
We are concerned with the existence of solutions of (p, q)-Laplacian problems that include nonlinear perturbation terms in both the differential equations and the boundary. Using variational methods and critical point theory, we prove the existence of weak solutions for the nonlinear problem when the nonlinearities involved remain asymptotically below the infimum of the set of eigenvalues of the (p, q)-Laplacian problem with weights and a spectral parameter present in both the differential equation and the boundary. Additionally, we establish an existence result for the nonlinear problem when the nonlinearities involved remain asymptotically below …
Of Metaphors And Measurements: Cross-Disciplinary Learning In K-8 English Language Arts And Mathematics,
2026
Western Michigan University
Of Metaphors And Measurements: Cross-Disciplinary Learning In K-8 English Language Arts And Mathematics, Morgan Shiver, Janet Shiver
New Jersey English Journal
English Language Arts and mathematics may seem like an unlikely pair, but together, literature and math can foster meaningful cross-disciplinary learning. This article presents strategies for using literature in K-8 classrooms to meet both ELA and math standards, enhancing student engagement and comprehension.
ℤ3-Graded Cartan Calculus On 𝒪(ℂQ1|1|1),
2026
TÜBİTAK
ℤ3-Graded Cartan Calculus On 𝒪(ℂQ1|1|1), Sultan Çeli̇k, Sali̇h Çeli̇k
Turkish Journal of Mathematics
After a brief introduction of the basic concepts of ℤ3-grading, the paper continues by introducing ℤ3-graded differential calculus and ℤ3-graded Cartan calculus. Then, using a matrix R which is a solution of the Yang-Baxter equation, a new ℤ3-graded quantum group and a ℤ3-graded quantum space are introduced. The scheme of the ℤ3-graded differential calculus developed on the algebra of functions on this quantum space is extended to the ℤ3-graded Cartan calculus and all the results obtained are formulated using the matrix R.
G-Topological Groupoids,
2026
TÜBİTAK
G-Topological Groupoids, Osman Mucuk
Turkish Journal of Mathematics
In the groupoid theory, it is unclear that a topological groupoid's quotient groupoid with the quotient topology is topological. In this paper, we approach this problem considering G-methods and G-convergence. We define G-topological groupoid, which agrees with the sequential version of a topological groupoid in the particular case G=lim, and give some counterexamples. Then, we extend the usual properties of topological groupoids to the G-topological groupoids. We also prove that a G-topological groupoid's quotient groupoid is G-topological groupoid when a normal subgroupoid is suitably chosen. This result enables us to obtain examples of topological quotient groupoids in a particular case.
The Variation Of Eigenvalues Of The Two-Dimensional Magnetic Schrödinger Operator With Respect To The Angle Of A Flat Sector,
2026
TÜBİTAK
The Variation Of Eigenvalues Of The Two-Dimensional Magnetic Schrödinger Operator With Respect To The Angle Of A Flat Sector, Araz R. Aliev, Elshad H. Eyvazov
Turkish Journal of Mathematics
A two-dimensional Schrödinger operator with a spherically symmetric electric potential and an Aharonov Bohm magnetic field in a circular sector under Neumann boundary conditions is considered. The intervals of the angular variation of the flat region are found, where the eigenvalues of the Neumann problem for the Schrödinger operator with a spherically symmetric electric potential strictly decrease monotonically in the Aharonov-Bohm magnetic field.
Further Geometric Properties Of The Generalized K-Bessel Functions,
2026
TÜBİTAK
Further Geometric Properties Of The Generalized K-Bessel Functions, Merve Görgülü, İbrahi̇m Aktaş
Turkish Journal of Mathematics
This study investigates certain geometric properties of the normalized k-Bessel function, which is a natural generalization of classical and modified Bessel functions of the first kind. These geometric properties include η-starlikeness, η-uniform convexity, starlikeness associated with exponential function and Bernoulli’s lemniscate, and convexity associated with exponential function and Bernoulli’s lemniscate. Moreover, certain corollaries related to classical and modified Bessel functions are presented by specialising parameters. In addition, some examples and their graphical representations are provided to support the findings of this study.
Some Methods For Finding The Number Of Partitions Of N With M−Parts, P(N, M),
2026
Hakkari Üniversitesi
Some Methods For Finding The Number Of Partitions Of N With M−Parts, P(N, M), Yusuf Soyvural, Ali̇ Bülent Eki̇n
Turkish Journal of Mathematics
P(n, m) denotes the number of partitions of n with m parts, while Pm(n) denotes the number of partitions of n with parts at most m. It is a well-known result that the number of partitions of n ≥ 0 into m or fewer parts is equal to Pm(n). In the literature, there are some results for P(n, m) and Pm(n) for some values of m. In this work, we give more compact results for P(n …
On Almost Kenmotsu Manifolds Admitting Nearly Vacuum Static Equations With Applications,
2026
TÜBİTAK
On Almost Kenmotsu Manifolds Admitting Nearly Vacuum Static Equations With Applications, Uday Chand De, Krishnendu De, Sudhakar Kumar Chaubey
Turkish Journal of Mathematics
In this article, we study certain characteristics of nearly vacuum static equations on almost Kenmotsu manifolds. It is established that an η-Einstein almost Kenmotsu manifold allowing nearly vacuum static equations is of constant scalar curvature and either the solution is trivial or, the manifold reduces to an Einstein manifold. Next, nearly vacuum static equations on (κ,μ)-almost Kenmotsu manifolds and generalized (κ,μ)'-nullity distribution are considered and we obtain several interesting results. Moreover, we illustrate that if a 3-dimensional Kenmotsu manifold allows nearly vacuum static equations, then the manifold is locally isometric to the hyperbolic space Η3(-1). After that, we investigate a …
Cover And Contents,
2026
TÜBİTAK
Fubini Collocation Method For Numerical Solutions Of Differential Equations With Quadratic And Cubic Nonlinearities,
2026
Manisa Celal Bayar University
Fubini Collocation Method For Numerical Solutions Of Differential Equations With Quadratic And Cubic Nonlinearities, Kübra Erdem Bi̇çer, Havva Türkhan
Turkish Journal of Mathematics
In this study, the Fubini collocation method is proposed for the approximate solution of nonlinear differential equations. The method utilizes fundamental relations involving Fubini polynomials and their derivatives, employing collocation points to enhance solution accuracy. Within this framework, the given differential equation is transformed into a system of nonlinear algebraic equations involving the unknown coefficients of the approximate solution. This resulting system is then solved using appropriate numerical techniques to obtain the approximate solution. The effectiveness of the proposed method is demonstrated through several test problems, with accuracy evaluated using absolute error functions. Furthermore, illustrative examples and residual-based error analysis …
The Derivative Of Spectral Function Of The Problem With The Boundary Condition Dependent On Spectral Parameter,
2026
TÜBİTAK
The Derivative Of Spectral Function Of The Problem With The Boundary Condition Dependent On Spectral Parameter, Eli̇f Başkaya, Haskiz Coşkun
Turkish Journal of Mathematics
In this study, the computation of the derivative of the spectral function for Sturm-Liouville problem with eigenvalue dependent boundary condition at the finite left end is considered.
Representation Of Inverse Ordered Semigroups By Means Of Symmetric Inverse Semigroups On A Set,
2026
TÜBİTAK
Representation Of Inverse Ordered Semigroups By Means Of Symmetric Inverse Semigroups On A Set, Michael Tsingelis
Turkish Journal of Mathematics
A partial one-to-one mapping on a set X is a mapping whose domain is a subset of X. The set of partial one-one mappings on a set X is an inverse semigroup (the symmetric inverse semigroup on X). An element x of an ordered semigroup (S, ·, ≤) is called an inverse element of α ∈ S if α ≤ xαx and x ≤ xαx. An inverse ordered semigroup is an ordered semigroup S for which every element of S possesses an inverse element and the inverse elements of any element of S are in …
Cospectrality Results For Signed Graphs With Two Eigenvalues Unequal To ±1,
2026
Tilburg University
Cospectrality Results For Signed Graphs With Two Eigenvalues Unequal To ±1, Willem H. Haemers, Hati̇ce Topcu
Turkish Journal of Mathematics
Recently the collection G of all signed graphs for which the adjacency matrix has all but at most two eigenvalues equal to ±1 has been determined. Here we investigate G for cospectral pairs, and for signed graphs determined by their spectrum (up to switching). If the order is at most 20, the outcome is presented in a clear table. If the spectrum is symmetric we find all signed graphs in G determined by their spectrum, and we obtain all signed graphs cospectral with the bipartite double of the complete graph. In addition we determine all signed graphs cospectral with the …
