Tootfinder

An explicit computational approach for a three-dimensional system of nonlinear elastodynamic sine-Gordon problem
Eric Ngondiep
https://arxiv.org/abs/2506.14807

An explicit computational approach for a three-dimensional system of nonlinear elastodynamic sine-Gordon problem
This paper proposes an explicit computational method for solving a three-dimensional system of nonlinear elastodynamic sine-Gordon equations subject to appropriate initial and boundary conditions. The time derivative is approximated by interpolation technique whereas the finite element approach is used to approximate the space derivatives. The developed numerical scheme is so-called, high-order explicit computational technique. The new algorithm efficiently treats the time derivative term and p…

On the Robustness of Derivative-free Methods for Linear Quadratic Regulator
Weijian Li, Panagiotis Kounatidis, Zhong-Ping Jiang, Andreas A. Malikopoulos
https://arxiv.org/abs/2506.12596

On the Robustness of Derivative-free Methods for Linear Quadratic Regulator
Policy optimization has drawn increasing attention in reinforcement learning, particularly in the context of derivative-free methods for linear quadratic regulator (LQR) problems with unknown dynamics. This paper focuses on characterizing the robustness of derivative-free methods for solving an infinite-horizon LQR problem. To be specific, we estimate policy gradients by cost values, and study the effect of perturbations on the estimations, where the perturbations may arise from function approx…

On nth Level Fractional Derivatives: An Equivalent Representation and Applications to Inverse Problem
Asim Ilyas, Salman A. Malik, Kamran Suhaib
https://arxiv.org/abs/2506.12614

On nth Level Fractional Derivatives: An Equivalent Representation and Applications to Inverse Problem
This work contributes to the theory of nth level fractional derivative, where $n$ is a positive integer. An equivalent representation of 2nd level fractional derivative in terms of Riemann-Liouville fractional derivative is presented. We generalized our result and provide representation of nth level fractional derivative. As an application, we solve an inverse problem defined for a diffusion equation involving 2nd level fractional derivative.

A survey of Chernoff and Hoeffding bounds
Alexandros V. Gerbessiotis
https://arxiv.org/abs/2506.15612 https://arxiv.org/pdf/2506.1561…

A survey of Chernoff and Hoeffding bounds
This is a survey paper that discusses the original bounds of the seminal papers by Chernoff and Hoeffding. Moreover, it includes a variety of derivative bounds in a variety of forms. Complete proofs are provided as needed. The intent is to provide a repository of reference bounds for the interested researcher.

The fundamental theorem of the local theory for non-smooth curves
Domenico Mucci, Alberto Saracco
https://arxiv.org/abs/2506.12564 https://

The fundamental theorem of the local theory for non-smooth curves
We extend the classical fundamental theorem of the local theory of smooth curves to a wider class of non-smooth data. Curvature and torsion are prescribed in terms of the distributional derivative measures of two given functions of bounded variation. The essentially unique non-smooth curve solution has both finite total curvature and total absolute torsion. In case of continuous data, we preliminarly discuss a more general problem involving a linear system of distributional derivative equations.

Tensor perturbations in higher derivative gravity theories in $D$ dimensions
Ercan Kilicarslan
https://arxiv.org/abs/2506.10563 https://

Tensor perturbations in higher derivative gravity theories in $D$ dimensions
We study tensor perturbations of the ghost-free generic non-local gravity theory constructed infinite series of higher derivative terms in $D$ dimensions. The infinite series of higher derivative terms are encoded by form factors, the forms of which can be restricted by requiring that the action remains perturbatively free of ghosts and tachyons around maximally symmetric backgrounds for transverse traceless fluctuations. To demonstrate this, we obtain field equations for AdS plane wave metric …

Seeking a quadratic refinement of Sendov's conjecture
Michael J. Miller
https://arxiv.org/abs/2506.12951 https://arxiv.org/pdf/25…

Seeking a quadratic refinement of Sendov's conjecture
A conjecture of Sendov states that if a polynomial has all its roots in the unit disk and if $β$ is one of those roots, then within one unit of $β$ lies a root of the polynomial's derivative. If we define $r(β)$ to be the greatest possible distance between $β$ and the closest root of the derivative, then Sendov's conjecture claims that $r(β) \le 1$. In this paper, we conjecture that there is a constant $c>0$ so that $r(β) \le 1-cβ(1-β)$ for all $β\in [0,1]$. We find such constants fo…

A shape optimisation of mutual inductances among coils
Toru Takahashi, Tatsuya Tokito, Yi Cui, Toshiro Matsumoto
https://arxiv.org/abs/2506.14085 https://

A shape optimisation of mutual inductances among coils
This paper introduces a shape optimisation framework for achieving desired mutual inductances (MIs) among coils in 3D space. Utilising a wire modelling approach, the coils are discretised using B-spline curves, with control points (CPs) serving as design variables. The key contribution is the derivation of the shape derivative of the objective function in terms of MIs, enabling the use of gradient-based quasi-Newton optimisation methods. A coil length constraint is also incorporated. The study …

Henry Clay Frick was a union buster

In 1892, he hired hundreds of Pinkerton detectives
— a private army of thugs with guns
— to quell a strike against a Pennsylvania steel mill.
Ten men were killed, dozens injured, and the situation became so inflamed that the state militia was called in to break the workers’ resistance.
Frick, who made a fortune supplying the coal derivative known as coke
to Andrew Carnegie’s steel company, where Frick later served…

At the Frick, a grand Gilded Age collection shows its intimate side
A five-year, $220-million expansions has transformed the Frick, without changing anything fundamental to the experience.

Fractional order derivative approach of viscoelastic behavior of tropical wood
Loic Chrislin Nguedjio (IP), Rostand Moutou Pitti (CENAREST, IP), Benoit Blaysat (IP), Pierre Kisito Talla (IP), Nicolas Sauvat (IP), Joseph Gril (IP)
https://arxiv.org/abs/2506.13208

Fractional order derivative approach of viscoelastic behavior of tropical wood
For some time now, wood has offered itself as an alternative to other modern construction materials, and has become the material of choice for structures, mainly because of its renewable nature, durability and ease of shaping. However, once in service, even at room temperature and under low stresses, it deforms and faces the problems of creep and recovery. The aims of this work is to model and predict the viscoelastic deformations of tropical wood by a rheological approach based on fractional c…

Structural Characterizations of Marginal Policy Effects
Zhixin Wang, Yu Zhang, Zhengyu Zhang
https://arxiv.org/abs/2506.11694 https://

Structural Characterizations of Marginal Policy Effects
This paper investigates the structural interpretation of the marginal policy effect (MPE) within nonseparable models. We demonstrate that, for a smooth functional of the outcome distribution, the MPE equals its functional derivative evaluated at the outcome-conditioned weighted average structural derivative. This equivalence is definitional rather than identification-based. Building on this theoretical result, we propose an alternative identification strategy for the MPE that complements existi…

Detecting local topology with the spectral localizer
Alexander Cerjan, Hermann Schulz-Baldes
https://arxiv.org/abs/2506.14174 https://

Detecting local topology with the spectral localizer
The spectral localizer is a predictive framework for the computation of topological invariants of natural and artificial materials. Here, three crucial improvements on the criterion for the validity of the framework are reported: first, merely a properly defined local spectral gap of the Hamiltonian is required, second, only relative bounds on the Hamiltonian and its noncommutative derivative are relevant, and, third, the numerical constant in a tapering estimate is improved. These developments…

Legendre-Gauss-Lobatto Collocation Method for Optimal Control via Polynomial Approximations of Differential Equation Vector Fields
Gabriela Abadia-Doyle, William W. Hager, Anil V. Rao
https://arxiv.org/abs/2506.13938

Legendre-Gauss-Lobatto Collocation Method for Optimal Control via Polynomial Approximations of Differential Equation Vector Fields
A new method is described for solving optimal control problems using direct collocation at Legendre-Gauss-Lobatto points. The approach of this paper employs a polynomial approximation of the right-hand side vector field of the differential equations and leads to the following important outcomes. First, the first-order optimality conditions of the LGL integral form are derived, which lead to a full-rank transformed adjoint system and novel costate estimate. Next, a derivative-like form of the LG…

This https://arxiv.org/abs/2402.02793 has been replaced.
link: https://scholar.google.com/scholar?q=a

On the shape derivative of polygonal inclusions in the conductivity problem
We consider the conductivity problem for a homogeneous body with an inclusion of a different, but known, conductivity. Our interest concerns the associated shape derivative, i.e., the derivative of the corresponding electrostatic potential with respect to the shape of the inclusion. For a smooth inclusion it is known that the shape derivative is the solution of a specific inhomogeneous transmission problem. We show that this characterization of the shape derivative is also valid when the inclus…

This https://arxiv.org/abs/2503.06005 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

Remarks on nonperturbative perturbations
We consider the linearized perturbations of near-horizon extremal Reissner-Nordström black holes in $d$-dimensional Einstein-Maxwell-Gauss-Bonnet gravity and seven-dimensional third-order Lovelock gravity. We find the solutions for the gravitational perturbations as a function of the higher-derivative coupling coefficients, which we treat nonperturbatively. Consequently, we observe a breakdown in perturbation theory for large harmonics for the six-derivative corrections.

Failure of the Flat Chain Conjecture and non-regularity of the prescribed Jacobian equation
Jakub Tak\'a\v{c}
https://arxiv.org/abs/2506.13718 https://…

Failure of the Flat Chain Conjecture and non-regularity of the prescribed Jacobian equation
We show that the Flat Chain Conjecture in Lang's formulation (that is, without requiring finite mass of the underlying currents) fails for metric $k$-currents in $\mathbb{R}^d$ whenever $d\geq 2$ and $k\in\{1, \dots, d\}$. In all other cases, it holds. We first connect the conjecture to a regularity statement concerning the prescribed Jacobian equation near $L^\infty$. We then show that the equation does not have the required regularity. For a Lipschitz vector field $π$, its derivative $\mathr…

On slice regular fractal-fractional Dirichlet type spaces
Jos\'e Oscar Gonz\'alez-Cervantes, Carlos Alejandro Moreno-Mu\~noz, Juan Bory-Reyes
https://arxiv.org/abs/2506.14172

On slice regular fractal-fractional Dirichlet type spaces
In this paper, we study some families of right modules of quaternionic slice regular functions induced by a generalized fractal-fractional derivative with respect to a truncated quaternionic exponential function on slices. Important Banach spaces of slice regular functions, namely the Bergman and the Dirichlet modules, are two important elements of one of our families.

This https://arxiv.org/abs/2504.19466 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

The partial derivative of ratios of Schur polynomials and applications to symplectic quotients
We show that a ratio of Schur polynomials $s_λ/s_ρ$ associated to partitions $λ$ and $ρ$ such $λ\subsetneqρ$ has a negative partial derivative at any point where all variables are positive. This is accomplished by establishing an injective map between sets of pairs of skew semistandard Young tableaux that preserves the product of the corresponding monomials. We use this result and the description of the first Laurent coefficient of the Hilbert series of the graded algebra of regular funct…

The stochastic heat inclusion with fractional time driven by time-space Brownian and L\'evy white noise
Olfa Draouil, Rahma Yasmina Moulay Hachemi, Bernt {\O}ksendal
https://arxiv.org/abs/2506.08275

The stochastic heat inclusion with fractional time driven by time-space Brownian and Lévy white noise
We study a time-fractional stochastic heat inclusion driven by additive time-space Brownian and Lévy white noise. The fractional time derivative is interpreted as the Caputo derivative of order $α\in (0,2).$ We show the following: \\ a) If a solution exists, then it is a fixed point of a specific set-valued map.\\ b) Conversely, any fixed point of this map is a solution of the heat inclusion.\\ c) Finally, we show that there is at least one fixed point of this map, thereby proving that there …

Pointwise-in-time error bounds for semilinear and quasilinear fractional subdiffusion equations on graded meshes
Natalia Kopteva, Sean Kelly
https://arxiv.org/abs/2506.12954

Pointwise-in-time error bounds for semilinear and quasilinear fractional subdiffusion equations on graded meshes
Time-fractional semilinear and quasilinear parabolic equations with a Caputo time derivative of order $α\in(0,1)$ are considered, solutions of which exhibit a singular behaviour at an initial time of type $t^σ$ for any fixed $σ\in (0,1) \cup (1,2)$. The L1 scheme in time is combined with a general class of discretizations for the semilinear term. For such discretizations, we obtain sharp pointwise-in-time error bounds on graded temporal meshes with arbitrary degree of grading. Both semi-disc…

AI4Contracts: LLM & RAG-Powered Encoding of Financial Derivative Contracts
Maruf Ahmed Mridul, Ian Sloyan, Aparna Gupta, Oshani Seneviratne
https://arxiv.org/abs/2506.01063

AI4Contracts: LLM & RAG-Powered Encoding of Financial Derivative Contracts
Large Language Models (LLMs) and Retrieval-Augmented Generation (RAG) are reshaping how AI systems extract and organize information from unstructured text. A key challenge is designing AI methods that can incrementally extract, structure, and validate information while preserving hierarchical and contextual relationships. We introduce CDMizer, a template-driven, LLM, and RAG-based framework for structured text transformation. By leveraging depth-based retrieval and hierarchical generation, CDMi…

Prym varieties and projective structures on Riemann surfaces
Indranil Biswas, Alessandro Ghigi, Luca Vai
https://arxiv.org/abs/2506.02871 https://

Prym varieties and projective structures on Riemann surfaces
Given an étale double covering $π\, :\, \widetilde{C}\, \longrightarrow\, C$ of compact Riemannsurfaces with $C$ of genus at least two, we use the Prym variety of the cover to construct canonical projective structures on both $\widetilde C$ and $C$. This construction can be interpreted as a section of an affine bundle over the moduli space of étale double covers. The $\overline{\partial}$--derivative of this section is a (1,1)--form on the moduli space. We compute this derivative in terms of…

Isoperimetric Problem and Weierstrass Necessary Condition for Fractional Calculus of Variations
Shakir Sh. Yusubov, Shikhi Sh. Yusubov, Elimhan N. Mahmudov
https://arxiv.org/abs/2506.12926

Isoperimetric Problem and Weierstrass Necessary Condition for Fractional Calculus of Variations
Summary]{In this paper, we study problems of minimization of a functional depending on the fractional Caputo derivative of order $0<α\leq 1$ and the fractional Riemann- Liouville integral of order $β> 0$ at fixed endpoints. A fractional analogue of the Du Bois-Reymond lemma is proved, and the Euler-Lagrange conditions are proved for the simplest problem of fractional variational calculus with fixed ends and for the fractional isoperimetric problem. An approach is proposed to obtain the necess…

On fractional differential equations, dimensional analysis, and the double gamma function
J. Vaz, E. Capelas de Oliveira
https://arxiv.org/abs/2506.00026 h…

On fractional differential equations, dimensional analysis, and the double gamma function
In this paper we discuss some issues that arise in the process of writing a fractional differential equation (FDE) by replacing an integer order derivative by a fractional order derivative in a given differential equation. To address these issues, we propose a dimensional regularization of the Caputo fractional derivative, ensuring consistency in physical dimensions. Then we solve some FDEs using this proposed dimensional regularization. We show that the solutions of these FDEs are most conveni…

I really disliked Star Wars E8 #TheLastJedi. I thought it wasn't just offensive to established canon of decades of #StarWars, it was obnoxiously derivative & just laden with bad storytelling.
I mean, when one's suspension of disbelief is repeatedly broken, that's a seriou…

This https://arxiv.org/abs/2505.22707 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_hept…

The non-relastivistic limit of HSZ Theory
We study the non-relativistic (NR) limit of HSZ theory, a higher-derivative theory of gravity with exact and manifest T-duality invariance. Since the theory can be formulated using the generalized metric formalism, the HSZ Lagrangian remains convergent to all orders in derivatives when taking the NR limit. In this work, we analyze the three-derivative corrections to the symmetry transformations of the fields in the NR case, as well as the four-derivative action in the absence of a b-field. Inte…

Expansion of a bivariate symmetric mean in the neighborhood of the first bisector
Bakir Farhi
https://arxiv.org/abs/2506.07601 https://

Expansion of a bivariate symmetric mean in the neighborhood of the first bisector
In this paper, we investigate the behavior of a bivariate mean $M$ near the first bisector by establishing, in several significant cases, an important expansion of $M$ derived from the Taylor expansion of a single-variable function. These expansions are made explicit for a number of classical means. This motivates the introduction of the concept of the characteristic function $Q_M$ of a mean $M$, defined as the second partial derivative of $M$ with respect to its first variable, evaluated along…

Fast Derivative Valuation from Volatility Surfaces using Machine Learning
Lijie Ding, Egang Lu, Kin Cheung
https://arxiv.org/abs/2505.22957 https://…

Fast Derivative Valuation from Volatility Surfaces using Machine Learning
We introduce a fast and flexible Machine Learning (ML) framework for pricing derivative products whose valuation depends on volatility surfaces. By parameterizing volatility surfaces with the 5-parameter stochastic volatility inspired (SVI) model augmented by a one-factor term structure adjustment, we first generate numerous volatility surfaces over realistic ranges for these parameters. From these synthetic market scenarios, we then compute high-accuracy valuations using conventional methodolo…

Swapped the nVidia RTX 4070Ti with a nice, regular-sized AMD Radeon 9070 XT. Everything is running perfectly though I did have to reinstall Linux because I couldn't undo the futzing I did to clear up a few issues with Wayland with the 4070Ti. Not a huge deal, but still annoying. However, everything is fine and now just enjoying some gaming.
#linux

This https://arxiv.org/abs/2409.08469 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Improved Finite-Particle Convergence Rates for Stein Variational Gradient Descent
We provide finite-particle convergence rates for the Stein Variational Gradient Descent (SVGD) algorithm in the Kernelized Stein Discrepancy ($\mathsf{KSD}$) and Wasserstein-2 metrics. Our key insight is that the time derivative of the relative entropy between the joint density of $N$ particle locations and the $N$-fold product target measure, starting from a regular initial distribution, splits into a dominant `negative part' proportional to $N$ times the expected $\mathsf{KSD}^2$ and a smalle…

This https://arxiv.org/abs/2411.16666 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_sta…

CatNet: Controlling the False Discovery Rate in LSTM with SHAP Feature Importance and Gaussian Mirrors
We introduce CatNet, an algorithm that effectively controls False Discovery Rate (FDR) and selects significant features in LSTM. CatNet employs the derivative of SHAP values to quantify the feature importance, and constructs a vector-formed mirror statistic for FDR control with the Gaussian Mirror algorithm. To avoid instability due to nonlinear or temporal correlations among features, we also propose a new kernel-based independence measure. CatNet performs robustly on different model settings …

Second-Order Linear Relaxation Schemes for Time-Fractional Phase-Field Models
Hui Yu, Zhaoyang Wang, Ping Lin
https://arxiv.org/abs/2506.11817 https://

Second-Order Linear Relaxation Schemes for Time-Fractional Phase-Field Models
This work uses a linear relaxation method to develop efficient numerical schemes for the time-fractional Allen-Cahn and Cahn-Hilliard equations. The L1+-CN formula is used to discretize the fractional derivative, and an auxiliary variable is introduced to approximate the nonlinear term by solving an algebraic equation rather than a differential equation as in the invariant energy quadratization (IEQ) and scalar auxiliary variable (SAV) approaches. The proposed semi-discrete scheme is linear, se…

The Fourier transform in variable exponent Lebesgue spaces
Andr\'e Pedroso Kowacs, Wagner Augusto Almeida de Moraes
https://arxiv.org/abs/2506.08891 ht…

The Fourier transform in variable exponent Lebesgue spaces
In this work we define a Fourier transform for each $f\in L^{p(\cdot)}(\mathbb{R})$, for a large class of exponent functions $p(\cdot)$, as the distributional derivative of a Hölder continuous function. A norm is defined in the space of such Fourier transforms so that it is isometrically isomorphic to $L^{p(\cdot)}(\mathbb{R})$. We also prove several properties of this Fourier transform, such as inversion in norm and an exchange theorem.

Source Identification Problem for a Nonlinear Subdiffusion Equation
R. R. Ashurov, O. T. Mukhiddinova
https://arxiv.org/abs/2506.11519 https://

Source Identification Problem for a Nonlinear Subdiffusion Equation
The work is devoted to the study of the inverse problem of determining the right-hand side of a nonlinear subdiffusion equation with a Caputo derivative with respect to time. Nonlinearity of the equation means that the right-hand side of the equation depends nonlinearly on the solution of the equation. The inverse problem consists of reconstructing the coefficient of the right-hand side, which depends on both time and spatial variables, under a measurement in an integral form. Similar inverse p…

Uncertainty-Aware Strategies: A Model-Agnostic Framework for Robust Financial Optimization through Subsampling
Hans Buehler, Blanka Horvath, Yannick Limmer, Thorsten Schmidt
https://arxiv.org/abs/2506.07299

Uncertainty-Aware Strategies: A Model-Agnostic Framework for Robust Financial Optimization through Subsampling
This paper addresses the challenge of model uncertainty in quantitative finance, where decisions in portfolio allocation, derivative pricing, and risk management rely on estimating stochastic models from limited data. In practice, the unavailability of the true probability measure forces reliance on an empirical approximation, and even small misestimations can lead to significant deviations in decision quality. Building on the framework of Klibanoff et al. (2005), we enhance the conventional ob…

Study of $p^{k}$-Eulerian polynomials and $p^{k}$-Fibonacci numbers for every odd prime $p$ and $k\geq0$
M. Parvathi, A. Tamilselvi, D. Hepsi
https://arxiv.org/abs/2506.09941

Study of $p^{k}$-Eulerian polynomials and $p^{k}$-Fibonacci numbers for every odd prime $p$ and $k\geq0$
In this paper, we define the notion of descent for the paths in the $p$-Bratteli diagram. This leads to the definition of $p^{k}$-Eulerian polynomials, whose coefficients count the number of paths with a given number of descents. We provide a method for constructing the $p^{k}$-Eulerian polynomials at each vertex. Furthermore, we compute the total number of descents of all paths ending at a given vertex as the corresponding $p^{k}$-Fibonacci numbers. We show that the derivative of the $p^{k}$-E…

EFT Corrections to Charged Black Hole Quasinormal Modes
William L. Boyce, Jorge E. Santos
https://arxiv.org/abs/2506.10074 https://ar…

EFT Corrections to Charged Black Hole Quasinormal Modes
We study the impact of higher-derivative corrections from Effective Field Theory on the quasinormal mode spectrum of Reissner-Nordström black holes. While previous work has explored corrections to Schwarzschild and Kerr black holes - typically using small-rotation approximations - a comprehensive analysis near extremality remains lacking. We focus on Reissner-Nordström black holes as a tractable model admitting an extremal limit, enabling investigation of the effect of these corrections on th…

QCD sum rule study on excited light meson operators
Wei-Han Tan, Wen-Ying Liu, Hong-Zhou Xi, Hua-Xing Chen
https://arxiv.org/abs/2505.24376 https://…

QCD sum rule study on excited light meson operators
We apply the QCD sum rule method to systematically study excited light meson operators and calculate their decay constants. These operators are constructed by explicitly adding one covariant derivative to the quark-antiquark pair. In total, twelve such operators are constructed, among which ten are subjected to detailed numerical analyses. The considered quark contents include $\bar{q}q$, $\bar{q}s$, and $\bar{s}s$ ($q = u/d$), allowing the formation of various $SU(3)$ flavor nonets. For instan…

Depth to magnetic source estimation using TDX contour
Hammed Oyekan
https://arxiv.org/abs/2505.22780 https://arxiv.org/pdf/2505.22780…

Depth to magnetic source estimation using TDX contour
Accurate depth estimation of magnetic sources plays a crucial role in various geophysical applications, including mineral exploration, resource assessments, regional hydrocarbon exploration, and geological mapping. Thus, this abstract presents a fast and simple method of estimating the depth of a magnetic body using the TDX derivative of the total magnetic field. TDX is a first-order derivative of the magnetic field that, in addition to edge detection, is less affected by noise, allowing for be…

Transformed Diffusion-Wave fPINNs: Enhancing Computing Efficiency for PINNs Solving Time-Fractional Diffusion-Wave Equations
Jing Li, Zhengqi Zhang
https://arxiv.org/abs/2506.11518

Transformed Diffusion-Wave fPINNs: Enhancing Computing Efficiency for PINNs Solving Time-Fractional Diffusion-Wave Equations
We propose transformed Diffsuion-Wave fractional Physics-Informed Neural Networks (tDWfPINNs) for efficiently solving time-fractional diffusion-wave equations with fractional order $α\in(1,2)$. Conventional numerical methods for these equations often compromise the mesh-free advantage of Physics-Informed Neural Networks (PINNs) or impose high computational costs when computing fractional derivatives. The proposed method avoids first-order derivative calculations at quadrature points by introdu…

This https://arxiv.org/abs/2504.13423 has been replaced.
link: https://scholar.google.com/scholar?q=a

Mixed Fractional Information: Consistency of Dissipation Measures for Stable Laws
Symmetric alpha-stable (S alpha S) distributions with alpha<2 lack finite classical Fisher information. Building on Johnson's framework, we define Mixed Fractional Information (MFI) via the initial rate of relative entropy dissipation during interpolation between S alpha S laws with differing scales, v and s. We demonstrate two equivalent formulations for MFI in this specific S alpha S-to-S alpha S setting. The first involves the derivative D'(v) of the relative entropy between the two S alpha …

Fractional order derivative characterizations of Besov-Morrey type spaces with applications
Chen Lu, Mingjin Li, Jianren Long
https://arxiv.org/abs/2505.20709

Fractional order derivative characterizations of Besov-Morrey type spaces with applications
On the one hand, the fractional order derivative characterization of the Besov-Morrey type space $B_{p}^{K}(s)$ is established by $K$-Carleson measures, and it was also shown that $f \in B_{p}^{K}(s_1) \Leftrightarrow f^{\left(\frac{s_2 - s_1}{p}\right)} \in B_{p}^{K}(s_2)$, which extended the results of Sun et al. on the fractional derivative of Morrey type space. On the other hand, some sufficient conditions for the growth of solutions to linear complex differential equations have been obtain…

This https://arxiv.org/abs/2409.13353 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Global existence for wave equations with scale-invariant time-dependent damping and time derivative nonlinearity
This paper addresses the Cauchy problem for wave equations with scale-invariant time-dependent damping and nonlinear time-derivative terms, modeled as $$\partial_{t}^2u- Δu +\fracμ{1+t}\partial_tu= f(\partial_tu), \quad x\in \mathbb{R}^n, t>0,$$ where $f(\partial_tu)=|\partial_tu|^p $ or $|\partial_tu|^{p-1}\partial_tu$ with $p>1$ and $μ>0$. We prove global existence of small data solutions in low dimensions $1\leq n\leq 3$ by using energy estimates in appropriate Sobolev…

Fractional Nonlinear Schrodinger Equation Revisited
Morteza Nattagh Najafi, Fatemeh Foroughirad
https://arxiv.org/abs/2505.19202 https://

Fractional Nonlinear Schrodinger Equation Revisited
We investigate the space time fractional nonlinear Schrodinger equation (FNLSE) incorporating the modified Riemann Liouville derivative introduced by Jumari. The equation is characterized by two parameters: the fractional derivative parameter (alpha, which captures the memory effects) and the non linearity parameter a. We present analytical solutions via three complementary approaches: the fractional Riccati method, the Adomian decomposition method, and the scaling method. The FNLSE is formulat…

Some results on generalized Hukuhara diamond-{\alpha} derivative and integral of fuzzy valued functions and on time scales
Selami Baye\u{g}, Funda Raziye Mert, Billur Kaymak\c{c}alan
https://arxiv.org/abs/2506.00016

Some results on generalized Hukuhara diamond-α derivative and integral of fuzzy valued functions and on time scales
In this paper, we define generalized Hukuhara diamond-alpha integral for fuzzy functions on time scales and obtain some of its fundamental properties and also we establish the relationship between diamond-alpha differentiation and integration.

This https://arxiv.org/abs/2502.07313 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Critical exponent for the one-dimensional wave equation with a space-dependent scale invariant damping and time derivative nonlinearity
We investigate in this paper the Cauchy problem of the one-dimensional wave equation with space-dependent damping of the form $μ_0(1+x^2)^{-1/2}$, where $μ_0>0$, and time derivative nonlinearity. We establish global existence of mild solutions for small data compactly supported by employing energy estimates within suitable Sobolev spaces of the associated homogeneous problem. Furthermore, we derive a blow-up result under some positive initial data by employing the test function method. …

This https://arxiv.org/abs/2408.02541 has been replaced.
initial toot: https://mastoxiv.page/@arX…

Modelling power-law ultrasound absorption using a time-fractional, static memory, Fourier pseudo-spectral method
We describe and implement a numerical method for modelling the frequency-dependent power-law absorption of ultrasound in tissue, as governed by the first order linear wave equations with a loss taking the form of a fractional time derivative. The (Caputo) fractional time derivative requires the full problem history which is contained within an iterative procedure. The resulting numerical method requires a fixed (static) memory cost irrespective of the number of time steps. The spatial domain is…

Dynamics of rotationally invariant polynomial root sets under iterated differentiations
Andr\'e Galligo, Joseph Najnudel, Truong Vu
https://arxiv.org/abs/2506.06263

Dynamics of rotationally invariant polynomial root sets under iterated differentiations
We associate to an $N$-sample of a given rotationally invariant probability measure $μ_0$ with compact support in the complex plane, a polynomial $P_N$ with roots given by the sample. Then, for $t \in (0,1)$, we consider the empirical measure $μ_t^{N}$ associated to the root set of the $\lfloor t N\rfloor$-th derivative of $P_N$. A question posed by O'Rourke and Steinerberger \cite{o2021nonlocal}, reformulated as a conjecture by Hoskins and Kabluchko \cite{hoskins2021dynamics}, and recently…

This https://arxiv.org/abs/2501.11694 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Gravitational Wave Propagation in a Geometric Condensate in Starobinsky Cosmology
In this paper we propose a new paradigm for cosmology: a time dependent scalar condensate background originated from the quadratic $(R + αR^2)$ Starobinski model, where $R$ is the Ricci scalar and $α$ the coupling constant. In weak gravity limit the system decouples into a conventional graviton and a higher derivative scalar. It was shown earlier through works from our group, \cite{ssg,sg,us}, that the latter can sustain an oscillatory lowest energy configuration or a {\it{Geometric Condensat…

Shape derivative approach to fractional overdetermined problems
Sidy M. Djitte, Ignace A. Minlend
https://arxiv.org/abs/2506.00268 https://

Shape derivative approach to fractional overdetermined problems
We use shape derivative approach to prove that balls are the only convex and $C^{1,1}$ regular domains in which the fractional overdetermined problem \begin{equation*} \left\{\begin{aligned} \Ds u&= λ_{s, p} u^{p-1}\quad\text{in}\quad\Om \\ u &= 0\quad \text{in}\quad\R^N\setminus \Om\\ u/d^s&=C_0\quad\text{on\;\; $\partialØ$} \end{aligned} \right. \end{equation*} admits a nontrivial solution for $p\in [1, 2]$ and where $λ_{s, p}= λ_{s, p}(Ø)$ is the best constant in the family of Subcritic…

Characterization of Hilbertizable spaces via convex functions
Nicolas Borchard, Gerd Wachsmuth
https://arxiv.org/abs/2506.04686 https://

Characterization of Hilbertizable spaces via convex functions
We show that the existence of a strongly convex function with a Lipschitz derivative on a Banach space already implies that the space is isomorphic to a Hilbert space. Similarly, if both a function and its convex conjugate are $C^2$ then the underlying space is also isomorphic to a Hilbert space.

Shape optimization under width constraint: the Cheeger constant and the torsional rigidity
Beniamin Bogosel
https://arxiv.org/abs/2506.07708 https://

Shape optimization under width constraint: the Cheeger constant and the torsional rigidity
In this article it is shown that the equilateral triangle maximizes the Cheeger constant and minimizes the torsional rigidity among shapes having a fixed minimal width. The proof techniques use direct comparisons with simpler shapes, consisting of disks with three disjoint caps. Comparison results for harmonic functions help establish that in non-equilateral configurations the shape derivative has an appropriate sign, contradicting optimality.

Electromagnetism: an intrinsic approach to Hadamard's method of descent
Giuliano Angelone, Elisa Ercolessi, Paolo Facchi, Rocco Maggi, Giuseppe Marmo, Saverio Pascazio, Francesco V. Pepe
https://arxiv.org/abs/2506.05255

Electromagnetism: an intrinsic approach to Hadamard's method of descent
We present a systematic geometric framework for the dimensional reduction of classical electromagnetism based on the concept of descent along vector fields of invariance. By exploring the interplay between the Lie derivative and the Hodge star operator, we implement descent conditions on differential forms that reduce Maxwell's equations in four-dimensional spacetime to electromagnetic theories in lower dimensions. We also consider multiple descent along pairwise commuting vector fields of inva…

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations
Subhash Paudel, Nail K. Yamaleev
https://arxiv.org/abs/2506.10820

A Combined Parallel-in-time Direct Inverse (ParaDIn)-Parareal Method for Nonlinear Differential Equations
As has been shown in our previous work, the parallel-in-time direct inverse (ParaDIn) method introduced by Yamaleev and Paudel in (arXiv: 2406.00878v1, 2024) imposes some constraint on the maximum number of time levels, $N_t$, that can be integrated in parallel. To circumvent this problem and further increase the speedup, we combine the ParaDIn method with the Parareal algorithm to efficiently parallelize the first-order time derivative term in nonlinear partial differential equations discretiz…

This https://arxiv.org/abs/2405.04989 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Paley-Wiener Type Theorems associated to Dirac Operators of Riesz-Feller type
This paper explores Paley-Wiener type theorems within the framework of hypercomplex variables. The investigation focuses on a space-fractional version of the Dirac operator $\mathbf{D}_θ^α$ of order $α$ and skewness $θ$. The pseudo-differential reformulation of $\mathbf{D}_θ^α$ in terms of the Riesz derivative $(-Δ)^{\fracα{2}}$ and the so-called {\textit Riesz-Hilbert transform} $H$, allows for the description of generalized Hardy spaces on the upper and lower half-spaces of $\mathbf{R…

Classification of the real Painlev\'{e} I transcendents by zeros and connection problem: an asymptotic study
Yan Huang, Yu-Tian Li, Wen-Gao Long
https://arxiv.org/abs/2506.03648

Classification of the real Painlevé I transcendents by zeros and connection problem: an asymptotic study
In this paper, we study the asymptotic behavior and connection problem of Painlevé I (PI) equation through a detailed analysis of the Stokes multipliers associated with its solutions. Focusing on the regime where the derivative at the real zeros of the solution becomes large, we apply the complex WKB method to derive full asymptotic expansions of the Stokes multipliers. These expansions allow us to classify real solutions of PI according to their behavior at the zeros, distinguishing between o…

Robust Moment Identification for Nonlinear PDEs via a Neural ODE Approach
Shaoxuan Chen, Su Yang, Panayotis G. Kevrekidis, Wei Zhu
https://arxiv.org/abs/2506.05245

Robust Moment Identification for Nonlinear PDEs via a Neural ODE Approach
We propose a data-driven framework for learning reduced-order moment dynamics from PDE-governed systems using Neural ODEs. In contrast to derivative-based methods like SINDy, which necessitate densely sampled data and are sensitive to noise, our approach based on Neural ODEs directly models moment trajectories, enabling robust learning from sparse and potentially irregular time series. Using as an application platform the nonlinear Schrödinger equation, the framework accurately recovers govern…

This https://arxiv.org/abs/2505.06681 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Local well-posedness for a system of quadratic derivative nonlinear Schrödinger equations
We consider the Cauchy problem for a system of quadratic derivative nonlinear Schrödinger equations introduced by M. Colin and T. Colin (2004) as a model of laser-plasma interaction. Under the condition that the flow map fails to be twice differentiable, Hirayama, Kinoshita, and Okamoto (2022) proved the well-posedness by constructing a modified energy and applying the energy method. In the present paper, we improve the well-posedness result under the above condition by using the short-time Fo…

This https://arxiv.org/abs/2501.10306 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Micro-Macro Decomposition of Particle Swarm Optimization Methods
Solving non-convex minimization problems using multi-particle metaheuristic derivative-free optimization methods is still an active area of research. Popular methods are Particle Swarm Optimization (PSO) methods, that iteratively update a population of particles according to dynamics inspired by social interactions between individuals. We present a modification to include constrained minimization problems using exact penalization. Additionally, we utilize the hierarchical structure of PSO to in…

Vanishing, Unbounded and Angular Shifts on the Quotient of the Difference and the Derivative of a Meromorphic Function
Lasse Asikainen, Yu Chen, Risto Korhonen
https://arxiv.org/abs/2505.21150

Vanishing, Unbounded and Angular Shifts on the Quotient of the Difference and the Derivative of a Meromorphic Function
We show that for a vanishing period difference operator of a meromorphic function \( f \), there exist the following estimates regarding proximity functions, \[ \lim_{η\to 0} m_η\left(r, \frac{Δ_ηf - aη}{f' - a} \right) = 0 \] and \[ \lim_{r \to \infty} m_η\left(r, \frac{Δ_ηf - aη}{f' - a} \right) = 0, \] where \( Δ_ηf = f(z + η) - f(z) \), and \( |η| \) is less than an arbitrarily small quantity \( α(r) \) in the second limit. Then, under certain assumptions on the grow…

Uncertainty principles for free metaplectic transformation and associated metaplectic operators
Ping Liang, Pei Dang, Weixiong Mai
https://arxiv.org/abs/2506.03724

Uncertainty principles for free metaplectic transformation and associated metaplectic operators
In this paper, we systematically investigate the Heisenberg-Pauli-Weyl uncertainty principle for free metaplectic transformation, as well as metaplectic operators. Specifically, we obtain two different types of the uncertainty principle for free metaplectic transformations in terms of the so-called phase derivative, one of which can be generalized to the $L^p$-case with $1\le p\le 2$. The obtained results are valid not only for free metaplectic transformations but also for general metaplectic o…

This https://arxiv.org/abs/2203.06002 has been replaced.
link: https://scholar.google.com/scholar?q=a

Experiments on the Violation of Electromagnetic Gauge Symmetry by Yang-Mills Gravity Using Josephson Effects in Superconductors
Yang-Mills gravity is a quantum theory of gravity with translational gauge symmetry that is based on a flat space-time. The universal coupling of all quantum fields to quantum Yang-Mills gravity is based on the replacement of $\partial_μ$ by the translational gauge covariant derivative $(\partial_μ+gϕ_μ^ν\partial_ν)$ in the Lagrangians of non-gravitational fields. Near the surface of the Earth, Yang-Mills gravity causes the phase gradient $\partial_k θ$ to be altered by a factor of $h_1\…

On the Generalized Hukuhara Nabla Differentiability of Fuzzy Functions on Time Scales via Characterization Theorem
Funda Raziye Mert, Selami Baye\u{g}, Billur Kaymak\c{c}alan
https://arxiv.org/abs/2506.00015

On the Generalized Hukuhara Nabla Differentiability of Fuzzy Functions on Time Scales via Characterization Theorem
In this paper, we provide a comprehensive investigation of the generalized Hukuhara nabla derivative for fuzzy functions on time scales. We establish some characterizations of generalized Hukuhara nabla differentiable fuzzy functions on time scales via the nabla differentiability of their endpoint functions. These characterizations complete and extend previous findings of fuzzy number valued functions from the real domain to those on time scales. Additionally, we generalize the product rule, pr…

This https://arxiv.org/abs/2403.05322 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_mat…

Direct-search methods in the year 2025: Theoretical guarantees and algorithmic paradigms
Optimizing a function without using derivatives is a challenging paradigm, that precludes from using classical algorithms from nonlinear optimization, and may thus seem intractable other than by using heuristics. Nevertheless, the field of derivative-free optimization has succeeded in producing algorithms that do not rely on derivatives and yet are endowed with convergence guarantees. One class of such methods, called direct-search methods, is particularly popular thanks to its simplicity of im…

A General Version of Carath\'{e}odory's Existence and Uniqueness Theorem
Paulo M. de Carvalho-Neto, C\'icero L. Frota, Pedro G. P. Torelli
https://arxiv.org/abs/2505.24516

A General Version of Carathéodory's Existence and Uniqueness Theorem
In this paper, we establish a general version of Carathéodory's existence and uniqueness theorem for a semilinear system of integro-differential equations arising from differential equations with distinct orders of Caputo fractional derivative. The main result of our work demonstrates that the integrability order of the Carathéodory function $f$ must be at least greater than the maximum of the reciprocals of all differentiation orders in the system; otherwise, even the existence of a solution…

Refined regularity at critical points for linear elliptic equations
Jongkeun Choi, Hongjie Dong, Seick Kim
https://arxiv.org/abs/2506.08281 https://…

Refined regularity at critical points for linear elliptic equations
We investigate the regularity of solutions to linear elliptic equations in both divergence and non-divergence forms, particularly when the principal coefficients have Dini mean oscillation. We show that if a solution $u$ to a divergence-form equation satisfies $Du(x^o)=0$ at a point, then the second derivative $D^2u(x^o)$ exists and satisfies sharp continuity estimates. As a consequence, we obtain ``$C^{2,α}$ regularity'' at critical points when the coefficients of $L$ are $C^α$. This result …

Active flux for ideal magnetohydrodynamics: A positivity-preserving scheme with the Godunov-Powell source term
Junming Duan, Praveen Chandrashekar, Christian Klingenberg
https://arxiv.org/abs/2506.04857

Active flux for ideal magnetohydrodynamics: A positivity-preserving scheme with the Godunov-Powell source term
The Active Flux (AF) is a compact, high-order finite volume scheme that allows more flexibility by introducing additional point value degrees of freedom at cell interfaces. This paper proposes a positivity-preserving (PP) AF scheme for solving the ideal magnetohydrodynamics, where the Godunov-Powell source term is employed to deal with the divergence-free constraint. For the evolution of the cell average, apart from the standard conservative finite volume method for the flux derivative, the non…

A fast and memoryless numerical method for solving fractional differential equations
Nicola Guglielmi, Ernst Hairer
https://arxiv.org/abs/2506.04188 https:…

A fast and memoryless numerical method for solving fractional differential equations
The numerical solution of implicit and stiff differential equations by implicit numerical integrators has been largely investigated and there exist many excellent efficient codes available in the scientific community, as Radau5 (based on a Runge-Kutta collocation method at Radau points) and Dassl, based on backward differentiation formulas, among the others. When solving fractional ordinary differential equations (ODEs), the derivative operator is replaced by a non-local one and the fractional …

AFIRE: Accurate and Fast Image Reconstruction Algorithm for Geometric-inconsistency Multispectral CT
Yu Gao, Chong Chen
https://arxiv.org/abs/2505.24793 ht…

AFIRE: Accurate and Fast Image Reconstruction Algorithm for Geometric-inconsistency Multispectral CT
For nonlinear multispectral computed tomography (CT), accurate and fast image reconstruction is challenging when the scanning geometries under different X-ray energy spectra are inconsistent or mismatched. Motivated by this, we propose an accurate and fast algorithm named AFIRE to address such problem in the case of mildly full scan. We discover that the derivative operator (gradient) of the involved nonlinear mapping at some special points, for example, at zero, can be represented as a composi…

Adams-Trudinger-Moser inequalities of Adimurthi-Druet type regulated by the vanishing phenomenon and its extremals
Abiel Costa Macedo, Jos\'e Francisco de Oliveira, F\'abio Sodr\'e Rocha
https://arxiv.org/abs/2505.24297

Adams-Trudinger-Moser inequalities of Adimurthi-Druet type regulated by the vanishing phenomenon and its extremals
Let $W^{m,\frac{n}{m}}(\mathbb{R}^n)$ with $1\le m < n$ be the standard higher order derivative Sobolev space in the critical exponential growth threshold. We investigate a new Adams-Adimurthi-Druet type inequality on the whole space $\mathbb{R}^n$ which is strongly influenced by the vanishing phenomenon. Specifically, we prove \begin{equation}\nonumber \sup_{\underset{\|\nabla^{m} u\|_{\frac{n}{m}}^{^{\frac{n}{m}}}+\|u\|_{\frac{n}{m}}^{\frac{n}{m}} \leq 1}{u\in W^{m,\fr…