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Local and global well-posedness for the kinetic derivative NLS on $\mathbb{R}$
Nobu Kishimoto, Kiyeon Lee
https://arxiv.org/abs/2507.20271 https://arxiv.or…

Local and global well-posedness for the kinetic derivative NLS on $\mathbb{R}$
We investigate the local and global well-posedness of the kinetic derivative nonlinear Schrödinger equation(KDNLS) on $\mathbb{R}$, described by \[ i\partial_t u + \partial_x^2 u = iα\partial_x (|u|^2 u) + iβ\partial_x (\mathcal{H} (|u|^2) u), \] where $α, β\in \mathbb{R}$, and $\mathcal{H}$ represents the Hilbert transformation. For KDNLS, the $L^2$ norm of a solution is decreasing (resp. increasing, conserved) when $β$ is negative (resp. positive, zero). Focusing on …

D3PINNs: A Novel Physics-Informed Neural Network Framework for Staged Solving of Time-Dependent Partial Differential Equations
Xun Yang, Guanqiu Ma
https://arxiv.org/abs/2508.20440

D3PINNs: A Novel Physics-Informed Neural Network Framework for Staged Solving of Time-Dependent Partial Differential Equations
In this paper, we propose a novel framework, Dynamic Domain Decomposition Physics-Informed Neural Networks (D3PINNs), for solving time-dependent partial differential equations (PDEs). In this framework, solutions of time-dependent PDEs are dynamically captured. First, an approximate solution is obtained by the Physics-Informed Neural Networks (PINNs) containing the domain decomposition, then the time derivative terms in the PDE will be retained and the other terms associated with the solution…

Generalized Uncertainty Principle as a Mechanism for CP Violation
Hector Gisbert, Victor Ilisie, Ezequiel Valero
https://arxiv.org/abs/2507.20727 https://a…

Generalized Uncertainty Principle as a Mechanism for CP Violation
Within quantum electrodynamics we show that the Generalized Uncertainty Principle induces higher-derivative corrections that promote the topological invariant $F_{μν}\,\widetilde F^{μν}$ to the dynamical, non-topological operator $\partial^λF_{μν}\,\partial_λ\widetilde F^{μν}$. We explore the resulting phenomenology, focusing on the generation of electric dipole moments. Our findings open a new low-energy window for testing quantum-gravity scenarios through precision measurements of c…

The Partial Theta Operator and Multivariate Generalized Lambert Series
Ronald Orozco L\'opez
https://arxiv.org/abs/2507.15160 https://

The Partial Theta Operator and Multivariate Generalized Lambert Series
In this paper, we introduce the Theta Partial operator $θ(y\mathbf{D}_λ)$, based on the $λ$-derivative operator $\mathbf{D}_λ$, and use it to define the following generalization of the Lambert series \begin{equation*} \sum_{n=0}^{\infty}a_{n}\frac{x^{n+1}}{x-λ^ny}z^n. \end{equation*} Also, we define generalized Lambert-Mehler and Lambert-Rogers type series, double-sum bivariate generalized Lambert series and multivariate generalized Lambert series. A list of interesting generalized Lambert…

SPP location with spherical ray tracing by refractive index
Hui Qian, Xiaosan Zhu, Dongliang Liu
https://arxiv.org/abs/2506.19859 https://

SPP location with spherical ray tracing by refractive index
Atmospheric layer structure is a primary factor affecting the precision of single-point satellite positioning. The assumption of electromagnetic wave rectilinear propagation hinders the accurate implementation of ionospheric and tropospheric corrections, whereas curvilinear positioning methods fully account for ray deflection. This study aims to derive partial derivative formulas for theoretical travel time with respect to latitude, longitude, elevation, and velocity models by formulating elect…

Gravitational Baryogenesis Constraints on Nojiri-Odintsov $f(R)$ Gravity
Kalyan Malakar, Mrinnoy M Gohain, Kalyan Bhuyan
https://arxiv.org/abs/2506.18949 h…

Gravitational Baryogenesis Constraints on Nojiri-Odintsov $f(R)$ Gravity
This paper focuses on exploring the imbalance between matter and antimatter via the gravitational baryogenesis mechanism within the framework of Nojiri-Odintsov $f(R)$ gravity models in a spatially flat FLRW universe, where $R$ is the Ricci curvature scalar. This mechanism is based on \(\mathcal{CP}\)-violation generated via introducing an interaction between baryonic matter current (\(J^μ\)) and the derivative of curvature scalar (\(\partial_μR\)), which finally results in the baryon asymmet…

Pontryagin Maximum Principle for McKean-Vlasov Reaction-Diffusion Equations
Johan Benedikt Spille, Wilhelm Stannat
https://arxiv.org/abs/2507.16288 https:/…

Pontryagin Maximum Principle for McKean-Vlasov Reaction-Diffusion Equations
We consider the stochastic control of a semi-linear stochastic partial differential equations (SPDE) of McKean-Vlasov type. Based on a recent novel approach to the Lions derivative for Banach space valued functions, we prove the Gateaux differentiability of the control to state map and, using adjoint calculus, we derive explicit representations of the gradient of the cost functional and a Pontryagin maximum principle. On the way, we also prove a novel existence and uniqueness result for linear …

A Novel Homotopy Perturbation Sumudu Transform Method for Nonlinear Fractional PDEs: Applications and Comparative Analysis
Maryam Jalili
https://arxiv.org/abs/2506.20457

A Novel Homotopy Perturbation Sumudu Transform Method for Nonlinear Fractional PDEs: Applications and Comparative Analysis
This study introduces the Homotopy Perturbation Sumudu Transform Method (HPSTM), a novel hybrid approach combining the Sumudu transform with homotopy perturbation to solve nonlinear fractional partial differential equations (FPDEs), including fractional porous medium, heat transfer, and Fisher equations, using the Caputo fractional derivative. HPSTM leverages the linearity-preserving properties of the Sumudu transform and the flexibility of homotopy perturbation, achieving faster convergence th…

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…

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…

Frechet and Mordukhovich Derivative (Coderivative) and Covering Constant for Single-Valued Mapping in Euclidean Space with Applications (I)
Jinlu Li
https://arxiv.org/abs/2508.10766

Frechet and Mordukhovich Derivative (Coderivative) and Covering Constant for Single-Valued Mapping in Euclidean Space with Applications (I)
In this paper, we study Frechet derivatives and Mordukhovich derivatives (or coderivatives) of single-valued mappings in Euclidean spaces. At first, we prove the guideline for calculating the Frechet derivatives of single-valued mappings by their partial derivatives. Then, by using the connections between Frechet derivatives and Mordukhovich derivatives (or coderivatives) of single-valued mappings in Banach spaces, we derive the useful rules for calculating the Mordukhovich derivatives of singl…

A kernel compression method for distributed-order fractional partial differential equations
Jonas Beddrich, Barbara Wohlmuth
https://arxiv.org/abs/2508.13631 https://

A kernel compression method for distributed-order fractional partial differential equations
We propose a kernel compression method for solving Distributed-Order (DO) Fractional Partial Differential Equations (DOFPDEs) at the cost of solving corresponding local-in-time PDEs. The key concepts are (1) discretization of the integral over the order of the fractional derivative and (2) approximation of linear combinations of integral kernels with exponential sums, expressing the non-local history term as a sum of auxiliary variables that solve a weakly coupled, local in time system of PDEs.…

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…

Pointwise explicit estimates for derivatives of solutions to linear parabolic PDEs with Neumann boundary conditions
C Ciccarella
https://arxiv.org/abs/2507.08622

Pointwise explicit estimates for derivatives of solutions to linear parabolic PDEs with Neumann boundary conditions
We establish a pointwise bound on the spatial derivative $\left| \frac{\partial V}{\partial x} \right|$ of the solution to a parabolic PDE with Neumann boundary conditions. The bound is fully explicit in the sense that it depends only on the coefficients of the PDE and the domain, including closed-form expression for all constants. The proof is purely probabilistic. We first extend to time inhomogeneous diffusions a result concerning the derivative of the solution of a reflected SDE…

Forward and inverse problems for a mixed-type equation with the Caputo fractional derivative and Dezin-type non-local condition
Ravshan Ashurov, Umida Dusanova, Navbahor Nuraliyeva
https://arxiv.org/abs/2507.12129

Forward and inverse problems for a mixed-type equation with the Caputo fractional derivative and Dezin-type non-local condition
This work is dedicated to the study of a mixed-type partial differential equation involving a Caputo fractional derivative in the time domain $t > 0$ and a classical parabolic equation in the domain $t < 0$, along with Dezin-type non-local boundary and gluing conditions. The forward and inverse problems are studied in detail. For the forward problem, the existence and uniqueness of solutions are established using the Fourier method, under appropriate assumptions on the initial data and the righ…

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…

Pricing Fractal Derivatives under Sub-Mixed Fractional Brownian Motion with Jumps
Nader Karimi
https://arxiv.org/abs/2506.24111 https://arxiv.org/pdf/2506.…

A stability-enhanced nonstandard finite difference framework for solving one and two-dimensional nonlocal differential equations
Shweta Kumari, Mani Mehra
https://arxiv.org/abs/2508.13542

A stability-enhanced nonstandard finite difference framework for solving one and two-dimensional nonlocal differential equations
Standard finite difference (SFD) schemes often suffer from limited stability regions, especially when applied in explicit setup to partial differential equations. To address this challenge, this study investigates the efficacy of nonstandard finite difference (NSFD) schemes in enhancing stability of explicit SFD schemes for 1D and 2D Caputo-type time-fractional diffusion equations (TFDEs). A nonstandard L1approximation is proposed for the Caputo fractional derivative, and its local truncation e…

Fractional Dirichlet problems with an overdetermined nonlocal Neumann condition
Michele Gatti, Julian Scheuer, Tobias Weth
https://arxiv.org/abs/2507.13715

Fractional Dirichlet problems with an overdetermined nonlocal Neumann condition
We investigate symmetry and quantitative approximate symmetry for an overdetermined problem related to the fractional torsion equation in a regular open, bounded set $Ω\subseteq \mathbb{R}^n$. Specifically, we show that if $\overlineΩ$ has positive reach and the nonlocal normal derivative introduced in (Dipierro, Ros-Oton, Valdinoci, Rev. Mat. Iberoam. 33 (2017), no. 2, 377-416) is constant on an external surface parallel and sufficiently close to $\partial Ω$, then $Ω$ must be a ball. Rema…

It\^{o}-Stratonovich Conversion in Infinite Dimensions for Unbounded, Time-Dependent, Nonlinear Operators
Daniel Goodair
https://arxiv.org/abs/2508.03424 https://

Itô-Stratonovich Conversion in Infinite Dimensions for Unbounded, Time-Dependent, Nonlinear Operators
We prove that a solution, in a variational framework, to the Stratonovich stochastic partial differential equation with noise $G\left(t, Ψ_t\right) \circ dW_t$ is given by a solution to the Itô equation with Itô-Stratonovich corrector $\frac{1}{2}\sum_{i=1}^\infty D_uG_i\left(t, Ψ_t\right)\left[G_i(t,Ψ_t)\right]dt$. Here $G_i$ denotes the action of $G$ on the $i^{th}$ component of the cylindrical noise, and $D_uG_i$ its Fréchet partial derivative in the Hilbert space for which the Itô fo…

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…

Muckenhoupt-weighted $L_q(L_p)$ boundedness for time-space fractional nonlocal operators
Yong Zhen Yang, Yong Zhou
https://arxiv.org/abs/2507.01890 https:/…

Muckenhoupt-weighted $L_q(L_p)$ boundedness for time-space fractional nonlocal operators
Based on the $ϕ(Δ)$-type operator studied by Kim \cite[\emph{Adv.~Math.}]{Kim2}, where $ϕ$ is a Bernstein function, we establish weighted $L_{q}(L_{p})$ estimates for solutions to the following fractional evolution equation: $$ \partial_{t}^αw(t,x) = ϕ(Δ)w(t,x) + h(t,x), \quad t > 0, \; x \in \mathbb{R}^{d}, $$ where $\partial_{t}^α$ denotes the Caputo derivative of $0 < α< 1$. To be specific, for all $1 < p, q < \infty$, we demonstrate that $$ \int_{0}^{\infty} \left( \int_{\mathbb{R}^…

Hybrid Shifted Gegenbauer Integral-Pseudospectral Method for Solving Time-Fractional Benjamin-Bona-Mahony-Burgers Equation
Kareem T. Elgindy
https://arxiv.org/abs/2507.23099 htt…

Hybrid Shifted Gegenbauer Integral-Pseudospectral Method for Solving Time-Fractional Benjamin-Bona-Mahony-Burgers Equation
This paper presents a high-order hybrid shifted Gegenbauer integral-pseudospectral (HSG-IPS) method for solving the time-fractional Benjamin-Bona-Mahony-Burgers (FBBMB) equation. A key innovation of our approach is the transformation of the original equation into a fractional partial-integro differential form that contains only a first-order derivative, which can be accurately approximated using a first-order shifted Gegenbauer differentiation matrix (SGDM), while all other terms in the transfo…

Yudovich theory under geometric regularity for density-dependent incompressible fluids
Francesco Fanelli
https://arxiv.org/abs/2506.23365 https://

Yudovich theory under geometric regularity for density-dependent incompressible fluids
This paper focuses on the study of the density-dependent incompressible Euler equations in space dimension $d=2$, for low regularity (\textsl{i.e.} non-Lipschitz) initial data satisfying assumptions in spirit of the celebrated Yudovich theory for the classical homogeneous Euler equations. We show that, under an \textsl{a priori} control of a non-linear geometric quantity, namely the directional derivative $\partial_Xu$ of the fluid velocity $u$ along the vector field $X:=\nabla^\perpρ$, wher…