Tootfinder

On irrationals with Lagrange value exactly 3
Zhe Cao, Harold Erazo, Carlos Gustavo Moreira
https://arxiv.org/abs/2509.01867 https://arxiv.org/pdf/2509.0186…

On irrationals with Lagrange value exactly 3
For $c>0$, let $X_c$ denote the set of $x\in\mathbb{R}\backslash\mathbb{Q}$ such that $\left| x-\frac{p}{q} \right|<\frac{1}{cq^2}$ has only finitely many rational solutions $\frac{p}{q}$. It is a classical fact, known since the 1950s, that $X_c$ is uncountable for $c>3$ and countable for $c<3$. However, the cardinality of $X_3$ does not appear to be present in the literature. We prove that $X_3$ is uncountable. More generally, we show that for any $n\in\mathbb{N}\cup\{\infty\}$, th…

Structural Equations for Critical Points of Conformally Invariant Curvature Energies in 4d
Yann Bernard
https://arxiv.org/abs/2509.01179 https://arxiv.org/…

Structural Equations for Critical Points of Conformally Invariant Curvature Energies in 4d
This paper considers the Euler-Lagrange equations satisfied by the critical points of a large class of conformally invariant extrinsic energies for 4-manifolds immersed into Euclidean space (any codimension). Using invariances and Noether's theorem, we convert the Euler-Lagrange equation in a system of equations with analytically favourable structures. The present paper generalises to the four-dimensional setting ideas originally developed by Tristan Rivière in his study of the Willmore energy…

Was able to grab and install Lagrange (for accessing Gopher/Gemini sites) here on my laptop that has Mint on it, just by searching for Lagrange in the Software Manager (gotta love Linux). Installed, launched-- and yeah, it really is a great, clean GUI. Also, you can see my Rogue desktop background 😂
#Gemini #Gopher …

Optimising reference library selection for reference-star differential imaging of discs with SPHERE/IRDIS
S. Stasevic, J. Milli, J. Mazoyer, A. -M. Lagrange, S. Bergeon
https://arxiv.org/abs/2509.03325

Optimising reference library selection for reference-star differential imaging of discs with SPHERE/IRDIS
The direct detection of circumstellar discs through high-contrast imaging provides key insights into the history and dynamics of planetary systems. Pole-on discs, especially faint debris discs, are difficult to detect and require careful consideration during post-processing to remove stellar residuals from the data while preserving the disc signal. Reference-star differential imaging (RDI) serves as one of the primary post-processing methods for disc observations. We aim to develop a method of …

This https://arxiv.org/abs/2505.23679 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_grqc_…

Boundary terms in cosmology
In the derivation of the Einstein field equations via Hamilton's principle, the inclusion of a boundary term is essential to render the variational problem well-posed, as it addresses variations that do not vanish at the boundary of the spacetime manifold. Typically, this term is chosen as the Gibbons-Hawking-York boundary term. In this work, we propose an alternative treatment of the boundary term within a cosmological framework by employing the Lagrange multiplier method. This approach enforc…

Synergy between Roman and PRIMA imaging capabilities for large extragalactic surveys
M\'ed\'eric Boquien (Universit\'e C\^ote d'Azur, Observatoire de la C\^ote d'Azur, CNRS, Laboratoire Lagrange, Nice, France), Laure Ciesla (Aix Marseille Univ, CNRS, CNES, LAM, Marseille, France), Roman Amestoy (Aix Marseille Univ, CNRS, CNES, LAM, Marseille, France), Jason Glenn (NASA Goddard Space Flight Center, Greenbelt, Maryland, United States), Carlotta Gruppioni (Istituto Naz…

Synergy between Roman and PRIMA imaging capabilities for large extragalactic surveys
The Roman Space Telescope will be instrumental for characterizing the physical properties of galaxies and understanding their evolution across time. However, a complete view of galaxy star formation activity will only be possible with the addition of far-infrared observations that a telescope such as PRobe far-Infrared Mission for Astrophysics (PRIMA) will be able to provide. Indeed, PRIMA's far-infrared camera will be highly sensitive to dust emission, whereas Roman will probe the stellar emis…

Sharp gradient stability for a class of Hardy-Sobolev-Maz'ya inequalities
Wei Dai, Jingze Fu, An Zhang
https://arxiv.org/abs/2509.00814 https://arxiv.o…

Sharp gradient stability for a class of Hardy-Sobolev-Maz'ya inequalities
This paper investigates the stability problem for a class of Hardy-Sobolev-Maz'ya inequalities with non-radial extremal functions. We prove that the Euler-Lagrange equations are non-degenerate and obtain a sharp global quantitative stability. The presence of partial (stronger) singular weight brings substantial new challenges, requiring us to significantly refine the techniques from \cite{DT1,FN,FZ} and introduce some new ideas to handle both the cylindrical symmetry of non-radial extremal func…

Laser M\"ossbauer spectroscopy of ^{229}Th
Takahiro Hiraki, Takahiko Masuda, Sayuri Takatori, Fabian Schaden, Michael Bartokos, Kjeld Beeks, Yuta Fukunaga, Andreas Gr\"uneis, Ming Guan, Georgy Kazakov, Thomas LaGrange, Adrian Leitner, Ira Morawetz, Ryoichiro Ogake, Koichi Okai, Martin Pimon, Martin Pressler, Thomas Riebner, Noboru Sasao, Felix Schneider, Thorsten Schumm, Kotaro Shimizu, Luca Toscani de Col, Tomas Sikorsky, Akihiro Yoshimi, Koji Yoshimura

Laser Mössbauer spectroscopy of ^{229}Th
Mössbauer spectroscopy is widely used in biochemistry, geology, and solid-state physics to obtain structural information on materials. Here, we extend this technique into the optical range using a vacuum ultraviolet laser to probe the low-energy nuclear transitions of thorium-229, doped in calcium fluoride crystals. We discover four distinct doping sites for the thorium ions, determine the characteristic electric field gradients emerging in the interaction with the host crystal, and identify t…

Smoothness of extremizers for certain inequalities of the Radon transform
Taryn C. Flock
https://arxiv.org/abs/2508.00783 https://arxiv.org/pdf/2508.00783

Smoothness of extremizers for certain inequalities of the Radon transform
The Radon transform is a bounded operator from $L^p$ of Euclidean space to $L^q$ of the manifold of all affine hyperplanes in $\mathbb{R}^n$ for certain exponents depending dimension. Extremizers have been determined for certain values of $q$ and $p$, but most remain open. We show that extremizers are infinitely differentiable whenever the exponents in the associated Euler-Lagrange equation, $q-1$ and $\frac1{p-1}$, are integers. The proof adapts the method of Christ and Xue, to the case wher…

Deep Uzawa for Kinetic Transport with Lagrange-Enforced Boundaries
Charalambos Makridakis, Aaron Pim, Tristan Pryer, Nikolaos Rekatsinas
https://arxiv.org/abs/2507.19907 https:/…

Deep Uzawa for Kinetic Transport with Lagrange-Enforced Boundaries
We propose a neural network framework for solving stationary linear transport equations with inflow boundary conditions. The method represents the solution using a neural network and imposes the boundary condition via a Lagrange multiplier, based on a saddle-point formulation inspired by the classical Uzawa algorithm. The scheme is mesh-free, compatible with automatic differentiation and extends naturally to problems with scattering and heterogeneous media. We establish convergence of the conti…

Nonlocal free boundary minimal surfaces
Marco Badran, Serena Dipierro, Enrico Valdinoci
https://arxiv.org/abs/2508.00337 https://arxiv.org/pdf/2508.00337…

Nonlocal free boundary minimal surfaces
We introduce the nonlocal analogue of the classical free boundary minimal hypersurfaces in an open domain $Ω$ of $\mathbb{R}^n$ as the (boundaries of) critical points of the fractional perimeter $\operatorname{Per}_s(\cdot,\,Ω)$ with respect to inner variations leaving $Ω$ invariant. We deduce the Euler-Lagrange equations and prove a few surprising features, such as the existence of critical points without boundary and a strong volume constraint in $Ω$ for unbounded hypersurfaces. Moreover,…

Event-Triggered Resilient Consensus of Networked Euler-Lagrange Systems Under Byzantine Attacks
Yuliang Fu, Guanghui Wen, Dan Zhao, Wei Xing Zheng, Xiaolei Li
https://arxiv.org/abs/2507.15283

Event-Triggered Resilient Consensus of Networked Euler-Lagrange Systems Under Byzantine Attacks
The resilient consensus problem is investigated in this paper for a class of networked Euler-Lagrange systems with event-triggered communication in the presence of Byzantine attacks. One challenge that we face in addressing the considered problem is the inapplicability of existing resilient decision algorithms designed for one-dimensional multi-agent systems. This is because the networked Euler-Lagrange systems fall into the category of multi-dimensional multi-agent systems with coupling among …

Emergent musical properties of a transformer under contrastive self-supervised learning
Yuexuan Kong, Gabriel Meseguer-Brocal, Vincent Lostanlen, Mathieu Lagrange, Romain Hennequin
https://arxiv.org/abs/2506.23873

Emergent musical properties of a transformer under contrastive self-supervised learning
In music information retrieval (MIR), contrastive self-supervised learning for general-purpose representation models is effective for global tasks such as automatic tagging. However, for local tasks such as chord estimation, it is widely assumed that contrastively trained general-purpose self-supervised models are inadequate and that more sophisticated SSL is necessary; e.g., masked modeling. Our paper challenges this assumption by revealing the potential of contrastive SSL paired with a transf…

On an Abstraction of Lyapunov and Lagrange Stability
Michelangelo Bin, David Angeli
https://arxiv.org/abs/2507.15047 https://arxiv.or…

On an Abstraction of Lyapunov and Lagrange Stability
This paper studies a set-theoretic generalization of Lyapunov and Lagrange stability for abstract systems described by set-valued maps. Lyapunov stability is characterized as the property of inversely mapping filters to filters, Lagrange stability as that of mapping ideals to ideals. These abstract definitions unveil a deep duality between the two stability notions, enable a definition of global stability for abstract systems, and yield an agile generalization of the stability theorems for basi…

Arnol'd's limit and the Lagrange inversion
Martin Klazar
https://arxiv.org/abs/2507.22743 https://arxiv.org/pdf/2507.22743

Arnol'd's limit and the Lagrange inversion
We show how to prove by means of the Lagrange inversion the limit of Arnol'd that $$ \lim_{x\to0}\frac{\sin(\tan x)-\tan(\sin x)}{\arcsin(\arctan x)-\arctan(\arcsin x)}=1\,. $$ In fact, we obtain a more general result in terms of formal power series.

Faddeev-Jackiw Quantization of Classical Constrained Systems
Shaza Abdul Majid, Ansha S Nair, Saurabh Gupta
https://arxiv.org/abs/2507.22505 https://arxiv.…

Faddeev-Jackiw Quantization of Classical Constrained Systems
We accomplish the quantization of a few classical constrained systems à la (modified) Faddeev-Jackiw formalism. We analyze the constraint structure and obtain basic brackets of the theory. In addition, we disclose the gauge symmetries within the symplectic framework. We also provide new interpretation for Lagrange multipliers and outline a MATLAB implementation algorithm for symplectic formulation.

@… @… I use Lagrange as well but for the cli I think bombadillo is great.

🇺🇦 #NowPlaying on KEXP's #Expansions
gyrofield:
🎵 Lagrange
#gyrofield
https://gyrofield.bandcamp.com/track/lagrange
https://open.spotify.com/track/13BuUIQlL6MC3tt7pbEl1v

Galton-Watson processes, simple varieties of trees and Khinchin families
V\'ictor J. Maci\'a
https://arxiv.org/abs/2506.18370 https://

Galton-Watson processes, simple varieties of trees and Khinchin families
In this note, we introduce a unified analytic framework that connects simple varieties of trees, Bienayme-Galton-Watson processes and Khinchin families. Using Lagrange's inversion formula, we derive new coefficient-based expressions for extinction probabilities and reinterpret them as boundary phenomena tied to the domain of the inverse of the solution to Lagrange's equation. This perspective reveals a structural bridge between combinatorial and probabilistic models, simplifying classical argum…

Facets of Brachistochronic Trajectories
David Agmon, Ady Mann
https://arxiv.org/abs/2507.00084 https://arxiv.org/pdf/2507.00084

Facets of Brachistochronic Trajectories
This paper studies brachistochrone trajectories. Four rules are formulated as sufficient conditions. Two rules apply for a general conservative force. Two rules apply for a central force. A central force allows wire replacement. The wire is replaced by appropriate magnetic field. This enables solving motion equations directly. We replace Euler Lagrange with direct integration.

A Data-Driven Approach for Predicting Hydrodynamic Forces on Spherical Particles Using Volume Fraction Representations
Alexander Metelkin, Sam Jacob Jacob, Bernhard Vowinckel
https://arxiv.org/abs/2507.20767

A Data-Driven Approach for Predicting Hydrodynamic Forces on Spherical Particles Using Volume Fraction Representations
Particle-laden flows are simulated at various scales using numerical techniques that range from particle-resolved Direct Numerical Simulations (pr-DNS) for small-scale systems to Lagrange point-particle methods for laboratory-scale problems, and Euler-Euler approaches for larger-scale applications. Recent research has been particularly focused on the development of both physics-based and data-driven closures to enhance the accuracy of the Lagrangian point-particle approach by leveraging highly …

Lagrange multiplier expressions for matrix polynomial optimization and tight relaxations
Lei Huang, Jiawang Nie, Jiajia Wang, Lingling Xie
https://arxiv.org/abs/2506.12579

Lagrange multiplier expressions for matrix polynomial optimization and tight relaxations
This paper studies matrix constrained polynomial optimization. We investigate how to get explicit expressions for Lagrange multiplier matrices from the first order optimality conditions. The existence of these expressions can be shown under the nondegeneracy condition. Using Lagrange multiplier matrix expressions, we propose a strengthened Moment-SOS hierarchy for solving matrix polynomial optimization. Under some general assumptions, we show that this strengthened hierarchy is tight, or equiva…

Existence and multiplicity of normalized solutions for the quasi-linear Schr\"{o}dinger equations with mixed nonlinearities
Qihan He, Hao Wang
https://arxiv.org/abs/2507.00375

Existence and multiplicity of normalized solutions for the quasi-linear Schrödinger equations with mixed nonlinearities
In this paper, we study the existence and multiplicity of the normalized solutions to the following quasi-linear problem \begin{equation*} -Δu-Δ(|u|^2)u+λu=|u|^{p-2}u+τ|u|^{q-2}u, \text{ in }\mathbb{R}^N,~ 1\leq N\leq4, \end{equation*} with prescribed mass $$\int_{\mathbb{R}^N}|u|^2dx=a ,$$ where $λ\in\mathbb{R}$ appears as a Lagrange multiplier and the parameters $a,τ$ are all positive constants. We are concerned about the mass-mixed case $2

Convergence analysis of the dynamically regularized Lagrange multiplier method for the incompressible Navier-Stokes equations
Cao-Kha Doan, Thi-Thao-Phuong Hoang, Lili Ju, Rihui Lan
https://arxiv.org/abs/2508.14007

Convergence analysis of the dynamically regularized Lagrange multiplier method for the incompressible Navier-Stokes equations
This paper is concerned with temporal convergence analysis of the recently introduced Dynamically Regularized Lagrange Multiplier (DRLM) method for the incompressible Navier-Stokes equations. A key feature of the DRLM approach is the incorporation of the kinetic energy evolution through a quadratic dynamic equation involving a time-dependent Lagrange multiplier and a regularization parameter. We apply the backward Euler method with an explicit treatment of the nonlinear convection term and show…

Revisiting Coincident GR in Internal STEGR Formulation
Kyosuke Tomonari, Taishi Katsuragawa, Shin'ichi Nojiri
https://arxiv.org/abs/2506.22158 https://…

Revisiting Coincident GR in Internal STEGR Formulation
We revisit Coincident General Relativity (CGR) in the gauge approach to gravity based on Symmetric Teleparallel Equivalent to General Relativity (STEGR) in the {\it internal-space formulation}, which one of the authors recently proposed in Ref.~[J. Math. Phys. 66 (2025) 5, 052505]. First, we review the standard formulation of STEGR theories in the Palatini approach to gravity, in which formulation we impose the teleparallel and torsion-free conditions by using Lagrange multipliers. Second, we i…

Conditionally adaptive augmented Lagrangian method for physics-informed learning of forward and inverse problems using artificial neural networks
Qifeng Hu, Shamsulhaq Basir, Inanc Senocak
https://arxiv.org/abs/2508.15695

Conditionally adaptive augmented Lagrangian method for physics-informed learning of forward and inverse problems using artificial neural networks
We present several advances to the physics and equality constrained artificial neural networks (PECANN) framework that substantially improve its capability to learn solutions of canonical partial differential equations (PDEs). First, we generalize the augmented Lagrangian method (ALM) to support multiple independent penalty parameters, enabling simultaneous enforcement of heterogeneous constraints. Second, we reformulate pointwise constraint enforcement and Lagrange multipliers as expectations …

One year of ASPEX-SWIS operation -- Characteristic features, observations and science potential
Abhishek Kumar, Shivam Parashar, Prashant Kumar, Dibyendu Chakrabarty, Bhas Bapat, Aveek Sarkar, Manan S. Shah, Hiteshkumar L. Adalja, Arpit R. Patel, Pranav R. Adhyaru, M. Shanmugam, Swaroop B. Banerjee, K. P. Subramaniam, Tinkal Ladiya, Jacob Sebastian, Bijoy Dalal, Aakash Gupta, M. B. Dadhania, Santosh V. Vadawale, Shiv Kumar Goyal, Neeraj Kumar Tiwari, Aaditya Sarda, Sushil Kumar, Nishan…

One year of ASPEX-SWIS operation -- Characteristic features, observations and science potential
The Aditya-L1 mission, India's first dedicated solar observatory positioned at the first Lagrange point (L1) of the Sun-Earth system, carries the Solar Wind Ion Spectrometer (SWIS) as part of the ASPEX payload suite. Even before settling into its Halo orbit, SWIS has been providing nearly continuous in-situ measurements of solar wind ion spectra. Moments of the velocity distribution functions (VDFs) have been calculated to derive key solar wind parameters such as density, bulk speed, and temper…

Phases of a Bose-Einstein condensate of microwave-shielded dipolar molecules
Chiara J. Polterauer, Robert E. Zillich
https://arxiv.org/abs/2507.18986 https://

Phases of a Bose-Einstein condensate of microwave-shielded dipolar molecules
Bose-Einstein condensation of dipolar molecules can be achieved by shielding loss channels with microwave fields. The microwave coupling can be approximated by effective dipole-dipole interactions with a short-range repulsion. We study properties and stability of these molecular Bose gases with a many-body variational method, the hypernetted-chain Euler-Lagrange method for a wide range of densities and repulsion strengths of the microwave shield. We find a homogeneous gas-like phase which, howe…

Large deviations of ionic currents in dilute electrolytes
Jafar Farhadi, David T. Limmer
https://arxiv.org/abs/2507.18556 https://arxiv.org/pdf/2507.18556

Large deviations of ionic currents in dilute electrolytes
We evaluate the exponentially rare fluctuations of the ionic current for a dilute electrolyte by means of macroscopic fluctuation theory. We consider the fluctuating hydrodynamics of a fluid electrolyte described by a stochastic Poisson-Nernst-Planck equation. We derive the Euler-Lagrange equations that dictate the optimal concentration profiles of ions conditioned on exhibiting a given current, whose form determines the likelihood of that current in the long-time limit. For a symmetric electro…

Finite-Dimensional Quantum Systems under the Fourth Law of Thermodynamics
Rohit Kishan Ray
https://arxiv.org/abs/2508.14389 https://arxiv.org/pdf/2508.1438…

Finite-Dimensional Quantum Systems under the Fourth Law of Thermodynamics
The Steepest Entropy Ascent (SEA) ansatz, recently recognized as the fourth law of thermodynamics, governs the irreversible evolution of a system from a non-equilibrium state toward a unique maximum-entropy equilibrium. SEA builds upon the second law to unify mechanics and thermodynamics. Due to its nonlinear nature, exact solutions to the SEA equation of motion are scarce. To address this, the Fixed Lagrange Multiplier (FLM) method is developed as an approximate analytical tool, applicable to …

Persistence of Invariant Tori for Stochastic Nonlinear Schr\"{o}dinger in the Sense of Most Probable Paths
Xinze Zhang, Yong Li, Kaizhi Wang
https://arxiv.org/abs/2508.17284

Persistence of Invariant Tori for Stochastic Nonlinear Schrödinger in the Sense of Most Probable Paths
This paper investigates the application of KAM theory to the stochastic nonlinear Schrödinger equation on infinite lattices, focusing on the stability of low-dimensional invariant tori in the sense of most probable paths. For generality, we provide an abstract proof within the framework of stochastic Hamiltonian systems on infinite lattices. We begin by constructing the Onsager-Machlup functional for these systems in a weighted infinite sequence space. Using the Euler-Lagrange equation, we ide…

On some examples and counterexamples about weighted Lagrange interpolation with Exponential and Hermite weights
Patricia Szokol
https://arxiv.org/abs/2508.18029 https://

On some examples and counterexamples about weighted Lagrange interpolation with Exponential and Hermite weights
The famous Bernstein conjecture about optimal node systems of classical polynomial Lagrange interpolation, standing unresolved for over half a century, was solved by T. Kilgore in 1978. Immediately following him, also the additional conjecture of Erdős was solved by deBoor and Pinkus. These breakthrough achievements were built on a fundamental auxiliary result on nonsingularity of derivative (Jacobian) matrices of certain interval maxima in function of the nodes. After the above breakthrough, …

Size and Shape of Jupiter Trojan (2207) Antenor from Stellar Occultations
Feliphe S. Ferreira, Julio I. B. Camargo, Bruno E. Morgado, Viviane Peixoto, Josselin Desmars, Felipe Braga-Ribas, Altair Gomes-Junior, Bruno Sicardy, Jose Ortiz, R. Vieira-Martins, C. Pereira, Luana Liberato, Marcelo Assafin, Yucel Kilic, Rodrigo Boufleur, Flavia Rommel, Gustavo Benedetti-Rossi, Martin Banda-Huarca, Franck Marchis, Paolo Tanga, Benoit Blanc, Erick Bondoux, Alexandra Burnett, S. Calavia-Belloc, O…

Size and Shape of Jupiter Trojan (2207) Antenor from Stellar Occultations
Librating around the Lagrange L5, the Jupiter's Trojan (2207) Antenor has been observed in recent years and its rotational light curve suggests it to be a very likely binary asteroid candidate. From stellar occultations, we report results from three events from Europe and North America to estimate the 2D apparent size and shape of Jupiter's Trojan (2207) Antenor. For the best-fitted ellipse in the sky-plane, we determined that Antenor has a 2D apparent equatorial radius of 54.30 +/- 0.99 km at …

Structure-preserving parametric finite element methods for two-phase Stokes flow based on Lagrange multiplier approaches
Harald Garcke, Dennis Trautwein, Ganghui Zhang
https://arxiv.org/abs/2508.12326 …

Structure-preserving parametric finite element methods for two-phase Stokes flow based on Lagrange multiplier approaches
We present a novel formulation for parametric finite element methods to approximate two-phase Stokes flow. The new formulation is based on the classical Stokes equation in the bulk and a novel choice of interface conditions with additional Lagrange multipliers. This new Lagrange multiplier approach ensures that the numerical methods exactly preserve two physical structures of two-phase Stokes flow at the fully discrete level: (i) the energy-decaying and (ii) the volume-preserving properties. Mo…

Collision-Free Bearing-Driven Formation Tracking for Euler-Lagrange Systems
Haoshu Cheng, Martin Guay, Shimin Wang, Yunhong Che
https://arxiv.org/abs/2508.09908 https://

Collision-Free Bearing-Driven Formation Tracking for Euler-Lagrange Systems
In this paper, we investigate the problem of tracking formations driven by bearings for heterogeneous Euler-Lagrange systems with parametric uncertainty in the presence of multiple moving leaders. To estimate the leaders' velocities and accelerations, we first design a distributed observer for the leader system, utilizing a bearing-based localization condition in place of the conventional connectivity assumption. This observer, coupled with an adaptive mechanism, enables the synthesis of a nove…

Dislocation-Driven Nucleation Type Switching Across Repeated Ultrafast Magnetostructural Phase Transition
Jan Hajdu\v{c}ek, Antoine Andrieux, Jon Ander Arregi, Martin Tich\'y, Paolo Cattaneo, Beatrice Ferrari, Fabrizio Carbone, Vojt\v{e}ch Uhl\'i\v{r}, Thomas LaGrange
https://arxiv.org/abs/2507.18364

Dislocation-Driven Nucleation Type Switching Across Repeated Ultrafast Magnetostructural Phase Transition
Controlling magnetic order on ultrafast timescales, driven by spintronic and recording applications, is one of the main directions of current research in magnetism. Despite major advances in understanding the temporal evolution of magnetic order upon its emergence or quenching, experimental demonstration of the local link between microstructure and dynamic nucleation is missing. Here, taking advantage of the high structural and magnetic resolution of in situ transmission electron microscopy, we…

Holographic flavour and neural networks
Veselin G. Filev
https://arxiv.org/abs/2506.20115 https://arxiv.org/pdf/2506.20115

Holographic flavour and neural networks
In holography, flavour probe branes are used to introduce fundamental matter to the AdS/CFT correspondence. At a technical level, the probes are described by extremizing the DBI action and solving the Lagrange-Euler equations of motion. I report on applications of artificial neural networks that allow direct minimization of the regularized DBI action (interpreted as a free energy) without the need to derive and solve the equations of motion. I consider, as examples, magnetic catalysis of chiral…

Lagrange-like interpolation in unitary rings, Boolean algebras and Boolean posets
Ivan Chajda, Helmut L\"anger
https://arxiv.org/abs/2508.04836 https://

Lagrange-like interpolation in unitary rings, Boolean algebras and Boolean posets
It is known that every function with a finite support over a given field can be interpolated by means of the Lagrangian polynomial. The question is if a similar interpolation is possible if one considers a unitary ring or a Boolean algebra instead of a field. We get a positive answer to this question provided the similarity type of the algebra in question is enriched with one more unary operation, the so-called Baaz delta. We get an explicit construction of this interpolation polynomial in both…

A first-order condition for discrete-time distribution steering
Alberto Dom\'inguez Corella, David Gonz\'alez-S\'anchez
https://arxiv.org/abs/2508.21026 https://

A first-order condition for discrete-time distribution steering
We study a class of distribution-steering problems from a variational point of view. Under some differentiability assumptions, we derive necessary conditions for optimal Markov policies in the spirit of the Lagrange multiplier approach. We also provide a heuristic gradient-based method derived from the variational principle.

S-shaped Utility Maximization with VaR Constraint and Partial Information
Dongmei Zhu, Ashley Davey, Harry Zheng
https://arxiv.org/abs/2506.10103 https://

S-shaped Utility Maximization with VaR Constraint and Partial Information
We study S-shaped utility maximisation with VaR constraint and unobservable drift coefficient. Using the Bayesian filter, the concavification principle, and the change of measure, we give a semi-closed integral representation for the dual value function and find a critical wealth level that determines if the constrained problem admits a unique optimal solution and Lagrange multiplier or is infeasible. We also propose three algorithms (Lagrange, simulation, deep neural network) to solve the prob…

Determining the chemical potential via universal density functional learning
Florian Samm\"uller, Matthias Schmidt
https://arxiv.org/abs/2506.15608 ht…

Determining the chemical potential via universal density functional learning
We demonstrate that the machine learning of density functionals allows one to determine simultaneously the equilibrium chemical potential across simulation datasets of inhomogeneous classical fluids. Minimization of an implicit loss function based on an Euler-Lagrange equation yields both the universal one-body direct correlation functional, which is represented locally by a neural network, as well as the system-specific unknown chemical potential values. The method can serve as an efficient al…

Replaced article(s) found for physics.ins-det. https://arxiv.org/list/physics.ins-det/new
[1/1]:
- Shot-to-shot acquisition ultrafast electron diffraction
Remi Claude, Michele Puppin, Bruce Weaver, Paolo Usai, Thomas LaGrange, Fabrizio Carbone

Identifying Unmeasured Confounders in Panel Causal Models: A Two-Stage LM-Wald Approach
Bang Quan Zheng
https://arxiv.org/abs/2508.10342 https://arxiv.org/…

Identifying Unmeasured Confounders in Panel Causal Models: A Two-Stage LM-Wald Approach
Panel data are widely used in political science to draw causal inferences. However, these models often rely on the strong and untested assumption of sequential ignorability--that no unmeasured variables influence both the independent and outcome variables across time. Grounded in psychometric literature on latent variable modeling, this paper introduces the Two-Stage LM-Wald (2SLW) approach, a diagnostic tool that extends the Lagrange Multiplier (LM) and Wald tests to detect violations of this …

Integer continued fractions for complex numbers
Cormac O'Sullivan
https://arxiv.org/abs/2508.15078 https://arxiv.org/pdf/2508.15078

Integer continued fractions for complex numbers
We study a natural extension to complex numbers of the standard continued fractions. The basic algorithm is due to Lagrange and Gauss, though it seems to have gone mostly unnoticed as a way to create continued fractions. The new representations are shown to be unique, and to have useful properties. They also admit a geometric cutting sequence interpretation.

A new Lagrange multiplier approach for constructing structure preserving schemes, III. Bound preserving and energy dissipating
Qing Cheng, Tingfeng Wang, Xiaofei Zhao
https://arxiv.org/abs/2506.12402

A new Lagrange multiplier approach for constructing structure preserving schemes, III. Bound preserving and energy dissipating
In the third part of this series, we continue to explore the idea of the Lagrange multiplier introduced in the first part [2020, Comput. Methods Appl. Mech. Engr., 391, 114585] and refined in the second part [2022, SIAM J. Numer. Anal., 60, 970-998] to further develop efficient and accurate numerical schemes that preserve the maximum bound principle (MBP) and energy dissipation for solving gradient flows. The proposed framework allows us to begin with any conventional scheme as a predictor step…

Finite energy foliations in the restricted three-body problem
Lei Liu, Pedro A. S. Salom\~ao
https://arxiv.org/abs/2506.17867 https://

Finite energy foliations in the restricted three-body problem
This paper is about using pseudo-holomorphic curves to study the circular planar restricted three-body problem. The main result states that for mass ratios sufficiently close to $\frac{1}{2}$ and energies slightly above the first Lagrange value, the flow on the regularized component $\mathbb R P^3 \# \mathbb R P^3$ of the energy surface admits a finite energy foliation with three binding orbits, namely two retrograde orbits around the primaries and the Lyapunov orbit in the neck region about th…

Fast Equivariant Imaging: Acceleration for Unsupervised Learning via Augmented Lagrangian and Auxiliary PnP Denoisers
Guixian Xu, Jinglai Li, Junqi Tang
https://arxiv.org/abs/2507.06764

Fast Equivariant Imaging: Acceleration for Unsupervised Learning via Augmented Lagrangian and Auxiliary PnP Denoisers
We propose Fast Equivariant Imaging (FEI), a novel unsupervised learning framework to efficiently train deep imaging networks without ground-truth data. From the perspective of reformulating the Equivariant Imaging based optimization problem via the method of Lagrange multipliers and utilizing plug-and-play denoisers, this novel unsupervised scheme shows superior efficiency and performance compared to vanilla Equivariant Imaging paradigm. In particular, our PnP-FEI scheme achieves an order-of-m…

Follow-Up Exploration of the TWA 7 Planet-Disk System with JWST NIRCam
Katie A. Crotts, Aarynn L. Carter, Kellen Lawson, James Mang, Beth Biller, Mark Booth, Rodrigo Ferrer-Chavez, Julien H. Girard, Anne-Marie Lagrange, Michael C. Liu, Sebastian Marino, Maxwell A. Millar-Blanchaer, Andy Skemer, Giovanni M. Strampelli, Jason Wang, Olivier Absil, William O. Balmer, Rapha\"el Bendahan-West, Ellis Bogat, Rachel Bowens-Rubin, Ga\"el Chauvin, Cl\'emence Fontanive, Kyle Franson,…

Follow-Up Exploration of the TWA 7 Planet-Disk System with JWST NIRCam
The young M-star TWA 7 hosts a bright and near face-on debris disk, which has been imaged from the optical to the submillimeter. The disk displays multiple complex substructures such as three disk components, a large dust clump, and spiral arms, suggesting the presence of planets to actively sculpt these features. The evidence for planets in this disk was further strengthened with the recent detection of a point-source compatible with a Saturn-mass planet companion using JWST/MIRI at 11 $μ$m, …

Anisotropic Spacetimes in $f(G)$-gravity: Bianchi I, Bianchi III and Kantowski-Sachs Cosmologies
R. Bogadi, A. Giacomini, M. Govender, C. Hansraj, G. Leon, A. Paliathanasis
https://arxiv.org/abs/2508.18055

Anisotropic Spacetimes in $f(G)$-gravity: Bianchi I, Bianchi III and Kantowski-Sachs Cosmologies
We investigate the evolution of cosmological anisotropies within the framework of $f\left(G\right)$-gravity. Specifically, we consider a locally rotationally symmetric geometry in four-dimensional spacetime that describes the Bianchi I, Bianchi III, and the Kantowski-Sachs spacetimes. Within this context, we introduce a Lagrange multiplier which allows us to reformulate the geometric degrees of freedom in terms of a scalar field. The resulting theory is dynamically equivalent to an Einstein-Gau…

Integrals of motion on extremals of the equation Euler-Lagrange
V. P. Koshcheev
https://arxiv.org/abs/2508.11735 https://arxiv.org/pdf/2508.11735

Integrals of motion on extremals of the equation Euler-Lagrange
It is shown that a chain of closed systems of first order ordinary differential equations describing the evolution of moments can be constructed using the Jacobi equation. It is shown that Wronsky determinants for fundamental matrices of closed systems of first order ordinary differential equations are integrals of motion on extremals of the Euler-Lagrange equation.

The symmetric groups $S_n, n\geq 4$, and finite non-abelian simple groups are not embeddable in any Riordan group
Tian-Xiao He, Nikolai A. Krylov
https://arxiv.org/abs/2508.03056

The symmetric groups $S_n, n\geq 4$, and finite non-abelian simple groups are not embeddable in any Riordan group
We prove that the symmetric group of degree greater than three cannot be embedded into the Riordan group with coefficients in any commutative ring. We also prove the impossibility to embed finite non-abelian simple groups. As a closely related topic, we show why all truncated Riordan groups are solvable, in stark contrast to the unsolvability of the infinite-sized Riordan groups. Finally, we give an explicit embedding of the alternating group $A_4$ into the Lagrange subgroup with coefficients i…

Multi-Class-Token Transformer for Multitask Self-supervised Music Information Retrieval
Yuexuan Kong, Vincent Lostanlen, Romain Hennequin, Mathieu Lagrange, Gabriel Meseguer-Brocal
https://arxiv.org/abs/2507.12996

Multi-Class-Token Transformer for Multitask Self-supervised Music Information Retrieval
Contrastive learning and equivariant learning are effective methods for self-supervised learning (SSL) for audio content analysis. Yet, their application to music information retrieval (MIR) faces a dilemma: the former is more effective on tagging (e.g., instrument recognition) but less effective on structured prediction (e.g., tonality estimation); The latter can match supervised methods on the specific task it is designed for, but it does not generalize well to other tasks. In this article, w…

This https://arxiv.org/abs/2407.16363 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_qu…

Variational quantum algorithm based on Lagrange polynomial encoding to solve differential equations
Differential equations (DEs) serve as the cornerstone for a wide range of scientific endeavors, their solutions weaving through the core of diverse fields such as structural engineering, fluid dynamics, and financial modeling. DEs are notoriously hard to solve, due to their intricate nature, and finding solutions to DEs often exceeds the capabilities of traditional computational approaches. Recent advances in quantum computing have triggered a growing interest from researchers for the design of…

Superconvergent quadriatic finite element on uniform tetrahedral meshes
Yunqing Huang, Shangyou Zhang
https://arxiv.org/abs/2506.12407 https://

Superconvergent quadriatic finite element on uniform tetrahedral meshes
By a direct computation, we show that the $P_2$ interpolation of a $P_3$ function is also a local $H^1$-projection on uniform tetrahedral meshes, i.e., the difference is $H^1$-orthogonal to the $P_2$ Lagrange basis function on the support patch of tetrahedra of the basis function. Consequently, we show the $H^1$ and $L^2$ rconvergence of the $P_2$ Lagrange finite element on uniform tetrahedral meshes. Using the standard 20-points Lagrange $P_3$ interpolation, where the 20 nodes are exactly some…

Density dependent embedding potentials for piecewise exact densities
Tomasz Adam Wesolowski
https://arxiv.org/abs/2506.08744 https://…

Density dependent embedding potentials for piecewise exact densities
Frozen Density Embedding Theory (FDET) [Wesolowski {\it Phys. Rev. A} {\bf 77}, 012504 (2008)] provides the interpretation of the eigenvalue equations for an embedded $N'$-electron wavefunction, in which the embedding operator is multiplicative, as the Euler-Lagrange equation corresponding to the constrained minimisation of the Hohenberg-Kohn energy functional. The constraint is given by a non-negative function integrating to an integer $N-N'>0$ with $N$ being the total number of electrons in t…

Introduction to Nonlinear Spectral Analysis
Leon Bungert, Yury Korolev
https://arxiv.org/abs/2506.08754 https://arxiv.org/pdf/2506.08…

Introduction to Nonlinear Spectral Analysis
These notes are meant as an introduction to the theory of nonlinear spectral theory. We will discuss the variational form of nonlninear eigenvalue problems and the corresponding non-linear Euler--Lagrange equations, as well as connections with gradient flows. For the latter ones, we will give precise conditions for finite time extinction and discuss convergence rates. We will use this theory to study asymptotic behaviour of nonlinear PDEs and present applications in $L^\infty$ variational probl…

Normalized solutions for the NLS equation with mixed fractional Laplacians and combined nonlinearities
Shubin Yu, Chen Yang, Chun-Lei Tang
https://arxiv.org/abs/2506.20943

Normalized solutions for the NLS equation with mixed fractional Laplacians and combined nonlinearities
We look for normalized solutions to the nonlinear Schrödinger equation with mixed fractional Laplacians and combined nonlinearities $$ \left\{\begin{array}{ll} (-Δ)^{s_{1}} u+(-Δ)^{s_{2}} u=λu+μ|u|^{q-2}u+|u|^{p-2}u \ \text{in}\;{\mathbb{R}^{N}}, \\[0.1cm] \int_{\mathbb{R}^{N}}|u|^2\mathrm dx=a^2, \end{array} \right. $$ where $N\geq 2,\;00$ and $λ\in\mathbb R$ appears as an unknown Lagrange multiplier. We mainly focus on some special cases, inc…

The Constrained Symplectic Area Functional and its Floer Homology
Emilia Konrad
https://arxiv.org/abs/2507.06084 https://arxiv.org/pd…

The Constrained Symplectic Area Functional and its Floer Homology
This paper introduces a new Floer homology for periodic Reeb orbits on the boundaries of Liouville domains. The construction of this Constrained Floer Homology (CFH) is based on the symplectic area functional, restricted to loops satisfying a vanishing Hamiltonian mean value condition. While CFH shares its chain groups with Rabinowitz Floer homology (RFH), it avoids the use of a Lagrange multiplier, enabling a more intrinsic product structure. Our first main result shows that the Fredholm theor…

Replaced article(s) found for math.NT. https://arxiv.org/list/math.NT/new
[1/1]:
- The Markoff and Lagrange spectra on the Hecke group H4
Dong Han Kim, Deokwon Sim

Two classification results for stationary surfaces of the least moment of inertia
Rafael L\'opez
https://arxiv.org/abs/2507.12398 https://

Two classification results for stationary surfaces of the least moment of inertia
A surface in Euclidean space $\r^3$ is said to be an $α$-stationary surface if it is a critical point of the energy $\int_Σ|p|^α$, where $α\in\r$. These surfaces are characterized by the Euler-Lagrange equation $H(p)=α\frac{\langle N(p),p\rangle}{|p|^2}$, $p\inΣ$, where $H$ and $N$ are the mean curvature and the normal vector of $Σ$. If $α\not=0$, we prove that vector planes are the only ruled $α$-stationary surfaces. The second result of classification asserts that…

A Gauge-Theoretic Action Principle for Viscous Incompressible Fluids
Rashmi R. Nayak
https://arxiv.org/abs/2506.11202 https://arxiv.o…

A Gauge-Theoretic Action Principle for Viscous Incompressible Fluids
We propose a novel action principle for two dimensional incompressible fluid dynamics that naturally incorporates both vorticity and viscous dissipation via gauge field couplings. The action features a Chern Simons like term, $ε^{μνρ} A_μ\partial_νA_ρ$, capturing the topological structure of vorticity, alongside a quadratic term $(ε^{μνρ} \partial_νA_ρ)^2$ representing viscous damping. Incompressibility is enforced through a Lagrange multiplier, while coupling to an external potent…

A deep first-order system least squares method for the obstacle problem
Gabriel Acosta, Eugenia Bel\'en, Francisco M. Bersetche, Juan Pablo Borthagaray
https://arxiv.org/abs/2508.19412

A deep first-order system least squares method for the obstacle problem
We propose a deep learning approach to the obstacle problem inspired by the first-order system least-squares (FOSLS) framework. This method reformulates the problem as a convex minimization task; by simultaneously approximating the solution, gradient, and Lagrange multiplier, our approach provides a flexible, mesh-free alternative that scales efficiently to high-dimensional settings. Key theoretical contributions include the coercivity and local Lipschitz continuity of the proposed least-square…

Elastic bilayer membranes under confinement -- Existence, regularity, and rigidity
Matthias R\"oger, Fabian Rupp
https://arxiv.org/abs/2506.14520 http…

Elastic bilayer membranes under confinement -- Existence, regularity, and rigidity
Motivated by applications to cell biology, we study the constrained minimization of the Helfrich energy among closed surfaces confined to a container. We show existence of minimizers in the class of bubble trees of spherical weak branched immersions and derive the Euler--Lagrange equations which involve a measure-valued Lagrange multiplier that is concentrated on the coincidence set with the container boundary. We provide a careful analysis of this elliptic system and prove optimal regularity f…

X-SHYNE: X-Shooter spectra of young exoplanet analogs II. Presentation and analysis of the full library
Simon Petrus, Ga\"el Chauvin, Micka\"el Bonnefoy, Pascal Tremblin, Caroline Morley, Benjamin Charnay, Genaro Suarez, Jonathan Gagn\'e, Paulina Palma-Bifani, Allan Denis, Matthieu Ravet, Amelia Bayo, Bruno B\'ezard, Beth Biller, Philippe Delorme, Jacqueline Faherty, Jayesh M. Goyal, Kielan Hoch, Kevin Hoy, James S Jenkins, Anne-Marie Lagrange, Baptiste Lavie, Michael…

X-SHYNE: X-Shooter spectra of young exoplanet analogs II. Presentation and analysis of the full library
The X-SHYNE library is a homogeneous sample of 43 medium-resolution (R=8000) infrared (0.3-2.5um) spectra of young (<500Myr), low-mass (<20Mjup), and cold (Teff=600-2000K) isolated brown dwarfs and wide-separation companions observed with the VLT/X-Shooter instrument. To characterize our targets, we performed a global comparative analysis. We first applied a semi-empirical approach. By refining their age and bolometric luminosity, we derived key atmospheric and physical properties, such as Teff…

Enforcing Speech Content Privacy in Environmental Sound Recordings using Segment-wise Waveform Reversal
Modan Tailleur, Mathieu Lagrange, Pierre Aumond, Vincent Tourre
https://arxiv.org/abs/2507.08412

Enforcing Speech Content Privacy in Environmental Sound Recordings using Segment-wise Waveform Reversal
Environmental sound recordings often contain intelligible speech, raising privacy concerns that limit analysis, sharing and reuse of data. In this paper, we introduce a method that renders speech unintelligible while preserving both the integrity of the acoustic scene, and the overall audio quality. Our approach involves reversing waveform segments to distort speech content. This process is enhanced through a voice activity detection and speech separation pipeline, which allows for more precise…

A Taylor-Hood finite element method for the surface Stokes problem without penalization
Alan Demlow, Michael Neilan
https://arxiv.org/abs/2506.20419 https:…

A Taylor-Hood finite element method for the surface Stokes problem without penalization
Finite element approximation of the velocity-pressure formulation of the surfaces Stokes equations is challenging because it is typically not possible to enforce both tangentiality and $H^1$ conformity of the velocity field. Most previous works concerning finite element methods (FEMs) for these equations thus have weakly enforced one of these two constraints by penalization or a Lagrange multiplier formulation. Recently in [A tangential and penalty-free finite element method for the surface Sto…

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…

New examples of $M\setminus L$: intruder sets
Harold Erazo
https://arxiv.org/abs/2508.09872 https://arxiv.org/pdf/2508.09872…

New examples of $M\setminus L$: intruder sets
We exhibit new examples of regions of $M\setminus L$ where $M$ and $L$ denote the Markov and Lagrange spectra, respectively. These regions have a different nature from all known regions studied so far: they contain \emph{intruder sets} associated with distinct combinatorics that trespass the region where self-replication holds. Our construction follows the usual self-replication method but replaces the standard local uniqueness condition with a more flexible and weaker property. These examples …

On an Iterative Scheme for the Spinorial Yamabe Equation on Manifolds with Boundary
Eric Tr\'ebuchon
https://arxiv.org/abs/2506.18546 https://

On an Iterative Scheme for the Spinorial Yamabe Equation on Manifolds with Boundary
We study the existence of solutions to the spinorial Yamabe equation -- that is, the Euler--Lagrange equation associated with the conformal invariant introduced by S. Raulot -- for compact manifolds with boundary. For the inhomogeneous equation, we employ an iterative scheme to establish existence under smallness assumptions on the relevant parameters. Using bootstrapping methods, we extend the regularity of the solution to $C^\infty$ away from its zero set in the interior, and up to the bounda…

Quantum variational calculus on a lattice
Shahn Majid, Francisco Sim\~ao
https://arxiv.org/abs/2508.02628 https://arxiv.org/pdf/2508.02628

Quantum variational calculus on a lattice
We solve the long-standing problem of variational calculus on a noncommutative space or spacetime for a significant class of models with trivial jet bundle. Our approach entails a quantum version of the Anderson variational double complex $Ω(J^\infty)$ and includes Euler-Lagrange equations and a partial Noether's theorem. We show in detail how this works for a free field on a $\Bbb Z^m$ lattice regarded as a discrete noncommutative geometry, obtaining the Klein-Gordon equation for a scalar fie…

Mixed virtual element methods for a stress-velocity-rotation formulation in viscoelasticity
Sarvesh Kumar, Utkarsh Rajput, Ricardo Ruiz-Baier
https://arxiv.org/abs/2506.18168

Mixed virtual element methods for a stress-velocity-rotation formulation in viscoelasticity
In this paper we propose a new mixed virtual element formulation for the numerical approximation of viscoelasticity equations with weakly imposed stress symmetry. The governing equations use the Zener model and are expressed in terms of the principal unknowns of additively decomposed stress into elastic and internal viscoelastic contributions, while the rotation tensor and velocity act as Lagrange multipliers. The time discretisation uses Crank--Nicolson's scheme. We demonstrate the unique solv…

On the Markoff spectrum on the 6th Hecke group
Byungchul Cha, Dong Han Kim, Deokwon Sim
https://arxiv.org/abs/2506.08358 https://arxi…

On the Markoff spectrum on the 6th Hecke group
The discrete part of the Markoff spectrum on the 6th Hecke group $\mathbf H_6$ was known by A. Schmidt. In this paper, we study the Markoff and Lagrange spectra on $\mathbf H_6$ after the smallest accumulation point $4/\sqrt{3}$. We show that both spectra below $4/\sqrt{3} + ε$ have positive Hausdorff dimension for any positive $ε$. We also find maximal gaps and an isolated point in the spectra.

Higher dimensional Sacks-Uhlenbeck-type functionals and applications
Gianmichele Di Matteo, Tobias Lamm
https://arxiv.org/abs/2506.17166 https://

Higher dimensional Sacks-Uhlenbeck-type functionals and applications
In this work, we generalize Sacks-Uhlenbeck's existence result for harmonic spheres, constructing for $n \ge 2$, regular, non-trivial, $n$-harmonic $n$-spheres into suitable target manifolds. We obtain an infinite family of new null-homotopic such maps. The proof follows a similar perturbative argument, which in high dimensions leads to a degenerate and double-phase-type Euler-Lagrange system, making the uniform regularity needed to formalize the bubbling harder to achieve. Then, we develop a r…

A thorough study of Riemannian Newton's Method
Caio O. da Silva, Yuri A. Aoto, Felipe F. G. S. Costa, M\'arcio F. da Silva
https://arxiv.org/abs/2506.09297

A thorough study of Riemannian Newton's Method
This work presents a thorough numerical study of Riemannian Newton's Method (RNM) for optimization problems, with a focus on the Grassmannian and on the Stiefel manifold. We compare the Riemannian formulation of Newton's Method with its classical Euclidean counterpart based on Lagrange multipliers by applying both approaches to the important and challenging Hartree--Fock energy minimization problem from Quantum Chemistry. Experiments on a dataset of 125 molecules show that the Riemannian approa…

Optimal velocity fields for instantaneous magnetic field growth
Nicholas J. Moore, Stefan G. Llewellyn Smith
https://arxiv.org/abs/2508.03573 https://arxiv…

Optimal velocity fields for instantaneous magnetic field growth
We consider a variant of the kinematic dynamo problem. Rather than prescribing a velocity field and searching for high-growth magnetic fields via an eigenvalue problem, we treat the seed magnetic-field structure as given and ask which velocity field maximally enhances its instantaneous growth. We show this second problem has an elegant formulation in terms of variational calculus. Upon simultaneously constraining the velocity's kinetic energy and enstrophy, the Euler-Lagrange equation leads to …

Suppressed Intrinsic Curvature Gravity
Ido Ben-Dayan, Elena Emtsova
https://arxiv.org/abs/2507.04502 https://arxiv.org/pdf/2507.04502…

Suppressed Intrinsic Curvature Gravity
We consider various mechanisms of modifying the effect of intrinsic curvature in gravity with respect to general relativity. Two primary approaches are studied. First, by considering a Lagrange multiplier or an auxiliary field. Second, by non-minimal coupling between a scalar field and the intrinsic curvature scalar. We reproduce the basic solutions of FLRW cosmology, black hole solutions, Lense-Thirring effect, and gravitational waves. The speed of gravitational waves is modified in comparison…

Tree-based adaptive finite element methods for deformable image registration
Nicol\'as A. Barnafi, Alberto F. Mart{\i}n, Ricardo Ruiz-Baier
https://arxiv.org/abs/2506.15876

Tree-based adaptive finite element methods for deformable image registration
In this work we propose an adaptive Finite Element Method (FEM) formulation for the Deformable Image Registration problem (DIR) together with a residual-based a posteriori error estimator, whose efficiency and reliability are theoretically established. This estimator is used to guide Adaptive Mesh Refinement and coarsening (AMR). The nonlinear Euler-Lagrange equations associated with the minimisation of the relevant functional are solved with a pseudo time-stepping fixed-point scheme which is f…

Global Lipschitz regularity in anisotropic elliptic problems with natural gradient growth
Carlo Alberto Antonini, Andrea Cianchi
https://arxiv.org/abs/2507.14606

Global Lipschitz regularity in anisotropic elliptic problems with natural gradient growth
We deal with homogeneous Dirichlet and Neumann boundary-value problems for anisotropic elliptic operators of p-Laplace type. They emerge as Euler-Lagrange equations of integral functionals of the Calculus of Variations built upon possibly anisotropic norms of the gradient of trial functions. We establish global Lipschitz regularity of solutions under the weakest possible assumption on right-hand side of the equation, which may also include the gradient term with natural growth exponent. The res…

Structure-preserving space discretization of differential and nonlocal constitutive relations for port-Hamiltonian systems
Antoine Bendimerad-Hohl, Ghislain Haine, Laurent Lef\`evre, Denis Matignon
https://arxiv.org/abs/2507.06869

Structure-preserving space discretization of differential and nonlocal constitutive relations for port-Hamiltonian systems
We study the structure-preserving space discretization of port-Hamiltonian (pH) systems defined with differential constitutive relations. Using the concept of Stokes-Lagrange structure to describe these relations, these are reduced to a finite-dimensional Lagrange subspace of a pH system thanks to a structure-preserving Finite Element Method. To illustrate our results, the 1D nanorod case and the shear beam model are considered, which are given by differential and implicit constitutive relati…

Existence and asymptotical behavior of normalized solutions to focusing biharmonic HLS upper critical Hartree equation with a local perturbation
Jianlun Liu, Hong-Rui Sun, Ziheng Zhang
https://arxiv.org/abs/2507.14896

Existence and asymptotical behavior of normalized solutions to focusing biharmonic HLS upper critical Hartree equation with a local perturbation
This paper is concerned with the following focusing biharmonic HLS upper critical Hartree equation with a local perturbation $$ \begin{cases} Δ^2u-λu-μ|u|^{p-2}u-(I_α*|u|^{4^*_α})|u|^{4^*_α-2}u=0\ \ \mbox{in}\ \mathbb{R}^N, \\[0.1cm] \int_{\mathbb{R}^N} u^2 dx = c, \end{cases} $$ where $0<α0$, $2+\frac{8}{N}=:\bar{p}\leq p<4^*:=\frac{2N}{N-4}$, $4^*_α:=\frac{N+α}{N-4}$, $λ\in \mathbb{R}$ is a Lagrange multiplier and $I_α$ is th…

$\textit{A Priori}$ Error Analysis for the $p$-Stokes Equations with Slip Boundary Conditions: A Discrete Leray Projection Framework
Alex Kaltenbach, J\"orn Wichmann
https://arxiv.org/abs/2507.15016

$\textit{A Priori}$ Error Analysis for the $p$-Stokes Equations with Slip Boundary Conditions: A Discrete Leray Projection Framework
We present an $\textit{a priori}$ error analysis for the kinematic pressure in a fully-discrete finite-differences/-elements discretization of the unsteady $p$-Stokes equations, modelling non-Newtonian fluids. This system is subject to both impermeability and perfect Navier slip boundary conditions, which are incorporated either weakly via Lagrange multipliers or strongly in the discrete velocity space. A central aspect of the $\textit{a priori}$ error analysis is the discrete Leray projection,…

Quantum Hamiltonian Descent based Augmented Lagrangian Method for Constrained Nonconvex Nonlinear Optimization
Mingze Li, Lei Fan, Zhu Han
https://arxiv.org/abs/2508.02969 https…

Quantum Hamiltonian Descent based Augmented Lagrangian Method for Constrained Nonconvex Nonlinear Optimization
Nonlinear programming (NLP) plays a critical role in domains such as power energy systems, chemical engineering, communication networks, and financial engineering. However, solving large-scale, nonconvex NLP problems remains a significant challenge due to the complexity of the solution landscape and the presence of nonlinear nonconvex constraints. In this paper, we develop a Quantum Hamiltonian Descent based Augmented Lagrange Method (QHD-ALM) framework to address largescale, constrained noncon…

Rigidity of solutions to singular/degenerate semilinear critical equations
Giovanni Catino, Dario Daniele Monticelli, Alberto Roncoroni
https://arxiv.org/abs/2506.15611

Rigidity of solutions to singular/degenerate semilinear critical equations
This paper deals with singular/degenerate semilinear critical equations which arise as the Euler-Lagrange equation of Caffarelli-Kohn-Nirenberg inequalities in $\mathbb{R}^d$, with $d\geq 2$. We prove several rigidity results for positive solutions, in particular we classify solutions with possibily infinite energy when the intrinsic dimension $n$ satisfies $2

A Cubed Sphere Fast Multipole Method
Anthony Chen, Robert Krasny
https://arxiv.org/abs/2508.13550 https://arxiv.org/pdf/2508.13550

A Cubed Sphere Fast Multipole Method
This work describes a new version of the Fast Multipole Method for summing pairwise particle interactions that arise from discretizing integral transforms and convolutions on the sphere. The kernel approximations use barycentric Lagrange interpolation on a quadtree composed of cubed sphere grid cells. The scheme is kernel-independent and requires kernel evaluations only at points on the sphere. Results are presented for the Poisson and biharmonic equations on the sphere, barotropic vorticity eq…

Long time behavior of the Vlasov-Maxwell-Fokker-Planck system with a strong external magnetic field
Anh-Tuan Vu
https://arxiv.org/abs/2508.12231 https://ar…

Long time behavior of the Vlasov-Maxwell-Fokker-Planck system with a strong external magnetic field
The subject matter of this paper concerns the magnetic confinement of plasma. We investigate the long time behavior of the Vlasov-Maxwell-Fokker-Planck system under the effect of a strong external magnetic field. We first formally derive an asymptotically reduced model. In three space dimensions, a constraint occurs along the parallel direction to the magnetic field. To eliminate the corresponding Lagrange multiplier, we then study the Vlasov-Maxwell-Fokker-Planck system in two spatial dimensio…

Combining Nonlinear FETI-DP Methods and Quasi-Newton Methods using an SQP Approach
Stephan K\"ohler, Oliver Rheinbach
https://arxiv.org/abs/2508.11309 https://

Combining Nonlinear FETI-DP Methods and Quasi-Newton Methods using an SQP Approach
The combination of nonlinear FETI-DP (Dual Primal Finite Element Tearing and Interconnecting) and Quasi-Newton methods using a sequential quadratic programming (SQP) approach is considered. Nonlinear FETI-DP methods are parallel iterative solution methods for nonlinear finite element problems, based on divide and conquer, using Lagrange multipliers. In the method, we use Quasi-Newton approximations of Hessian for the quadratic programs, where the initial approximation uses the exact Hessian. To…

Optimal ${L^2}$ error estimates for 2D/3D incompressible Cahn--Hilliard--magnetohydrodynamic equations
Haiyan Su, Jilu Wang, Zeyu Xia, Ke Zhang
https://arxiv.org/abs/2506.13080

Optimal ${L^2}$ error estimates for 2D/3D incompressible Cahn--Hilliard--magnetohydrodynamic equations
This paper focuses on an optimal error analysis of a fully discrete finite element scheme for the Cahn--Hilliard--magnetohydrodynamic (CH-MHD) system. The method use the standard inf-sup stable Taylor--Hood/MINI elements to solve the Navier--Stokes equations, Lagrange elements to solve the phase field, and particularly, the Nédélec elements for solving the magnetic induction field. Suffering from the strong coupling and high nonlinearity, the previous works just provide suboptimal error estim…

Nonrelativistic limit of ground states to $L^2$-supercritical nonlinear Dirac equations
Pan Chen, Yanheng Ding, Qi Guo
https://arxiv.org/abs/2507.11203 htt…

Nonrelativistic limit of ground states to $L^2$-supercritical nonlinear Dirac equations
In this paper, we study the existence and nonrelativistic limit of normalized ground states for the following nonlinear Dirac equation with power-type potentials \begin{equation*} \begin{cases} &-i c\sum\limits_{k=1}^3α_k\partial_k u +mc^2 β{u}- |{u}|^{p-2}{u}=ω{u}, \\ &\displaystyle\int_{\mathbb{R}^3}\vert u \vert^2 dx =1. \end{cases} \end{equation*} We demonstrate the existence of ground states for large $c$ and establish the uniqueness of the associated Lagrange multiplier f…

Quasi-optimality of the Crouzeix-Raviart FEM for p-Laplace-type problems
Johannes Storn
https://arxiv.org/abs/2507.12742 https://arxi…

Quasi-optimality of the Crouzeix-Raviart FEM for p-Laplace-type problems
We verify quasi-optimality of the Crouzeix-Raviart FEM for nonlinear problems of $p$-Laplace type. More precisely, we show that the error of the Crouzeix-Raviart FEM with respect to a quasi-norm is bounded from above by a uniformly bounded constant times the best-approximation error plus a data oscillation term. As a byproduct, we verify a novel more localized a priori error estimate for the conforming lowest-order Lagrange FEM.

A hybrid isogeometric and finite element method: NURBS-enhanced finite element method for hexahedral meshes
Duygu Sap
https://arxiv.org/abs/2506.13694 http…

A hybrid isogeometric and finite element method: NURBS-enhanced finite element method for hexahedral meshes
In this paper, we present a NURBS-enhanced finite element method that integrates NURBS-based boundary representations of geometric domains into standard finite element frameworks applied to hexahedral meshes. We decompose an open, bounded, convex three-dimensional domain with a NURBS boundary into two parts, define the NURBS-enhanced finite elements over the boundary layer, and use piecewise-linear Lagrange finite elements in the interior region. We introduce a novel quadrature rule and a novel…

Normalized solutions for a Sobolev critical quasilinear Schr\"odinger equation
Yuxin Li, Meijie Yang, Xiaojun Chang
https://arxiv.org/abs/2506.10870 h…

Normalized solutions for a Sobolev critical quasilinear Schrödinger equation
In this paper, we study the existence of normalized solutions for the following quasilinear Schrödinger equation with critical exponent: \begin{equation*} -Δu-uΔ(u^2)+λu=τ|u|^{q-2}u+|u|^{2\cdot2^*-2}u,~~~~x\in\R^N, \end{equation*} under the mass constraint $\int_{\R^N}|u|^2dx=c$ for some prescribed $c>0$. Here $τ\in \mathbb{R}$ is a parameter, $λ\in\R$ appears as a Lagrange multiplier, $N\ge3$, $2^*:=\frac{2N}{N-2}$ and $2

Unsteady Navier-Stokes Equations On A Stationary Surface
Charles M. Elliott, Achilleas Mavrakis
https://arxiv.org/abs/2508.09266 https://arxiv.org/pdf/2508…

Unsteady Navier-Stokes Equations On A Stationary Surface
In this paper we consider a fully discrete numerical method for the unsteady Navier-Stokes equations on a smooth closed stationary surface in $\mathbb{R}^3$. We use the surface finite element method (SFEM) with a generalized Taylor-Hood finite element pair $\mathrm{\mathbf{P}}_{k_u}$/$\mathrm{P}_{k_{pr}}$/$\mathrm{P}_{k_λ}$, where we enforce the tangential condition of the velocity field weakly, by introducing an extra Lagrange multiplier $λ$. Depending on the richness of the finite element s…

Elliptic interface problem approximated by CutFEM: I. Conservative flux recovery and numerical validation of adaptive mesh refinement
Daniela Capatina, Aimene Gouasmi, Cuiyu He
https://arxiv.org/abs/2507.03492

Elliptic interface problem approximated by CutFEM: I. Conservative flux recovery and numerical validation of adaptive mesh refinement
We study an elliptic interface problem with discontinuous diffusion coefficients on unfitted meshes using the CutFEM method. Our main contribution is the reconstruction of conservative fluxes from the CutFEM solution and their use in a posteriori error estimation. We introduce a hybrid mixed formulation with locally computable Lagrange multipliers and reconstruct the flux in the immersed Raviart-Thomas space. Based on this, we propose a new a posteriori error estimator that includes both volume…

Numerical solution of the wave equation outside a sphere
Michael J. Carley
https://arxiv.org/abs/2506.04809 https://arxiv.org/pdf/250…

Numerical solution of the wave equation outside a sphere
A method is presented for the fast evaluation of the transient acoustic field generated outside a spherical surface by sources inside the surface. The method employs Lebedev quadratures, which are the optimal method for spatial integration, and Lagrange interpolation and differentiation in an advanced time algorithm for the evaluation of the transient field. Numerical testing demonstrates that the approach gives near machine-precision accuracy and a speed-up in evaluation time which depends on …