A coupled Kolmogorov-Arnold Network and Level-Set framework for evolving interfacesKolmogorov-Arnold Networks (KANs) require significantly smaller architectures compared to multilayer perceptron (MLP)-based approaches, while retaining expressive power through spline-based…Tarus Pande, V M S K Minnikanti, Shyamprasad Karagadde·Jan 14, 2026SaveLearn
Quantization Commutes with Reduction of Chern-Simons Gauge TheoryWe prove an infinite-dimensional version of "quantization commutes with reduction" in the framework of geometric quantization of Chern-Simons gauge theory, focusing on the genus one case. The proof…Geyang Dai, Ruiming Liang, Yang Zhang·Jan 14, 2026SaveLearn
Stochastic Implicit Lagrange-Poincar\'e ReductionIn this paper we consider reduction of the stochastic Hamilton-Pontryagin principle formulated on the Pontryagin bundle of a manifold Q. We prove that a stochastic action invariant under the free…Archishman Saha·Jan 13, 2026SaveLearn
Newell-Whitehead-Segel equation,A Simpler ProofPrevious analysis of the Newell-Whitehead-Segel equation proved the best solution is null; although, the method of solution generated complex nested integrals, therefore, difficult to analyze…Luisiana X. Cundin·Jan 13, 2026SaveLearn
Upper and Lower Bounds for The Quantum Dynamics of One-Dimensional Divergence-Type Random Jacobi OperatorsWe study quantum transport for the discrete one-dimensional random Jacobi operator of divergence-gradient type. For strictly positive and bounded random variables, we analyze the q-moments of the…Long Li, Wei Wang, Shiwen Zhang·Jan 13, 2026SaveLearn
Application of the theory of C*-algebras to the emergence of hydrodynamics in quantum many-body systemsThis Ph.D. thesis reports on progress in rigorously establishing hydrodynamic principles from the microscopic Hamiltonian dynamics of quantum many-body systems in a general, non-model-specific…Dimitrios Ampelogiannis·Jan 13, 2026SaveLearn
Conservation laws and exact solutions of a nonlinear acoustics equation by classical symmetry reductionSymmetries and conservation laws are studied for a generalized Westervelt equation which is a nonlinear partial differential equation modelling the propagation of sound waves in a compressible…Almudena del Pilar Márquez, Elena Recio, María Luz Gandarias·Jan 13, 2026SaveLearn
Square roots of complexified quaternionsSquare roots of complexified (complex) quaternions, namely, the Hamilton quaternion, coquaternion, nectorine, and conectorine are investigated. The isomorphisms between the complex quaternions and…Adolfas Dargys, Arturas Acus·Jan 13, 2026SaveLearn
Algebras of distributions suitable for phase-space quantum mechanics. IThe twisted product of functions on R2N is extended to a *-algebra of tempered distributions which contains the rapidly decreasing smooth functions, the distributions of compact support, and…José M. Gracia-Bondía, Joseph C. Várilly·Jan 13, 2026SaveLearn
A Non-Renormalization Theorem for Local Functionals in Ghost-Free Vector Field Theories Coupled to Dynamical GeometryWe establish a non-renormalization theorem for a class of ghost-free local functionals describing massive vector field theories coupled to dynamical geometry. Under the assumptions of locality,…Lavinia Heisenberg, Shayan Hemmatyar, Nadine Nussbaumer·Jan 12, 2026SaveLearn
On eigenvalues of the Landau Hamiltonian with a periodic electric potentialWe consider the Landau Hamiltonian HB+V on L2( R2) with a periodic electric potential V. For every m∈ N we prove that there exist nonconstant periodic…Leonid Danilov·Jan 12, 2026SaveLearn
On the weak coupling limit of the periodic quantum Lorentz gasWe report partial progress on the weak coupling limit behavior of observables for the periodic quantum Lorentz gas. Our results indicate that for certain observables, the limit behavior is trivial…Massimiliano Gubinelli, Vishnu Sanjay·Jan 12, 2026SaveLearn
A proposal for the algebra of a novel noncommutative spacetimeWe investigate the quantum structure of spacetime at fundamental scales via a novel, Lorentz-invariant noncommutative coordinate framework. Building on insights from noncommutative geometry, spectral…Markus B. Fröb, Albert Much, Kyriakos Papadopoulos·Jan 12, 2026SaveLearn
Finslerian geometrodynamicsWe construct a unified framework of geometrodynamics based on the Finsler geometry to reveal the relationship between spacetime and dynamics.The Lagrangian of electron in electromagnetic field as the…Mingwei Zhou, Shi-Dong Liang·Jan 12, 2026SaveLearn
Integrable Stochastic Processes Associated with the D2 AlgebraWe introduce an integrable stochastic process associated with the D2 quantum group, which can be decomposed into two symmetric simple exclusion processes. We establish the integrability of the…Guang-Liang Li, Xin Zhang, Junpeng Cao et al.·Jan 12, 2026SaveLearn
A Non-Reciprocal Elliptic Spectral Solution of the Right-Angle Penetrable Wedge Transmission ProblemWe study the two-dimensional time-harmonic scalar transmission problem for an impedance-matched penetrable right-angle wedge: the exterior medium has wavenumber k0 and the interior sector |theta| <…Jonas Matuzas·Jan 11, 2026SaveLearn
A PDE approach for the invariant measure of stochastic oscillators with hysteresisThis paper presents a PDE approach as an alternative to Monte Carlo simulations for computing the invariant measure of a white-noise-driven bilinear oscillator with hysteresis. This model is widely…Lihong Guo, Harry L. F. Ip, Mingyang Wang·Jan 11, 2026SaveLearn
Classical elliptic BC1 Ruijsenaars-van Diejen model: relation to Zhukovsky-Volterra gyrostat and 1-site classical XYZ model with boundariesWe present a description of the classical elliptic BC1 Ruijsenaars-van Diejen model with 8 independent coupling constants through a pair of BC1 type classical Sklyanin algebras…A. Mostovskii, A. Zotov·Jan 11, 2026SaveLearn
Inverse problem for the divisor of the good Boussinesq equationA third-order operator with periodic coefficients is an L-operator in the Lax pair for the Boussinesq equation on a circle. The projection of the divisor of the Floquet solution poles for this…Andrey Badanin, Evgeny Korotyaev·Jan 10, 2026SaveLearn
Comminution as a Non-Hermitian Quantum Field Theory: Log-Size Jump Generators, Branching Embeddings, and the Airy Solvable SectorPure-breakage population balance equations (PBEs) give the standard deterministic description of fragmentation and comminution. They predict mean particle size distributions, but they do not…Juan J. Segura·Jan 10, 2026SaveLearn
Non-Linear Generalization of the DLR Equations: q-Specifications and q-Equilibrium MeasuresWe introduce a non-linear generalization of the classical Dobrushin-Lanford-Ruelle (DLR) framework by developing the concept of a q-specification and the associated q-equilibrium measures.…F. H. Haydarov, B. A. Omirov, U. A. Rozikov·Jan 10, 2026SaveLearn
An Operator-Algebraic Framework for Anyons and Defects in Quantum Spin SystemsIn this dissertation, we detail an operator algebraic approach to studying topological order in the infinite volume setting. We give a thorough and self-contained review of the DHR-style approach on…Siddharth Vadnerkar·Jan 9, 2026SaveLearn
10-plectic formulation of gravity and Cartan connectionsWe give a Hamiltonian formulation of %the first order Weyl--Einstein--Cartan gravity which is covariant from the viewpoint of the geometry of the principal fiber bundle. The connection is represented…Dimitri Vey·Jan 8, 2026SaveLearn
Modeling phononic band gap in microstructured solids using the Riemann-Cartan geometric frameworkThis paper discusses the modeling of acoustic wave fields in microstructured elastic solids within the framework of Riemann-Cartan geometry. We consider a scenario in which microstructural…Ilya Peshkov, Loïc Le Marrec·Jan 8, 2026SaveLearn
Multiplicative Averages of Plancherel Random Partitions: Elliptic Functions, Phase Transitions, and ApplicationsWe consider random integer partitions λ that follow the Poissonized Plancherel measure of parameter t2. Using Riemann-Hilbert techniques, we establish the asymptotics of the…Mattia Cafasso, Matteo Mucciconi, Giulio Ruzza·Jan 8, 2026SaveLearn