5443 papers
This paper applies the classical Lie symmetry method to a nonlinear heat-diffusion equation with variable coefficients to classify admitted symmetries, reduce the partial differential equation to ordinary differential equations, and construct invariant solutions for physically relevant cases such as Storm-type materials and power-law dependencies.
This paper establishes that embedded infinite plane triangulations within ergodic scale-free environments converge to their circle packing and Riemann uniformization embeddings on a large scale, provided that specific moment and connectivity conditions are met.
This paper presents new deformation and involutivity theorems for Poisson quasi-Nijenhuis manifolds under factorization hypotheses on their defining forms, supported by examples of involutive structures, to advance the application of this geometry to classical completely integrable systems.
This paper proposes a heuristic MIMO-CC delivery framework that enables asymmetric stream allocation while guaranteeing linear decodability through a newly derived criterion, thereby expanding the achievable Degrees of Freedom region beyond the limitations of existing symmetric-constrained designs.
This paper establishes that both geometric and homological finiteness properties of group pairs remain invariant under a suitably defined notion of quasi-isometry for group pairs.
This short note resolves a problem posed by Wickstead regarding the sequential monotone closure of spaces, a topic arising from the study of Riesz completions of regular operator spaces between Banach lattices.
This paper constructs infinitely many -component Brunnian links of 3-balls in the 4-sphere for each integer by utilizing and providing a new proof for a result concerning splitting spheres for trivial two-component links of 2-spheres.
This paper introduces and analyzes a broad class of continuous directed polymers in driven by Gaussian environments, establishing their structural properties, proving a sharp measure-theoretic dichotomy regarding their relation to Wiener measure, and demonstrating diffusive behavior in high dimensions and high temperatures, thereby extending the Alberts--Khanin--Quastel framework to higher-dimensional settings.
Inspired by R. Heitmann's proof of the Direct Summand Conjecture and G. Faltings' normalized length, this paper establishes new results on local cohomology modules in mixed characteristic using the Frobenius map, with significant implications for the study of splinters.
This paper introduces a new poset property defined via a variation of the Banach-Mazur game that strengthens -strategic closedness, proves that the Proper Forcing Axiom (PFA) is preserved under forcing with such posets, and applies this result to reproduce Magidor's theorem on the consistency of PFA with weak square principles while distinguishing the property from -operational closedness.
This paper proposes and analyzes a novel class of modified averaged vector field methods that simultaneously preserve multiple invariants for conservative Stratonovich stochastic differential equations, proving their mean square convergence order of 1 under commutative noises and demonstrating their superiority in long-time simulations through numerical experiments.
This paper establishes the probabilistic superiority of stochastic symplectic methods over non-symplectic ones by proving that the former asymptotically preserve the large deviations principles governing the exponential decay of hitting probabilities for the mean position and velocity of stochastic Hamiltonian systems, a result demonstrated via the Gärtner–Ellis theorem on the linear stochastic oscillator.
This paper determines the all-genus Hodge-Gromov-Witten theory for smooth hypersurfaces in weighted projective spaces defined by chain, loop, or general invertible polynomials, providing the first genus-zero Gromov-Witten invariants for non-Gorenstein ambient spaces where convexity fails.
This paper establishes that symplectic discretizations, including spectral Galerkin spatial semi-discretization and temporal full discretization, weakly asymptotically preserve the large deviations principle of the stochastic linear Schrödinger equation, thereby providing an effective numerical approach for approximating the LDP rate function in infinite-dimensional spaces.
This paper establishes convergence rates for scalable pseudo-likelihood-based -estimators of random graph models with dependent edges and increasing parameter dimensions, addressing challenges like phase transitions and near-degeneracy through a novel class of generalized -models.
This paper presents a convergence analysis for minimum action methods coupled with finite difference schemes, establishing that the convergence orders of the discrete Freidlin-Wentzell action functional are $1/21\theta$-method for small-noise stochastic differential equations in the context of large deviations.
This paper establishes the convergence of the probability density for a fully discrete finite difference method solving the stochastic Cahn--Hilliard equation with multiplicative space-time white noise by introducing a novel localization argument to overcome the non-Lipschitz drift and partially resolving an open problem regarding the numerical computation of the solution's density.
This paper introduces a unified definition of Anosov representations for relatively hyperbolic groups that encompasses various existing notions of geometrically finite behavior and proves their stability under deformations satisfying specific dynamical conditions on peripheral subgroups.
This paper proposes a co-design framework that jointly optimizes communication topology and differential privacy levels in multi-agent formation control to balance privacy protection, network connectivity, and steady-state performance.
This paper introduces and analyzes the Generalized Multiplicative Gradient (GMG) method for solving convex optimization problems over symmetric cones with non-Lipschitz gradients, establishing an convergence rate through novel theoretical results and demonstrating its superior computational complexity compared to other first-order methods across several key applications.