3729 papers
This paper establishes the existence, uniqueness, and sharp boundary asymptotics of large solutions to semilinear elliptic equations with gradient-dependent terms and singular weights, while also proving their strict convexity and identifying them as value functions for infinite-horizon stochastic optimal control problems.
This paper answers a question posed by Ben Yaacov, Ibarlucía, and Tsankov by demonstrating an explicit construction of an affine formula using quantifier alternations to calculate distances between -tuples in -valued -structures.
This paper establishes the existence and uniqueness of strong solutions for a stochastic differential equation driven by the sum of two correlated fractional Brownian sheets with distinct Hurst parameters, demonstrating that the additive noise regularizes the system to ensure well-posedness even under weak drift assumptions.
This paper presents a simple construction of algebro-geometric solutions to the Gelfand–Dickey hierarchy using an -type infinite ODE system and Dubrovin's method, while also deriving a formula for the -point function of the associated Riemann -function.
This paper establishes the existence of sign-changing solutions to a critical elliptic equation involving a Yamabe type operator on a compact manifold with boundary, contingent upon specific geometric conditions.
This paper constructs simplified oscillatory reconstructions based on the nontrivial zeros of Dirichlet L-functions to visualize how interference patterns act as analytic filters that separate primes into congruence classes, thereby providing a visual bridge between the zero distributions of L-functions and the algebraic structure of cyclotomic fields.
This paper establishes an extreme value theorem for the geodesic flow on the hyperbolic surface associated with the theta group by introducing a spliced continued fraction algorithm, proving its dynamical equivalence to the flow's first return map, and deriving a Galambos-type extreme value law for maximal cusp excursions via spectral analysis of the transfer operator.
This paper demonstrates that entropy acts as a driving force in various evolution equations because it characterizes the invariant measure of an underlying stochastic process, thereby unifying diverse examples from stochastic processes, gradient flows, and GENERIC systems under a single principle.
This paper proposes TV-Select, a unified framework that simultaneously identifies relevant variables and distinguishes between constant and time-varying effects in longitudinal models by employing a doubly penalized B-spline approach with group Lasso and roughness penalties to achieve accurate structural recovery, smooth estimation, and improved predictive performance.
This paper establishes the existence and uniqueness of solutions to rough differential equations driven by tempered fractional Brownian motion with Hurst index by canonically lifting the noise to a geometric rough path and employing a Doss-Sussmann transformation combined with a greedy stopping time sequence, while also deriving quantitative growth bounds for the solutions.
This paper presents a data-driven numerical approach using Flow Map Learning to construct a deep neural network model of drag and lift forces, enabling real-time active flow control for over 20% drag reduction in cylinder flow without requiring online flow field simulations.
This paper establishes the existence and asymptotic behavior of foliations by area-minimizing hypersurfaces in arbitrary-dimensional asymptotically flat manifolds with multiple ends, while also proving a global regularity result for free-boundary area-minimizing hypersurfaces in dimensions up to eight.
This paper proposes HSM-ADMM, a novel distributed stochastic algorithm for nonconvex composite optimization that achieves optimal complexity with a single-loop structure and minimal communication by employing node-specific adaptive step sizes to decouple convergence stability from global network properties.
This paper investigates BCH and LCD cyclic codes of length over finite fields by analyzing cyclotomic cosets to determine code dimensions, improve minimal distance bounds, establish conditions for dually-BCH codes when is odd, and enumerate all LCD cyclic codes, with some constructed codes proven to be optimal.
This paper constructs the parametrix for elliptic Gevrey pseudodifferential operators by establishing a Banach algebra structure for formal Gevrey symbols, which is then applied to derive estimates for adiabatic projectors in the Gevrey setting.
This paper constructs and proves the existence of an infinite sequence of strongly regular digraphs with parameters by utilizing block circulant matrices, polynomial arithmetic, and computational tools to derive explicit adjacency formulas and propose a conjecture regarding their automorphism groups.
This paper introduces a new notion of -chains for continuous-time semiflows inspired by the shadow-orbit property and proves that, for systems with strong compact dynamics, this definition generates the same chain-recurrent structure as Conley's classical -chains.
This paper rigorously establishes the low Mach number limit and derives explicit convergence rates for a three-dimensional viscous compressible two-fluid model with algebraic pressure closure, proving that its well-prepared strong solutions converge to the incompressible Navier–Stokes equations as the Mach number tends to zero.
This paper establishes that Tensor-Based Modulation (TBM) is a geometrically uniform coded modulation scheme derived from a non-binary linear block code over , demonstrating its algebraic structure through explicit generator matrix derivation and validating its robustness in both single-user and multi-user wireless channels.
The paper establishes that topological symplectic manifolds possess a canonical bi-Lipschitz structure, a result that yields the first known examples demonstrating both the non-existence and non-uniqueness of topological symplectic structures.