4625 papers
This paper demonstrates that for a symplectic manifold with a monoidal Fukaya category, the monoidal structure uniquely determines the homological mirror functor to the derived category of coherent sheaves on its mirror , thereby filling a gap in the literature regarding the reconstruction of the mirror from categorical data.
This paper establishes that while measure-valued sources on lower-dimensional sets degrade global convergence rates for finite element methods due to solution singularities, optimal local and error estimates are still achievable in subdomains strictly separated from the source support.
This paper constructs an instanton cochain complex using the eigenspaces of a deformed mapping cone Laplacian and proves its cochain isomorphism to the topologically defined mapping cone Thom-Smale complex, thereby establishing a bridge between analytic and topological approaches to the wedge by a smooth closed form.
This paper derives a discrete-time channel model for optical communications with intensity modulation and direct detection affected by laser relative intensity noise, revealing that signal-dependent noise with memory causes achievable information rates to saturate with dense constellations when the receiver ignores this memory.
This paper presents a discontinuous Galerkin numerical analysis of a nonlinear multiphysics model coupling the Westervelt wave equation and a convection-diffusion equation to simulate ultrasound-enhanced drug delivery, establishing well-posedness and optimal convergence rates for the semi-discrete system under suitable assumptions.
This paper addresses the performance degradation caused by fiber Kerr nonlinearity in high-power optical satellite uplinks by developing a realistic system model and proposing low-complexity digital signal processing techniques, including constellation shaping via a look-up table and nonlinear phase rotation, which collectively increase the maximum acceptable link loss by up to 6 dB while enabling adaptive rate tuning.
This paper investigates random walks in finite Abelian groups governed by Markov chains within specific Birkhoff subpolytopes, demonstrating that their evolving probability distributions converge within a time-dependent shrinking polytope characterized by various statistical metrics, and illustrates these findings through physical implementations involving non-selective quantum measurements in both additive and Heisenberg-Weyl groups.
This paper derives the polar-finite decomposition for odd-spin admissible-level characters and establishes new mock theta conjecture-like identities for the corresponding string functions at levels $2/32/5$.
This paper establishes that the -deformed modular group specializes to a finite group at a complex parameter if and only if is a primitive -th root of unity for , in which cases the resulting groups are isomorphic to specific binary polyhedral groups, while the case yields an infinite but "mild" structure with applications to Jones polynomials.
This paper establishes the convergence of Lie-Trotter and Strang splitting schemes for the Gross-Pitaevskii equation with time-dependent potentials and non-zero boundary conditions in Zhidkov spaces, while demonstrating the conservation of generalized mass, near-preservation of energy, and investigating quantum vortex nucleation in relevant experimental settings.
This paper proposes a joint subcarrier assignment and power allocation framework for bistatic OFDM-based ISAC systems that maximizes communication data rate while satisfying delay sensing accuracy constraints, revealing that sensing subcarriers should be allocated only when their Fisher information gain outweighs the communication rate loss.
This paper establishes a general sparse domination principle that respects the cancellative structure of functions across various measure spaces, including martingale and Euclidean settings, leading to new sharp weighted results for operators acting on spaces and a sparse characterization of the norm.
This paper characterizes the spectrum of Hausdorff operators acting on weighted Bergman and power weighted Hardy spaces defined over the upper half-plane.
This paper investigates the statistical distributions, including proportions, variance, and maximal proportions, of the number of left prime truncations for integers and irreducible truncations for polynomials over finite fields.
This paper classifies unital cubic maps from the cyclic group of order 3 into arbitrary non-abelian groups, demonstrating that the associated universal group is an infinite arithmetic lattice in and establishing the existence of finite nilpotent groups of arbitrarily large nilpotency class admitting such maps.
This paper confirms that G.A. Dirac's conjecture regarding the existence of pairwise order-compatible, edge-disjoint paths holds for infinite graphs with bounded path lengths and establishes that such paths form an equivalence relation for all infinite cardinals , with the full conjecture being true if and only if has uncountable cofinality.
This paper demonstrates that a specific polynomial-time decision problem, defined by causal token traversal constraints, inherently requires linear time to execute and cannot be accelerated by parallel computation, thereby revealing a fundamental gap between logical parallelism and causal executability that places the problem outside the classical complexity class.
This paper establishes Banach, Newton-Raphson, and Brouwer fixed point theorems within the framework of generalized smooth functions, thereby enabling the rigorous solution of nonlinear singular equations involving distributions that fall outside the scope of classical fixed point theory.
This paper introduces a task-relative taxonomy of actuator inputs in feedback-linearizable nonlinear systems, defining "dexterity" inputs that can be deactivated to gracefully downgrade tasks while preserving linearization on shared outputs through a unified controller based on dynamic prolongation.
This paper demonstrates an asymmetry in uniqueness sets by constructing examples that fail to support measures with -summable Fourier coefficients while simultaneously supporting measures with rapidly decaying positive frequencies, thereby revealing a fundamental divergence between unilateral and bilateral uniqueness problems.