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Super-Exponential Convergence Rate of a Nonlinear Continuous Data Assimilation Algorithm: The 2D Navier–Stokes Equation Paradigm
We study a nonlinear-nudging modification of the Azouani–Olson–Titi continuous data assimilation (downscaling) algorithm for the 2D incompressible...
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Super-Exponential Rate of Convergence of the Cayley Transform Method for an Abstract Differential Equation
A boundary-value problem (BVP) for a second-order abstract differential equation with an operator coefficient in a Hilbert space is investigated. The...
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Blow-Up Analysis for Heat Equation with a Nonlocal Weighted Exponential Boundary Flux
This paper is concerned with the blow-up phenomenon for classical heat equation with a nonlocal weighted exponential boundary flux. Based on the...
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A super-localized generalized finite element method
This paper presents a novel multi-scale method for elliptic partial differential equations with arbitrarily rough coefficients. In the spirit of...
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Convergence to Sharp Traveling Waves of Solutions for Burgers-Fisher-KPP Equations with Degenerate Diffusion
This paper is concerned with the convergence to sharp traveling waves of solutions with semi-compactly supported initial data for Burgers-Fisher-KPP...
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The prescribed Gauduchon scalar curvature problem in almost Hermitian geometry
In this paper, we consider the prescribed Gauduchon scalar curvature problem on almost Hermitian manifolds. By deducing the expression of the...
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Microlocal analysis for Gelfand–Shilov spaces
We introduce an anisotropic global wave front set of Gelfand–Shilov ultradistributions with different indices for regularity and decay at infinity....
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Long-Time Behavior for Subcritical Measure-Valued Branching Processes with Immigration
In this work we study the long-time behavior for subcritical measure-valued branching processes with immigration on the space of tempered measures....
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The high-dimensional cohomology of the moduli space of curves with level structures II: punctures and boundary
We give two proofs that appropriately defined congruence subgroups of the map** class group of a surface with punctures/boundary have enormous...
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Semi-Martingales and Stochastic Integration
Predictable covariation, L2-martingale and semi-martingale integrals, quadratic variation and covariation, substitution rule, Doléans exponential,...
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Multiplicity Results for the Biharmonic Equation with Singular Nonlinearity of Super Exponential Growth in ℝ4
We consider the following elliptic problem of exponential-type growth posed in an open bounded domain with smooth boundary B 1 (0) ⊂ ℝ 4 :
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Hypocoercivity and sub-exponential local equilibria
Hypocoercivity methods are applied to linear kinetic equations without any space confinement, when local equilibria have a sub-exponential decay. By...
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Strong Approximations for a Class of Dependent Random Variables with Semi-Exponential Tails
We give rates of convergence in the almost sure invariance principle for sums of dependent random variables with semi-exponential tails, whose...
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Numerical Multiscale Methods for Waves in High-Contrast Media
Multiscale high-contrast media can cause astonishing wave propagation phenomena through resonance effects. For instance, waves could be exponentially...
