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We obtain improved Strichartz estimates for solutions of the Schr\"odinger equation on compact manifolds with nonpositive sectional curvatures which are related to the classical universal results of Burq, G\'erard and Tzvetkov [11]. More…

The paper surveys the basic properties of generalized Stieltjes functions including some new ones. We introduce the notion of the exact Stieltjes order and give a criterion of exactness, simple sufficient conditions and some prototypical…

Let $k\geq 1$ be an integer. Let $\delta_k(n)$ denote the maximum divisor of $n$ which is co-prime to $k$. We study the error term of the general $m$-th Riesz mean of the arithmetical function $\delta_k(n)$ for any positive integer $m \ge…

We applied the method of finite-part integration [Galapon E.A Proc.R.Soc A 473, 20160567(2017)] to evaluate in closed-form the exact one-loop integral representations of the Heisenberg-Euler Lagrangian from QED for a constant magnetic field…

In this article we establish central limit theorems for multilevel Polyak-Ruppert averaged stochastic approximation schemes. We work under very mild technical assumptions and consider the slow regime in wich typical errors decay like…

We derive a fully computable aposteriori error estimator for a Galerkin finite element solution of the wave equation with explicit leapfrog time-stepping. Our discrete formulation accommodates both time evolving meshes and leapfrog based…

From known effective bounds on the prime counting function of the form \[ |\pi(x)-\mathrm{Li}(x)| < a \;x \;(\ln x)^{b} \; \exp\left(-{c}\; \sqrt{\ln x}\right); \qquad (x \geq x_0); \] it is possible to establish exponentially tight…

Infinitesimal contraction analysis provides exponential convergence rates between arbitrary pairs of trajectories of a system by studying the system's linearization. An essentially equivalent viewpoint arises through stability analysis of a…

We prove novel convergence results for a stochastic proximal gradient algorithm suitable for solving a large class of convex optimization problems, where a convex objective function is given by the sum of a smooth and a possibly non-smooth…

For an infinite word $\mathbf{x}$, Bugeaud and Kim introduced a new complexity function $\text{rep}(\mathbf{x})$ which is called the exponent of repetition of $\mathbf{x}$. They showed $1\le \text{rep}(\mathbf{x}) \le \sqrt{10}-\frac{3}{2}$…

This article investigates time-discrete approximations of Allen-Cahn type SPDEs driven by space-time white noise near the sharp interface limit $\epsilon\to 0$, where the small parameter $\epsilon$ is the diffuse interface thickness. We…

We derive logarithmic gradient estimate and universal boundedness estimate for semilinear elliptic equations on \RCD\, metric measure spaces, which contains the class of Riemannian manifolds with Ricci curvature bounded below. These…

In this paper, we establish new bounds for classical prime-counting functions. All of our bounds are explicit and assume the Riemann Hypothesis. First, we prove that $|\psi(x) - x|$ and $|\vartheta(x) - x|$ are bounded from above by…

We prove a Weitzenb\"ock identity for general pairs of constant coefficient homogeneous first order partial differential operators, and deduce from it sufficient algebraic conditions for coerciveness and Morrey estimates under the natural…

In this paper, a new axiomatization for unbounded functional calculi is proposed and the associated theory is elaborated comprising, among others, uniqueness and compatibility results and extension theorems of algebraic and topological…

Consider a sequence of estimators $\hat \theta_n$ which converges almost surely to $\theta_0$ as the sample size $n$ tends to infinity. Under weak smoothness conditions, we identify the asymptotic limit of the last time $\hat \theta_n$ is…

A new sampling methodology based on incomplete cosine expansion series is presented as an alternative to the traditional sinc function approach. Numerical integration shows that this methodology is efficient and practical. Applying the…

We propose a derivative-free trust-region method based on finite-difference gradient approximations for smooth optimization problems with convex constraints. The proposed method does not require computing an approximate stationarity…

We develop a higher regularity theory for general quasilinear elliptic equations and systems in divergence form with random coefficients. The main result is a large-scale $L^\infty$-type estimate for the gradient of a solution. The estimate…

We obtain an error estimate between viscosity solutions and \delta-viscosity solutions of nonhomogeneous fully nonlinear uniformly elliptic equations. The main assumption, besides uniform ellipticity, is that the nonlinearity is…