Related papers: Improved cutoff functions for short-range potentia…
Explicit divergences and counterterms do not appear in the differential renormalization method, but they are concealed in the neglected surface terms in the formal partial integration procedure used. A systematic real space cutoff procedure…
We prove functional inequalities in any dimension controlling the iterated derivatives along a transport of the Coulomb or super-Coulomb Riesz modulated energy in terms of the modulated energy itself. This modulated energy was introduced by…
We provide two methods for constructing smooth bump functions and for smoothly cutting off smooth functions on fractals, one using a probabilistic approach and sub-Gaussian estimates for the heat operator, and the other using the analytic…
In this paper, we first obtain a refined Bohr radius for invariant families of bounded analytic functions on unit disk $ \mathbb{D} $. Then, we obtain Bohr inequality for certain integral transforms, namely Fourier (discrete) and Laplace…
We examine the conditions under which the sum of random multiplicative functions in short intervals, given by $\sum_{x<n \leqslant x+y} f(n)$, exhibits the phenomenon of \textit{better than square-root cancellation}. We establish that the…
A compression algorithm is introduced for multi-determinant wave functions which can greatly reduce the number of determinants that need to be evaluated in quantum Monte Carlo calculations. We have devised an algorithm with three levels of…
We present two new classes of orthogonal functions, log orthogonal functions (LOFs) and generalized log orthogonal functions (GLOFs), which are constructed by applying a $\log$ mapping to Laguerre polynomials. We develop basic approximation…
The sharp Wolff-type decoupling estimates of Bourgain--Demeter are extended to the variable coefficient setting. These results are applied to obtain new sharp local smoothing estimates for wave equations on compact Riemannian manifolds,…
This paper introduces and develops novel coderivative-based Newton methods with Wolfe linesearch conditions to solve various classes of problems in nonsmooth optimization. We first propose a generalized regularized Newton method with Wolfe…
This article generalizes the small noise cutoff phenomenon to the strong solutions of the stochastic heat equation and the damped stochastic wave equation over a bounded domain subject to additive and multiplicative Wiener and L\'evy noises…
Let $f(z) = \sum_{k=0}^\infty d_k z^k$, $d_k\in\mathbb{C}\backslash\{ 0 \}$, $d_0=1$, be a power series with a non-zero radius of convergence $\rho$: $0 <\rho \leq +\infty$. Denote by $f_n(z)$ the n-th partial sum of $f$, and $R_{2n}(z) =…
Ewald summation is an important technique used to deal with long-range Coulomb interaction. While it is widely used in simulations of molecules and solid state materials, many important results are dispersed in literature and their…
Within the last fifteen years, a program of establishing relationships between algorithmic randomness and almost-everywhere theorems in analysis and ergodic theory has developed. In harmonic analysis, Franklin, McNicholl, and Rute…
The canonical models for studying the unjamming scenario in systems of soft repulsive particles assume pairwise potentials with a sharp cut-off in the interaction range. The sharp cut-off renders the potential non-analytic, but makes it…
We consider extensions of the Shannon relative entropy, referred to as $f$-divergences.Three classical related computational problems are typically associated with these divergences: (a) estimation from moments, (b) computing normalizing…
We present a first numerical study of lattice QCD with O(a) improved Wilson quarks and a chirally twisted mass term. Renormalized correlation functions are derived from the Schroedinger functional and evaluated in an intermediate space-time…
We propose a novel framework, called moving window method, for solving the linear Schr\"odinger equation with an external potential in $\mathbb{R}^d$. This method employs a smooth cut-off function to truncate the equation from Cauchy…
In this paper we first consider another version of the Rogosinski inequality for analytic functions $f(z)=\sum_{n=0}^\infty a_nz^n$ in the unit disk $|z| < 1$, in which we replace the coefficients $a_n$ $(n= 0,1,\ldots ,N)$ of the power…
The properties of strongly gravitating systems suggest that field theory overcounts the states of a system. Reducing the number of degrees of freedom, without abandoning the notion of effective field theory, may be achieved through a…
Our recent method to calculate renormalized functional determinants, the partial wave cutoff method, is extended for the evaluation of 4-D fermion one-loop effective action with arbitrary mass in certain types of radially symmetric,…