相关论文: The Error Function and The Kink Soliton
We present simple, user-friendly bounds for the expected operator norm of a random kernel matrix under general conditions on the kernel function $k(\cdot,\cdot)$. Our approach uses decoupling results for U-statistics and the non-commutative…
We investigate the thermal equilibrium properties of kinks in a classical $\F^4$ field theory in $1+1$ dimensions. From large scale Langevin simulations we identify the temperature below which a dilute gas description of kinks is valid. The…
In this paper a spline based integral approximation is utilized to propose a sequence of approximations to the error function that converge at a significantly faster manner than the default Taylor series. The approximations can be improved…
This article shows that on a closed interval $[a,b]$ a continuous function may be approximated to an arbitrary degree of accuracy using scattered translates of the general multiquadric $(x^2+c^2)^{k-1/2}$.
We present a method for constructing global analytical expressions that approximate a function over its entire range. These approximations not only mirror the original function as accurately as desired, but are purposefully created to…
We present an alternative way to determine the unknown parameter associated to a gaussian approximation in a generic two-dimensional model. Instead of the standard variational approach, we propose a procedure based on a quantitative…
The sine-Gordon model with space- and time-dependent parameters is considered. A highly accurate effective model with two degrees of freedom is constructed, allowing the description of the kink movement in this model even for extremely long…
The paper study the discrete sets of translations of the Gaussian function that span the spaces L1(R) and L2(R).
Let $E_{kk}^{(n)}$ denote the minimax (i.e., best supremum norm) error in approximation of $x^n$ on $[\kern .3pt 0,1]$ by rational functions of type $(k,k)$ with $k<n$. We show that in an appropriate limit $E_{kk}^{(n)} \sim 2\kern .3pt…
Calculations of quantum corrections to soliton masses generally require both the vacuum sector and the soliton sector to be regularized. The finite part of the quantum correction depends on the assumed relation between these regulators when…
The representation in terms of Ernst's complex potential is used to describe and analyze dilaton-axion theories with potential. The set of such systems is divided into pairs of dual systems with respect to the inversion of the Ernst…
Two approximations of the integral of a class of sinusoidal composite functions, for which an explicit form does not exist, are derived. Numerical experiments show that the proposed approximations yield an error that does not depend on the…
Let $\mathcal{D}$ be the dictionary of Gaussian mixtures: the functions created by affine change of variables of a single Gaussian in $n$ dimensions. $\mathcal{D}$ is used pervasively in scientific applications to a degree that…
We study a class of phase-space distribution functions that is generated from a Gaussian convolution of the Wigner distribution function. This class of functions represents the joint count probability in simultaneous measurements of…
Stein's method for Gaussian process approximation can be used to bound the differences between the expectations of smooth functionals $h$ of a c\`adl\`ag random process $X$ of interest and the expectations of the same functionals of a well…
In this paper, we derive rates of convergence in the high-dimensional central limit theorem for Polyak--Ruppert averaged iterates generated by entropy-regularized asynchronous Q-learning with linear function approximation and a polynomial…
Two residual-type error estimators for the mortar staggered discontinuous Galerkin discretizations of second order elliptic equations are developed. Both error estimators are proved to be reliable and efficient. Key to the derivation of the…
A posteriori error estimators are studied for discontinuous Galerkin methods for solving a frictional contact problem, which is a representative elliptic variational inequality of the second kind. The estimators are derived by relating the…
Submodularity is one of the most important properties in combinatorial optimization, and $k$-submodularity is a generalization of submodularity. Maximization of a $k$-submodular function requires an exponential number of value oracle…
We study the asymptotic behaviour of the entire function \[ E(z) = \sum_{n\ge 0} \frac{z^n}{\gamma (n+1)} \] and the analytic function \[ K(z) = \frac1{2\pi {\rm i}}\, \int_{c-{\rm i}\infty}^{c+{\rm i}\infty} z^{-s}\gamma (s)\, {\rm d}s\,,…