相关论文: Higher order Glaeser inequalities and optimal regu…
Many problems in applied mathematics require root finding algorithms. Unfortunately, root finding methods have limitations. Firstly, regarding the convergence, there is a trade-off between the size of it's domain and it's rate. Secondly the…
We extend several well-known tools from the theory of second-order divergence-form elliptic equations to the case of higher-order equations. These tools are the Caccioppoli inequality, Meyers's reverse Holder inequality for gradients, and…
In this paper we established a class of optimal fourth-order methods which is obtained by existing third-order method for solving nonlinear equations for simple roots by using weight functions. Some physical examples are given to illustrate…
In this paper we investigate the gamma-relative differentiation by the motivation of amending the order of the weighted polynomial approximation on the semiaxis for certain functions. With the help of this we give some definitions of…
This paper considers optimization of smooth nonconvex functionals in smooth infinite dimensional spaces. A H\"older gradient descent algorithm is first proposed for finding approximate first-order points of regularized polynomial…
In this paper, we study lower order terms of the $1$-level density of low-lying zeros of quadratic Hecke L-functions in the Gaussian field. Assuming the Generalized Riemann Hypothesis, our result is valid for even test functions whose…
This work is devoted to the study of the existence and sign of Green's functions for first order linear problems with constant coefficients and initial (one point) conditions. We first prove a result on the existence of solutions of $n$-th…
The representation for the sharp constant ${\rm K}_{n, p}$ in an estimate of the modulus of the $n$-th derivative of an analytic function in the upper half-plane ${\mathbb C}_+$ is considered. It is assumed that the boundary value of the…
We establish a form of the Gotzmann representation of the Hilbert polynomial based on rank and generating degrees of a module, which allow for a generalization of Gotzmann's Regularity Theorem. Under an additional assumption on the…
In this paper we investigate the approximation of continuous functions on the Wasserstein space by smooth functions, with smoothness meant in the sense of Lions differentiability. In particular, in the case of a Lipschitz function we are…
Gowers norms have been studied extensively both in the direct sense, starting with a function and understanding the associated norm, and in the inverse sense, starting with the norm and deducing properties of the function. Instead of…
In this paper, we discuss the more general Hessian inequality $\sigma_{k}^{\frac{1}{k}}(\lambda (D_i (A\left(|Du|\right) D_j u)))\geq f(u)$ including the Laplacian, p-Laplacian, mean curvature, Hessian, k-mean curvature operators, and…
Hardy-Littlewood-Sobolev (HLS) Inequality fails in the "critical" case: \mu=n. However, for discrete HLS, we can derive a finite form of HLS inequality with logarithm correction for a critical case: \mu=n and p=q, by limiting the inequality…
We study the following problem: given n real arguments a1, ..., an and n real weights w1, ..., wn, under what conditions does the inequality w1 f(a1) + w2 f(a2) + ... + wn f(an) >= 0 hold for all functions f with nonnegative kth derivative…
In this paper we study the right differentiability of a parametric infimum function over a parametric set defined by equality constraints. We present a new theorem with sufficient conditions for the right differentiability with respect to…
It has been well established that first order optimization methods can converge to the maximal objective value of concave functions and provide constant factor approximation guarantees for (non-convex/non-concave) continuous submodular…
The paper is concerned with the completeness problem of root functions of general boundary value problems for first order systems of ordinary differential equations. Namely, we introduce and investigate the class of \emph{weakly regular…
It is well-known that every convex function admits an affine support at every interior point of a domain. Convex functions of higher order (precisely of an odd order) have a similar property: they are supported by the polynomials of degree…
In this paper we study the auxiliary problems that appear in $p$-order tensor methods for unconstrained minimization of convex functions with $\nu$-H\"{o}lder continuous $p$th derivatives. This type of auxiliary problems corresponds to the…
This study focuses on convex functions and their generalized. Thus, we start this study by giving the definition of convex functions and some of their properties and discussing a simple geometric property. Then we generalize E-convex…