Related papers: Interpolation inequalities in pattern formation
In this paper we study some determinant inequalities and matrix inequalities which have a geometrical flavour. We first examine some inequalities which place work of Macbeath [13] in a more general setting and also relate to recent work of…
The paper contains a survey of the results obtained by the author in recent years. These results concern the application in multivariate polynomial interpolation of some geometric constructions and methods. In particular, we give estimates…
We use a probabilistic method to produce some combinatorial inequalities by considering pattern containment in permutations and words.
The success of first principles electronic structure calculation for predictive modeling in chemistry, solid state physics, and materials science is constrained by the limitations on simulated length and time scales due to computational…
We treat the interpolation problem $ \{f(x_j)=y_j\}_{j=1}^N $ for polynomial and rational functions. Developing the approach by C.Jacobi, we represent the interpolants by virtue of the Hankel polynomials generated by the sequences $…
Jensen inequalities for positive linear maps of Choi and Hansen-Pedersen type are established for a large class of operator/matrix means. These results are also extensions of the Minkowski determinantal inequality. To this end we develop…
We report the generation of polarization-entangled photons, using a quantum dot single photon source, linear optics and photodetectors. Two photons created independently are observed to violate Bell's inequality. The density matrix…
This paper introduces an interpolation-based method, called the reconstruction approach, for nonparametric regression. Based on the fact that interpolation usually has negligible errors compared to statistical estimation, the reconstruction…
We explore inequalities on linear extensions of posets and make them effective in different ways. First, we study the Bj\"orner--Wachs inequality and generalize it to inequalities on order polynomials and their $q$-analogues via direct…
I review recent progress in the extraction of unpolarized parton distributions in the proton and in nuclei from a unified point of view that highlights how the interplay between high energy particle physics and lower energy nuclear physics…
When approximating a function that depends on a parameter, one encounters many practical examples where linear interpolation or linear approximation with respect to the parameters prove ineffective. This is particularly true for responses…
We prove Ehrhard's inequality using interpolation along the Ornstein-Uhlenbeck semi-group. We also provide an improved Jensen inequality for Gaussian variables that might be of independent interest.
We give a complete characterization of limiting interpolation spa\-ces for the real method of interpolation using extrapolation theory. For this purpose the usual tools (e.g., Boyd indices or the boundedness of Hardy type operators) are not…
We study matrix inequalities involving partial traces for positive semidefinite block matrices. First of all, we present a new method to prove a celebrated result of Choi [Linear Algebra Appl. 516 (2017)]. Our method also allows us to prove…
Interatomic potentials approximate the potential energy of atoms as a function of their coordinates. Their main application is the effective simulation of many-atom systems. Here, we review empirical interatomic potentials designed to…
In this paper, we present some extensions of interpolation between the arithmetic-geometric means inequality. Among other inequalities, it is shown that if $A, B, X$ are $n\times n$ matrices, then \begin{align*}…
In this paper, we study the H\"older-type interpolation inequality and observability inequality from measurable sets in time for parabolic equations either with L^p unbounded potentials or with electric potentials. The parabolic equations…
Interpolation polynomials were introduced by Knop--Sahi in type $A$, and Okounkov in type $BC$. They are inhomogeneous polynomials whose top terms are Jack and Macdonald polynomials. Thus the expansion coefficients for the product of two…
We introduce a general class of (quasi-)interpolants of functions defined on a Bravais lattice, and establish several technical results for these interpolants that are crucial ingredients in the analysis of atomistic models and…
The structure of certain types of quasi shift-invariant spaces, which take the form $V(\psi,\mathcal{X}):=\overline{\text{span}}^{L_2}\{\psi(\cdot-x_j):j\in\mathbb{Z}\}$ for a discrete set $\mathcal{X}=(x_j)\subset\mathbb{R}$ is…