We present a higher order stabilization-free virtual element method applied to plane elasticity problems. utilize serendipity approach reduce the total number of degrees freedom from corresponding high-order approximations. The well-posedness problem is numerically studied via an eigenanalysis. then several benchmark problems linear and we show that delivers optimal convergence rates in $L^2$ n...

The aim of this paper is to provide new upper bounds ω(T), which denotes the numerical radius a bounded operator T on Hilbert space (H,⟨·,·⟩). We show Aczél inequality in terms |T|. Next, we give certain inequalities about A-numerical ωA(T) and A-operator seminorm ∥T∥A an T. also present several results related 2×2 block matrices semi-Hilbert operators, by using symmetric matrices.

Let $$r_A(T)$$ denote the A-spectral radius of an operator T which is bounded with respect to seminorm induced by a positive A on complex Hilbert space $${\mathcal {H}}$$ . In this paper, we aim establish several inequalities for products, sums and commutators A-bounded operators. Some applications our results are provided. Moreover, give affirmative answer question recently posed Baklouti Namo...

Abstract In this manuscript two BMO estimates are obtained, one for Linear Elasticity and Nonlinear Elasticity. It is first shown that the BMO-seminorm of gradient a vector-valued mapping bounded above by constant times symmetric part its gradient, is, Korn inequality in BMO. The uniqueness equilibrium finite deformation whose principal stresses everywhere nonnegative then considered. when seco...

In this paper we address two questions about the synchronization of coupled oscillators in Kuramoto model with all-to-all coupling. first part use some classical results convex geometry to prove bounds on size frequency set supporting existence stable, phase locked solutions and show that such frequencies can be expressed by a seminorm which call norm. second ideas from extreme order statistics...

In this work, we present a novel error analysis for recovering spatially dependent diffusion coefficient in an elliptic or parabolic problem. It is based on the standard regularized output least-squares formulation with $H^1(\Omega)$ seminorm penalty and then discretized using Galerkin finite element method conforming piecewise linear elements both state backward Euler time case. We derive prio...

We show that, under finitely many ergodicity assumptions, any multicorrelation sequence defined by invertible measure preserving $\mathbb{Z}^d$-actions with multivariable integer polynomial iterates is the sum of a nilsequence and null sequence, extending recent result second author. To this end, we develop new seminorm bound estimate for multiple averages improving results in previous work fir...