scholarly journals On best constants in L2 approximation

2020 ◽  
Author(s):  
Andrea Bressan ◽  
Michael S Floater ◽  
Espen Sande
Keyword(s):  
Asymptotic Behaviour ◽  
Numerical Method ◽  
Lower Bounds ◽  
Isogeometric Analysis ◽  
Numerical Results ◽  
Best Constants ◽  
Upper And Lower Bounds

Abstract In this paper we provide explicit upper and lower bounds on certain $L^2$$n$-widths, i.e., best constants in $L^2$ approximation. We further describe a numerical method to compute these $n$-widths approximately and prove that this method is superconvergent. Based on our numerical results we formulate a conjecture on the asymptotic behaviour of the $n$-widths. Finally, we describe how the numerical method can be used to compute the breakpoints of the optimal spline spaces of Melkman and Micchelli, which have recently received renewed attention in the field of isogeometric analysis.

scholarly journals Optimization of a k-covering of a bounded set with circles of two given radii

2021 ◽  
Vol 11 (1) ◽  
pp. 232-240
Author(s):  
Alexander V. Khorkov ◽  
Shamil I. Galiev
Keyword(s):  
Linear Programming ◽  
Numerical Method ◽  
Lower Bounds ◽  
Integer Linear Programming ◽  
Numerical Results ◽  
Programming Models ◽  
Bounded Set ◽  
The Given

Abstract A numerical method for investigating k-coverings of a convex bounded set with circles of two given radii is proposed. Cases with constraints on the distances between the covering circle centers are considered. An algorithm for finding an approximate number of such circles and the arrangement of their centers is described. For certain specific cases, approximate lower bounds of the density of the k-covering of the given domain are found. We use either 0–1 linear programming or general integer linear programming models. Numerical results demonstrating the effectiveness of the proposed methods are presented.

Reliability of a system with Poisson inspection times

1999 ◽  
Vol 36 (4) ◽  
pp. 1140-1154 ◽  
Author(s):  
Laurence Dieulle
Keyword(s):  
Asymptotic Behaviour ◽  
Failure Rate ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Analytic Method ◽  
Random Times

For systems subject to inspections at Poisson random times, we present an analytic method which gives upper and lower bounds for the reliability. We also study its asymptotic behaviour and derive the asymptotic failure rate.

Reliability of a system with Poisson inspection times

1999 ◽  
Vol 36 (04) ◽  
pp. 1140-1154 ◽  
Author(s):  
Laurence Dieulle
Keyword(s):  
Asymptotic Behaviour ◽  
Failure Rate ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Analytic Method ◽  
Random Times

For systems subject to inspections at Poisson random times, we present an analytic method which gives upper and lower bounds for the reliability. We also study its asymptotic behaviour and derive the asymptotic failure rate.

Stability of a dislocation : Discrete model

1998 ◽  
Vol 9 (4) ◽  
pp. 373-396 ◽  
Author(s):  
A. B. MOVCHAN ◽  
R. BULLOUGH ◽  
J. R. WILLIS
Keyword(s):  
Shear Stress ◽  
Lower Bounds ◽  
Nonlinear Model ◽  
Discrete Model ◽  
Critical Shear Stress ◽  
Numerical Results ◽  
Upper And Lower Bounds ◽  
Evolution Problem ◽  
Stability Of Solutions ◽  
The Stability

An algorithm, based on a discrete nonlinear model, is presented for evaluation of the critical shear stress required to move a dislocation through a lattice. The stability of solutions of the corresponding evolution problem is analysed. Numerical results provide upper and lower bounds for the critical shear stress.

scholarly journals Long-time asymptotics of the long-range Emch-Radin model

Open Physics ◽  
2012 ◽  
Vol 10 (3) ◽  
Author(s):  
Michael Kastner
Keyword(s):  
Asymptotic Behaviour ◽  
Long Range ◽  
Lower Bounds ◽  
Time Scale ◽  
System Size ◽  
Upper And Lower Bounds ◽  
Expectation Values ◽  
Time Asymptotics ◽  
Long Time ◽  
Long Time Asymptotics

AbstractThe long-time asymptotic behaviour is studied for a long-range variant of the Emch-Radin model of interacting spins. We derive upper and lower bounds on the expectation values of a class of observables. We prove analytically that the time scale at which the system relaxes to equilibrium diverges with the system size N, displaying quasistationary nonequilibrium behaviour. This finding implies that, for large enough N, equilibration will not be observed in an experiment of finite duration.

Upper and Lower Bounds of Frequencies for Cantilever Bars of Variable Cross Sections

1966 ◽  
Vol 33 (4) ◽  
pp. 948-950 ◽  
Author(s):  
J. H. Gaines ◽  
Enrico Volterra
Keyword(s):  
Lower Bounds ◽  
Cross Sections ◽  
Transverse Shear ◽  
Natural Frequencies ◽  
Numerical Results ◽  
Upper And Lower Bounds ◽  
Variable Cross ◽  
Tabular Form ◽  
Rotatory Inertia ◽  
Transverse Vibrations

Upper and lower bounds of frequencies of transverse vibrations of cantilever bars of variable cross sections are presented, taking into account the effects of transverse shear and of rotatory inertia. Numerical results for the first four natural frequencies are presented in tabular form for different inertia characteristics of the bars.

Sway Added-Mass of Cylinders in a Canal Using Dual-Extremum Principles

1977 ◽  
Vol 21 (04) ◽  
pp. 193-199
Author(s):  
Kwang June Bai
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Lower Bounds ◽  
Added Mass ◽  
Numerical Results ◽  
Upper And Lower Bounds ◽  
Two Dimensional ◽  
Rectangular Section ◽  
Circular Section ◽  
Element Method

This paper describes a finite-element method based on the dual extremum principles. As an application of the dual-extremum principles, the upper and lower bounds of the added mass of two-dimensional cylinders in a canal are computed for the zero-and infinite-frequency limits. Specifically, the upper and lower bounds of the added mass of a rectangular section, a triangular section, a circular section, and a Lewis-form section at the center of a rectangular canal are computed. The added mass is also computed for a rectangular section at off-center locations in a canal. Present numerical results are compared with previous results obtained by the hypercircle method [1].

scholarly journals On the Generalized Distance Energy of Graphs

Mathematics ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 17 ◽  
Author(s):  
Abdollah Alhevaz ◽  
Maryam Baghipur ◽  
Hilal A. Ganie ◽  
Yilun Shang
Keyword(s):  
Lower Bounds ◽  
Complete Graph ◽  
Connected Graph ◽  
Distance Matrix ◽  
Wiener Index ◽  
Diagonal Matrix ◽  
Upper And Lower Bounds ◽  
Star Graph ◽  
Extremal Graphs ◽  
Generalized Distance

The generalized distance matrix D α ( G ) of a connected graph G is defined as D α ( G ) = α T r ( G ) + ( 1 − α ) D ( G ) , where 0 ≤ α ≤ 1 , D ( G ) is the distance matrix and T r ( G ) is the diagonal matrix of the node transmissions. In this paper, we extend the concept of energy to the generalized distance matrix and define the generalized distance energy E D α ( G ) . Some new upper and lower bounds for the generalized distance energy E D α ( G ) of G are established based on parameters including the Wiener index W ( G ) and the transmission degrees. Extremal graphs attaining these bounds are identified. It is found that the complete graph has the minimum generalized distance energy among all connected graphs, while the minimum is attained by the star graph among trees of order n.

scholarly journals Hadamard k-fractional inequalities of Fejér type for GA-s-convex mappings and applications

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Hui Lei ◽  
Gou Hu ◽  
Zhi-Jie Cao ◽  
Ting-Song Du
Keyword(s):  
Lower Bounds ◽  
Hypergeometric Functions ◽  
Upper And Lower Bounds ◽  
Weighted Inequalities ◽  
Convex Mappings ◽  
Special Means

Abstract The main aim of this paper is to establish some Fejér-type inequalities involving hypergeometric functions in terms of GA-s-convexity. For this purpose, we construct a Hadamard k-fractional identity related to geometrically symmetric mappings. Moreover, we give the upper and lower bounds for the weighted inequalities via products of two different mappings. Some applications of the presented results to special means are also provided.

Sign in / Sign up

Export Citation Format

Share Document