Search results for "Number"

Menger curvature and Lipschitz parametrizations in metric spaces

2005

On Pietsch measures for summing operators and dominated polynomials

2012

We relate the injectivity of the canonical map from $C(B_{E'})$ to $L_p(\mu)$, where $\mu$ is a regular Borel probability measure on the closed unit ball $B_{E'}$ of the dual $E'$ of a Banach space $E$ endowed with the weak* topology, to the existence of injective $p$-summing linear operators/$p$-dominated homogeneous polynomials defined on $E$ having $\mu$ as a Pietsch measure. As an application we fill the gap in the proofs of some results of concerning Pietsch-type factorization of dominated polynomials.

Hamel-isomorphic images of the unit ball

2010

In this article we consider linear isomorphisms over the field of rational numbers between the linear spaces ℝ2 and ℝ. We prove that if f is such an isomorphism, then the image by f of the unit disk is a strictly nonmeasurable subset of the real line, which has different properties than classical non-measurable subsets of reals. We shall also consider the question whether all images of bounded measurable subsets of the plane via a such mapping are non-measurable (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Elastic Deformation of Dispersely Failing Unidirectionally Reinforced Composites

2003

A phenomenological model is proposed for describing the elastic deformation of a unidirectionally reinforced composite capable of accumulating scattered microdamages during its loading. The composite is considered as a homogeneous transversely isotropic solid. Its damaged state at every point is characterized by a centrally symmetric scalar function on the unit sphere (the damage function), which is used to account for variations in the elastic properties of the material during its deformation. The damage itself depends on the history of some equivalent strain, for which four simplified variants are suggested. The relation between strains and stresses is defined in a differential form. Depe…

Spectral rigidity and invariant distributions on Anosov surfaces

2014

This article considers inverse problems on closed Riemannian surfaces whose geodesic flow is Anosov. We prove spectral rigidity for any Anosov surface and injectivity of the geodesic ray transform on solenoidal 2-tensors. We also establish surjectivity results for the adjoint of the geodesic ray transform on solenoidal tensors. The surjectivity results are of independent interest and imply the existence of many geometric invariant distributions on the unit sphere bundle. In particular, we show that on any Anosov surface $(M,g)$, given a smooth function $f$ on $M$ there is a distribution in the Sobolev space $H^{-1}(SM)$ that is invariant under the geodesic flow and whose projection to $M$ i…

Evaluation of bond strength of orthodontic brackets without enamel etching

2015

Background: to compare the shear bond strength of brackets with and without enamel etching. Material and Methods: In this study, 60 sound premolars were randomly divided into four different groups: 1- TXE group: Enamel etching + Transbond XT adhesive + Transbond XT composite. 2- TXS group: Transbond plus self-etch adhesive + Transbond XT composite. 3- PQ1E group: Enamel etching + PQ1 adhesive + Transbond XT composite. 4- PQ1 group: PQ1 adhesive + Transbond XT composite. The shear bond strengths of brackets were evaluated using universal testing machine at cross head speed of 0.5 mm/ min. The Adhesive Remnant Index (ARI) was also measured. One-way ANOVA, Tukey’s post hoc, Kruskal-wallis and …

Effect of thermocycling and surface treatment on repair bond strength of composite.

2017

BACKGROUND Repair of composite restorations is a conservative method that can increase the longevity and durability of restorations while preserving the tooth structure. Achieving a suitable bond between the old and new composite is difficult. To overcome this problem, some methods have been recommended to increase the repair bond strength of composite.This study aimed to assess the effect of aging by thermocycling (5,000 and 10,000 cycles) and mechanical surface treatments (Er,Cr:YSGG laser and bur) on repair shear bond strength of composite resin. MATERIAL AND METHODS Totally, 120 composite blocks measuring 6x4x4 mm were fabricated of Filtek Z250 composite and were randomly divided into t…

Deformation of Polypropylene Foam Neopolen® P in Compression

2004

Neopolen® P is a two-phase cellular composite foam material produced by BASF AG, Germany. In most of the practical applications, Neopolen® P works under a range of small and compressive deformations. Therefore it is necessary to determine the moduli in compression and compressive strength in the most effective way for a wide range of foam densities: 22≤ρ84≤kg/m3. Several experimental methods of different precision for deformation properties of Neopolen® P were compared. The direct measurements performed by a universal testing machine were used for the main part of the experiments. They were compared with results obtained by a more precise and time-consuming method, using an inductive exten…

Influence of preheating on mechanical and surface properties of nanofilled resin composites

2019

Background Resin composite preheating is an innovative method that could be clinically beneficial by improving the handling properties, marginal adaptation, and surface properties of uncured nanofilled resin composite materials. There is conflict and unclear information regarding the effect of preheating on the microhardness, fracture toughness and surface roughness of nanofilled resin composites. Thus, it is important to assess whether dental clinicians can adopt preheating procedures without compromising composite mechanical strength. Objective: The purpose of this study was to evaluate the effect of preheating on microhardness, fracture toughness and surface roughness of nanofilled resin…

Strength and Ductility of Hollow Circular Steel Columns Filled with Fibre Reinforced Concrete

1999

Publisher Summary This chapter investigates the behavior of hollow circular steel cross-sections filled with Fiber Reinforced Concrete (FRC), subjected to monotonic loads. The casting of different types of composite members—steel columns, steel columns filled with Normal Strength Concrete (NSC), and steel columns filled with Fiber Reinforced Concrete (FRC) was employed. The columns were tested in uniaxial compression utilizing a universal testing machine operating in displacement control. The maximum strength of composite members filled with FRC was 20% higher than that recorded for steel pipes filled with FRC. After the peak load was reached, failure was due to the crushing of concrete and…