Search results for "BES"
showing 10 items of 3692 documents
A note on topological dimension, Hausdorff measure, and rectifiability
2020
The purpose of this note is to record a consequence, for general metric spaces, of a recent result of David Bate. We prove the following fact: Let $X$ be a compact metric space of topological dimension $n$. Suppose that the $n$-dimensional Hausdorff measure of $X$, $\mathcal H^n(X)$, is finite. Suppose further that the lower n-density of the measure $\mathcal H^n$ is positive, $\mathcal H^n$-almost everywhere in $X$. Then $X$ contains an $n$-rectifiable subset of positive $\mathcal H^n$-measure. Moreover, the assumption on the lower density is unnecessary if one uses recently announced results of Cs\"ornyei-Jones.
Existence of doubling measures via generalised nested cubes
2012
Working on doubling metric spaces, we construct generalised dyadic cubes adapting ultrametric structure. If the space is complete, then the existence of such cubes and the mass distribution principle lead into a simple proof for the existence of doubling measures. As an application, we show that for each $\epsilon>0$ there is a doubling measure having full measure on a set of packing dimension at most $\epsilon$.
Approximation and quasicontinuity of Besov and Triebel–Lizorkin functions
2016
We show that, for $0<s<1$, $0<p<\infty$, $0<q<\infty$, Haj\l asz-Besov and Haj\l asz-Triebel-Lizorkin functions can be approximated in the norm by discrete median convolutions. This allows us to show that, for these functions, the limit of medians, \[ \lim_{r\to 0}m_u^\gamma(B(x,r))=u^*(x), \] exists quasieverywhere and defines a quasicontinuous representative of $u$. The above limit exists quasieverywhere also for Haj\l asz functions $u\in M^{s,p}$, $0<s\le 1$, $0<p<\infty$, but approximation of $u$ in $M^{s,p}$ by discrete (median) convolutions is not in general possible.
Interactions of carbon nanotubes with aqueousaquatic media containing organicinorganic contaminants and selected organisms of aquatic ecosystems – A …
2015
Due to their unique molecular architecture translating into numerous every-day applications, carbon nanotubes (CNTs) will be ultimately an increasingly significant environmental contaminant. This work reviews qualitative/quantitative analyses of interactions of various types of CNTs and their chemically modified analogues with aqueous/aquatic media containing organic and inorganic contaminants and selected organisms of aquatic ecosystems. A special emphasis was placed on physicochemical interactions between CNTs as adsorbents of heavy metal cations and aromatic compounds (dyes) with its environmental consequences. The studies revealed CNTs as more powerful adsorbents of aromatic compounds (…
Effects of high intensity resistance aquatic training on body composition and walking speed in women with mild knee osteoarthritis : a 4-month RCT wi…
2017
Objective: To investigate the effects of 4-months intensive aquatic resistance training on body composition and walking speed in post-menopausal women with mild knee osteoarthritis (OA), immediately after intervention and after 12-months follow-up. Additionally, influence of leisure time physical activity (LTPA) will be investigated. Design: This randomised clinical trial assigned eighty-seven volunteer postmenopausal women into two study arms. The intervention group (n = 43) participated in 48 supervised intensive aquatic resistance training sessions over 4-months while the control group (n = 44) maintained normal physical activity. Eighty four participants continued into the 12-months' fo…
Separation of halloysite/kaolinite mixtures in water controlled by sucrose addition: The influence of the attractive forces on the sedimentation beha…
2022
In this work, we propose an easy strategy for the separation of halloysite/kaolinite mixtures in sucrose aqueous solution. Preliminarily, we investigated the influence of the sucrose addition on the colloidal stability of kaolinite nanoplates and halloysite nanotubes (HNTs) dispersed in water. Dynamic Light Scattering (DLS) measurements revealed that the HNTs aqueous mobility is dependent on the sucrose concentration, while the ζ-potential is negligibly affected by the addition of the carbohydrate in the aqueous solvent. On the other hand, any variations on the surface charge and dynamic behavior of kaolinite were detected in the presence of sucrose. The obtained ζ-potential and DLS results…
Halloysite nanotubes filled with MgO for paper reinforcement and deacidification
2021
Abstract A novel material for the deacidification and protection of paper has been designed by using MgO filled halloysite nanotubes (Hal). The ability of MgO loaded nanotubes to control the acidic conditions was evaluated by pH measurements in aqueous solvent. Afterwards, paper was impregnated into hydroxypropyl cellulose dispersions containing the consolidating material. A simulation of strong acidic conditions allowed us to evaluate the deacidification effect of the composite material on the samples. In particular, the paper reaches a pH of 7.7 after 1 h exposition to HNO3 vapours when MgO-Hal nanoparticles are added to the impregnation mixture at a concentration of 10 wt% and it remains…
Polyfunctional Tetraaza-Macrocyclic Ligands: Zn(II), Cu(II) Binding and Formation of Hybrid Materials with Multiwalled Carbon Nanotubes
2017
The binding properties of HL1, HL2, and HL3 ligands toward Cu(II) and Zn(II) ions, constituted by tetraaza-macrocyclic rings decorated with pyrimidine pendants, were investigated by means of potentiometric and UV spectrophotometric measurements in aqueous solution, with the objective of using the related HL-M(II) (HL = HL1–HL3; M = Cu, Zn) complexes for the preparation of hybrid MWCNT-HL-M(II) materials based on multiwalled carbon nanotubes (MWCNTs), through an environmentally friendly noncovalent procedure. As shown by the crystal structure of [Cu(HL1)](ClO4)2, metal coordination takes place in the macrocyclic ring, whereas the pyrimidine residue remains available for attachment onto the s…
Probing the internal environment of PVP networks generated by irradiation with different sources
2010
Poly(N-vinyl-2-pyrrolidone) (PVP) hydrogels have been synthesised from the aqueous solutions of the same linear polymer by two different radiation sources: electron beams and UV rays. The present investigation couples conventional hydrogel characterisation techniques with the study of the partition equilibria, fluorescence behaviour and release of two different molecular probes, 1-anilino-8-naphthalene sulphonate (ANS) and Thioflavin T (ThT). The two probes have comparable molecular weight and different structural and optical properties. The chemical networks produced upon irradiation in different experimental conditions presented quite distinctive mechanical spectra, yielded to different…