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.

Applied MathematicsGeneral Mathematics010102 general mathematicsMetric Geometry (math.MG)01 natural sciencesMeasure (mathematics)funktioteoriaCombinatoricsMetric spacesymbols.namesakeCompact spaceMathematics - Metric GeometryMathematics - Classical Analysis and ODEs0103 physical sciencesClassical Analysis and ODEs (math.CA)FOS: MathematicssymbolsHausdorff measuremittateoria010307 mathematical physics0101 mathematicsLebesgue covering dimensionMathematicsProceedings of the American Mathematical Society
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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 $\epsilon$.

Applied MathematicsGeneral MathematicsDyadic cubesStructure (category theory)Space (mathematics)Measure (mathematics)CombinatoricsMetric spacePacking dimension28C15 (Primary) 54E50 (Secondary)Mathematics - Classical Analysis and ODEsSimple (abstract algebra)Classical Analysis and ODEs (math.CA)FOS: MathematicsUltrametric spaceMathematicsProceedings of the American Mathematical Society
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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.

Applied MathematicsGeneral Mathematicsmedian010102 general mathematicsMathematical analysista111QuasicontinuityMedianMetric measure space010103 numerical & computational mathematicsTriebel–Lizorkin spaceTriebel–Lizorkin space01 natural sciencesFractional Sobolev spaceCombinatoricsmetric measure spaceBesov spacequasicontinuityLimit (mathematics)0101 mathematicsBesov spacefractional Sobolev spaceMathematicsTRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY
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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 (…

Aquatic OrganismsEnvironmental EngineeringHealth Toxicology and MutagenesisMetal ions in aqueous solutionchemistry.chemical_elementCarbon nanotubeEnvironmentHydrophilizationlaw.inventionAdsorptionlawMetals HeavyAnimalsEnvironmental ChemistryOrganic matterOrganic ChemicalsColoring AgentsEcosystemchemistry.chemical_classificationAqueous solutionNanotubes CarbonChemistryPublic Health Environmental and Occupational HealthGeneral MedicineGeneral ChemistryPollutionDaphniaEnvironmental chemistryAdsorptionEcotoxicityCarbonWater Pollutants ChemicalChemosphere
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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…

Aquatic exerciseOsteoarthritisWalking speedBody compositionlaw.invention0302 clinical medicineRandomized controlled triallawMedicineOrthopedics and Sports MedicineVolunteerOBESE ADULTSHigh intensityta3141HIP OSTEOARTHRITISMiddle AgedOsteoarthritis KneeRANDOMIZED CONTROLLED-TRIAL3. Good healthPostmenopauseFemaleWATER IMMERSIONLIMITATIONSmedicine.medical_specialtyPhysical ExertionBiomedical EngineeringEXERCISEwalking speed03 medical and health sciencesPhysical medicine and rehabilitationRheumatologyInternal medicineOsteoarthritisHumansOLDER-ADULTSMETAANALYSISAgedHydrotherapykehonkoostumus030203 arthritis & rheumatologybusiness.industryaquatic exerciseResistance Training030229 sport sciencesARTICULAR-CARTILAGEmedicine.disease3126 Surgery anesthesiology intensive care radiologyRheumatologyPreferred walking speedosteoarthritisOrthopedic surgeryLean body massPhysical therapyPatient ComplianceWEIGHTbusinesshuman activitiesFollow-Up Studies
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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…

Aqueous colloidal stabilityTGAColloid and Surface ChemistryHalloysite nanotubesNanoclaysSeparationSettore CHIM/02 - Chimica FisicaColloids and Surfaces A: Physicochemical and Engineering Aspects
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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…

Aqueous solutionMaterials scienceHydroxypropyl celluloseHalloysite nanotubesNanoparticleGeologyDynamic mechanical analysisengineering.materialDMAHydroxypropyl cellulosemedicine.diseaseHalloysitechemistry.chemical_compoundchemistryChemical engineeringGeochemistry and PetrologyDeacidificationUltimate tensile strengthmedicineengineeringCelluloseCelluloseVapoursPaper consolidationSettore CHIM/02 - Chimica Fisica
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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…

Aqueous solutionMaterials sciencePyrimidine010405 organic chemistryGeneral Chemical EngineeringInorganic chemistryPotentiometric titrationStackingGeneral ChemistryCrystal structure010402 general chemistryRing (chemistry)01 natural sciencesArticle0104 chemical sciencesMetallcsh:Chemistrychemistry.chemical_compoundchemistrylcsh:QD1-999visual_artPolymer chemistryvisual_art.visual_art_mediumHybrid materialcarbon nanotubes copper zinc macrocycles hybrid materials functionalized carbon nanotubesACS Omega
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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…

Aqueous solutionPolymers and PlasticsChemistryUV irradiationPhotochemistryFluorescenceSpectral lineHydrogelColloid and Surface ChemistryRheologyElectron beam irradiationPolymer chemistrySelf-healing hydrogelsFluorescent probesMaterials ChemistryMoleculeSettore CHIM/07 - Fondamenti Chimici Delle TecnologieIrradiationPhysical and Theoretical ChemistryRheologyMolecular probeColloid and Polymer Science
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Von Arabesken. Neues zu einer Theorie des Ornaments bei Goethe

2004

Arabesques Goethe Theory of Ornament
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