Geodesic metrics on fractals and applications to heat kernel estimates

It is well known that for a Brownian motion, if we change the medium to be inhomogeneous by a measure μ, then the new motion(the time-changed process) will diffuse according to a different metric D(·, ·).In 2009, Kigami initiated a general scheme to construct such metrics through some self-similar weight functions g on the symbolic space. In order to provide concrete models to Kigami’s theoretical construction, in this paper,we give a thorough study of his metric on two classes of fractals of pr...     

Applications of esr techniques to the study of free radical processes and kinetics in acrylic polymerizations

Electron spin resonance (ESR) techniques have been applied to a detailed study of batch and semicontinuous emulsion polymerization of methyl methacrylate; butyl acrylate and styrene have been briefly studied. Quenching of samples from the polymerization reactor followed by ESR analysis are useful, but we have developed continuous flow techniques which are preferable in many cases. ESR techniques can provide valuable information relating to the nature of free radical reactions, the concentration of propagating free radicals, and the kinetic processes in these reactions. Direct ESR analysis is most valuable but is not applicable to all systems. Spin trapping techniques can be useful for systems not accessible by direct analysis.     

Bimanes (1,5-diazabicyclo[3.3.0]octadienediones): Laser activity in syn-bimanes

The conversion of 3-methyl-4-benzyl-4-chloro-2-pyrazolin-5-one 10b was catalyzed by a mixture of potassium fluoride and alumina to give syn-(methyl, benzyl)bimane 6 (62%) without detectable formation of the anti isomer, A6 [a 1 : 1 mixture (87%) of the isomers 6 and A6 was obtained when the catalyst was potassium carbonate]. In a similar reaction syn-(methyl,carboethoxymethyl)bimane 7 (15%) with the anti isomer A7 (36%) was obtained from 3-methyl-4-carboethoxymethyl-4-chloro-2-pyrazolin-5-one 10c . syn-(Methyl, β-acetoxyethyl)bimane 8 (70%) was obtained from 3-methyl-4-β-acetoxyethyl-4-chloro-2-pyrazolin-5-one 10d (potassium carbonate catalysis) and was converted by hydrolysis to syn-(methyl, β-hydroxyethyl)bimane 9 (40%). Acetyl nitrate (nitric acid in acetic anhydride) converted anti-(amino,hydrogen)bimane 11 to anti-(amino,nitro)bimane 15 (91%), anti-(methyl,hydrogen)bimane 13 to anti-(methyl,nitro)(methyl,hydrogen)bimane 16 (57%), and degraded syn-(methyl,hydrogen)bimane 12 to an intractable mixture. Treatment with trimethyl phosphite converted syn-(bromomethyl,methyl)bimane 17 to syn-(dimethoxyphosphinylmethyl,methyl)bimane 18 (78%) that was further converted to syn-(styryl,methyl)bimane 19 (29%) in a condensation reaction with benzaldehyde. Treatment with acryloyl chloride converted syn-(hydroxymethyl,methyl)bimane 20 to its acrylate ester 21 (22%). Stoichiometric bromination of syn-(methyl,methyl)bimane 1 gave a monobromo derivative that was converted in situ by treatment with potassium acetate to syn-(acetoxymethyl,methyl)(methyl,methyl)bimane 47 . N-Amino-μ-amino-syn-(methylene,methyl)bimane 24 (68%) was obtained from a reaction between the dibromide 17 and hydrazine. Derivatives of the hydrazine 24 included a perchlorate salt and a hydrazone 25 derived from acetone. Dehydrogenation of syn-(tetramethylene)bimane 26 by treatment with dichlorodicyanobenzoquinone (DDQ) gave syn-(benzo,tetramethylene)bimane 27 (58%) and syn-(benzo)bimane 28 (29%). Bromination of the bimane 26 gave a dibromide 29 (92%) that was also converted by treatment with DDQ to syn-(benzo)bimane 28 . Treatment with palladium (10%) on charcoal dehydrogenated 5, 6, 10, 11-tetrahydro-7H,9H-benz [6, 7] indazol [1, 2a]benz[g]indazol-7,9-dione 35 to syn-(α-naphtho)bimane 36 (71%). The bimane 35 was prepared from 1,2,3,4-tetrahydro-1-oxo-2-naphthoate 37 by stepwise treatment with hydrazine to give 1,2,4,5-tetrahydro-3H-benz[g]indazol-3-one 38 , followed by chlorine to give 3a-chloro-2,3a,4,5-tetrahydro-3H-benz[g]indazol-3-one 39 , and base. Dehydrogenation over palladium converted the indazolone 34 to 1H-benz[g] indazol-3-ol 36 . Helicity for the hexacyclic syn-(α-naphtho)bimane 36 was confirmed by an analysis based on molecular modeling. The relative efficiencies (RE) for laser activity in the spectral region 500–530 nm were obtained for 37 syn-bimanes by reference to coumarin 30 (RE 100): RE > 80 for syn-bimanes 3, 5, 18 , and μ-(dicarbomethoxy)methylene-syn-(methylene,methyl)bimane 22 : RE 20–80: for syn-bimanes 1,2,4,20,24,26 , and μ-thia-syn-(methylene,methyl)bimane 50 : and RE 0-20 for 26 syn-bimanes. The bimane dyes tended to be more photostable and more water-soluble than coumarin 30. The diphosphonate 18 in dioxane showed laser activity at 438 nm and in water at 514 nm. Presumably helicity, that was demonstrated by molecular modeling, brought about a low fluorescence intensity for syn-(α-naphtho)bimane 36 , Φ0.1, considerably lower than obtained for syn-(benzo)bimane 28 , Φ0.9.     

Quantitative analysis of MWCNT agglomeration in polymeric‐based membranes using atomic force microscope

In this work, we performed an analysis on the surface properties of polyethersulfone (PES)‐based ultrafiltration membranes that were prepared by incorporating acid functionalized multiwalled carbon nanotube (f‐MWCNT) and polyvinylpyrrolidone into membrane matrix via simple blending method. The bonding‐chemistry of the nanocomposites implanted within the PES membrane was investigated by Fourier transform infrared spectrometer while atomic force microscope was employed to observe the distribution of f‐MWCNT in the membrane matrix and further measured its agglomeration quantitatively. The resultant 3D atomic force microscope images provided the most satisfactory way to examine the distribution of nanomaterials in the membranes, and with the help of ‘point profile data’ the maximum height and width of the agglomerated cluster could be quantitatively calculated. Moreover, the surface profile studies of the membrane surface provided the information about the length, volume, area, perimeter, radius and diameter of grains. It was observed that PES/nanocomposite blended membranes were held together via strong hydrogen bonding, but poor dispersion of MWCNT in the membrane matrix reduced the membrane performance in terms of protein (pepsin and bovine albumin serum) rejection and increased the surface roughness. Copyright © 2016 John Wiley & Sons, Ltd.     

Determination of potential curve parameters of excited electronic states of polyatomic molecules by resonance CARS

Resonance CARS line-shape analysis has been applied to determine the parameters of the excited electronic state potential curves of a cyanine dye and its short-lived photoisomers during the process of photoisomerization. For this very complicated situation other methods for the estimation of these values would fail. The origin shift parameters determined are very small and the homogeneous line width is smaller than the line width of the absorption band.     

The effect of functionalization on structure and electrical conductivity of multi-walled carbon nanotubes

Nanosized powders of Ti-Nb oxide core-shell nanocrystals with atomic ratios of Nb/Ti = 0.11, 0.25, and 0.38 have been prepared by two preparation routes. The first route was co-precipitation, followed by␣annealing, using NbCl₅ as a source of Nb. The second route was coating of pure TiO₂ nanocrystals by Nb-isopropoxide in liquid medium, followed by impregnation of the Nb into the nanoparticles by annealing. Both methods yielded anatase nanocrystals with a Nb-rich shell and a core, which had much lower Nb loadings. The anatase structure solid solution (with Nb incorporated) was stable under annealing up to 760°C. The particle size remained within the nanometric scale (<50 nm) under heat-treatment up to 760°C. It has been shown that the fabricated powders can be redispersed in aqueous media by simple ultrasound treatment, resulting in nanosized dispersions. Using a variety of analytical techniques, including depth profiling of single nanocrystallites by AES combined with sputtering by Ar ions, the mechanism of the core-shell structure creation was studied. It is proposed that the formation of the core-shell structure is governed by solubility limitations in the co-precipitation route and by solubility and diffusion limitations in the coating-incorporation route.     

Electronic band structure of solid CO2 as determined from the hv-dependence of photoelectron emission

Photoelectron energy distribution curves from solid CO₂ have been determined for excitation energies from hv = 14 up to 40 eV using synchrotron radiation. A 1:1 correspondence to the gas-phase photoelectron spectrum is observed for the occupied molecular orbitals. The vertical binding energies E_B^v (E_VAC = 0) and widths (fwhm) of the valence bands of solid CO₂ are determined to be 13.0 and 0.95 eV (1π_g); 16.7 and 1.1 eV (1π_u); 17.6 and 0.85 eV (3σ_u) and 18.8 and 0.8 eV (4σ_g) for the individual bands respectively. The partial photoemission cross sections differ importantly from those of the gas phase in exhibiting pronounced maxima at 5.2 eV (1π_g), 4.4–5.3 eV (1π_u + 3σ_u) and 4.2 eV (4σ_g) above the vacuum level, which is attributed to effects of high density of final (conduction-band) states. Further weaker maxima are observed at higher photon energies. Contrary to the case for the gas phase, the resonances are unperturbed in the solid by degenerate autoionizing molecular Rydberg states. The molecular origin of the resonances in the continuum is discussed and related to X-ray absorption spectra, electron-scattering data and to theoretical cross-section calculations. It is shown that the same set of resonances is observed in the different experiments. The resonances occur however at different energies due to different Coulomb interactions. The photoemission results presented provide also a key to the hitherto unexplained optical spectrum of solid CO₂ in the VUV range, making possible an assignment of the structures observed to Frenkel-type excitons (hv ≤ 15 eV) and interband transitions (hv ? 15 eV).