Comparison of Different Definitions of Traces for a Class of Ramified Domains with Self-Similar Fractal Boundaries

We consider a class of ramified bidimensional domains Ω with a self-similar fractal boundary Γ^?∞?, which is supplied with a probability measure μ called the self-similar measure. Emphasis is put on the case when the domain is not a ε???δ domain as defined by Jones and the fractal set is not totally disconnected. We compare two notions of trace on Γ^?∞? for functions in W ^1,q (Ω): the classical one, see for instance the book by Jonnson and Wallin, 1984, using the strict definition of a function at a point of $\overline{\Omega}$ , and another one proposed in 2007 and heavily relying on self-similarity. We prove that the two traces coincide μ-almost everywhere on Γ^?∞?. As a corollary, we characterize the critical number $\bar q$ for which for all $q<\bar q$ (resp. $q > \bar q$ ) there is a (resp. no) continuous extension operator from W ^1,q (Ω) to W ^1,q (?²).     

Homologous SNV Reaction: Synthesis of l‐Methyl‐4‐[4′‐phenylsulfonyl‐1′,3′‐butadienyl]pyridinium Iodide and Its Reactivity with Thiol Groups Giving Rise to the Chromophoric Thioether

Thioether 4‐[(1′E,3′E)‐4′‐phenylsulfanyl‐1,3′‐butadienyl]pyridine 8 and sulfone 4‐(4′‐phenylsulfonyl‐1′,3′‐butadienyl)pyridine 14 were prepared by reaction of the carbanions derived from allylic thioether or allylic sulfone with isonicotinaldehyde. The reaction with the sulfonyl carbanion occurred at the α position and on heating the alcolate gave the dienic sulfone 14 . The corresponding pyridinium iodide 10 and 15 were prepared by reaction with methyl iodide, respectively, on pyridine derivates 8 and 14 . The dienic pyridinium thioether 10 showed a long wavelength absorption band centered at 420 nm. The reaction of dienic pyridinium sulfone 15 with thiophenol gave the dienic pyridinium thioether 10 by a nucleophilic vinylic substitution. The reaction of sulfone 15 with glutathione was of second order and the rate constant was 8.5 M^?1s^?1 at 30°C and pH 7, about 500 times smaller than the rate constant observed with (E)‐1‐methyl‐4‐(2‐methylsulfonyl‐1‐ethenyl)pyridinium iodide 1 . The dienic pyridinium thioether 10 was a negative solvatochrome.     

Metal-organic deposition of YBa2Cu3Ox and Bi2Sr2Ca1Cu2Ox films on various substrates starting from different fluorine-free metallorganic compounds

YBa₂Cu₃O_x (Y-123) and Bi₂Sr₂Ca₁Cu₂O_x (Bi-2212) films on various substrates have been prepared by Metal-Organic Deposition starting from different metallorganic fluorine-free compounds and using a very simple instrumentation. The processing conditions include a rapid pyrolysis step in air and an annealing step in oxygen for Y-123 and in air for Bi-2212. The films obtained have been characterized by X-ray diffraction (XRD) and the formation of a superconducting phase of Y-123 or Bi-2212 was confirmed measuring the critical temperature (T _c) with Ac-susceptibility and resistive measurements. Microstructure and final cationic ratios have been studied by scanning electron microscopy (SEM) and energy dispersive spectroscopy (EDS).     

Stress-concentration factors for elliptical holes near an edge

Experimental and theoretical stress-concentration factor and stress-intensity factor solutions exist for a large number of hole shapes and configurations. However, little work has been done on the interaction between holes and free edges. This paper reports the results of an experimental study which investigated elliptical holes close to each edge of a tension plate. The holes were symmetric with respect to the longitudinal axis of the models and had their major axes normal to the edge of the plate. The ellipse ratio and the distance between the center and the edge were varied. A statistical model is developed which shows that the stress concentrationK _g at both ends of the ellipses is linearly dependent on a geometric function ? such thatK _g = αΦ + γ. The values for the function ? are given.     

Organocatalytic,Asymmetric Eliminative [4+2] Cycloaddition of Allylidene Malononitriles with Enals: Rapid Entry to Cyclohexadiene‐Embedding Linear and Angular Polycycles

A direct aminocatalytic synthesis has been developed for the chemo‐, regio‐, diastereo‐, and enantioselective construction of densely substituted polycyclic carbaldehydes containing fused cyclohexadiene rings. The chemistry utilizes, for the first time, remotely enolizable π‐extended allylidenemalononitriles as electron‐rich 1,3‐diene precursors in a direct eliminative [4+2] cycloaddition with both aromatic and aliphatic α,β‐unsaturated aldehydes. The generality of the process is demonstrated by approaching 6,6‐, 5,6‐, 7,6‐, 6,6,6‐, and 6,5,6‐fused ring systems, as well as biorelevant steroid‐like 6,6,6,6,5‐ and 6,6,6,5,6‐rings. A stepwise reaction mechanism for the key [4+2] addition is proposed as a domino bis‐vinylogous Michael/Michael/retro‐Michael reaction cascade. The utility of the malononitrile moiety as traceless activating group of the dicyano nucleophilic substrates is demonstrated.     

Material properties in thermal-stress analysis

With simple techniques and not too-costly laboratory equipment, the significant material properties in modeling transient thermal stresses by photothermoelasticity are evaluated. The results are presented for a room-temperature-cured epoxy, a hot-cured epoxy and a polycarbonate. The materials tested are also evaluated on their applicability to a transient-thermal-stress analysis.     

MRI-guided neutron capture therapy by use of a dual gadolinium/boron agent targeted at tumour cells through upregulated low-density lipoprotein transporters

The upregulation of low-density lipoprotein (LDL) transporters in tumour cells has been exploited to deliver a sufficient amount of gadolinium/boron/ligand (Gd/B/L) probes for neutron capture therapy, a binary chemio-radiotherapy for cancer treatment. The Gd/B/L probe consists of a carborane unit (ten B atoms) bearing an aliphatic chain on one side (to bind LDL particles), and a Gd(III)/1,4,7,10-tetraazacyclododecane monoamide complex on the other (for detection by magnetic resonance imaging (MRI)). Up to 190 Gd/B/L probes were loaded per LDL particle. The uptake from tumour cells was initially assessed on cell cultures of human hepatoma (HepG2), murine melanoma (B16), and human glioblastoma (U87). The MRI assessment of the amount of Gd/B/L taken up by tumour cells was validated by inductively coupled plasma-mass-spectrometric measurements of the Gd and B content. Measurements were undertaken in vivo on mice bearing tumours in which B16 tumour cells were inoculated at the base of the neck. From the acquisition of magnetic resonance images, it was established that after 4-6 hours from the administration of the Gd/B/L-LDL particles (0.1 and 1 mmol kg(-1) of Gd and (10)B, respectively) the amount of boron taken up in the tumour region is above the threshold required for successful NCT treatment. After neutron irradiation, tumour growth was followed for 20 days by MRI. The group of treated mice showed markedly lower tumour growth with respect to the control group.     

Synthesis of a chloro protected iridium nitrido complex

Intramolecular activation processes of vulnerable ligand C-H bonds frequently limit the thermal stability and accessibility of late transition metal complexes with terminal metal nitrido units. In this study chloro substitution of the 2,6-ketimine N-aryl substituents (2,6-C(6)H(3)R(2), R = Cl) of the pyridine, diimine ligand is probed to increase the stability of square-planar iridium nitrido compounds. The thermal stability of iridium azido precursor and nitrido compounds was studied by a combination of thermoanalytical methods (DTG/MS and DSC) and were compared to the results for the related complexes with 2,6-dialkyl substituted N-aryl groups (R = Me, iPr). The investigations were complemented by DFT calculations, which allowed us to unravel details of the thermal decomposition pathways and provided mechanistic insights of further conversion steps and fluctional processes. The DTG/MS and DSC measurements revealed two different types of thermolysis pathways for the azido compounds. For the complexes with R = Cl and iPr substituents, two well-separated exothermic processes were observed. The first moderately exothermic loss of N(2) is followed by a second, strongly exothermic transformation. This contrasts the experimental results for the compound with 2,6-dimethyl substituents (R = Me), where both steps proceed concurrently in the same temperature range. The separation of the two thermal steps in the 2,6-dichloro substituted derivative allowed us to develop a protocol for the isolation of the highly insoluble nitrido complex, which was characterized by UV/vis, IR-spectroscopy and elemental analysis. Its constitution was further confirmed by reaction with silanes, which gave the corresponding silyl amido complexes.