Remarks on an overdetermined boundary value problem

We modify and extend proofs of Serrin’s symmetry result for overdetermined boundary value problems from the Laplace-operator to a general quasilinear operator and remove a strong ellipticity assumption in Philippin (Maximum principles and eigenvalue problems in partial differential equations (Knoxville, TN, 1987), Longman Sci. Tech., Pitman Res. Notes Math. Ser., Harlow, 175, pp. 34–48, 1988) and a growth assumption in Garofalo and Lewis (A symmetry result related to some overdetermined boundary value problems, Am. J. Math. 111, 9–33, 1989) on the diffusion coefficient A, as well as a starshapedness assumption on Ω in Fragalà et al. (Overdetermined boundary value problems with possibly degenerate ellipticity: a geometric approach. Math. Zeitschr. 254, 117–132, 2006).     

Preparation of 3-substituted-2-pyridin-2-ylindoles: regioselectivity of Larock’s indole annulation with 2-alkynylpyridines

A regioselective Larock approach to 3-substituted-2-pyridin-2-ylindoles from 2-alkynylpyridines and 2-iodoanilines is described herein. The unexpectedly high regioselectivity can be rationalized by a combination of steric, coordinative and electronic effects.     

Pressure-driven flow of a rate-type fluid with stress threshold in an infinite channel

In this paper we extend some of our previous works on continua with stress threshold. In particular here we propose a mathematical model for a continuum which behaves as a non-linear upper convected Maxwell fluid if the stress is above a certain threshold and as a Oldroyd-B type fluid if the stress is below such a threshold. We derive the constitutive equations for each phase exploiting the theory of natural configurations (introduced by Rajagopal and co-workers) and the criterion of the maximization of the rate of dissipation. We state the mathematical problem for a one-dimensional flow driven by a constant pressure gradient and study two peculiar cases in which the velocity of the inner part of the fluid is spatially homogeneous.     

Neutral to Ionic Pressure-Induced Phase Transition in the Mixed Stack Charge-Transfer Crystal ClMePD-DMeDCNQI

In the present work we report a spectroscopic investigation of the pressure-induced neutral to ionic (NI) phase transition in the mixed stack charge-transfer crystal 2-chloro-5-methyl-p-phenylenediamine 2,5-dimethyl-dicyanoquinonediimine, ClMePD-DMeDCNQI. The pressure induced phase change is studied by calculating, from spectroscopic data, the degree of ionicity, 𝜌 , which undergoes a continuous change as a function of pressure, reaching a value of about 0.65 at 3 GPa. The NI crossing reveals unique properties with respect to previously studied cases on similar compounds.     

Stability of charged impurities in a coupled single electron transistor and antidot system

We have fabricated devices on GaAs/AlGaAs heterostructures, containing two-dimensional electron gases, that consist of three point contacts surrounding an etched antidot with an Al/AlO_x/Al single electron transistor. The single electron transistor measurement shows rearrangement of neighboring charged impurities with a characteristic stability time scale of 20 s in one device and greater than 1 h in a second device. We also measured the resistance of the point contact–antidot constriction versus magnetic field. In a device with a 20 s stability time, we see a high noise level and poor reproducibility. In a device with a long stability time, much greater than 1 h, we are able to see reproducible features including Aharonov–Bohm oscillations.     

Transverse effects in superfluorescence

We demonstrate that off-axial emission can be responsible for the pulse envelope ringing, transverse effects, and large shot-to-shot pulse shape fluctuations observed in recent superfluorescence experiments.     

Generation of highly directional beams from a globally incoherent source

We have carried out a series of observations of the far field intensity distribution produced by a class of partially coherent planar sources. Our results confirm that, under the Collett-Wolf quasi-homogeneity conditions, highly directional beams can be produced even from a source which is globally incoherent. The far-zone pattern is shown to be largely independent of the intensity profile in the source plane and that the beam radius varies as predicted by Foley and Zubairy in the paraxial approximation. We show experimentally how the coherence length in the source plane can be measured directly from the far zone intensity distribution.     

A Few Properties of Just Infinite Algebras

In this article we prove a few interesting properties of just infinite algebras. Bartholdi (2006 Bartholdi , L. ( 2006 ). Branch rings, thinned rings, tree enveloping rings . Israel J. Math. 154 : 93 – 139 .[Crossref], [Web of Science ®] , [Google Scholar]), defines a particular class of just infinite algebras and demonstrates various properties of these examples. One such property, which is tedious to prove for his specific examples, is primality. We prove here that, in fact, all just infinite algebras are prime. We then consider two corollaries of this theorem; one suggests a weaker definition of just infinite for finitely generated algebras and the other examines the specific case of just infinite algebras which also satisfy a polynomial identity.     

Anionic N-Fries rearrangement of N-alkyl-2-iodo anilides induced by iodine-magnesium exchange: application for synthesis of strained 1,2,3-trisubstituted indoles

A superior, mild, high-yielding one-pot process for rapid access to oxo anilides has been developed that involves three cascade reactions: iodine-magnesium exchange, regiospecific ortho N-Fries rearrangement, and in situ trapping of the formed aniline anion. Coupled with McMurry cyclization, the two-step process allows ready synthesis of strained 1,2,3-trisubstituted indoles regioselectively.     

Microsurface potential measurements: repulsive forces between polyelectrolyte brushes in the presence of multivalent counterions

We propose a new way to determine weak repulsive forces operative between colloidal particles by measuring the rate of slow coagulation. The rate of slow coagulation is directly related to the competition of the repulsion with thermal motion. Since the thermal forces are weak, measurements of the coagulation rate can lead to precise information on repulsive potentials having a magnitude of just a few kT. We demonstrate this novel way by studying colloidal spherical polyelectrolyte brush (SPB) particles in aqueous solution containing trivalent La3+ counterions. The particles consist of a monodisperse polystyrene core of 121 nm radius from which linear sodium poly(styrenesulfonate) (PSS) chains are densely grafted (contour length 48 nm). We determine the rate of coagulation by time-resolved simultaneous static and dynamic light scattering in the presence of LaCl3 (0.2 to 150 mM). Direct measurements of the repulsive force between macroscopic brush layers demonstrate that the potential is decaying exponentially with distance. This is in good agreement with a simple theoretical treatment that furthermore leads to the effective surface potential Psi0. The good agreement of data obtained by the novel microscopic method with direct macroscopic measurements underscores the general validity of our approach.