Comparison of number–average molecular weights calculated by GPC and membrane osmometry

Data are presented which show that when a polymer contains an appreciable amount of low molecular weight species below the diffusion limit of the osmometer membrane, the osmotic molecular weight, M?_n, is generally higher than the M?_n calculated from gel-permeation chromatography (GPC). Experiments were performed on samples of poly(vinyl chloride) (PVC) and high-cis polybutadiene polymers. Osmotic data were obtained in the usual manner, while GPC data were obtained using the universal calibration approach. It was found that when all polymer species below approximately 10,000 molecular weight were excluded from the calculation of M?_n by GPC, agreement in M?_n was obtained between membrane osmometry and GPC. The data obtained suggest that the choice of M?_n as measured by membrane osmometry in the calibration of the GPC should not be done casually, as the measured M?_n may not reflect the “true” value of that sample, especially when the polymer sample contains an appreciable amount of low molecular weight material.     

Effect of Pr-Ca substitution on the transport and magnetic behavior of LaMnO3 perovskite

The effect of simultaneous substitution of a fluctuating cation and a divalent cation in LaMnO₃ perovskite modifies the properties of the material to exhibit large valence colossal magnetoresistance (CMR) effect. A good example of these properties is (La_1−2x Pr _x Ca _x )MnO₃ (LPCMO) type CMR material. In this communication it is reported that, with the increase in x (for x=0.1, 0.15, 0.2), the T _c varies between 100 and 120 K with improvisation in metal-insulator transition. Interestingly, resistance increases with x from few hundred ohms to few kilo ohms with corresponding decrease in the unit cell volume. The results of the studies using X-ray diffraction (XRD), electrical resistivity, magnetoresistance and ac susceptibility measurements on LPCMO samples for understanding the structural, transport and magnetic properties are discussed in detail.     

Novel tricyclic diamines 2. Synthesis of 1,7-diazaisoadamantane, 1,5-diazaisoadamantane and 1,6-diazahomobrendane

Three novel tricyclic diamines (1,7-diazaisoadamantane, 1,5-diazaisoadamantane and 1,6-diazahomobrendane) were prepared. A flexible synthetic strategy was employed which used flat, aromatic azaindoles as the starting materials. The requisite azaindoles were prepared by a tandem Sonogashira coupling/intramolecular cyclization reaction. Ring saturation, appropriate functionalization and intramolecular alkylation provided the three novel tricyclic diamines cores.     

On Fuglede's Conjecture and the Existence of Universal Spectra

Recent methods developed by Tao [18], Kolountzakis and Matolcsi [7] have led to counterexamples to Fugelde’s Spectral Set Conjecture in both directions. Namely, in Tao produced a spectral set which is not a tile, while Kolountzakis and Matolcsi showed an example of a nonspectral tile. In search of lower dimensional nonspectral tiles we were led to investigate the Universal Spectrum Conjecture (USC) of Lagarias and Wang [14]. In particular, we prove here that the USC and the "tile → spectral" direction of Fuglede’s conjecture are equivalent in any dimensions. Also, we show by an example that the sufficient condition of Lagarias and Szabó [13] for the existence of universal spectra is not necessary. This fact causes considerable difficulties in producing lower dimensional examples of tiles which have no spectra. We overcome these difficulties by invoking some ideas of Révész and Farkas [2], and obtain nonspectral tiles in . Fuglede’s conjecture and the Universal Spectrum Conjecture remains open in 1 and 2 dimensions. The one-dimensional case is closely related to a number theoretical conjecture on tilings by Coven and Meyerowitz [1].     

Integral equation formulation for buoyancy-driven convection problems

An integral equation formulation for buoyancy-driven convection problems is developed and illustrated. Buoyancy-driven convection in a bounded cylindrical geometry with a free surface is studied for a range of aspect ratios and Nusselt numbers. The critical Rayleigh number, the nature of the cellular motion, and the heat transfer enhancement are computed using linear theory. Green's functions are used to convert the linear problem into linear Fredholm integral equations. Theorems are proved which establish the properties of the eigenvalues and eigenfunctions of the linear integral operator which appears in these equations.     

Pointwise ergodic theorem along the prime numbers

The pointwise ergodic theorem is proved for prime powers for functions inL ^p,p>1. This extends a result of Bourgain where he proved a similar theorem forp>(1+√3)/2. This paper is a part of the author’s Ph.D. thesis supervised by V. Bergelson.     

On the Magnitude of the Sum of Bases of the Natural Numbers

We construct two bases of the natural numbers B₁ and B₂, eachof order two, such that (B₁ + B₂ (n) <n^{+c/(log n)}. For alower estimate, it is proved that if B₂ and are two bases, eachof order two, then (B₁+B₂)(n) > n. Generalisations to sumsof bases of order h > 2 are also given.     

The Nonsmooth Dynamics of Combined Slip and Spin Motion Under Dry Friction

Journal of Nonlinear Science - The isothermal quasistatic (i.e. acceleration neglected) hardening-free plasticity at large strains is considered, based on the standard multiplicative decomposition...