Littlewood-Paley Inequalities on Manifolds with Ends

Potential Analysis - Let M be a manifold with ends $mathbb {R}^{m}sharp mathcal {R}^{n}$ with m > n >?2 which is a non-doubling manifold. In this paper we prove a...     

On Locally Nilpotent Subgroups of GL 1(D)

In this article we study locally nilpotent subgroups of D*: = GL ₁(D), where D is a division ring. It is proved that every locally nilpotent subnormal subgroup of D* is central. If D is algebraic over its centre then every locally solvable subnormal subgroup of D* is central. Also, in this case, it is shown that every locally nilpotent maximal subgroup of D* can occur as the multiplicative group of some maximal subfield of D.     

Weighted Lorentz estimates for parabolic equations with non-standard growth on rough domains

The main aim of this paper is to prove the Calderón–Zygmund estimates for a general nonlinear parabolic equation of p(x, t)-Laplacian type in the weighted Lorentz spaces. Note that we only require some mild conditions on the nonlinearity of coefficients and the underlying domain. The result for these nonlinear parabolic equations is new even in the particular case when the growth p(x, t) is a constant.     

An improvement of the binary merge algorithm

In this paper, we are concerned with the merging of two linearly-ordered listsA andB consisting of elements:a ₁<a ₂<...<b _n . The Hwang-Lin merging algorithm was considered very efficient for merging two lists of arbitrary sizes. Recently, Manacher was able to develop methods which reduce the number of pairwise comparisons required in the Hwang-Lin algorithm by a factor 31/336m. We develop in this paper a new method which further improves this factor to 52/336m. It is possible that even larger improvements could be achieved.     

Some remarks about the formulation of three-dimensional thermoelastoplastic problems by integral equations

The extended form of the identity of Somigliana, giving the displacement rate in terms of the traction and the displacement rate on the boundary, involves plastic and thermal strain rate. Because of strong singularity of some kernel, die gradient of the displacement rate may be strictly evaluated by an integro-differential expression. The paper shows how to derive the integral form of the gradient rate which corrects some erroneous expressions reported in the literature.     

Specific acoustic impedances of piezoelectric ceramic and polymer composites used in medical applications

The specific acoustic impedance of the piezoelectric composites over the frequency range of 0.5-7.5 MHz was measured using the reflection, the echo-shift, and the resonance techniques. There was a significant difference between the values obtained by the reflection technique in comparison with the other two techniques. It is argued that the difference is inherent in the measurement techniques and they measure different properties of the composite such as acoustic impedance and reflectivity. The specific acoustic impedance and the reflectivity were found to be a function of the volume fraction of the ceramic and not a function of frequency.     

Mechanistic insights into the chiral phosphoramide-catalyzed, enantioselective crossed-aldol reactions of aldehydes

[reaction: see text] The mechanism of the phosphoramide-catalyzed enantioselective aldol additions of trichlorosilyl enolate 1 to aldehydes has been studied. Natural abundance 12C/13C kinetic isotope analysis showed that the rate-determining step of the reaction is the aldolization. Arrhenius activation parameters for the aldol addition reaction were determined. The entropy of activation is large and highly negative, whereas the enthalpy of activation is relatively small. Despite the different trends in selectivity observed for electron-rich and electron-poor aldehydes, similar entropic and enthalpic contributions to the free energies of activation are found for both classes of substrates. The experimental results from the Arrhenius and the kinetic isotope effect studies allowed the formulation of an interpretation for the divergent selectivity trends in the aldol reaction.     

Synthesis of (-)-delobanone

On irradiation in the presence of Fe(CO)(5) under a CO atmosphere, the alkenyl cyclopropane 2 underwent smooth ring expansion to give the sesquiterpene (-)-delobabone 3. The alkenyl cyclopropane 2 was prepared from the enantiomerically enriched epoxide 1.