A remark on the polytopality of an interesting 3-sphere

We give a simple proof establishing the polytopality of the 3-sphere described in [3].     

Compactly supported tight affine spline frames in

The theory of fiberization is applied to yield compactly supported tight affine frames (wavelets) in from box splines. The wavelets obtained are smooth piecewise-polynomials on a simple mesh; furthermore, they exhibit a wealth of symmetries, and have a relatively small support. The number of ``mother wavelets', however, increases with the increase of the required smoothness.

Two bivariate constructions, of potential practical value, are highlighted. In both, the wavelets are derived from four-direction mesh box splines that are refinable with respect to the dilation matrix .

     

Radiation from a Uniformly Accelerated Charge

The emission of radiation by a uniformly accelerated charge is analyzed. According to the standard approach, a radiation is observed whenever there is a relative acceleration between the charge and the observer. Analyzing difficulties that arose in the standard approach, we propose that a radiation is created whenever a relative acceleration between the charge and its own electric field exists. The electric field induced by a charge accelerated by an external (nongravitational) force is not accelerated with the charge. Hence the electric field is curved in the instantaneous rest frame of the accelerated charge. This curvature gives rise to a stress force, and the work done to overcome the stress force is the source of the energy carried by the radiation. In this way, the energy balance paradox finds its solution.     

Kaon electroproduction from the deuteron and the Λn final state interaction

Inclusive and exclusive cross sections are calculated for thed(e,eK ⁺)n reaction using amplitudes describing the elementary photo,p(,K ⁺), and electroproduction,p(e, eK ^–), processes. The sensitivity of the theoretical cross section to the final staten interaction is examined for severalN potentials. The utility of this reaction for investigating possible strange dibaryon resonances is discussed.Presented at the symposium Mesons and Light Nuclei, Bechyn, Czechoslovakia, May 27–June 1, 1985.The authors gratefully acknowledge Dr. Lacy Petris and Professor Ian Morrison for very beneficial interactions and assistance. This research was supported in part by the U.S. Derpatment of Energy and the Australian Research Grants Scheme. One of the authors (S.C.) also acknowledges the support and hospitality extended by the School of Physics, University of Melbourne during a short term visit.     

Self-similar spherical gravitational collapse and the cosmic censorship hypothesis

We show that a self-similar general relativistic spherical collapse of a perfect fluid with an adiabatic equation of statep=(–1) and low enough values, results in a naked singularity. The singularity is tangent to an event horizon which surrounds a massive singularity and the redshift along a null geodesic from the singularity to an external observer is infinite. We believe that this is the most serious counter example to cosmic censorship obtained so far.This Essay received the fifth award from the Gravity Research Foundation for 1987-Ed.     

Exponential box splines

In a recent paper by Nira Dyn and the author, univariate cardinal exponential B-splines are shown to have a representation similar to the wellknown box spline representation of the univariate cardinal polynomialB-splines. Motivated by this, we construct, for a set ofn directions inZ ^s and a vector of constants λ ?R ⁿ, an “exponential box spline” which has the same smoothness and support as the polynomial box spline, and is a positive piecewise exponential in its support. We derive recurrence relations for the exponential box splines which are simpler than those for the polynomial case. A relatively simple structure of the space spanned by the translates of an exponential box spline is obtained for λ in a certain open dense set ofR ⁿ—the “simple” λ. In this case, the characterization of the local independence of the translates and related topics, as well as the proofs involved, are quite simple when compared with the polynomial case (corresponding toλ = 0).     

Synthesis and C70 complexation studies of a fluorescent 5,5’-bi-p-tert-butylcalix[4]arene scaffold

Abstract

In this paper, we report the synthesis and C70 complexation studies of a new fluorescent 5,5′-bi-p-tert-butylcalix[4]arene capsule with an extended hydrophobic cavity. The synthetic route required development of a series of selective protection and de-protection reactions, such as esterification and ester cleavage, as well as a cross-coupling reaction at the lower rim. The resulting 5,5′-bi-p-tert-butylcalixarene was fully characterised, including by X-ray crystallography. In the solid state, the compound exists in an ‘open-capsule’ orientation, with a perfectly planar bridging biphenylene unit resulting in high fluorescence with a maximum emission peak at 390 nm. Preliminary fluorescence-based complexation experiments with C70 fullerene did not provide conclusive evidence for formation of inclusion complexes.     

Avermectin-Milbemycin Studies. 3. Synthesis of a Milbemycin-Avermectin Hybrid

An efficient synthesis of a milbemycin-avermectin hybrid ($\text{i.e.}$ 1) has been achieved.     

Total syntheses of (+)-zampanolide and (+)-dactylolide exploiting a unified strategy

The first total syntheses of (+)-zampanolide (1) and (+)-dactylolide (2), members of a new class of tumor cell growth inhibitory macrolides, have been achieved. Key features of the unified synthetic scheme included the stereocontrolled construction of the cis-2,6-disubstituted tetrahydropyran via a modified Petasis-Ferrier rearrangement, a highly convergent assembly of the macrocyclic domain, and, in the case of zampanolide, a Curtius rearrangement/acylation tactic to install the N-acyl hemiaminal. The complete relative and absolute stereochemistries for both (+)-zampanolide and (+)-dactylolide were also assigned, albeit tentatively in the case of (+)-zampanolide (1).     

Design, synthesis, and evaluation of analogues of (+)-14-normethyldiscodermolide

[Structure: see text] The design, syntheses, and biological evaluation of nine totally synthetic analogues of the microtubule-stabilizing agent (+)-14-normethyldiscodermolide (2) are reported. Simplification at the C(21)-C(24) terminal diene and at the C(1)-C(5) lactone moieties reveals significant structure-activity relationships.