The states of the character ring of a compact group

Deligne’s generalization of the Hadamard—Vallée Poussin method in classical number theory is formulated as the representability of certain states of the character ring of a compact group, and the determination of all the representable states is carried out. Research partially supported by NSF Grant 85-01742.     

A Brownian-ratchet DNA pump with applications to single-nucleotide polymorphism genotyping

We have fabricated a micron-scale device capable of transporting DNA oligomers using Brownian ratchets. The ratchet potential is generated by applying a voltage difference to interdigitated electrodes. Cycling between the charged state and a discharged, free-diffusion state rectifies the Brownian motion of charged particles. The observed macroscopic transport properties agree with the transport rate predicted from microscopic parameters including the DNA diffusivity, the dimensions of the ratchet potential, and the cycling time. Applications to human genetics, primarily genotyping of single-nucleotide polymorphisms (SNPs), are discussed. Received: 7 November 2001 / Accepted: 14 January 2002 / Published online: 22 April 2002     

Addition photochimique (2+2) de composes organometalliques α-insatures aux derives carbonyles α,β-insatures: addition d'alcynylsilanes a la cyclopentenone

Alkynylsilanes add photochemically to cyclopentenone to give bicyclo[3.2.0]heptenones. The photochemical rearrangement of adducts was studied. A method to eliminate the trimethylsilyl substituent is proposed. The structure of adducts is proved by spectroscopy, mainly ¹³C NMR.     

Boundedness and differentiability for nonlinear elliptic systems

We consider the elliptic system eratorname{div} (\mathcal{A}^j (x,u,\nabla u)) = \mathcal{B}^j (x,u,\nabla u)$">, and an obstacle problem for a similar system of variational inequalities. The functions and satisfy certain ellipticity and boundedness conditions with a -admissible weight and exponent e2$">. The growth of in ert\nabla u\vert$"> and ert u\vert$"> is of order . We show that weak solutions of the above systems are locally bounded and differentiable almost everywhere in the classical sense.

     

A method for finding Lanczos coefficients with the aid of symmetries

A set of algorithms involving the Lanczos potential and certain kinematical quantities for some arbitrary space-times, obtained using timelike vector fields, is considered. It is shown that such algorithms appear most naturally in the context of the spin coefficient formalism. Furthermore, explicit solutions are derived for the new spin coefficient algorithms.     

Near-infrared diode laser spectroscopy of the HCSi radical

The eight="20" border="0" style="vertical-align:bottom" width="172" alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022285203003011-si21.gif">, eight="20" border="0" style="vertical-align:bottom" width="172" alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022285203003011-si22.gif">, and eight="20" border="0" style="vertical-align:bottom" width="172" alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022285203003011-si23.gif"> band spectra of HCSi radical were investigated by means of near-infrared diode laser spectroscopy to determine precise molecular constants for the eight="20" border="0" style="vertical-align:bottom" width="73" alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022285203003011-si24.gif"> and eight="20" border="0" style="vertical-align:bottom" width="90" alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022285203003011-si25.gif"> states. The detailed analysis of the rotationally resolved eight="20" border="0" style="vertical-align:bottom" width="172" alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022285203003011-si26.gif"> band spectra, studied for the first time in the present investigation, leads to the precise determination of molecular constants for the eight="20" border="0" style="vertical-align:bottom" width="73" alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022285203003011-si27.gif"> state associated with the Renner-Teller interaction. We obtained −0.15126663(53) and 495.00698(30) cm⁻¹ as the Renner-Teller parameter <em>εem> and the bending vibrational frequency <em>ωem>₂, respectively. Based on the molecular constants for the eight="20" border="0" style="vertical-align:bottom" width="73" alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022285203003011-si28.gif"> and eight="20" border="0" style="vertical-align:bottom" width="73" alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022285203003011-si29.gif"> states, the rotational levels of the eight="20" border="0" style="vertical-align:bottom" width="90" alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022285203003011-si30.gif"> state were analyzed to obtain molecular constants and information on upper state perturbations. Using the available spectroscopic data, valence force fields for both the eight="16" border="0" style="vertical-align:bottom" width="32" alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022285203003011-si31.gif"> and eight="16" border="0" style="vertical-align:bottom" width="45" alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022285203003011-si32.gif"> states were estimated to aid in understanding the vibrational energy levels of the HCSi radical.     

Branched crystal morphology of linear polyethylene crystallized in a two-dimensional diffusion-controlled growth field

The branched crystal morphology of linear polyethylene formed at various temperatures from thin films has been studied by atomic-force microscopy (AFM), transmission electron microscopy (TEM), electron diffraction (ED) pattern and polymer decoration technique. Two types of branched patterns, i.e. dendrite and seaweed patterns, have been visualized. The fractal dimension d _f = 1.65 of both dendrite and some of seaweed patterns was obtained by using the box-counting method, although most of the seaweed patterns are compact. Selected-area ED patterns indicate that the fold stems tilt about 34.5^° around the b-axis and polymer decoration patterns show that the chain folding direction and regularity in two (200) regions are quite different from each other. Because of chain tilting, branched crystals show three striking features: 1) the lamella-like branches show two (200) regions with different thickness; 2) the crystals usually bend towards the thin region; 3) the thick region grows faster by developing branches, thus branches usually occur outside the thick region. The branched patterns show a characteristic width w, which gives a linear relationship with the crystallization temperature on a semilogarithmic plot. Received 15 March 2002 and Received in final form 29 April 2002     

High-spin proton and alpha-particle emission as probes for nuclear structure

During recent years the nuclear decay modes of discrete prompt proton and α-particle emission from (super)deformed high-spin states have been discovered in nuclei in the vicinity of ⁵⁶Ni. The latest news from experiments performed at EUROBALL and GAMMASPHERE regarding these decays are presented and discussed. Published online: 31 October 2002 RID="a" ID="a"e-mail: dirk.rudolph@kosufy.lu.se