Riemannian Manifolds in Which Certain Curvature Operator Has Constant Eigenvalues along Each Circle

Riemannian manifolds for which a natural curvature operator has constant eigenvalues on circles are studied. A local classification in dimensions two and three is given. In the 3-dimensional case one gets all locally symmetric spaces and all Riemannian manifolds with the constant principal Ricci curvatures r ₁ = r ₂ = 0, r ₃= 0 , which are not locally homogeneous, in general.     

Effective Mode Volume of Nanoscale Plasmon Cavities

The controlled squeezing of electromagnetic energy into nanometric volumes via surface plasmon-polariton excitations in plasmonic nanoresonators is analyzed using the concept of an effective electromagnetic mode volume V _eff, while taking careful account of the plasmon-polariton dispersion and the electromagnetic energy stored in the metal. Together with the quality factor Q of the cavity resonance, this enables a comparison with dielectric optical cavities, where V _eff is limited by diffraction. For a Fabry–Perot type planar metallic cavity, a one-dimensional analytic model as well as a three-dimensional finite-difference time-domain simulation reveal that V _eff is not bounded by diffraction, and that Q/V _eff increases for decreasing cavity size. In this picture, matter–plasmon interactions can be quantified in terms of Q and V _eff, and a resonant cavity model for the enhancement of spontaneous Raman scattering is presented.     

Mineralogical analysis of auriferous ores from the El Diamante mine, Colombia

X-ray diffraction (XRD), Mössbauer spectrometry (MS), secondary ions mass spectroscopy (SIMS) and laser-ablation microprobe–inductively coupled plasma–mass spectrometry (LAM–ICP–MS) were used to study mineral samples of Colombian auriferous ores collected from the “El Diamante” mine, located in the municipality of Guachavez-Nariño, in Colombia. The samples were prepared as polished thin sections and polished sections. From XRD data, quartz, sphalerite and pyrite were detected and their respective cell parameters were estimated. From MS analyses, pyrite, arsenopyrite and chalcopyrite were identified; their respective hyperfine parameters and respective texture were deduced. Multiple regions of approximately 200 × 200 μm in each sample were analyzed with SIMS; the occurrence of “invisible gold” associated mainly with pyrite and secondarily with arsenopyrite could thus be assigned. It was also found that pyrite is of the arsenious type. Spots from 30 to 40 μm in diameter were analyzed with LAM–ICP–MS for pyrite, arsenopyrite and sphalerite; Au is “homogeneously” distributed inside the structure of the arsenious pyrite and the arsenopyrite (not as inclusions); the chemical composition indicates similarities of this “invisible gold”, forming a solid solution with arsenious pyrite and arsenopyrite. One hundred nineteen and 62 ppm of ‘invisible gold’ was quantified in 21 spots analyzed on pyrite and in 14 spots on arsenopyrite, respectively.     

Surface polarity of cellulose derivates observed by coumarin 151 and 153 as solvatochromic and fluorochromic probes

Solvent‐dependent ultraviolet–visible (UV–vis) absorption and Stokes shifts including strong hydrogen‐bond‐donating (HBD) solvents such as 2,2,2‐trifluoroethanol and 1,1,1,3,3,3‐hexafluoro‐2‐propanol of two coumarine dyes (Co 151 and Co 153) were analyzed with multiple‐square analyses of linear solvation energy relationships and the Kamlet–Taft solvent parameter set to α (HBD capacity), β (hydrogen‐bond‐accepting capacity), and π* (dipolarity/polarizability). The UV–vis absorption and emission spectra of Co 151 and Co 153 were measured when adsorbed on various polysaccharides such as different cellulose batches, carboxymethylcelluloses with different degrees of substitution, and chitine. As a result of this evaluation, Co 153 is recommended as an alternative UV–vis probe for evaluating the dipolarity/polarizability of cellulose and cellulose derivates. Multiple adsorption of Co 153 on Linters cellulose took place indicating a wide‐surface polarity distribution, which makes the determination of a rigid polarity parameter questionable. Thus, fluorescence measurements of adsorbed Co 153 are suitable to detect inhomogenities on a surface but not for the determination of empirical polarity parameters. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 1210–1218, 2003     

Zeros of functions with finite Dirichlet integral

In this paper, we refine a result of Nagel, Rudin, and Shapiro (1982) concerning the zeros of holomorphic functions on the unit disk with finite Dirichlet integral.

     

SASEGASA: A New Generic Parallel Evolutionary Algorithm for Achieving Highest Quality Results

This paper presents a new generic Evolutionary Algorithm (EA) for retarding the unwanted effects of premature convergence. This is accomplished by a combination of interacting generic methods. These generalizations of a Genetic Algorithm (GA) are inspired by population genetics and take advantage of the interactions between genetic drift and migration. In this regard a new selection scheme is introduced, which is designed to directedly control genetic drift within the population by advantageous self-adaptive selection pressure steering. Additionally this new selection model enables a quite intuitive heuristics to detect premature convergence. Based upon this newly postulated basic principle the new selection mechanism is combined with the already proposed Segregative Genetic Algorithm (SEGA), an advanced Genetic Algorithm (GA) that introduces parallelism mainly to improve global solution quality. As a whole, a new generic evolutionary algorithm (SASEGASA) is introduced. The performance of the algorithm is evaluated on a set of characteristic benchmark problems. Computational results show that the new method is capable of producing highest quality solutions without any problem-specific additions.     

Pentopyranosyl Oligonucleotide Systems. 9th Communication

Pyranosyl‐RNA (‘p‐RNA’ ) is an oligonucleotide system isomeric to natural RNA and composed of the very same building blocks as RNA. Its generational, chemical, and informational properties are deemed to be those of an alternative nucleic acid system that could have been a candidate in Nature's evolutionary choice of the molecular basis of genetic function. We consider the study of the chemistry of p‐RNA as etiologically relevant in the sense that knowledge of its structural, chemical, and informational properties on the chemical level offers both a perspective and reference points for the recognition of specific structural assets of the RNA structure that made it the (supposedly) superior system among possible alternatives and, therefore, the system that became part of biology as we know it today. The paper describes the chemical synthesis of β‐d‐ (and L )‐ribopyranosyl‐(4′→2′)‐oligonucleotide sequences, presents a resume of their structural and chemical properties, and cautiously discusses what we may and may not have learned from the pyranosyl isomer of RNA with respect to the conundrum of RNA's origin.