Global saddle-point duality for quasi-concave programs

General and quasi-concave non-differentiable cases of the maximization of the minimun between two functions are considered. With the aid of duality theory for mathematical programming involving conjugate-like operators and by defining a bifunction we construct a new Lagrangian and generate a class of perturbations. New saddle-point theorems are presented, and equivalence is proved between the existence of a saddle-point and the existence of a certain cone-supporting property of the perturbation function. These results suggest possible improvements in multiplier methods.This work was partially supported by a grant from Control Data.     

Graded parafermions: standard and quasiparticle bases

Two bases of states are presented for modules of the graded parafermionic conformal field theory associated to the coset . The first one is formulated in terms of the two fundamental (i.e., lowest-dimensional) parafermionic modes. In that basis, one can identify the completely reducible representations, i.e., those whose modules contain an infinite number of singular vectors; the explicit form of these vectors is also given. The second basis is a quasiparticle basis, determined in terms of a modified version of the exclusion principle. A novel feature of this model is that none of its bases are fully ordered and this reflects a hidden structural exclusion principle.     

ATMOS (ATM optical switching)—system perspective

The expected traffic growth from new broadband services will require network capacities that can be beneficially provided by optical WDM transport networks. Optical packet techniques are essential for large networks to provide flexibility and granularity. A layered network architecture with a transparent optical layer and optical packet layers has been elaborated. Four switching concept options for large optical ATM switch fabrics in the public network and small access nodes are presented. The technology for the related key functions of space and wavelength switching was developed in the RACE ATMOS project and the feasibility of concepts and technologies was verified in four system demonstrators.     

There are uncountably many universal topological planes

We prove the existence of uncountably many nonisomorphic topological projective planes, each universal in the sense that it contains an isomorphic copy of every pseudoline arrangement.     

pH‐controlled reaction divergence of decarboxylation versus fragmentation in reactions of dihydroxyfumarate with glyoxylate and formaldehyde: parallels to biological pathways

The reactions of dihydroxyfumarate with glyoxylate and formaldehyde exhibit a unique pH‐controlled mechanistic divergence leading to different product suites by two distinct pathways. The divergent reactions proceed via a central intermediate (2,3‐dihydroxy‐oxalosuccinate, 3 , in the reaction with glyoxylate and 2‐hydroxy‐2‐hydroxymethyl‐3‐oxosuccinate, 14 , in the reaction with formaldehyde). At pH 7–8, products ( 7 , 8 , and 15 ) exclusively from a decarboxylation of the intermediate are observed, while at pH 13–14, products ( 9 , 10 , and 16 ) solely derived from a hydroxide‐promoted fragmentation of the intermediate are formed. The decarboxylative and fragmentation pathways are mutually exclusive and do not appear to coexist under the range of pH (7–14) conditions investigated. Herein, we employ a combination of quantitative ¹³C NMR measurements and density functional theory calculations to provide a rationale for this pH‐driven reaction divergence. These rationalizations also hold true for the reactions of dihydroxyfumarate produced in situ by the catalytic cyanide‐mediated dimerization of glyoxylate. In addition, the non‐enzymatic decarboxylation and fragmentation transformations of these central intermediates ( 3 and 14 ) appear to have intriguing parallels to the enzymatic reactions of oxalosuccinate and formation of glyceric acid derivatives in extant metabolism – the high and low pH mimicking the precise control exerted by the enzymes over reaction pathways. Copyright © 2016 John Wiley & Sons, Ltd.     

Characterization of Al(III) complexes with hematein in artistic alum logwood inks

The complexes between Al(III) and hematein, the main coloring matter in alum logwood inks, were characterized by Raman and ²⁷Al NMR (nuclear magnetic resonance) spectroscopies. Raman spectra of the crystallized complexes and of the compounds applied on a paper substrate are presented and assigned based on published data for the parent compounds. These Raman spectra show that the coordination of the hematein to the Al(III) ions takes place in both cases through the carbonyl and hydroxyl groups in the molecule, and that the aromatic rings are also involved in the interaction. The Raman spectra of the pure hematein–Al(III) complexes were found to be consistent with those recorded for a logwood ink prepared following a late 19th century recipe, using logwood chips instead of pure hematein, and applied on a paper substrate. These spectra can be used as references for the noninvasive identification of the compounds in works of art. ²⁷Al solid‐state NMR showed that the coordination of the Al(III) atoms in the crystallized powder is predominantly octahedral, while when applied on a paper substrate the colorant is present mainly as a tetrahedral complex, with an octahedral coordination also present in a smaller proportion. The fact that the predominant coordinations for the complexes in the crystallized material and for the ones present on the paper substrate are different is relevant for the study of the lightfastness and thermal stability of works of art bearing these media. Copyright © 2009 John Wiley & Sons, Ltd.     

Fabrication and characterization of a PbTe quantum dots multilayer structure

Multilayer PbTe quantum dots (QDs) and SiO₂ were grown by pulsed laser deposition (PLD) and Plasma enhanced chemical vapor deposition (PECVD) techniques. The crystalline structure, QD size and size dispersion were observed by high-resolution transmission electron microscopy (HRTEM) measurements. This technique allows one to grow PbTe QDs as small as 1.8 nm diameter and 0.6 nm size dispersion. The whole structure can be used in a Fabry–Perot cavity for an optical device operating at the mid-infrared region.     

Mechanism of thermal transport in dilute nanocolloids

Thermal conduction modes in a nanocolloid (nanofluid) are quantitatively assessed by combining linear response theory with molecular dynamics simulations. The microscopic heat flux is decomposed into three additive fluctuation modes, namely, kinetic, potential, and collision. For low volume fractions (<1%) of nanosized platinum clusters which interact strongly with xenon host liquid, a significant thermal conductivity enhancement results from the self correlation in the potential flux. Our findings reveal a molecular-level mechanism for enhanced thermal conductivity in nanocolloids with short-ranged attraction and offer predictions that can be experimentally tested.