Compensating intermodal dispersion in photonic crystal directional couplers

Intermodal dispersion between the supermodes of a directional coupler may induce undesirable pulse breakup in a sufficiently large device. When this happens the device will no longer exchange power between its arms, and the extinction ratio is completely canceled. It is shown that, by carefully designing the coupling area of the directional coupler, one may compensate for intermodal dispersion. The compensating device should accomplish three basic requirements: inverse intermodal dispersion, balanced coupling of each supermode, and maximum power transfer while preserving the sign of the slope of the coupling coefficient with frequency for multiplexing-demultiplexing applications. This structure is designed and optimized with a genetic algorithm.     

Highly stereoselective aldol reactions of titanium enolates from lactate-derived chiral ketones

[reaction: see text] Highly stereoselective titanium-mediated aldol reactions based on lactate-derived ketones are reported. The stereochemical outcome of the process depends on the protecting group (PMB or Bn) and the Lewis acid (i-PrOTiCl(3) or TiCl(4)) used in the enolization step, the corresponding anti-syn or syn-syn aldols being prepared in high yields and with diastereomeric ratios up to 99:1.     

First highly regio- and diastereoselective [3+2] cycloaddition of chiral nonracemic Fischer carbene complexes with azomethine ylides: an enantioselective synthesis of (+)-rolipram

A new procedure for the synthesis of 1,3,4-trisubstituted and 1,4-disubstituted pyrrolidin-2-one derivatives in an enantioselective fashion is reported. The 1,3-dipolar cycloaddition of (+/-)-menthol and (-)-8-phenylmenthol derived Fischer alkoxy alkenyl carbene complexes with in situ generated functionalized azomethine ylides gives the corresponding cycloadducts as chelated tetracarbonyl Fischer carbene complexes. Only one regioisomer is detected in all cases, and the diastereoselectivity of the reaction is very high when (-)-8-phenylmenthol derived carbenes are employed. Oxidation and further transformation of the cycloadducts provide an easy access to pyrrolidin-2-ones. The anti-inflammatory and antidepressant drug (+)-Rolipram is readily prepared in four steps in a 20% overall yield by taking advantage of this newly developed methodology.     

Non-Transitive Generalizations of Subdirect Products of Linearly Ordered Rings

Weakly associative lattice rings (wal-rings) are non-transitive generalizations of lattice ordered rings (l-rings). As is known, the class of l-rings which are subdirect products of linearly ordered rings (i.e. the class of f-rings) plays an important role in the theory of l-rings. In the paper, the classes of wal-rings representable as subdirect products of to-rings and ao-rings (both being non-transitive generalizations of the class of f-rings) are characterized and the class of wal-rings having lattice ordered positive cones is described. Moreover, lexicographic products of weakly associative lattice groups are also studied here.     

Morita Equivalence of Sketches

Equivalence of sketches S and T means the equivalence of their categories Mod_S and Mod_T of all Set-valued models. E. Vitale and the second author have characterized equivalence of limit-sketches by means of bimodels, where a bimodel for limit sketches S and T is a model of S in the category Mod_T. For general sketches, we show that an analogous result holds provided that Mod_T is substituted by a more complex category; e.g., in case of limit-coproduct sketches, that category is (Mod_T), the free product completion of Mod_T.     

Development and Validation of an LC–ESI-MS Ion-Trap Method for Analysis of Impurities in Transkarbam 12, a Novel Transdermal Accelerant

A new, sensitive LC–MS method for evaluation of the purity of Transkarbam 12 (T12), a novel and highly effective accelerant of transdermal penetration, has been developed and validated. T12 and its impurities (6-aminohexanoic acid, AH, ε-caprolactam, CA, and dodecyl 6-(6-aminohexanamido)hexanoate, DAH) were characterized by MS and MS–MS analysis. Separation was achieved on a 150 mm × 3 mm, 5-μm particle, phenyl–hexyl column. The mobile phase was a gradient prepared from water, formic acid, and acetonitrile. The method was validated within the concentration range 50–250 ng mL^?1; correlation coefficients were >0.998. The accuracy of the method was from 98.6–105.0% for AH, 102.6–104.8% for CA, and 97.9–100.9% for DAH. Precision was in the range 3.19–4.42% for AH, 3.22–5.81% for CA, and 4.8–8.78% for DAH. The selectivity of the method and sample stability were also confirmed. The practical applicability of the method was proven by analysis of T12 bulk substance.     

Linear interval inequalities

We prove that a system of linear inequalities with interval-valued data is weakly solvable (each system obtained by fixing coefficeints in the intervals prescribed has a solution) if and only if it is strongly solvable (all such systems have a solution in common) and desribe an algorithm for checking strong solvability.