Length functions and Demazure operators for G(e,1,n), II

This note is the first part of consecutive two papers concerning with a length function and Demazure operators for the complex reflection group W = G(e, 1, n). In this first part, we study the word problem on W based on the work of Bremke and Malle [BM]. We show that the usual length function ?(W) associated to a given generator set S is completely described by the function n(W), introduced in [BM], associated to the root system of W.In the second part, we will study the Demazure operators of W on the symmetric algebra. We define a graded space H_W in terms of Demazure operators, and show that H_W is isomorphic to the coinvariant algebra S_W, which enables us to define a homogeneous basis on S_W parametrized by w?W.     

An infeasible (exterior point) simplex algorithm for assignment problems

The so called Modified Hung—Rom Algorithm, based upon theoretical considerations of Hirsch-paths, seems to be one of the most efficient algorithms for assignment problems. Since any two basic feasible solutions to a linear problem can always be connected with a short simplex path passing through the infeasible region, development of algorithms based upon theoretical considerations on infeasible paths seems to be of great practical interest. This paper presents an algorithm of this kind for assignment problems.     

Synthesis and biological evaluation of some 4-(isoxazolinyl or 1,2,4-oxadiazolyl) coumarins

Reaction of compound 3 with nitrile oxide 4a affords compounds 5a and 6 in 73% and 3% yield respectively, while reaction of 3 with 4b affords only compound 5b (85%). Reactions of compound 8 with the nitrile oxides 4a,b result in compounds 9a,b . The compound 10 , prepared from 1 and O-methylhydroxylamine, reacts with nitrile oxide 4b to give the oxadiazole derivative 12 . The above referred coumarins are screened for antiinflammatory activity in vivo using the carrageenin rat paw edema and in vitro through their antiproteolytic activity and their ability to inhibit β-glucuronidase and 12-Lipoxygenase.     

Insights into the Reaction Mechanism of Ethanol Conversion into Hydrocarbons on H‐ZSM‐5

Ethanol dehydration to ethene is mechanistically decoupled from the production of higher hydrocarbons due to complete surface coverage by adsorbed ethanol and diethyl ether (DEE). The production of C₃₊ hydrocarbons was found to be unaffected by water present in the reaction mixture. Three routes for the production of C₃₊ hydrocarbons are identified: the dimerization of ethene to butene and two routes involving two different types of surface species categorized as aliphatic and aromatic. Evidence for the different types of species involved in the production of higher hydrocarbons is obtained via isotopic labeling, continuous flow and transient experiments complemented by UV/Vis characterization of the catalyst and ab initio microkinetic modeling.     

Micro-Raman and X-ray fluorescence spectroscopy data fusion for the classification of ochre pigments

Two different data-fusion strategies are evaluated for the combination of the outputs of combined Raman/X-Ray fluorescence instrument. The studied application deals with the classification of ochre pigments investigated in the field of cultural heritage. The two fusion strategies are: (1) first level fusion: combines raw signals obtained from each technique and (2) second level fusion: combines extracted features provided individually by each technique. Classification tool is partial least squares-discriminant analysis (PLS-DA). Classification results obtained performing different data-fusion strategies are compared with those results obtained performing a single classification model for each data source. The results show that the combination of signal features is the most suitable for a rapid and unique processing of both types of spectra. Benefits and drawbacks of each strategy are also discussed.     

End-group characterisation of poly(propylene glycol)s by means of electrospray ionisation–tandem mass spectrometry (ESI-MS/MS)

The end-group functionalisation of a series of poly(propylene glycol)s has been characterised by means of electrospray ionisation–tandem mass spectrometry (ESI-MS/MS). A series of peaks with mass-to-charge ratios that are close to that of the precursor ion were used to generate information on the end-group functionalities of the poly(propylene glycol)s. Fragment ions resulting from losses of both of the end groups were noted from some of the samples. An example is presented of how software can be used to significantly reduce the length of time involved in data interpretation (which is typically the most time-consuming part of the analysis). Figure Screenshot from Polymerator software of annotated ESI-MS/MS spectrum from the lithiated heptamer of poly(propylene glycol) di-acrylate     

Ultrahuge cardinals

In this note, we start with the notion of a superhuge cardinal and strengthen it by requiring that the elementary embeddings witnessing this property are, in addition, sufficiently superstrong above their target . This modification leads to a new large cardinal which we call ultrahuge. Subsequently, we study the placement of ultrahugeness in the usual large cardinal hierarchy, while at the same time show that some standard techniques apply nicely in the context of ultrahuge cardinals as well.     

A novel strategy for the preparation of naturally occurring phosphocitrate and its partially esterified derivatives

A novel method for the synthesis of phosphocitrate (1, PC) starting from triethyl ester of citric acid and MeOPCl2 is described. The method is based on selective stepwise hydrolysis of ester moieties from the intermediate Me-O-P(O)(Cl)(Z) (Z = triethylcitrate), 4a, which also allows one to prepare partially esterified derivatives of PC with good yield and purity without chromatographic purifications.