Numerical aspects of computing the Moore-Penrose inverse of full column rank matrices

This paper presents a comparison of certain direct algorithms for computing the Moore-Penrose inverse, for matrices of full column rank, from the point of view of numerical stability. It is proved that the algorithm using Householder QR decomposition, implemented in floating point arithmetic, is forward stable but only conditionally mixed forward-backward stable. A similar result holds also for the Classical Gram-Schmidt algorithm with reorthogonalization (CGS2). This algorithm was developed and analyzed by Abdelmalek (BIT, 11(4):354–367, 1971) and its detailed error analysis was given in Giraud et al. (Numer. Math. 101(1):87–100, 2005).     

Correction to: Foreword to the memorial issue for Professor Roberto Marassi

Journal of Solid State Electrochemistry -     

Comparative investigation of reactivity of different kinds of fly ash in alkaline media

Comparison of the influence of temperature and different alkali activators on the reactivity of two types of fly ash (conventional, fluidized) was presented. The main emphasis was put on fluidized fly ash as potential component of binding mixtures containing low amount of cement. Conventional fly ash was used as a reference. It was found that for these materials the key differences affecting products of activation are: availability of calcium and sulfate ions as well as structure of fly ash grains influencing dissolution of aluminate and silicate species. Fluidized fly ash, contrary to conventional fly ash, undergoes reaction in 0.1 M solutions of hydroxides forming mainly ettringite. In the case of 4 M hydroxides, both fly ashes undergo hydration processes. Conventional fly ash formed mainly amorphous aluminosilicate gel, while fluidized fly ash may create zeolitic products especially in the case of elevated temperature of early hydration. Sulfate and alkali ions can be incorporated into aluminosilicate structure of new formed products; however, this process depends strictly on the type of used hydroxide and its concentration. The presence of Ca(OH)₂, carbonates and alkali sulfates was also registered in the case of hydrated fluidized fly ash.

     

Lipase-catalyzed kinetic resolution approach toward enantiomerically enriched 1-(β-hydroxypropyl)indoles

In a route towards enantiomerically enriched 1-(β-hydroxypropyl)indoles, which are potentially useful building blocks for high value-added chemicals synthesis, a kinetic resolution approach by means of lipase-catalyzed enantioselective acylation as well as hydrolysis/methanolysis has been elaborated for the first time. The enzymatic resolution of chiral N-substituted indole-based sec-alcohols was successfully accomplished, yielding both enantiomeric forms of the employed derivatives with up to >99% enantiomeric purity via an enantioselective transesterification under mild reaction conditions. The most selective resolutions were obtained using fungal (CAL-B and TLL) and bacterial (PFL and BCL) lipases and vinyl acetate as the acyl?group donor. The synthetic protocol described herein is very simple, user-friendly and efficient, thus paving the way for future access towards more complex compounds of this type. The absolute configurations of novel enantiomeric derivatives, and thus stereoselectivity of the described enzymatic reactions were confirmed by application of CDA-based NMR methodology and single-crystal X-ray diffraction analysis.     

Synthesis of the four enantiomers of diethyl 1,2-di(N-Boc-amino)propylphosphonates

A simple and efficient synthetic strategy to all four enantiomerically pure diethyl 1,2-di(N-Boc-amino)propylphosphonates has been elaborated starting from the corresponding N-[(R)-(1-phenylethyl)]aziridine-(2S)- and N-[(S)-(1-phenylethyl)]aziridine-(2R)-carboxaldehydes, employing a one-pot three-components Kabachnik-Fields reaction followed by the hydrogenolytic removal of the chiral auxiliary and aziridine ring opening with simultaneous protection of the amino groups as the N-Boc derivatives.     

Analysis of mechanisms with flexible beam-like links,rotary joints and assembly errors

The paper presents a method of modelling dynamics of mechanisms in which assembly errors can occur. One of the features of the method is that such errors can be included when the kinematics of the mechanism is modelled. A closed kinematic chain consisting of flexible and rigid links with one joint displaced and turned is discussed. Use of joint coordinates together with the rigid finite element method for discretisation of flexible links has allowed us to considerably decrease the size of the problem. Numerical simulations are carried out in order to analyse the influence of inaccurate assembly on the load on joints of a four-bar linkage.     

Synthesis of O-[4,6-Di-O-Acetyl-4-O-(2,3,4,6-Tetra-O-Acetyl-β-D-Galactopyranosyl)-2-Deoxy-2-Hydroxyimino-D-Arabino-Hexopyranosyl]-N-Benzyloxycarbonyl-L-Serine Methyl Esters And Their Transformations

ABSTRACT

3,6-Di-O-acetyl-4-O-(2,3,4,6-tetra-O-acetyl-β-D-galactopyranosyl)-2-deoxy-2-hydroxyimino-α- and -β-D-arabino-hexopyranosides of N-benzyloxycarbonyl-L-serine methyl ester as well as of ethanol have been synthesised from D-lactal hexaacetate via nitrosyl chloride, followed by condensation with L-serine derivatives and ethanol, respectively. The compounds of L-serine thus obtained were modified at C-2 and C-3 to afford L-serine derivatives attached to disaccharides containing terminal α-D-gluco-, 2-acetamido-α-D-gluco-, β-D-manno, 2-acetamido-β-D-manno-pyranosyl, 3-azido-2-hydroxyimino-α-D-arabino-, and α-D-ribo-hexopyranosyl residues.     

The hydrogen‐bonding network in deacetyl­cephalothin

The structural analysis of deacetyl­cephalothin [systematic name: (6R,7R)‐3‐hydroxy­methyl‐8‐oxo‐7‐(2‐thio­phen‐2‐yl­acetyl­amino)‐5‐thia‐1‐aza­bicyclo­[4.2.0]oct‐2‐ene‐2‐carboxylic acid], C₁₄H₁₄N₂O₅S₂, shows that the geometry of the central bicyclic moiety is close to the geometry exhibited by other biologically active cephalosporin antibiotics. The mol­ecules are arranged in a helical chain running parallel to the 2₁ axis via a strong O—H⋯O hydrogen bond. The main helices are zipped together via N—H⋯O inter­actions, forming infinite layers. The supramolecular architecture is stabilized by O—H⋯S and C—H⋯O hydrogen bonds.     

Crystal Structure and Solid State 13C Nmr Analysis of Methyl 3,4,6-Tri-O-Acetyl-2-Deoxy-2-(3-Phenylureido)-β-D-Glucopyranoside

ABSTRACT

The X-ray diffraction analysis of methyl 3,4,6-tri-O-acetyl-2-deoxy-(3-phenylureido)-β-D-glucopyranoside was performed and showed that the molecules are associated by two NHz.O=C hydrogen bonds. One molecule with disorder of an acetyl group at C-4 was found in the asymmetric crystal unit. The signals in ¹³C CPMAS NMR spectrum are duplicated indicating that local symmetry is lower than those of the crystal.     

A concise synthesis of tetrahydroisoquinoline-1-carboxylic acids using a Petasis reaction and Pomeranz–Fritsch–Bobbitt cyclization sequence

A sequence of two reactions: the Petasis reaction, in which an aminoacetaldehyde acetal was used as the amine component, followed by Pomeranz–Fritsch–Bobbitt cyclization, has been shown to be a convenient and simple method for the synthesis of tetrahydroisoquinoline-1-carboxylic acids. Using this method several acids have been prepared in good to excellent yields and characterized as hydrochloride salts.