A nearly optimal preconditioning based on recursive red–black orderings

Considering matrices obtained by the application of a five-point stencil on a 2D rectangular grid, we analyse a preconditioning method introduced by Axelsson and Eijkhout, and by Brand and Heinemann. In this method, one performs a (modified) incomplete factorization with respect to a so-called ‘repeated’ or ‘recursive’ red–black ordering of the unknowns while fill-in is accepted provided that the red unknowns in a same level remain uncoupled. Considering discrete second order elliptic PDEs with isotropic coefficients, we show that the condition number is bounded by 𝒪(n ${}^{\text{½ log}{}_{\text{2}}\text{(√(5) −1)}}$ ) where n is the total number of unknowns (½ log₂(√(5) − 1) = 0.153), and thus, that the total arithmetic work for the solution is bounded by 𝒪(n^1.077). Our condition number estimate, which turns out to be better than standard 𝒪(log² n) estimates for any realistic problem size, is purely algebraic and holds in the presence of Neumann boundary conditions and/or discontinuities in the PDE coefficients. Numerical tests are reported, displaying the efficiency of the method and the relevance of our analysis. © 1997 John Wiley & Sons, Ltd.     

Nonexistence of small,odd breathers for a class of nonlinear wave equations

In this note, we show that for a large class of nonlinear wave equations with odd nonlinearities, any globally defined odd solution which is small in the energy space decays to 0 in the local energy norm. In particular, this result shows nonexistence of small, odd breathers for some classical nonlinear Klein Gordon equations, such as the sine-Gordon equation and \(\phi ^4\) and \(\phi ^6\) models. It also partially answers a question of Soffer and Weinstein (Invent Math 136(1): 9–74, p 19 1999) about nonexistence of breathers for the cubic NLKG in dimension one.     

Screening approach for chiral separation of pharmaceuticals IV. Polar organic solvent chromatography

The aim of this work is to determine generic screening conditions and an initial simple separation strategy allowing the rapid separation of drug enantiomers in polar organic solvent chromatography (POSC). Four cellulose/amylose-based stationary phases were investigated in detail using two mobile phase basis solvents commonly applied in this mode, i.e. acetonitrile and methanol. Polar mode is interesting for use in purification of enantiomers. In a first step, the parameters potentially influencing the separation, such as addition of an alcohol to the polar organic solvent or the type of mobile phase additive(s), were examined by means of experimental designs. Afterwards, the factors found most important are investigated in more detail. Results showed that the cellulose- and amylose-based stationary phases have very broad and complementary enantiorecognition abilities in the POSC mode. The type of organic solvent for the mobile phase appeared to have a dramatic influence on the quality of the separation. Based on the results, a screening strategy was proposed. Enantioseparation was observed in more than 85% of the tested compounds and analysis times of last eluted peak were usually below 10 min.     

Precision study on capillary electrophoresis methods for metacycline

A CE method for metacycline (MTC) determination was investigated in an inter-laboratory experiment. Many problems were encountered in this study, most of which were related to the transfer of the method to different CE equipment. The reported problems could be classified into different categories: problems related to the precision, to the parameters in the protocol, and to the MTC peak shape. As the peak shape problem was partially responsible for the poor precision, a new CE method was developed in order to obtain a good MTC peak shape on all equipment. The precision of this new method for MTC determination was examined in an intermediate precision study, where the influence of the factors "time" and "equipment" was investigated. Although the new method could be transferred to different instruments, the precision remained poor mainly due to the contributions of the between-replicate and the between-injection variances.     

AES chemunex ADIAFOOD detection system for Listeria spp. environmental sample testing

The ADIAFOOD Detection System for the detection of Listeria species from environmental surfaces is based on real-time PCR technology and allows rapid pathogen detection within 21 h. The strength of the ADIAFOOD technology resides in its ability to rapidly and accurately detect Listeria species present on surfaces, such as stainless steel, plastic, ceramic, and sealed concrete. The technology is easy to use and versatile.     

Nucleotide Analogues Bearing a C2′ or C3′-Stereogenic All-Carbon Quaternary Center as SARS-CoV-2 RdRp Inhibitors

The design of novel nucleoside triphosphate (NTP) analogues bearing an all-carbon quaternary center at C2′ or C3′ is described. The construction of this all-carbon stereogenic center involves the use of an intramoleculer photoredox-catalyzed reaction. The nucleoside analogues (NA) hydroxyl functional group at C2′ was generated by diastereoselective epoxidation. In addition, highly enantioselective and diastereoselective Mukaiyama aldol reactions, diastereoselective N-glycosylations and regioselective triphosphorylation reactions were employed to synthesize the novel NTPs. Two of these compounds are inhibitors of the RNA-dependent RNA polymerase (RdRp) of SARS-CoV-2, the causal virus of COVID-19.     

Organometallic Derivatives of Cycloproparenes

The tricarbonylchromium complex of cyclopropa[b]naphthalene ( 3a ) is deprotonated at C(1) with BuLi. Quenching of the resulting anion with Mel results in a 1:1 mixture of stereoisomeric methyl derivatives 6a and 6b . Peterson olefination of the bis-silylated complex 3b affords the complexed alkylidenecycloproparene 5 in low yield. The tricarbonylchromium complex of cyclopropa[b]anthracene ( 10 ) is accessible via bis-hydro-desilylation of 9 . Its X-ray structure is also reported. All attempts to synthesize a tricarbonylchromium complex of benzocyclopropene ( 11a ) failed.     

A C-glycoside route to leukotrienes

The stereospecific syntheses of three isomers of 7-hydroxy-5,6-epoxy heptanoic acid methyl ester, $\text{7}$, $\text{12b}$ and $\text{19}$, have been achieved via a $\text{C}$-glycoside route.     

Preparation of ethyl 5(s),6-epoxy-3(r)-(methoxymethoxy)hexanoate: a key chiral intermediate for mevinolin and compactin.

The synthesis of Ethyl 5(S),6-Epoxy-3(R)-(methoxymethoxy)hexanoate, a key chiral synthon for the β-hydroxy-δ-lactone portion of Mevinolin and Compactin, $\text{via}$ a regiospecific ring opening of a tetrahydrofuran derivative by dimethylboron bromide, is described.     

Synthesis and stereochemistry of some new 1,3,5-tris(1,3-dioxan-2-yl)-benzene derivatives

The synthesis and the stereochemistry of new 1,3,5-tris(1,3-dioxan-2-yl)-benzene derivatives are reported. The anancomeric structure and the axial orientation of the aryl group with respect to all 1,3-dioxane rings, and the cis-trans isomerism of some of the compounds are revealed. The data are supported by NMR investigations and by the molecular structure of one compound determined by single crystal X-ray diffractometry.