Asymmetric Total Synthesis of (−)‐Erogorgiaene and Its C‐11 Epimer and Investigation of Their Antimycobacterial Activity

A short, nine‐step, highly enantioselective synthesis of (?)‐erogorgiaene and its C‐11 epimer is reported. The key stereochemistry controlling steps involve catalytic asymmetric crotylation, anionic oxy‐Cope rearrangement and cationic cyclisation. (?)‐Erogorgiaene exhibited promising antitubercular activity against multidrug‐resistant strains of Mycobacterium tuberculosis.     

On optimal high accuracy linear multistep methods for first kind volterra integral equations

General linear multistep methods which include those of Holyhead et al. [9] and Gladwin et al. [8] are introduced. A new simple root condition for stability is deduced. A theorem relating the coefficients of this new associated stability polynomial to those of the method is proved. This permits a constructive approach for obtaining high accuracy convergent methods. Two such methods are derived and numerical results are presented.This work was done under the financial support of: Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP), and Financiadora Nacional de Empreendimentos e Projetos (FINEP)—Ministério do Planejamento (Brazil).     

Generalized alternating-direction collocation methods for parabolic equations. I. Spatially varying coefficients

The alternating-direction collocation (ADC) method can be formulated for general parabolic partial differential equations. This is done using a piecewise cubic Hermite trial space defined on a rectangular discretization. As in all alternating-direction methods, the ADC algorithm produces errors that are additional to the standard discretization errors of multi-dimensional collocation. These errors increase when the coefficients of the governing equation are spatially variable. Analysis of the additional errors leads to several correction schemes. Numerical results indicate that a variant on the Laplace-modification procedure is an attractive choice as an improved ADC algorithm.     

Generalized alternating-direction collocation methods for parabolic equations. II. Transport equations with application to seawater intrusion problems

The alternating-direction collocation (ADC) method combines the attractive computational features of a collocation spatial approximation and an alternating-direction time marching algorithm. The result is a very efficient solution procedure for parabolic partial differential equations. To date, the methodology has been formulated and demonstrated for second-order parabolic equations with insignificant first-order derivatives. However, when solving transport equations, significant first-order advection components are likely to be present. Therefore, in this paper, the ADC method is formulated and analyzed for the transport equation. The presence of first-order spatial derivatives leads to restrictions that are not present when only second-order derivatives appear in the governing equation. However, the method still appears to be applicable to a wide variety of transport systems. A formulation of the ADC algorithm for the nonlinear system of equations that describes density-dependent fluid flow and solute transport in porous media demonstrates this point. An example of seawater intrusion into coastal aquifers is solved to illustrate the applicability of the method. An alternating-direction collocation solution algorithm has been developed for the general transport equation. The procedure is analogous to that for the model parabolic equations considered by Celia and Pinder [2]. However, the presence of first-order spatial derivatives requires special attention in the ADC formulation and application. With proper implementation, the ADC procedure effectively combines the efficient equation formulation inherent in the collocation method with the efficient equation solving characteristics of alternating-direction time marching algorithms. To demonstrate the viability of the method for problems with complex velocity fields, the procedure was applied to the problem of density-dependent flow and contaminant transport in groundwaters. A standard example of seawater intrusion into coastal aquifers was solved to illustrate the applicability of the method and to demonstrate its potential use in practical problems.     

13C NMR Analysis of some 4-hydroxy-2H-1,2-benzothiazine 1,1-dioxides

The ¹³C nmr spectra of some 4-hydroxy-2H-1,2-benzothiazine 1,1-dioxides I have been recorded and analyzed. Spectroscopic assignments were made on the basis of chemical shift theory, APT and fully coupled ¹³C nmr spectra. Spectral data support the enolic structure of these compounds.     

Synthesis of enantiopure 3-azabicyclo[3.2.0]heptanes by diastereoselective intramolecular [2+2] photocycloaddition reactions on chiral perhydro-1,3-benzoxazines

[2+2] photocycloadditions involving chiral 3-acryloyl-2-vinylperhydro-1,3-benzoxazines derived from (-)-8-aminomenthol are highly diastereoselective reactions. The facial selectivity depends on the type of substitution at the vinyl double bond, and always leads to cis-fused bicyclic derivatives. The de is good for compounds with one substituent at the outer carbon of the double bond at C-2, but only one diastereomer is formed in cyclizations of compounds with two substituents at that position. The elimination of the menthol appendage gives enantiopure 3-azabicyclo[3.2.0]heptanes.     

Stereoselective synthesis of pachastrissamine (jaspine B)

A stereoselective synthesis in enantiopure form of the natural anhydrophytosphingosine pachastrissamine (jaspine B), a metabolite isolated from sponges, is described. The chiral epoxide (R)-glycidol was the starting material. Key steps of this synthesis are a Sharpless asymmetric epoxidation, an intramolecular stereospecific epoxide opening mediated by a trichloroacetimidate group, and the formation of a tetrahydrofuran ring via intramolecular nucleophilic displacement.