Bounds on Codes Derived by Counting Components in Varshamov Graphs

We are interested in improving the Varshamov bound for finite values of length n and minimum distance d. We employ a counting lemma to this end which we find particularly useful in relation to Varshamov graphs. Since a Varshamov graph consists of components corresponding to low weight vectors in the cosets of a code it is a useful tool when trying to improve the estimates involved in the Varshamov bound. We consider how the graph can be iteratively constructed and using our observations are able to achieve a reduction in the over-counting which occurs. This tightens the lower bound for any choice of parameters n, k, d or q and is not dependent on information such as the weight distribution of a code. This work is taken from the author’s thesis [10]     

Three-component one-pot total syntheses of glyantrypine, fumiquinazoline F, and fiscalin B promoted by microwave irradiation

A microwave-promoted three-component one-pot reaction has been developed to provide access to the core pyrazino[2,1-b]quinazoline-3,6-dione (1) scaffold, which is common to several families of alkaloids with significant biological activities. By adapting this synthetic strategy through the use of selected Boc-amino acids and amino acid esters, we have accomplished highly efficient and concise total syntheses of glyantrypine (2), fumiquinazoline F (3), and fiscalin B (5), achieving overall yields of 55, 39, and 20%, respectively.     

The boron-mediated ketone-ketone aldol reaction

The first examples of the directed, boron-mediated aldol reaction between different ketones are presented. Transformation of a variety of ketones to their corresponding boron enolates with Chx₂BCl/Et₃N, followed by reaction with acceptor ketones in diethyl ether, and oxidation of the resultant boron aldolate (H₂O₂, MeOH/pH 7 buffer), provided the aldol addition products. The reaction was most facile when cyclic ketones were used, with the highest yields obtained for the reaction of boron enolates with cyclohexanone as the acceptor.     

Heterogeneous catalysts for cyclic carbonate synthesis from carbon dioxide and epoxides

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Reaktionen von α-Chlorcarbonsäurechloriden mit Trialkylaminen

The condensation of α,α-dichloropropionyl chloride (IVa) and of trichloroacetyl chloride (IVb) with α-chloropropionyl chloride (Ia) in the presence of triethylamine led to two acid chloride enol-esters, both as mixtures of cis- and trans-isomers, namely 1, 2-dichloropropenyl α,α-dichloropropionate (Va) and 1, 2-dichloropropenyl trichloroacetate (Vb). A mixture of triethylamine and trichloroacetyl chloride produced an oxidation-reduction reaction to give 48% 1, 2, 2, 2-tetrachloroethyltrichloroacetate (VIII) and 69% 1-diethylamino-4, 4, 4-trichloro-1-butene-3-one (IX). Basic hydrolysis of IX led to 43% of glutaconic acid (XIII). Tripropylamine reacted in the same way with trichloroacetyl chloride to yield 1-dipropylamino-2-methyl-4, 4, 4-trichloro-but-1-ene-3-one (XIX) which was readily hydrolyzed in acid solution to α-trichloroacetyl-propionaldehyde (XX).     

Rasterbare Texturen

Zusammenfassung Es wird eine KlasseR von beschränkten Punktmengen des s-dimensionalen Raumes eingeführt, die rasterbar genannt wird. Die KlasseR dürfte jene Punktmengen umfassen, die den theoretischen Bedürfnissen der Stereologie angepasst und in anschaulichem Sinne als normal zu bezeichnen sind.Der Ausdruck rasterbar bezeichnet die Eigenschaft dieser Punktmengen, dass sie durch das Raster jener Punkte einess-dimensionalen regulären Punktgitters repräsentierbar sind, die der Punktmenge angehören. Die Repräsentierbarkeit bezieht sich auf die Minkowskischen Quermasse und ist stochastisch zu interpretieren. Durch Auszählungen im Punktraster lassen sich die Minkowskischen Quermasse im Sinne der Statistik schätzen.Es wird weiter gezeigt, dass die Minkowskischen Quermasse der Punktmengen vonR als Entwicklungskoeffizienten einer ihnen zugeordneten Autokorrelationsfunktion interpretiert werden können. Insbesondere folgt hieraus, dass das Wienerspektrum einer zweidimensionalen, rasterbaren Textur die topologischen Eigenschaften der Textur nicht abbildet, weil das Wienerspektrum mit der Fouriertransformierten der reduzierten Autokorrelationsfunktion übereinstimmt.

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Summary In Euclidian space, (dimensionn=1, 2, 3), a general class of pointsets is introduced which is named rasterable.The term rasterable designates the important property of these pointsets that they can be represented by the raster of those points of a lattice which belong to the pointset.The representability of a pointset by a pointpicture concerns the directional Minkowski measures, which for rasterable pointsets can be interpreted as coefficients of the expansion of the corresponding auto-correlation function and therefore may be defined as derivatives.

     

Sustainable,mild and efficient p-methoxybenzyl ether deprotections utilizing catalytic DDQ

A procedure for the selective deprotection of p-methoxybenzyl ethers using catalytic amounts of DDQ and of sodium nitrite, with oxygen as the terminal oxidant, is reported.     

Batch versus Flow Photochemistry: A Revealing Comparison of Yield and Productivity

The use of flow photochemistry and its apparent superiority over batch has been reported by a number of groups in recent years. To rigorously determine whether flow does indeed have an advantage over batch, a broad range of synthetic photochemical transformations were optimized in both reactor modes and their yields and productivities compared. Surprisingly, yields were essentially identical in all comparative cases. Even more revealing was the observation that the productivity of flow reactors varied very little to that of their batch counterparts when the key reaction parameters were matched. Those with a single layer of fluorinated ethylene propylene (FEP) had an average productivity 20 % lower than that of batch, whereas three‐layer reactors were 20 % more productive. Finally, the utility of flow chemistry was demonstrated in the scale‐up of the ring‐opening reaction of a potentially explosive [1.1.1] propellane with butane‐2,3‐dione.