Reformatsky-type reactions in aqueous media. Use ofbronometryl-acrylic acid for the synthesis of α-methylene-γ-butyrolactones.

A new method for the preparation of α -methylene-γ -butyrolactones is described.     

Aggregation and the estimation of equation systems

Simulations based on two sets of data are used to assess the impact of combining equations on the accuracy of parameter estimates and their asymptotic standard errors.     

Conformal symplectic geometry,deformations, rigidity and geometrical (KMS) conditions

Deformations admitting a unit element of a local associative algebra defined on the space of functions on a manifold. Definition and properties of the * ^f -products and conformal symplectic geometry. Deformations of a * ^f -products. A theorem of rigidity. Application to statistical mechanics (KMS conditions).     

Formes quadratiques sur un semi-groupe involutif

Sans résumé     

Syntheses and NMR,MS and X‐ray investigations of homoadamantane‐fused pyridopyrimidinones

The reactions of ethyl 5‐oxotricyclo[4.3.1.1^3,8]undecane‐4‐carboxylate (2) with methyl‐substituted 2‐aminopyridines in polyphosphoric acid (PPA) gave two products, linearly‐condensed pyridopyrimidinones 4a‐c and 2‐pyridylcarboxamides 5a‐c , whereas the reactions with amino, hydroxy and nitro derivatives of 2‐aminopyridine furnished only linearly‐condensed pyridopyrimidinones (4g‐j). Use of a mixture of PPA and phosphorus oxychloride as solvent afforded both linearly‐ (4a‐c,e,f) and angularly‐condensed (6a–c,e,f) pyridopyrimidinones. In toluene, with p‐toluenesulfonic acid as catalyst, 2‐pyridylcarboxamides 5a‐f were obtained. In a mixture of PPA and phosphorus oxychloride at 80–120 °C, 5a‐f yielded angularly‐condensed pyridopyrimidinones 6a‐f. All the products exhibited characteristic features, as determined by NMR and electron ionization mass spectrometry and X‐ray crystallography.     

A time-domain approach to estimating the plucking point of guitar tones obtained with an under-saddle pickup

A method for estimating the plucking point of guitar tones is proposed. The algorithm is based on investigating the time lag between two consecutive pulses arriving at the bridge of the guitar. The signal is detected with an under-saddle pickup attached to the bridge. The method determines the minimum of the autocorrelation function for one period of the signal. The time lag of the minimum can be converted into the distance from the bridge where the string was plucked. The results obtained with the method are good, the error remains smaller than one centimetre, except for a few outliers. The algorithm is easy to implement and can be used to analyse playing styles. The efficiency of the method gives the potential to also use it in real-time computer music applications.