Duality in reconstruction systems

We consider reconstruction systems (RS’s), which are G-frames in a finite dimensional setting, and that includes the fusion frames as projective RS’s. We describe the spectral picture of the set of RS operators for the projective systems with fixed weights. We also introduce a functional defined on dual pairs of RS’s, called the joint potential, and study the structure of the minimizers of this functional. In the case of irreducible RS’s the minimizers are characterize as the tight systems. In the general case we give spectral and geometric characterizations of the minimizers of the joint potential. At the end of the paper we show several examples that illustrate our results.     

Thermal diffusivity study of cheese fats by thermal lens detection

In this paper we used thermal lens spectrometry to determine the thermal diffusivity of cheese fats. We have used equal concentrations of cheese fats from oaxaca, chihuahua, gouda, manchego and mozzarella cheeses at 42°C temperature. The two lasers mismatched mode experimental configuration was used with a He-Ne laser, as a probe beam and an Ar⁺ laser as the excitation one. The characteristic time constant of the transient thermal lens was obtained by fitting the theoretical expression to the experimental data in order to obtain the thermal diffusivity of the cheese fat samples. This measured thermal property may contribute to a better understanding of the cheese fats quality, which is very important in food industry.     

A novel cacalolide from Psacalium decompositum

A new cacalolide sesquiterpenoid, named as Romo-A, was isolated from the roots of Psacalium decompositum, Asteraceae, a Mexican medicinal shrub with antidiabetic properties. Its structure was elucidated by NMR, MS, IR, UV, and confirmed by X-ray diffraction studies.     

Novel acid-catalyzed rearrangement of tetrahydro-1,2,3,4-tetrazines: unexpected formation of glycosazones

The present contribution discloses a simple and unexpected acid-catalyzed cleavage of tetrahydrotetrazines leading to 1,2-bis(hydrazones). Incorporation of a chiral fragment derived from carbohydrates enables the rapid preparation of glycosazones, a family of compounds employed by Emil Fischer to elucidate the configuration of sugars. In addition, a mechanistic proposal accounts for experimental observations.     

Novel generation of an o-quinone methide from 2-(2'-cyclohexenyl)phenol by excited state intramolecular proton transfer and subsequent C-C fragmentation

Formation of an o-quinone methide via C-C fragmentation of a zwitterion formed by intramolecular excited state proton transfer from an o-allylphenol derivative is reported for the first time.