Structural Diversity from the Transannular Cyclizations of Natural Germacrone and Epoxy Derivatives: A Theoretical–Experimental Study

Treatment of germacrone ( 1 ) with different electrophiles, and of its epoxy derivatives germacrone‐4,5‐epoxide ( 2 ), germacrone‐1,10‐epoxide ( 3 ) and isogermacrone‐4,5‐epoxide ( 4 ) with Brönsted/Lewis acids and Ti^III, gives rise to a great structural diversity. Thus, by using a maximum of two steps, the production of more than 40 compounds corresponding to 14 skeletons is described. Computational calculations rationalizing the structural divergence produced are also described. Finally, since some of the compounds generated are bioactive natural sesquiterpenes, the mechanisms of formation of these substances will provide new insights in their biosynthesis.     

Synthesis and Conformational Analysis of Cyclic Homooligomers from Pyranoid ε‐Sugar Amino Acids

New pyranoid ε‐sugar amino acids were designed as building blocks, in which the carboxylic acid and the amine groups were placed in positions C2 and C3 with respect to the tetrahydropyran oxygen atom. By using standard solution‐phase coupling procedures, cyclic homooligomers containing pyranoid ε‐sugar amino acids were synthesized. Conformation analysis was performed by using NMR spectroscopic experiments, FTIR spectroscopic studies, X‐ray analysis, and a theoretical conformation search. These studies reveal that the presence of a methoxy group in the position C4 of the pyran ring produces an important structural change in the cyclodipeptides. When the methoxy groups are present, the structure collapses through interresidue hydrogen bonds between the oxygen atoms of the pyran ring and the amide protons. However, when the cyclodipeptide lacks the methoxy groups, a U‐shape structure is adopted, in which there is a hydrophilic concave face with four oxygen atoms and two amide protons directed toward the center of the cavity. Additionally, we found important evidence of the key role played by weak electrostatic interactions, such as the five‐membered hydrogen‐bonded pseudocycles (C₅) between the amide protons and the ether oxygen atoms, in the conformation equilibrium of the macrocycles and in the cyclization step of the cyclic tetrapeptides.     

Discovery of Homobivalent Bitopic Ligands of the Cannabinoid CB2 Receptor**

Single chemical entities with potential to simultaneously interact with two binding sites are emerging strategies in medicinal chemistry. We have designed, synthesized and functionally characterized the first bitopic ligands for the CB₂ receptor. These compounds selectively target CB₂ versus CB₁ receptors. Their binding mode was studied by molecular dynamic simulations and site-directed mutagenesis.     

A laser system for high accuracy measurement of small apertures in mechanical parts

A simple, high accuracy small gap measurement system for rough industrial environments was designed and constructed. The system could detect apertures as small as 60 μm with less than 6 μm error in metallic parts with finite (cm range) depth. The principle is based in the transient analysis of transmitted laser intensity which is focused and swept along the region of the gap. The system is composed of a low power visible laser (semiconductor or He–Ne), focusing system, rotating mirror scanner, detection optics and amplifier, control unit for signal processing, speed control and data delivery to the process control unit.     

An efficient splitting technique for two‐layer shallow‐water model

We consider the numerical approximation of the weak solutions of the two‐layer shallow‐water equations. The model under consideration is made of two usual one‐layer shallow‐water model coupled by nonconservative products. Because of the nonconservative products of the system, which couple both one‐layer shallow‐water subsystems, the usual numerical methods have to consider the full model. Of course, uncoupled numerical techniques, just involving finite volume schemes for the basic shallow‐water equations, are very attractive since they are very easy to implement and they are costless. Recently, a stable layer splitting technique was introduced [Bouchut and Morales de Luna, M2AN Math Model Numer Anal 42 (2008), 683–698]. In the same spirit, we exhibit new splitting technique, which is proved to be well balanced and non‐negative preserving. The main benefit issuing from the here derived uncoupled method is the ability to correctly approximate the solution of very severe benchmarks. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1396–1423, 2015     

Locally periodic Timoshenko rod: experiment and theory

The flexural vibrations of a locally periodic rod, which consists of N unit cells, are discussed both from the experimental and theoretical points of view. Timoshenko's beam theory and the transfer matrix method are used to calculate the normal-mode frequencies and amplitudes. The theoretical values are then compared with the experimental ones, which are obtained using an electromagnetic acoustic transducer (EMAT). Good agreement between the numerical results and the experimental measurements is obtained. It is shown that as N grows, a band spectrum emerges.     

Existence of (2, 8) GWhD( v) and (4, 8) GWhD( v) with $${ v \equi v 0,1 (mod 8)}$$

(2, 8) Generalized Whist tournament Designs (GWhD) on v players exist only if . We establish that these necessary conditions are sufficient for all but a relatively small number of (possibly) exceptional cases. For there are at most 12 possible exceptions: {177, 249, 305, 377, 385, 465, 473, 489, 497, 537, 553, 897}. For there are at most 98 possible exceptions the largest of which is v = 3696. The materials in this paper also enable us to obtain four previously unknown (4, 8)GWhD(8n+1), namely for n = 16,60,191,192 and to reduce the list of unknown (4, 8) GWhD(8n) to 124 values of v the largest of which is v = 3696.