Synthesis of Highly Substituted γ‐Butyrolactones by a Gold‐Catalyzed Cascade Reaction of Benzyl Esters

Easily accessible benzylic esters of 3‐butynoic acids in a gold‐catalyzed cyclization/rearrangement cascade reaction provided 3‐propargyl γ‐butyrolactones with the alkene and the carbonyl group not being conjugated. Crossover experiments showed that the formation of the new C?C bond is an intermolecular process. Initially propargylic–benzylic esters were used, but alkyl‐substituted benzylic esters worked equally well. In the case of the propargylic–benzylic products, a simple treatment of the products with aluminum oxide initiated a twofold tautomerization to the allenyl‐substituted γ‐butyrolactones with conjugation of the carbonyl group, the olefin, and the allene. The synthetic sequence can be conducted stepwise or as a one‐pot cascade reaction with similar yields. Even in the presence of the gold catalyst the new allene remains intact.     

Preparation of rhodium–phyllosilicate catalysts without leaching in liquid-phase 1-hexene hydrogenation

Rhodium catalysts have been prepared on palygorskite and montmorillonite (clay) supports by reduction with hydrogen (1 atmosphere) at room temperature of a cationic organometallic rhodium compound anchored to the support. The activity of these catalysts for the hydrogenation of liquid-phase 1-hexene remains constant with increase of prehydrogenation time and with re-use for several runs. No rhodium leaching is observed.     

Crystal field and magnetic properties of the tetragonal TbNi2Si2 compound

The magnetic properties of a TbNi₂Si₂ single crystal have been investigated experimentally by specific heat, anisotropy of the susceptibility and magnetization, and inelastic neutron scattering, leading to the determination of its fundamental coupling parameters. The lowest crystalline electric field states are two singlets close to each other, that explains the different magnetic structures evidenced in TbNi₂Si₂: an amplitude modulated structure, close to T _N , a simple antiferromagnetic one at low temperature and an antiphase one when an external magnetic field is applied along the c direction.     

Theoretical study of cyclization of 2′-hydroxychalcone

The isomerization mechanism of 2′(OH)chalcone (1) in flavanone (2) was studied. The calculations were performed with the semiempirical method AM1, using totally optimized molecular geometries. A 6-step mechanism including several equilibrium states was proposed. It was concluded that: (a) At the conformational equilibrium of 1 there could be 43.9% of s-cis conformer; (b) The acid dissociation of 1 trans-s-trans is considerable; (c) The E_E, ΔH_f and net charges show that the rotation of ring A of 1 and the formation of ring C of 2 occurs without greater impairments; (d) Although the keto structure is the most stable one, the enolate of 2 is present in the reaction medium; (e) The conversion of enol of 2 in the keto form would be the limiting step of the analyzed isomerization rate.     

Optimality and duality in multiobjective fractional programming involving ρ-semilocally type I-preinvex and related functions

Optimality conditions are obtained for a nonlinear fractional multiobjective programming problem involving η-semidifferentiable functions. Also, a general dual is formulated and a duality result is proved using concepts of generalized ρ-semilocally type I-preinvex functions.     

Limonene concentration in lemon (Citrus volkameriana) peel oil as a function of ripeness

The dependence of the limonene content of lemon (Citrus volkameriana) peel oil on the degree of ripeness of the fruit has been studied by using steam distillation and cold pressing to extract the oils from lemon fruit peel at different stages of maturation (green, greenish-yellow, and yellow-orange peel coloration). Samples of essential oils were analyzed by high resolution GC and GC-MS, using tetradecane as internal standard for quantitation. Forty components were detected; thirty eight were positively identified by comparison of their mass spectra (El, 70 eV) and Kováts retention indexes (determined using a non-logarithmic scale on capillary columns coated with both polar (DB-Wax) and non-polar (DB-1) stationary phases) with those of standards and with data reported in the literature. The limonene concentration reached a maximum level of 79.4% when the fruit was in the intermediate maturation stage characterized by greenish-yellow coloration.     

RECURSIVE BAIRE CLASSIFICATION AND SPEEDABLE FUNCTIONS

Using recursive variants of Baire notions of nowhere dense and meagre sets we study the topological size of speedable and infinitely often speedable functions in a machine-independent framework. We show that the set of speedable functions is not “small” whereas the set of infinitely often speedable functions is “large”. In this way we offer partial answers to a question in [4].     

Single electron tunneling rates in multijunction circuits

The rate of electron tunneling through normal metal tunnel junctions is calculated for the case of ultrasmall junction capacitances. The so-called Coulomb blockade of electron tunneling at low temperatures is shown to be strongly affected by the external electrical circuit. Under the common experimental condition of a low impedance environment the Coulomb blockade is suppressed for single tunnel junctions. However, a Coulomb gap structure emerges for junctions embedded in a high impedance environment. For a double junction setup a Coulomb blockade of tunneling arises even for low impedance environments due to the charge quantization on the metallic island between the junctions. An approach using circuit analysis is presented which allows to reduce the calculation of tunneling rates in multijunction circuits to those of a single junction in series with an effective capacitance. The range of validity of the socalled local rule and global rule rates is clarified. It is found that the tunneling rate tends towards the global rule rate as the number of junctions is increased. Some specific results are given for a one-dimensional array of tunnel junctions.