A theoretical approach to substituent effects: Stabilities and conformational preferences in β-substituted ethyl radicals

Ab initio molecular orbital theory is used to study substituent effects in a series of β-substituted Et radicals XCH₂CH₂. For X = BH₂ (plan.), CH₃, NH₂, OH and F, only slight conformational preferences and weak stabilizations are indicated. Such behaviour may be rationalized, using a PMO model, in terms of opposing changes, accompanying variation in X, in positive and negative hyperconjugation between the XCH₂ group and the CH₂ centre. On the other hand, for groups containing an appropriately oriented, low-lying vacant orbital, viz. X = Li, BeH and BH₂ (perp.), there is a pronounced preference for the perpendicular conformation of the radical. This is attributed to 1,3-interaction between the singly-occupied 2p(C) orbital and the vacant 2p(X) orbital.     

The bimolecular hydrogen-deuterium exchange behavior of protonated alkyl dipeptides in the gas phase

As part of an ongoing characterization of the intrinsic chemical properties of peptides, thermal hydrogen-deuterium exchange has been studied for a series of fast-atom-bombardment-generated protonated alkyldipeptides and related model compounds in the reaction with D₂O, CH₃OD, and ND₃ in a Fourier transform ion cyclotron resonance mass spectrometer. Despite the very large basicity difference between the dipeptides and the D₂O and CH₃OD exchange reagents, efficient exchange of all active hydrogen atoms occurs. From the kinetic data it appears that exchange of the amino, amide, and hydroxyl hydrogens proceeds with different efficiencies, which implies that the proton in thermal protonated dipeptides is immobile. The selectivity of the exchange at the different basic sites is governed by the nature of both the dipeptide and the exchange reagent. The results indicate that reversible proton transfer in the reaction complexes, which effectuates the deuterium incorporation, is assisted by formation of multiple hydrogen bonds between the reagents. Exchange is considered to proceed via the intermediacy of different competing intermediate complexes, each of which specifically leads to deuterium incorporation at different basic sites. The relative stabilization of the competing intermediate complexes can be related to the relative efficiencies of deuterium incorporation at different basic sites in the dipeptide. For all protonated dipeptides studied, the exchange in the reaction with ND₃ proceeds with unit efficiency, whereas all active hydrogen atoms are exchanged equally efficiently. Evidently specific multiple hydrogen bond formations are far less important in the reversible proton transfers with the relatively basic ammonia, which allows effective randomization of all active hydrogen atoms in the reaction complexes.     

Analysis of Sabine and Eyring equations and their application to concert hall audience and chair absorption

Historically, two equations have been used for predicting reverberation times, Sabine and Eyring. A precise means is presented for determining Eyring absorption coefficients alpha(eyring) when the Sabine coefficients alpha(sabine) are known, and vice versa. Thus, either formula can be used provided the absorption coefficients for the Sabine formula are allowed to exceed 1.0. The Sabine formula is not an approximation to the Eyring equation and is not a shortcoming. Given low reverberation times, the ratio of alpha(sabine) to alpha(eyring) may become greater than 2.0. It is vital that, for correct prediction of reverberation times, the absorption coefficients used in either formula must have been determined in spaces similar in size and shape, with similar locations of high absorption (audience) areas, and with similar reverberation times. For concert halls, it is found that, when the audience area (fully occupied) and midfrequency reverberation time are postulated, the hall volume is directly proportional to the audience absorption coefficient. Approximately 6% greater room volumes are needed when choosing nonrectangular versus classical-rectangular shaped halls and approximately 10% greater volumes when choosing heavily upholstered versus medium upholstered chairs. Determinations of audience sound absorption coefficients are presented, based on published acoustical and architectural data for 20 halls.     

Effect of Tomato Peel Extract Grown under Drought Stress Condition in a Sarcopenia Model

Tomatoes and their derivates represent an important source of natural biologically active components. The present study aims to investigate the protective effect of tomato peel extracts, grown in normal (RED-Ctr) or in drought stress (RED-Ds) conditions, on an experimental model of sarcopenia. The phenolic profile and total polyphenols content (TPC) of RED-Ctr and RED-Ds were determined by Ultra High-Performance Liquid Chromatography (UHPLC) analyses coupled to electrospray ionization high-resolution mass spectrometry (ESI-HR-MS). Human skeletal muscle myoblasts (HSMM) were differentiated in myotubes, and sarcopenia was induced by dexamethasone (DEXA) treatment. Differentiation and sarcopenia were evaluated by both real-time PCR and immunofluorescent techniques. Data show that myosin heavy chain 2 (MYH2), troponin T (TNNT1), and miogenin (MYOG) were expressed in differentiated myotubes. 5 μg Gallic Acid Equivalent (GAE/mL) of TPC from RED-Ds extract significantly reduced muscle atrophy induced by DEXA. Moreover, Forkhead BoxO1 (FOXO1) expression, involved in cell atrophy, was significantly decreased by RED-Ds extract. The protective effect of tomato peel extracts depended on their qualitative polyphenolic composition, resulting effectively in the in vitro model of sarcopenia.     

Inelastic tunneling in a double quantum dot coupled to a bosonic environment

Coupling a quantum system to a bosonic environment always give rise to inelastic processes, which reduce the coherency of the system. We measure energy-dependent rates for inelastic tunneling processes in a fully controllable two-level system of a double quantum dot. The emission and absorption rates are well reproduced by Einstein's coefficients, which relate to the spontaneous emission rate. The inelastic tunneling rate can be comparable to the elastic tunneling rate if the boson occupation number becomes large. In the specific semiconductor double dot, the energy dependence of the inelastic rate suggests that acoustic phonons are coupled to the double dot piezoelectrically.     

Matter and light wave interferometry in gravitational fields

We consider the problem of finding the quantum mechanical phase associated with the propagation of a particle in a given external gravitational field, and conclude that it ism ds. In weak fieldsh this allows us to calculate the gravitationally induced phase on a freely traveling particle as 1/2 h P dx whereP is the ordinary momentum. This formula has the expected Newtonian limit and is then used to calculate effects in matter wave interferometry such as those due to gravity waves and the dragging of the ether frame by rotating bodies. Light wave interferometry is then considered and is shown to be also described by 1/2 h K dx , whereK is the wave vector of the light, and the integral is along the path of the ray. Matter and light wave interferometry are compared in various cases.A preliminary version of this work was presented at the Grenoble Workshop on Neutron Interferometry, June 1978.     

THE BIOGENETIC LAW AND ITS INFLUENCE ON THEORIES OF LEARNING MATHEMATICS

Reference to the history of mathematics has been widely used in discussions of the development of curricula, the problems students have in learning mathematics, and the development of concepts in the individual. This paper examines the background to the "Biogenetic Law" [1] which has influenced so much thinking in educational theory, and the use of the "principle of parallelism" where individual development is claimed to mirror the historical development of the subject matter. Interpretations of the history of mathematics which are used to justify these claims are examined, and the universality of the supposed concepts is challenged. Questions are raised about some of the fundamental tenets of Piagetian epistemology.     

Numerical solution of the two-dimensional Poincaré equation

This paper deals with numerical approximation of the two-dimensional Poincaré equation that arises as a model for internal wave motion in enclosed containers. Inspired by the hyperbolicity of the equation we propose a discretisation particularly suited for this problem, which results in matrices whose size varies linearly with the number of grid points along the coordinate axes. Exact solutions are obtained, defined on a perturbed boundary. Furthermore, the problem is seen to be ill-posed and there is need for a regularisation scheme, which we base on a minimal-energy approach.