Algebraic approach to thermodynamic properties of diatomic molecules

A simple model extending Lie algebraic techniques is applied to the analysis of thermodynamic vibrational properties of diatomic molecules. Local anharmonic effects are described by means of a Morse-like potential and the corresponding anharmonic bosons are associated with the SU(2) algebra. The total number of anharmonic bosons, fixed by the potential shape, is determined for a large number of diatomic molecules. A vibrational high-temperature partition function and the related thermodynamic functions are derived and studied in terms of the parameters of the model. The idea of a critical temperature is introduced in relation to the specific heat. A physical interpretation in terms of a quantum deformation associated with the model is given.     

Acid catalyzed intramolecular attack of β‐phenylthioureido group on amide function. Parallel formation of thiodihydrouracil and 4‐iminothiodihydrouracil. Different pathways in the Edman degradation reaction in the formation of six‐ versus five‐membered cyclic intermediates

Contrary to the cleavage of α‐phenylthioureido peptides 1 proceeding through intermediate 2‐anilinothiazolinone 2 , the b‐analog cis‐2‐(3‐phenylthioureido)cyclopentane‐carboxamide 5 forms transiently 4‐imino‐2‐thioxopyrimidine 6 . Monitoring amide cyclization and hydrolysis of iminopyrimidine 6 in acid by UV showed that an equilibrium between 5 and 6 was reached followed by slower conversion of both compounds into 2‐oxo‐4‐thioxopyrimidine 7 . Both processes were characterized by isosbestic points, the first due to parallel conversion of 5 into 6 and 7 (or 6 into 5 and 7 ) at a constant ratio while the second identical for both reactants – to conversion of equilibrated 5 and 6 into 7 . The special isosbestic points allowed the determination of the individual constants of Scheme 2. Further confirmation was obtained from NMR product analysis and following the cyclization of amide 5 in DMSO:DCl. Product 2‐oxo‐4‐ thioxopyrimidine 7 hydrolyzed reversibly to thioureido acid 8 . The cyclization rate of 8 allowed the participation of 6‐oxothiazine 10 formed by sulfur attack to be excluded. The absence of sulfur attack in the six‐membered case is explained by the longer C? S bond bringing about greater bond angle strain at the tetrahedral ring atoms due to the geometrical characteristics of five‐ and six‐membered rings with planar segments. The cyclizations of amide 5 to iminopyrimidine 6 and to thiodihydrouracil 7 are first order in [H⁺], while the reactions of protonated imine 6 H⁺ are zero order to amide and ?1 to thiodihydrouracil. The reaction orders can be reconciled by assuming a rate determining proton transfer from the tetrahedral intermediate in amide cyclization. Copyright © 2007 John Wiley & Sons, Ltd.     

Relativistically invariant equations (βμ∂μ+ϱ)Ψ(x)=0 with singular ϱ, and detβ0 ≠ 0

We study relativistically invariant equations (β^μ?_μ+?)Ψ(x)=0 with a singular ?. The absence of a simple relation between these equations and their “conjugate” $\text{((β}{}^{\mathrm{\mu }}\text{)}{}^1\text{?}{}_{\mathrm{\mu }}\text{? ?}{}^1\text{)?(x) = 0}$ is pointed out. Assuming that Ψ(x) transforms under an arbitrary finite-dimensional representation of ISL(2,C), the problem of existence is investigated. It is shown that the assumption detβ⁰ ≠ 0 implies: all β^μ are invertible and the representation of ISL(2,C) is even- dimensional. The difficulties in the general treatment of the problem are discussed. A particular class of equations is illustrated by several examples.     

Inhomogeneities in the shape of the He 504.7 nm line excited in a hollow cathode discharge

The profile of the He 504.7 nm line emitted in the negative glow of a hollow cathode discharge is analyzed as a function of the distance from the emitting volume to the cathode axis. The value of the discharge current varied within the range of 10–30 mA, the helium pressure being 0.4–1.5 torr. A dependence was found of the Voigt parameter a on the location of the emitting volume. The simultaneous recording of two line shapes, emitted from different regions of the discharge, enables us to observe a shift δv of the line center observed off-axis compared with the line emitted along the axis. The electric field intensity at the periphery, 6 mm off-axis, is evaluated on the assumption that Starkbroadening is the cause of δv.     

The use of high energy laser-plasma sources in soft X-ray contact microscopy of living biological samples

In this paper the results of an experiment on soft X-ray contact microscopy using a laser-plasma source are presented. A resolution of 50 nm has been achieved imaging pig sperm cells, while other specimens, such as algae and yeast cells, showed internal details, proving the technique to be a powerful tool for biological investigations. Original biological information has been obtained and the conditions for optimal image formation have been studied. Received 5 June 2002 Published online 24 September 2002 RID="a" ID="a"e-mail: batani@mib.infn.it     

Unexpected Synthesis of a 5H‐chromeno[3,4‐c]pyridine Derivative from 4‐Chlorocoumarin‐3‐carbaldehyde and Malononitrile

In the reaction of 4‐chlorocoumarin‐3‐carbaldehyde with malononitrile in the presence of piperidine, a piperidinium salt of a novel tricyclic chromeno[3,4‐c]pyridine derivative was isolated instead of the expected “tert‐amino effect” product. When hexamethyleneimine (azepane) was used as a base, the corresponding azepanium salt (same anion) was obtained. Both structures have been formulated on the basis of their spectral (IR, NMR, MS) behavior and elemental analyses. In addition, the structure of the piperidinium salt was confirmed by means of X‐ray crystallographic analysis.     

Set-based corral control in stochastic dynamical systems: making almost invariant sets more invariant

We consider the problem of stochastic prediction and control in a time-dependent stochastic environment, such as the ocean, where escape from an almost invariant region occurs due to random fluctuations. We determine high-probability control-actuation sets by computing regions of uncertainty, almost invariant sets, and Lagrangian coherent structures. The combination of geometric and probabilistic methods allows us to design regions of control, which provide an increase in loitering time while minimizing the amount of control actuation. We show how the loitering time in almost invariant sets scales exponentially with respect to the control actuation, causing an exponential increase in loitering times with only small changes in actuation force. The result is that the control actuation makes almost invariant sets more invariant.     

Field induced phase transitions on NdRhIn5 and Nd2RhIn8 antiferromagnetic compounds

In this work, we have investigated the low temperature magnetic phase diagram of the tetragonal NdRhIn₅ and Nd₂RhIn₈ single crystals by means of temperature and field dependent heat capacity and magnetic susceptibility measurements. These compounds order antiferromagnetically with a Néel temperature (T_N) of 11 and 10.7 K for NdRhIn₅ and Nd₂RhIn₈, respectively. The constructed magnetic phase of both compounds are anisotropic and show, as expected, a decrease of T_N as a function of the magnetic field for c crystallographic direction. However when the magnetic field is applied along of the c-axis, which is the magnetic easy axis, first-order-like field induced transitions are observed within the antiferromagnetic state. We compare the phase diagrams obtained for NdRhIn₅ and Nd₂RhIn₈ with those for their cubic relative NdIn₃.