2-Dimension from the Topological Viewpoint

In this paper we study the 2-dimension of a finite poset from the topological point of view. We use homotopy theory of finite topological spaces and the concept of a beat point to improve the classical results on 2-dimension, giving a more complete answer to the problem of all possible 2-dimensions of an n-point poset.      

Signatures of counter-ion association and hydrogen bonding in vibrational circular dichroism spectra

We study the effect of counter-ion complexation on the example of Cl(-) ions interacting with the [Co(en)(3)](3+) complex. The H-bonding of the N-H groups of the ethylenediamine (en) ligands with the Cl(-) ions may lead to giant enhancement of the VCD intensity for the N-H stretches, but may also lead to VCD sign changes in the finger print region of N-H wagging, twisting and scissoring motions. Such sign changes should not be mistaken for signatures of the presence of the other enantiomer. We elucidate the mechanism for the sign changes and give a recommendation on how to deal with this problem. We also show that the experimental spectrum is only in good accord with the calculations if complexation of 5 Cl(-) ions (two axial, three equatorial) is assumed, but not with two (axial) or three (equatorial) Cl(-) ions, thus showing the potential of VCD to be used as an experimental probe for complexation.     

Study of solid state reactions in Nb/Al multilayer thin films

Solid state reactions of sputter-deposited Nb/Al multilayer thin films, with periodicities in the range 10–333 nm, have been studied by differential scanning calorimetry. The first phase to form upon annealing the films in NbAl₃. Constant-heating-rate calorimetric measurements show the presence of two peaks for the formation of this phase, while isothermal scans reveal that the first peak is associated with a nucleation and growth type transformation. The formation of NbAl₃ is thus interpreted as a two-stage process of nucleation and growth to coalescence (first peak) followed by growth until the consumption of one or both reactants (second peak).We thank NSF for support through DMR-9308651, K. Coffey, S. Vivekanand and B. Gadicharla for assistance and TA Instruments for the donation of a 1600°C furnace.     

An efficient synthesis of 5‐benzoyloxazolines by regio‐ and stereo‐controlled reaction of N‐substituted 2‐benzoylaziridines under microwave irradiation

Several N‐acyl‐2‐benzoylaziridines were prepared conveniently in good to high yields (71‐93%) and used in the preparation of 5‐benzoyloxazolines (76‐91%) by a regio‐ and stereo‐controlled reaction in the presence of Nal as an efficient catalyst under microwave irradiation in short reaction times (5‐10 mins). The structure of the regioisomeric product was confirmed by X‐ray analysis.     

Reductive amination of aldehydes and ketones to their corresponding amines with N-methylpyrrolidine zinc borohydride

A simple and convenient procedure for reductive amination of aldehydes and ketones using N-methylpyrrolidine zinc borohydride (ZBHNMP) as a reducing agent is described. The reactions are carried out with 1 equiv of amine and 1 equiv of aldehyde or ketone using 1 equiv of ZBHNMP in methanol under neutral conditions at room temperature.     

Phase unwrapping algorithm based on singularity compensation for three-dimensional shape measurement

Three-dimensional (3D) imaging continues to attract much research interest for its wide applications. In 3D shape measurement, the phase carries information about the object. However, phase mapping is ambiguous as the extracted phase is returned in a form that suffers from 2π phase jumps. In this case, the phase data must be unwrapped to be fit for use. Furthermore, sometimes the presence of noise in the measured data, in which many singular points (SPs) are found, makes general phase unwrapping algorithms fail to produce accurate unwrapped results. For this reason, we propose a new phase unwrapping method for dynamic 3D shape measurement. The new algorithm is based on compensating the singularity of discontinuity sources. It uses direct compensators for adjoining SP pairs and uses rotational compensators for other SP pairs. The proposed algorithm has been evaluated and compared with past phase unwrapping methods. Results show that the proposed method gives satisfactory unwrapped results with a low computation time.     

On the equivalence of conformational and enantiomeric changes of atomic configuration for vibrational circular dichroism signs

We study systematically the vibrational circular dichroism (VCD) spectra of the conformers of a simple chiral molecule, with one chiral carbon and an "achiral" alkyl substituent of varying length. The vibrational modes can be divided into a group involving the chiral center and its direct neighbors and the modes of the achiral substituent. Conformational changes that consist of rotations around the bond from the next-nearest neighbor to the following carbon, and bond rotations further in the chain, do not affect the modes around the chiral center. However, conformational changes within the chiral fragment have dramatic effects, often reversing the sign of the rotational strength. The equivalence of the effect of enantiomeric change of the atomic configuration and conformational change on the VCD sign (rotational strength) is studied. It is explained as an effect of atomic characteristics, such as the nuclear amplitudes in some vibrational modes as well as the atomic polar and axial tensors, being to a high degree determined by the local topology of the atomic configuration. They reflect the local physics of the electron motions that generate the chemical bonds rather than the overall shape of the molecule.