Zero-field spin splitting in a two-dimensional electron gas with the spin-orbit interaction revisited

We consider a two-dimensional electron gas (2DEG) with the Rashba spin-orbit interaction (SOI) in the presence of a perpendicular magnetic field. We derive analytical expressions of the density of states (DOS) of a 2DEG with the Rashba SOI in the presence of a magnetic field by using the Green's function technique. The DOS allows us to obtain the analytical expressions of the magnetoconductivities for spin-up and spin-down electrons. The conductivities for spin-up and spin-down electrons oscillate with different frequencies and give rise to the beating patterns in the amplitude of the Shubnikov-de Haas (SdH) oscillations. We find a simple equation which determines the zero-field spin splitting energy if the magnetic field corresponding to any beat node is known from the experiment. Our analytical results reproduce well the experimentally observed non-periodic beating patterns, number of oscillations between two successive nodes and the measured zero-field spin splitting energy.     

Zitterbewegung of electrons in quantum wells and dots in the presence of an in-plane magnetic field

We study the effect of an in-plane magnetic field on the zitterbewegung (ZB) of electrons in a semiconductor quantum well (QW) and in a quantum dot (QD) with the Rashba and Dresselhaus spin-orbit interactions (SOIs). We obtain a general expression of the time-evolution of the position vector and current of the electron in a semiconductor QW. The amplitude of the oscillatory motion is directly related to the Berry connection in momentum space. We find that in presence of the magnetic field the ZB in a QW does not vanish when the strengths of the Rashba and Dresselhaus SOIs are equal. The in-plane magnetic field helps to sustain the ZB in QWs even at a low value of k(0)d (where d is the width of the Gaussian wavepacket and k(0) is the initial wavevector). The trembling motion of an electron in a semiconductor QW with high Landé g-factor (e.g. InSb) is sustained over a long time, even at a low value of k(0)d. Further, we study the ZB of an electron in QDs within the two sub-band model numerically. The trembling motion persists in time even when the magnetic field is absent as well as when the strengths of the SOI are equal. The ZB in QDs is due to the superposition of oscillatory motions corresponding to all possible differences of the energy eigenvalues of the system. This is an another example of multi-frequency ZB phenomenon.     

Time minimizing transportation problems

A procedure for time minimization in a transportation problem is developed and consists of a finite number of interactions and is based on moving from a basic feasible solution to another till the last solution is arrived at. A numerical example is given in support of the theory.     

Revisiting Ramakrishnan's approach to relativity

The conditions under which the Velocity Addition Theorem (VAT) is formulated by Ramakrishnan gave rise to doubts about the uniqueness of the theorem. These conditions are rediscussed with reference to their algebraic and experimental implications.     

Nickel-catalyzed coupling of aryl iodides with aromatic aldehydes: chemoselective synthesis of ketones

Aryl iodides (ArI) couple with aryl aldehydes (Ar'CHO) in the presence of Ni(dppe)Br(2) and Zn to give the corresponding biaryl ketones (ArCOAr'). The use of a bidentate phosphine complex is critical to the success of this catalytic reaction. The reaction provides a new procedure for the synthesis of various functionalized biaryl ketones.     

Total synthesis of stevastelin B3

The total synthesis of stevastelin B3 was achieved using, as a key step, a method developed by us for the synthesis of 2-methyl-1,3-diols by Ti(III)-mediated diastereo- and regioselective opening of trisubstituted 2,3-epoxy alcohols, to carry out the stereoselective construction of its propionate-derived fatty acid segment.     

2-(α-pyridyl)thioquinaldinamide: a novel fluorimetric reagent in inorganic trace analysis. : Part 2. A simple selective determination of selenium(IV) at Ultratrace Levels

The very sensitive fluorimetric determination of selenium(IV) is based on its oxidation of the non-fluorescent 2-(α-pyridyl)thioquinaldinamide in slightly acidic solution (0.05–0.15 M sulphuric acid). The excitation and emission wavelengths are 350 nm and 500 nm, respectively. Linear calibration graphs are obtained for different ranges of selenium concentration between 0.01 ng ml^?1 and 0.5 μg ml^?1. Over sixty ions either do not interfere or can be masked in the determination of 1 ng ml^?1 Se(IV). The method is applied successfully to various synthetic mixtures and to a native sulphur sample. The reaction is fast and the fluorescent system is stable for 24 hours.     

Studies directed towards the total synthesis of lycoperdinosides: stereoselective construction of the C1-C9 and C10-C21 segments of the molecules

The three chiral centres of the C1-C9 moiety of the six-membered lactone glycosides, lycoperdinosides A and B, have been derived from a common starting material containing a single chiral centre. In contrast, the C10-C21 segment of these molecules has been synthesized using, as key steps, a highly stereoselective aldol reaction, a Ti(III)-mediated opening of a trisubstituted epoxy alcohol and an efficient directed hydrostannylation of a suitably substituted internal alkyne.     

Synthesis and conformational studies of amide-linked cyclic homooligomers of a thymidine-based nucleoside amino acid

Cyclic homooligomers of a thymidine-based nucleoside amino acid were synthesized from the linear dimer using BOP reagent in the presence of DIPEA under dilute conditions. Conformational analysis by NMR and constrained MD studies revealed that all the cyclic products had symmetrical structures. The NH and CO groups in these molecules point in opposite directions with near perpendicular orientation with respect to the plane of the macrocyclic ring having CO on the same side as the base.