An Improved Large Scale Synthesis of 2-Amino-4-chloropyridine and Its Use for the Convenient Preparation of Various Polychlorinated 2-Aminopyridines

An efficient large scale synthesis of 2-amino-4-chloropyridine (3) has been achieved through a modification of existing literature procedures. Compound 3 was used to prepare the previously unreported 2-amino-4,5-dichloropyridine (4). The known 2-amino-3,4-dichloropyridine (5) and 2-amino-3,4,5-trichloropyridine (6) were prepared from 3 by new routes and in higher yields than previously reported.     

Nonlinear interference in a mean-field quantum model

Using similar nonlinear stationary mean-field models for both a 2D axisymmetricalBose-Einstein Condensate and an electron pair in a parabolic trap, we propose to describethe original many-particle ground state as a one-particle mixed state (in contrast to apure state), i.e. as a statistical ensemble of several one-particle quantum states. Thesequantum states are the eigenfunctions of the corresponding stationary nonlinearSchrödinger equation (hence called “nonlinear eigenstates”). Due to their nonlinearity,they are not orthogonal. Therefore, taking the simple example of a two-level system, weshow that each of these two nonlinear eigenstates |i? and|j? occurs with a probability (or statistical weight) that isdefined by their non-orthogonality ?i|j? 0. We givethe corresponding density matrix. We search for physical grounds in the interpretation ofour two main results, namely, a quantum-classical nonlinear transition and theinterference between two “nonlinear eigenstates”.     

The far-infrared absorption of a periodic 2DEG in the transition regime between weak and strong modulation

We study the optical absorption of arrays of quantum dots and antidots in a perpendicular homogeneous magnetic field. The electronic system is described quantum mechanically using a Hartree approximation for the mutual Coulomb interaction of the electrons. The evolution of the absorption is traced from the homogeneous to the strongly modulated case identifying the ensuing collective modes, the magnetoplasmons, and their correlations with inherent length scales of the system.     

Harmonic morphisms from the Grassmannians and their non-compact duals

In this paper we give a unified framework for the construction of complex valued harmonic morphisms from the real, complex and quaternionic Grassmannians and their non-compact duals. This gives a positive answer to the corresponding open existence problem in the real and quaternionic cases. Mathematics Subject Classifications (2000): 58E20, 53C43, 53C12The author is a member of EDGE, Research Training Network HPRN-CT-2000-00101     

Sparse geometric graphs with small dilation

Given a set S of n points in , and an integer k such that 0k<n, we show that a geometric graph with vertex set S, at most n−1+k edges, maximum degree five, and dilation O(n/(k+1)) can be computed in time O(nlogn). For any k, we also construct planar n-point sets for which any geometric graph with n−1+k edges has dilation Ω(n/(k+1)); a slightly weaker statement holds if the points of S are required to be in convex position.     

Resistance minima in amorphous PdSi alloy

The resistivity minimum in amorphous PdSi containing transition metals is magnetic in origin. For high purity samples a weak minimum, possibly associated with residual Fe impurity, is removed by a mild heat-treatment known to reduce the density of localized “tunneling” states.     

Retarded transverse current-current response functions of a two-dimensional electron gas

The retarded transverse current-current response functions of an ideal two-dimensional electron gas at zero temperature are calculated. Introducing a new approximation scheme which allows one to take account of the reaction of the electromagnetic field to the induced current, i.e. the influence of the electronic induced current on the dynamics of the electromagnetic field, within the framework of the conventional linear response theory in a self-consistent way, a possible form of the dispersion relation for the transverse plasmon in the system is obtained. It is found that the energy of the transverse plasmon has a gap at k=0, if the thickness of the system is finite, in contrast to the longitudinal case.