Ground State of N Harmonically Bound Anyons in a Magnetic Field

The properties of the ground state of N anyons in an external magnetic field and a harmonic oscillator potential are computed in the large-N limit using the Thomas-Fermi approximation. The number of level crossings in the ground state as a function of the harmonic frequency, the strength and the direction of the magnetic field and N are also studied.

Recognition of Polycyclic Aromatic Hydrocarbons and Their Derivatives by the 1,3-Dinaphthalimide Conjugate of Calix4]arene: Emission, Absorption, Crystal Structures, and Computational Studies

Polycyclic aromatic hydrocarbons (PAHs) are environmental pollutants as well as well-known carcinogens. Therefore, it is important to develop an effective receptor for the detection and quantification of such molecules in solution. In view of this, a 1,3-dinaphthalimide derivative of calix4]arene (L) has been synthesized and characterized, and the structure has been established by single crystal XRD. In the crystal lattice, intermolecular arm-to-arm pi center dot center dot center dot pi overlap dominates and thus L becomes a promising receptor for providing interactions with the aromatic species in solution, which can be monitored by following the changes that occur in its fluorescence and absorption spectra. On the basis of the solution studies carried out with about 17 derivatives of the aromatic guest molecular systems, it may be concluded that the changes that occur in the fluorescence intensity seem to be proportional to the number of aromatic rings present and thus proportional to the extent of pi center dot center dot center dot pi interaction present between the naphthalimide moieties and the aromatic portion of the guest molecule. Though the nonaromatic portion of the guest species affects the fluorescence quenching, the trend is still based on the number of rings present in these. Four guest aldehydes are bound to L with K-ass of 2000-6000 M-1 and their minimum detection limit is in the range of 8-35 mu M. The crystal structure of a naphthaldehyde complex, L.2b, exhibits intermolecular arm-to-arm as well as arm-to-naphthaldehyde pi center dot center dot center dot pi interactions. Molecular dynamics studies of L carried out in the presence of aromatic aldehydes under vacuum as well as in acetonitrile resulted in exhibiting interactions observed in the solid state and hence the changes observed in the fluorescence and absorption spectra are attributable for such interactions. Complex formation has also been delineated through ESI MS studies. Thus L is a promising receptor that can recognize PAHs by providing spectral changes proportional to the aromatic conjugation of the guest and the extent of aromatic pi center dot center dot center dot pi interactions present between L and the guest.

Matrix method for eigenstructure assignment - The multi-input case with application

The eigenvalue and eigenstructure assignment procedure has found application in a wide variety of control problems. In this paper a method for assigning eigenstructure to a linear time invariant multi-input system is proposed. The algorithm determines a matrix that has eigenvalues and eigenvectors at the desired locations. It is obtained from the knowledge of the open-loop system and the desired eigenstructure. Solution of the matrix equation, involving unknown controller gams, open-loop system matrices, and desired eigenvalues and eigenvectors, results hi the state feedback controller. The proposed algorithm requires the closed-loop eigenvalues to be different from those of the open-loop case. This apparent constraint can easily be overcome by a negligible shift in the values. Application of the procedure is illustrated through the offset control of a satellite supported, from an orbiting platform, by a flexible tether.