Papoulis-like generalized sampling expansions in fractional Fourier domains and their application to superresolution

We present a generalized convolution theorem in the fractional Fourier domains that preserves the convolution theorem of the conventional Fourier transform. The Papoulis-like generalized sampling expansions in the fractional Fourier domains using this generalized convolution theorem are also derived and it is shown that the classical generalized Papoulis sampling expansion is a special case of it. Its application in the context of the image superresolution is also discussed.     

Quantum information processing by NMR using a 5-qubit system formed by dipolar coupled spins in an oriented molecule

Quantum information processing by NMR with small number of qubits is well established. Scaling to higher number of qubits is hindered by two major requirements (i) mutual coupling among qubits and (ii) qubit addressability. It has been demonstrated that mutual coupling can be increased by using residual dipolar couplings among spins by orienting the spin system in a liquid crystalline matrix. In such a case, the heteronuclear spins are weakly coupled, but the homonuclear spins often become strongly coupled. In such circumstances, the strongly coupled spins, which yield second order spectra, can no longer be individually treated as qubits. However, it has been demonstrated elsewhere, that the 2(N) energy levels of a strongly coupled N spin-1/2 system can be treated as an N-qubit system. For this purpose the various transitions have to be identified to well defined energy levels. This paper consists of two parts. In the first part, the energy level diagram of a heteronuclear 5-spin system is obtained by using a newly developed heteronuclear z-cosy (HET-Z-COSY) experiment. In the second part, implementation of logic gates, preparation of pseudopure states, creation of entanglement, and entanglement transfer is demonstrated, validating the use of such systems for quantum information processing.     

Experimental implementation of local adiabatic evolution algorithms by an NMR quantum information processor

Quantum adiabatic algorithm is a method of solving computational problems by evolving the ground state of a slowly varying Hamiltonian. The technique uses evolution of the ground state of a slowly varying Hamiltonian to reach the required output state. In some cases, such as the adiabatic versions of Grover's search algorithm and Deutsch-Jozsa algorithm, applying the global adiabatic evolution yields a complexity similar to their classical algorithms. However, using the local adiabatic evolution, the algorithms given by J. Roland and N.J. Cerf for Grover's search [J. Roland, N.J. Cerf, Quantum search by local adiabatic evolution, Phys. Rev. A 65 (2002) 042308] and by Saurya Das, Randy Kobes, and Gabor Kunstatter for the Deutsch-Jozsa algorithm [S. Das, R. Kobes, G. Kunstatter, Adiabatic quantum computation and Deutsh's algorithm, Phys. Rev. A 65 (2002) 062301], yield a complexity of order N (where N=2(n) and n is the number of qubits). In this paper, we report the experimental implementation of these local adiabatic evolution algorithms on a 2-qubit quantum information processor, by Nuclear Magnetic Resonance.     

Behaviour of a bz oscillating system at low temperatures

The BZ oscillating reaction has been studied at low temperatures and it was noted that strangely enough the oscillation period itself showed some sort of periodicity.     

Die quantitative Bestimmung von Triglyceriden mit Hilfe der Gaschromatographie

Ohne Zusammenfassung     

Ketone-zinc chloride combination as an initiator of polymerization

Dihydrocivetone, a macrocyclic ketone, has been found to be a weak initiator of vinyl polymerization. Anhydrous zinc chloride strongly promotes this to form a novel initiating system. Monomers tried successfully are methyl methacrylate, acrylonitrile and α-methylstyrene. The characteristic feature of polymerization of α-methylstyrene differs greatly from those of other monomers and those have been discussed and compared.     

The use of quinoxaline-2-carboxylic acid and its derivatives as analytical reagents

Quinoxaline-2-carboxylic acid and 3-chloro and 3-hydroxy derivatives have been studied as analytical reagents. The solubility products of the metal salts, the optimum pH range for complete precipitation and the thermal behaviours of the metal complexes have been established. Quinoxaline-2-carboxylic acid allows the gravimetric determination of Cu(II), Cd(II), Zn(II), Co(II), Ni(II) and Pd(II); with the 3-chloro and 3-hydroxy derivatives, only palladium(II) could be precipitated quantitatively.