Optimal rules with polynomial precision for Hilbert spaces possessing reproducing kernel functions

Numerische Mathematik - Optimal linear rules with polynomial precision, based on preassigned abscissas, are considered over a Hilbert space possessing a reproducing kernel function; the weights are...     

Optimal rules for numerical integration round the unit circle

The construction of optimal linear rules of numerical approximation by Davis' method has already been discussed for functions analytic in circles and in certain ellipses. In the present paper, introducing an appropriate Hilbert space, we discuss optimal linear rules for functions analytic in a circular annulus. We then consider the construction of optimal rules for numerical integration round the unit circleC ₁ : z=1. In Theorem 2 we obtain explicitly a family of optimal rules forc ₁ f(z)dz, withf analytic onC ₁; interestingly, in general, the optimal nodes do not lie onC ₁. For functionsf(1/2(z +z ^–1)), Theorem 2 gives a family of optimal quadrature formulas for integration over [–1,1].     

<Emphasis Type="Italic">SU</Emphasis>(2) invariants of symmetric qubit states

We express the density matrix for the N-qubit symmetric state or spin-j state (j = N/2) in terms of the well-known Fano statistical tensor parameters. Employing the multi-axial representation, where the spin-j density matrix is shown to be characterized by j(2j + 1) axes and 2j real scalars, we enumerate the number of invariants constructed out of these axes and scalars. We calculate these invariants explicitly in the particular case of the pure and mixed spin-1 state.     

Entangling capabilities of symmetric two-qubit gates

Our work addresses the problem ofgenerating maximally entangled two spin-1/2 (qubit) symmetric states using NMR, NQR, Lipkin–Meshkov–Glick Hamiltonians. Time evolution of such Hamiltonians provides various logic gates which can be used for quantum processing tasks. Pairs of spin-1/2s have modelled a wide range of problems in physics. Here, we are interested in two spin-1/2 symmetric states which belong to a subspace spanned by the angular momentum basis {|j = 1, μ〉; μ = + 1, 0, ?1}. Our technique relies on the decomposition of a Hamiltonian in terms of SU(3) basis matrices. In this context, we define a set of linearly independent, traceless, Hermitian operators which provides an alternate set of SU(n) generators. These matrices are constructed out of angular momentum operators J _x , J _y , J _z . We construct and study the properties of perfect entanglers acting on a symmetric subspace, i.e., spin-1 operators that can generate maximally entangled states from some suitably chosen initial separable states in terms of their entangling power.     

Determination of Solifenacin Succinate in Pure and Pharmaceutical Dosage forms by Spectrophotometry

Journal of Analytical Chemistry - Four simple, precise and sensitive visible spectrophotometric methods were developed for the determination of solifenacin succinate in pure and pharmaceutical...     

Quantification of Lupeol in Polyherbal Formulation by High-Performance Thin-Layer Chromatography Method Using Design of Experiments as a Tool to Assess Optimization of Method Development and Extraction Efficiency

JPC – Journal of Planar Chromatography – Modern TLC - A simple, specific, and quantitative high-performance thin-layer chromatographic (HPTLC) method has been developed for the...