Fourier analysis of the approximation power of principal shift-invariant spaces

The approximation order provided by a directed set {S _h } _h>0 of spaces, each spanned by thehZ ^d -translates of one function, is analyzed. The nearoptimal approximants of [R2] from eachs _h to the exponential functions are used to establish upper bounds on the approximation order. These approximants are also used on the Fourier transform domain to yield approximations for other smooth functions, and thereby provide lower bounds on the approximation order. As a special case, the classical Strang-Fix conditions are extended to bounded summable generating functions.The second part of the paper consists of a detailed account of various applications of these general results to spline and radial function theory. Emphasis is given to the case when the scale {s _h } is obtained froms ₁ by means other than dilation. This includes the derivation of spectral approximation orders associated with smooth positive definite generating functions.     

The Forwarding Indices of Random Graphs

A routing R of a graph G is a set of n(n ? 1) elementary paths R(u, v) specified for all ordered pairs (u, v) of vertices of G. The vertex-forwarding index ξ(G) of G, is defined by Where ξ(G, R) is the maximum number of paths of the routing R passing through any vertex of G and the minimum is taken over all the routings of G. Let G_p denote the random graph on n vertices with edge probability p and let m = np. It is proved among other things that, under natural growth conditions on the function p = p(n), the ratio Tends to 1 in probability as n tends to infinity.     

MPT versus: A manifestly covariant presentation of motion reversal and particle-antiparticle exchange

We show that particle-antiparticle exchange and covariant motion reversal are two physically different aspects of the same mathematical transformation, either in the prequantal relativistic equation of motion of a charged point particle, in the general scheme of second quantization, or in the spinning wave equations of Dirac and of Petiau-Duffin-Kemmer. While, classically, charge reversal and rest mass reversal are equivalent operations, in the wave mechanical case mass reversal must be supplemented by exchange of the two adjoint equations, implying .Denoting by M the rest mass reversal, P the parity reversal, T the Racah time reversal, and Z the exchange, the connection with the usual scheme of charge conjugation, parity reversal, and Wigner motion reversal, is with, of course,     

Limit on right handed weak coupling parameters from inelastic neutrino interactions

Right handed weak quark currents coupled to the usual left handed weak lepton current would be seen in inclusive antineutrino scattering on nuclei as a contribution at largey with the quark (not antiquark) structure function. We do not see such a term, and can therefore put an upper limit on the relative strengths of such right handed currents: \(\varrho ^2 = \frac{{\sigma _R }}{{\sigma _L }}< 0.009\) , 90% confidence. This measurement puts limits on the mixing angle of left-right symmetric models. In distinction to similar limits derived from muon decay or β decay, our limits are also valid if the right handed neutrino is heavy.     

Simultaneous spectrophotometric determination of cadmium, copper and zinc

A method for the simultaneous spectrophotometric determination of cadmium, copper and zinc based on the formation of their complexes with 1,5-bis(di-2-pyridylmethylene)thiocarbonohydrazide is proposed. The absorption curves of these complexes overlap severely in the scanning range 380–480 nm. The analyte concentrations are calculated by a least squares fit of the pure spectra to the mixture spectra. A linear determination range of 0.1–1.7 μg/ml for cadmium, 0.1–1.3 μg/ml for copper and 0.2–1.2 μg/ml for zinc were obtained. The effect of interference was studied. The method has been applied to the determination of these metal ions in various type of materials.     

High-performance liquid chromatography with on-line coupled UV, mass spectrometric and biochemical detection for identification of acetylcholinesterase inhibitors from natural products

A high-performance liquid chromatography (HPLC) method with on-line coupled ultraviolet (UV), mass spectrometry (MS) and biochemical detection for acetylcholinesterase (AChE) inhibitory activity has been developed. By combining the separation power of HPLC, the high selectivity of biochemical detection, and the ability to provide molecular mass and structural information of MS, AChE inhibitors can be rapidly identified. The biochemical detection was based on a colorimetric method using Ellman's reagent. The detection limit of galanthamine, an AChE inhibitor, in the HPLC-biochemical detection is 0.3 nmol. The three detector lines used, i.e., UV, MS and Vis for the biochemical detection were recorded simultaneously and the delay times of the peaks obtained were found to be consistent. This on-line post-column detection technique can be used for the identification of AChE inhibitors in plant extracts and other complex mixtures such as combinatorial libraries.     

Isolation and Absolute Configuration of β,β-Carotene Diepoxide

The 5,6:5′,6′-diepoxy-5,6:5′,6;-tetrahydro-β,β-carotene, isolated from tubers of a white-fleshed variety of sweet potato (Ipomoea batatas LAM .) has been assigned the (5R,6S,5′R,6′S)-chirality on the basis of its HPLC, UV/VIS, and CD data.     

Manganese pentacarbonyl bromide as candidate for a molecular qubit system operated in the infrared regime

Our concept for a quantum computational system is based on qubits encoded in vibrational normal modes of polyatomic molecules. The quantum gates are implemented by shaped femtosecond laser pulses. We adopt this concept to the new species manganese pentacarbonyl bromide [MnBr(CO)5] and show that it is a promising candidate in the mid-infrared (IR) frequency range to connect theory and experiment. As direct reference for the ab initio calculations we evaluated experimentally the absorption bands of MnBr(CO)5 in the mid-IR as well as the related transition dipole moments. The two-dimensional potential-energy surface spanned by the two strongest IR active modes and the dipole vector surfaces are calculated with density-functional theory. The vibrational eigenstates representing the qubit system are determined. Laser pulses are optimized by multitarget optimal control theory to form a set of global quantum gates: NOT, CNOT, Pi, and Hadamard. For all of them simply structured pulses with low pulse energies around 1 microJ could be obtained. Exemplarily for the CNOT gate we investigated the possible transfer to experimental shaping, based on the mask function for pulse shaping in the frequency regime as well as decomposition into a train of subpulses.