The coherence of an individual quantum state can be meaningfully discussed only when referring to a preferred basis. This arbitrariness can, however, lifted considering sets states. Here we introduce the concept set for characterizing systems in basis-independent way. We construct measures quantifying states as well measurements. These feature operational meaning terms discrimination games and ...

We show that there exists a bounded subset of $\mathbb{R}$ such no system exponentials can be Riesz basis for the corresponding Hilbert space. An additional result gives lower bound constant any putative two dimensional disk.

Intermolecular potential energy surface (IPS) for protein — protein has been examined using RHF, DFT-B3LYPand MP2 levels of theory with 6-31G, 6-31G* basis sets. A number of basis sets were used in order to evaluatethe basis set effects, at all three levels of theory, basis sets has significant effects on the calculated potentialenergy curves (including position, depth and width of the potentia...

Four new [NiH2L](ClO4)2 (1), [CuH2L](ClO4)2 (2), [MnH2L](ClO4)2 (3) and [CdH2L](ClO4)2 (4), complexes were prepared by the reaction of a new Schiff base ligand and Cu(II), Ni(II), Mn (II) and Zn (II) metal ions in equemolar ratios. The ligand, H2L was synthesized by reaction of 1, 4- bis (2- formylphenyl) piperazine and ethanol amine and characterized with IR and 1H,13C NMR spectroscopy. All co...

A method of evaluating matrix elements between polynomial basis functions is proposed involving the explicit expansion of the operator in terms of the polynomial. The method is shown to have several advantages over the direct evaluation of these matrix elements by Gaussian quadrature, including savings of up to a factor of 6N for an N-dimensional integral. Application to the calculation of poly...

2D curve representations usually take algebraic forms in ways not related to visual perception. This poses great difficulties in connecting curve representation with object recognition where information computed from raw images must be manipulated in a perceptually meaningful way and compared to the representation. In this paper we show that 2D curves can be represented compactly by imposing sh...

Three methods for improving the performance of (gaussian) radial basis function (RBF) networks were tested on the NETtaik task. In RBF, a new example is classified by computing its Euclidean distance to a set of centers chosen by unsupervised methods. The application of supervised learning to learn a non-Euclidean distance metric was found to reduce the error rate of RBF networks, while supervi...

Abstract: The performances of Normalised RBF (NRBF) nets and standard RBF nets are compared in simple classification and mapping problems. In Normalized RBF networks, the traditional roles of weights and activities in the hidden layer are switched. Hidden nodes perform a function similar to a Voronoi tessellation of the input space, and the output weights become the network's output over the pa...