Studies of silicophosphate derivatives by 31P-->29Si CP MAS NMR

We show that it is possible to efficiently transfer magnetization from ³¹P to ²⁹Si, using variable amplitude CP MAS experiment. This experiment is demonstrated by using Si₅O(PO₄)₆, the synthesis protocol of which is described. From the obtained results, we show that the experiment allows the spectral edition of ²⁹Si spectra from ³¹P→²⁹Si CP, enabling the studies of derivatives involving Si–O–P linkages, such as phosphosilicate glasses, microporous silicoaluminophosphates (SAPO) and bioactive phosphosilicates.     

A half-moment model for radiative transfer in a 3D gray medium and its reduction to a moment model for hot, opaque sources

We present in this paper a new 3D half-moment model for radiative transfer in a gray medium, called the model, which uses maximum entropy closure. This model is a generalization to 3D of the 1D version recently proposed in (J. Comp. Phys. 180 (2002) 584). The direction space Ω is divided into two pieces, Ω⁺ and Ω^-, in a dynamical way by the plane perpendicular to the total radiative flux, and the half moments are defined from these subspaces. The model closure and the integrations of the radiative transfer equation performed on the moving Ω^± spaces are detailed. 1D planar results, which have motivated the extension of the model of (J. Comp. Phys. 180 (2002) 584) to multi-dimensions, are shown. These results are very good. The model is thereafter derived for 3D spherically symmetric geometry, where the correctness of the non-trivial border terms can be checked. Two 3D spherically symmetric problems are numerically solved in order to show the accuracy of the closure and the role of the border terms. Once again, compared to the solution obtained with a ray tracing solver, results are very good. From the 3D half-moment model, a new moment model, called , is derived for the particular case of a 3D hot and opaque source radiating into a cold medium, for applications such as simulations of stellar atmospheres and fires. Two-dimensional numerical results are presented and compared to those obtained solving the RTE and with other moment models. They demonstrate the very good accuracy of the model, its good convergence properties, and better prediction compared to all other existing moment models in its domain of applicability.     

Density of integers which are discriminants of cyclic fields of odd prime degree

An asymptotic formula is given for the number of integers x which are discriminants of cyclic fields of odd prime degree.Received: 17 February 2004     

Computation of multiple Lie derivatives by algorithmic differentiation

Lie derivatives are often used in nonlinear control and system theory. In general, these Lie derivatives are computed symbolically using computer algebra software. Although this approach is well-suited for small and medium-size problems, it is difficult to apply this technique to very complicated systems. We suggest an alternative method to compute the values of iterated and mixed Lie derivatives by algorithmic differentiation.     

An implicit function approach to constrained optimization with applications to asymptotic expansions

In this article, an unconstrained Taylor series expansion is constructed for scalar-valued functions of vector-valued arguments that are subject to nonlinear equality constraints. The expansion is made possible by first reparameterizing the constrained argument in terms of identified and implicit parameters and then expanding the function solely in terms of the identified parameters. Matrix expressions are given for the derivatives of the function with respect to the identified parameters. The expansion is employed to construct an unconstrained Newton algorithm for optimizing the function subject to constraints.Parameters in statistical models often are estimated by solving statistical estimating equations. It is shown how the unconstrained Newton algorithm can be employed to solve constrained estimating equations. Also, the unconstrained Taylor series is adapted to construct Edgeworth expansions of scalar functions of the constrained estimators. The Edgeworth expansion is illustrated on maximum likelihood estimators in an exploratory factor analysis model in which an oblique rotation is applied after Kaiser row-normalization of the factor loading matrix. A simulation study illustrates the superiority of the two-term Edgeworth approximation compared to the asymptotic normal approximation when sampling from multivariate normal or nonnormal distributions.     

SQSQh: 1H‐detected SQ–SQ experiment for determination of signed silicon–carbon coupling constants

A new variant of SQ–SQ pulse sequence (SQSQh) for relative sign determination and detection of small silicon–carbon couplings over more than one bond is presented. In the SQSQh sequence, proton detection replaces carbon detection used in the original SQ–SQ pulse sequence (SQSQc). The theoretical gain in sensitivity was experimentally tested on two samples (trimethylsiloxyethane, 1, and 1,2,4‐tris(trimethylsiloxy)benzene, 2), the experimentally found gain provided by the SQSQh over the SQSQc method varied between 6 and 8. The method can be applied to linear spin systems, i.e. to systems where the silicon is coupled to the carbon in question and to any hydrogen not necessarily bonded to the carbon. Copyright © 2010 John Wiley & Sons, Ltd.     

Synthesis and Study of Two-Photon Induced Fluorescence of Novel Dyes

Morerecently,thesynthesisofnewdyeswithlargeupconvertedfluorescencebecomesthefocusoftheresearchandhasopenedupamyriadofapplications.Theapplicationsincludetwo-photoninducedlasing',two-photonopticalpowerlimiting',threedimensionalopticaldatastorage',andphotodynamictherapy'.Nevertheless,thistechniquehasneverreacheditsfullpotentialduetothelackofdyeswhichexhibithighupconvertedfluorescentilltensity.ThisrepoFtdescribesthesynthesisandpropertiesoftwo-photoninducedfluorescencedyeswhicharespecificallydesign…     

Class numbers with many prime factors

Here, we construct infinitely many number fields of any given degree d>1 whose class numbers have many prime factors.     

Monotone and Convex C 1 Hermite Interpolants Generated by a Subdivision Scheme

   Abstract. We propose C ¹ Hermite interpolants generated by the general subdivision scheme introduced by Merrien [17] and satisfying monotonicity or convexity constraints. For arbitrary values and slopes of a given function f at the end-points of a bounded interval, which are compatible with the contraints, the given algorithms construct shape-preserving interpolants. Moreover, these algorithms are quite simple and fast as well as adapted to CAGD. We also give error estimates in the case of interpolation of smooth functions.