Algorithms for generalized fractional programming

A generalized fractional programming problem is specified as a nonlinear program where a nonlinear function defined as the maximum over several ratios of functions is to be minimized on a feasible domain of ⁿ . The purpose of this paper is to outline basic approaches and basic types of algorithms available to deal with this problem and to review their convergence analysis. The conclusion includes results and comments on the numerical efficiency of these algorithms.This research was supported by NSERC (grant A8312) and Cooperation franco-québécoise (projet 20-02-13). Paper presented at Workshop on Mathematical Programming Catholic University of Rio de Janeiro, Brazil, October 10–14, 1988.     

Computing the real roots of a polynomial by the exclusion algorithm

We describe a new algorithm for localizing the real roots of a polynomialP(x). This algorithm determines intervals on whichP(x) does not possess any root. The remainder set contains the real roots ofP(x) and can be arbitrarily small.     

H2-broadening coefficients in the ν3 band of CH3D at low temperatures

Using a diode-laser spectrometer, we have measured H₂-broadening coefficients of CH₃D at low temperatures (153.5, 183.5, and 223.5 K) for four lines in the ν₃ band. The collisional widths are obtained by fitting each absorption line with three lineshape models: the Voigt, Rautian, and Galatry profiles. The broadening coefficients are also calculated on the basis of a semiclassical model of interacting linear molecules by considering an atom-atom Lennard-Jones potential in addition to electrostatic contributions. By comparing the broadening coefficients at room and low temperatures the temperature dependence of these broadenings has been determined both experimentally and theoretically.     

Spectral Measures Associated with the Factorization of the Lebesgue Measure on a Set via Convolution

Let \(Q\) be a fundamental domain of some full-rank lattice in \({\mathbb {R}}^d\) and let \(\mu \) and \(\nu \) be two positive Borel measures on \({\mathbb {R}}^d\) such that the convolution \(\mu *\nu \) is a multiple of \(\chi _Q\) . We consider the problem as to whether or not both measures must be spectral (i.e. each of their respective associated \(L^2\) space admits an orthogonal basis of exponentials) and we show that this is the case when \(Q = [0,1]^d\) . This theorem yields a large class of examples of spectral measures which are either absolutely continuous, singularly continuous or purely discrete spectral measures. In addition, we propose a generalized Fuglede’s Conjecture for spectral measures on \({\mathbb {R}}^1\) and we show that it implies the classical Fuglede’s Conjecture on \({\mathbb {R}}^1\) .     

Tight Gabor Frames Associated with Non-separable Lattices and the Hyperbolic Secant

We consider Gabor systems generated by a window given by the hyperbolic secant function. We show that such a system forms a Parseval frame for L ²(?) when the translations and modulations of the window are associated with certain non-separable lattices in ?² which we explicitly describe. We also study the more general problem of characterizing the positive Borel measures μ on ?²ⁿ with the property that the short-time Fourier transform defines an isometric embedding from L ²(? ⁿ ) to L _μ ² (?²ⁿ ) when the window belongs to the Schwartz class and, in particular, we characterize the extreme points of this set. In the case where the window is the hyperbolic secant function, we consider the situation where the measure is discrete with constant weights and supported on a non-separable lattice yielding a Parseval frame. We provide arithmetic conditions on the parameters defining the lattice characterizing when the associated measure is an extreme point.     

Characterization Theorem for Best Polynomial Spline Approximation with Free Knots,Variable Degree and Fixed Tails

In this paper, we derive a necessary condition for a best approximation by piecewise polynomial functions of varying degree from one interval to another. Based on these results, we obtain a characterization theorem for the polynomial splines with fixed tails, that is the value of the spline is fixed in one or more knots (external or internal). We apply nonsmooth nonconvex analysis to obtain this result, which is also a necessary and sufficient condition for inf-stationarity in the sense of Demyanov–Rubinov. This paper is an extension of a paper where similar conditions were obtained for free tails splines. The main results of this paper are essential for the development of a Remez-type algorithm for free knot spline approximation.     

Dissolution of Cellulose and Lignin with Biobased Ionic Liquids

Journal of Solution Chemistry - Choline-based ionic liquids, involving various alkyl chains lengths and carboxylates derived from biobased acids, have been synthetized with high yields through a...     

CuLn complexes with a single μ-oximato bridge

Two original dinuclear (LnYb, 3 and LnEr, 4) and one trinuclear Cu^IILn^IIICu^II (LnGd, 5) complexes derived from a polydentate non symmetrical Schiff base ligand H₂L have been prepared. The ligand possesses two functions (phenol and oxime) able to coordinate the Ln ions, but structural studies (X-ray diffraction and powder X-ray diffraction) show that the Cu^II and Ln^III ions are only bridged by the oximato (NO) pair. The missing phenoxo bridge is replaced by a surprising pseudo-bridge involving one oxygen atom of the nitrato anion linked to the Cu and Ln ions according to a η²: η¹: μ mode. Although this latter contact has no role from the magnetic point of view, it introduces a large deformation of the unique bridging network. The CuYb complex 3 and the trinuclear CuGdCu complex 5 present antiferromagnetic interactions, with a J_CuGd interaction equal to ?1.25 cm^?1 in 5. The genuine single bridge can be considered as responsible for the antiferromagnetic character of the interaction.     

Sterically congested uranyl complexes with seven-coordination of the UO2 unit: the peculiar ligation mode of nitrate in [UO2(NO3)2(Rbtp)] complexes

Addition of 1 or 2 molar equiv of Rbtp [Rbtp = 2,6-bis(5,6-dialkyl-1,2,4-triazin-3-yl)pyridine; R = Me, Pr ( n )] to UO 2(OTf) 2 in anhydrous acetonitrile gave the neutral compounds [UO 2(OTf) 2(Rbtp)] [R = Me ( 1), ( n )Pr ( 2)] and the cationic complexes [UO 2(Rbtp) 2][OTf] 2 [R = Me ( 3), Pr ( n ) ( 4)], respectively. No equilibrium between the mono and bis(Rbtp) complexes or between [UO 2(Rbtp) 2][OTf] 2 and free Rbtp in acetonitrile was detected by NMR spectroscopy. The crystal structures of 1 and 3 resemble those of their terpyridine analogues, and 3 is another example of a uranyl complex with the uranium atom in the unusual rhombohedral environment. In the presence of 1 molar equiv of Rbtp in acetonitrile, UO 2(NO 3) 2 was in equilibrium with [UO 2(NO 3) 2(Rbtp)] and the formation of the bis adduct was not observed, even with an excess of Rbtp. The X-ray crystal structures of [UO 2(NO 3) 2(Rbtp)] [R = Me ( 5), Pr ( n ) ( 6)] reveal a particular coordination geometry with seven coordinating atoms around the UO 2 fragment. The large steric crowding in the equatorial girdle forces the bidentate nitrate ligands to be almost perpendicular to the mean equatorial plane, inducing bending of the UO 2 fragment. The dinuclear oxo compound [U(CyMe 4btbp) 2(mu-O)UO 2(NO 3) 3][OTf] ( 7), which was obtained fortuitously from a 1:2:1 mixture of U(OTf) 4, CyMe 4btbp, and UO 2(NO 3) 2 [CyMe 4btbp = 6,6'-bis-(3,3,6,6-tetramethyl-cyclohexane-1,2,4-triazin-3-yl)-2,2'-bipyridine] is a very rare example of a mixed valence complex involving covalently bound U (IV) and U (VI) ions; its crystal structure also exhibits a seven coordinate uranyl moiety, with one bidentate nitrate group almost parallel to the UO 2 fragment. The distinct structural features of [UO 2(kappa (2)-NO 3) 2(Mebtp)], with its high coordination number and a noticeable bending of the UO 2 fragment, and of [UO 2(kappa (2)-NO 3)(kappa (1)-NO 3)(terpy)], which displays a classical geometry, were analyzed by Density Functional Theory, considering the bonding energy components and the molecular orbitals involved in the interaction between the uranyl, nitrate, and Mebtp or terpy moieties. The unusual geometry of the Mebtp derivative with the seven coordinating atoms around the UO 2 fragment was found very stable. In both the Mebtp and terpy complexes, the origin of the interaction appears to be primarily steric (Pauli repulsion and electrostatic); this term represents 62-63% of the total bonding energy while the orbital term contributes to about 37-38%.     

The determination of organochlorine compounds and petroleum hydrocarbons in a seaweed sample: results of a world-wide intercomparison exercise

A seaweed sample (Fucus sp.) was prepared, homogenised and distributed to laboratories worldwide as the IAEA-140 intercomparison material for the analysis of organochlorine compounds and petroleum hydrocarbons. A total of 80 laboratories from 51 countries reported results for this sample. The data sets reported by laboratories were evaluated statistically and the mean concentration values could be computed with 95% confidence limits for a large number of analytes. The accuracy of the analytical performance of each laboratory has been introduced by using Z-scores. The spread of results reported generally indicates that the accurate determination of many persistent organic pollutants, such as hexachlorobenzene, lindane, Aroclors or fluoranthene, is still difficult for many laboratories. The final results of this intercomparison exercise enable individual participants to assess their performance and, where necessary, to introduce appropriate modifications in their analytical procedures. Furthermore, as a series of statistical criteria was fulfilled for a number of compounds, the sample IAEA-140 can now be used as a reference material for quality control in the determination of chlorinated compounds and petroleum hydrocarbons in environmental samples.