Nondifferentiable mathematical programming and convex-concave functions

For a convex-concave functionL(x, y), we define the functionf(x) which is obtained by maximizingL with respect toy over a specified set. The minimization problem with objective functionf is considered. We derive necessary conditions of optimality for this problem. Based upon these necessary conditions, we define its dual problem. Furthermore, a duality theorem and a converse duality theorem are obtained. It is made clear that these results are extensions of those derived in studies on a class of nondifferentiable mathematical programming problems.This work was supported by the Japan Society for the Promotion of Sciences.     

Magnetic resonance in a [{Cr(CN)<Subscript>6</Subscript>} {Mn(S)-<Emphasis Type="Italic">pn</Emphasis>H-(H<Subscript>2</Subscript>O)}] · H<Subscript>2</Subscript>O single-crystal molecular ferrimagnet

The variations in the magnetic resonance spectra accompanying the transition from the paramagnetic to ferrimagnetic state in [{Cr(CN)₆} {Mn(S)-pnH-(H₂O) }] · H₂O orthorhombic chiral molecular crystals were studied. The dependence of the EPR linewidth on temperature in the proximity of the transition point T_C = 38 K argues for the two-dimensional character of spin ordering. The spin resonance line was found to undergo exchange narrowing at T > T_C. The ferrimagnetic phase has an easy magnetization axis coinciding with the a crystallographic axis.     

Electronic properties of CrF and CrCl in the X 6Sigma+ state: observation of the halogen hyperfine structure by Fourier transform microwave spectroscopy

The rotational spectra of the CrF and CrCl radicals in the X 6Sigma+ state were observed by employing a Fourier transform microwave spectrometer. The CrF and CrCl radicals were generated by the reaction of laser-ablated Cr with F2 and Cl2, respectively, diluted in Ar. A chromium rod made of chromium powder pasted with epoxy resin was ablated by a Nd:YAG laser. Rotational transitions were measured in the region between 8 and 26 GHz. Several hyperfine constants due to the halogen nuclei were determined by a least-squares analysis. The electronic properties of CrF and CrCl were derived from their hyperfine constants and were compared with those of other 3d transition metal monohalides: TiF, MnF, FeF, CoF, NiF, and FeCl.     

A New Indirect Electroanalytical Method to Monitor the Contamination of Natural Waters with 4‐Nitrophenol Using Multiwall Carbon Nanotubes

The electrochemical detection of the hazardous pollutant 4‐nitrophenol (4‐NP) at low potentials, in order to avoid matrix interferences, is an important research challenge. This study describes the development, electrochemical characterization and utilization of a multiwall carbon nanotube (MWCNT) film electrode for the quantitative determination of 4‐NP in natural water. Electrochemical impedance spectroscopy measurements showed that the modified surface exhibits a decrease of ca. 13 times in the charge transfer resistance when compared with a bare glassy carbon (GC) surface. Voltammetric experiments showed the possibility to oxidize a hydroxylamine layer (produced by the electrochemical reduction of 4‐NP on the GC/MWNCT surface) in a potential region which is approximately 700 mV less positive than that needed to oxidize 4‐NP, thus minimizing the interference of matrix components. The limit of detection for 4‐NP obtained using square‐wave voltammetry (0.12 μmol L^?1) was lower than the value advised by EPA. A natural water sample from a dam located in São Carlos (Brazil) was spiked with 4‐NP and analyzed by the standard addition method using the GC/MWCNT electrode, without any further purification step. The recovery procedure yielded a value of 96.5% for such sample, thus confirming the suitability of the developed method to determine 4‐NP in natural water samples. The electrochemical determination was compared with that obtained by HPLC with UV‐vis detection.     

On Freudenburg's counterexample to the Fourteenth Problem of Hilbert

In this paper we study Freudenburg's counterexample to the fourteenth problem of Hilbert and counterexamples derived from it. We shall construct a generating set of a nonfinitely generated G_a-invariant ring given in Freudenburg's counterexample by making use of an integral sequence which was constructed inductively by Freudenburg. This generating set shall be used in describing a generating set of a nonfinitely generated G_a-invariant ring given in Daigle and Freudenburg's counterexample. Using these generating sets, we shall determine the Hilbert series of the above Freudenburg's and Daigle and Freudenburg's nonfinitely generated G_a-invariant rings, and find that these Hilbert series are rational functions. Then we also show that the Hilbert series of nonfinitely generated invariant rings appearing in the author's linear counterexamples are rational functions.     

Preparation,Isolation and Characterization of all of the Regioisomeric 61, 6N-Bis-O-(Monomethoxytrityl) and-(Dimethoxytrityl) Derivatives of Cyclomalto-Olgosaccharides

Abstract

Regioisomeric 6¹, 6ⁿ-bis-O-(monomethoxytrityl) or 6¹, 6ⁿ-bis-O-(dimethoxytrityl) cyclomaltohexaose, -cyclomaltoheptaose (n = 2-4), and -cyclomaltooctaose derivatives (n = 2-5) were prepared by the reaction of cyclomaltohexaose (1, cG₆, αCD), cyclomaltoheptaose (11, cG₇, βCD) or cyclomaltooctaose (21, cG₈, γCD) and 4-monomethoxytrityl chloride or 4,4′-dimethoxytrityl chloride in pyridine. Products were isolated by HPLC. The regiochemical determination of these positional isomers was done by converting these compounds to the respective 6¹, 6ⁿ-bis-O-(tert-butyldimethylsilyl) derivatives¹ whose structures have been already established.     

Melt rheology of hyperbranched‐polystyrene synthesized with multisite macromonomer

Melt rheological behaviors of hyperbranched‐polystyrene (PS) copolymerized by dendric macromonomer technique are presented. The time–temperature superposition principle was applicable to the hyperbranched‐PS. The branched‐PS showed slightly lower zero‐shear viscosity in comparison with linear PS regardless of a presence of a number of branches expected from the dendric macromonomer technique. Although the influence of use of multimethacryloyl macromonomer in the polymerization process was marginal for linear viscoelastic regime, nonlinear shear and uniaxial elongational flows showed distinct differences between linear and branched‐PS. The strain dependence of the damping function became weak as increase of macromonomer content. The branched‐PS exhibited the growing elongational viscosity function comparing with linear PS. This prominent effect on the elongational flow behavior can be explained by the molecular architecture of the branched‐PS. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2226–2237, 2009