A simple Marquardt algorithm for the nonlinear least-squares problem

A new implementation of the Marquardt method for the nonlinear least-squares problem is presented. The algorithm is very simple but its performance with nine test functions is at least comparable with either Davidon-Fletcher-Powell's method or Moré's adaptive Marquardt method.     

Excess attenuation of millimeter waves at window region due to atmospheric water vapor

The attenuation of 245.52 GHz millimeter wave was measured through a near ground horizontal path in order to study the anomalous water vapor absorption at the window region. The result demonstrates that the attenuation coefficient includes the quadratic dependence on the water vapor density. The quadratic component of the water vapor density in the expression of the attenuation was assumed to arises from the contribution of water dimers alone, then the concentration of water dimers was estimated adopting the published theoretical water dimers absorption coefficient. The obtained concentration was 0.062% of monomers in number when the water vapor density is 7.5 g/m³. This concentration is in agreement with the published result obtained by way of another method.     

α,α‐Dibromotoluene as a monomer for poly (substituted methylene) synthesis: Magnesium‐mediated polycondensation of α,α‐dibromotoluene and magnesium/copper‐mediated copolycondensation of α,α‐dibromotoluene with 1,6‐dibromohexane

α,α‐Dibromotoluene 1 was found to be polymerized by the reaction with excess Mg to give poly(phenylmethylene)s 2 , whose main chains were partially dehydrogenated to carbon–carbon double bonds (C?C). The C?Cs in 2 can be brominated by treatment with Br₂. The polymerization mechanism was presumed to include the formation of Grignard reagents of various species with benzylic C? Br bonds and the nucleophilic attacks of the Grignard reagents to various compounds with benzylic C? Br bonds. Copolymerization of 1 with dichlorodimethylsilane successfully proceeded. Mg/Cu‐mediated copolycondensation of 1 with 1,6‐dibromohexane proceeded to give polymers that have similar compositions to those of random copolymers of ethylene and styrene. © 2006Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 5661–5671, 2006     

Selectivity enhancement for trans-2-(2,3-anthracenedicarboximido)-cyclohexane-derived diastereomers in HPLC by using an ordered organic stationary phase.

2-(2,3-anthracenedicarboximido)cyclohexane derivatives (AC) have been known as the evolutionary diastereomerizing reagents for enantiomer discrimination in HPLC with ODS. However, a substantial separation of diastereomers can be observed only at lower temperatures, such as -40 degrees C. Therefore, in this work, poly(octadecyl acrylate)-grafted silica, ODAn was applied as an alternative stationary phase to ODS for the separation of AC-derived diastereomers. As a result, complete separation was achieved even under the conventional condition: for example, methanol as the mobile phase and 0 degrees C as the column temperature. An investigation on the temperature dependency of the selectivity demonstrated that ODAn shows a remarkable increase in selectivity at temperatures below 30 degrees C, which almost agreed with the peak-top temperature of the endothermic peak in a DSC thermogram for ODA35 immersed in a mobile phase. The better separation would be derived from a highly ordered structure of ODAn and a carbonyl-pi interaction with AC-derived diastereomers.     

Radical copolymerization of alkyl 2‐norbornene‐2‐carboxylate with alkyl acrylates: Facile incorporation of norbornane framework into poly(alkyl acrylate)s

Radical copolymerization of alkyl 2‐norbornene‐2‐carboxylates (alkyl = Me 1a , nBu 1b ) with alkyl acrylates (alkyl = ethyl, methyl, and n‐butyl) was investigated. Copolymerization of 1a,b with the alkyl acrylates initiated by 1,1′‐azobis (cyclohexane‐1‐carbonitrile) at 85 °C proceeded to give random copolymers, although the homopolymerization of 1a,b did not proceed efficiently under the same conditions. Typically, bulk copolymerization of 1a with ethyl acrylate in a feed ratio of 1:3 ([ 1a ]:[EA]) afforded a copolymer with M_n = 33,300 containing 19.4 mol % of 1a unit in the composition. An increase of T_g derived from the incorporation of the rigid norbornane framework was observed, although the extent of the temperature rise was rather moderate. The ternary radical copolymerization of 1a,b /alkyl acrylate/N‐phenylmaleimide proceeded to give copolymers with the three repeating units in the main chain. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4597–4605, 2007     

XPS study on valence band structures of transition-metal trisulfides,TiS3, NbS3, and TaS3

Transition-metal trisulfides, TiS₃, NbS₃, and TaS₃, with a quasi-one-dimensional structure are investigated by X-ray photoelectron spectroscopic (XPS) measurements to obtain information on the valence band structures. The band structures at the Fermi level of these compounds correspond well to their transport properties. A shoulder is observed at the top of the valence band in NbS₃ and TaS₃, suggesting that this band is made up of the metal d_z² electrons. The d_z² band is occupied in NbS₃ and TaS₂ and empty in TiS₃. The characteristic features at the top of the valence band in NbS₃ imply the occurrence of d_z² band separation, which leads to a semiconducting nature.     

A Novel Affinity Capillary Electrophoresis for the Detection of Gene Mutation Using Immobilized Oligonucleotides-Polyacrylamide Conjugate

It has been found that small mutations of certain genes are the definitive origin of many heritable disorders and cancers with striking development of recent molecular biology. Such new findings have taken close-up of the importance of gene mutation assays based on the difference of DNA base sequences in diagnostic or medical field Capillary electrophoresis can be a good candidate for an ideal method on such gene analysis, because the methods can be performed with trace amount of samples, high resolution and shorter running time. We have established an effect of oligonucleotide, which was introduced onto capillary inner surface, on the recognition of an overall sequence of sample DNA fragments as an affinity ligand.     

Chromatographic resolution of dipeptide enantiomers and diastereomers on chiral stationary phases from poly(L-leucine) or poly(L-phenylalanine)

Two types of chiral stationary phase, polymer-bonded and non-bonded, containing poly(L-leucine) and poly(L-phenylalanine) were prepared. These stationary phases gave higher enantioselectivity for the optical resolution of various derivatives of leucylphenylalanine methyl ester by liquid chromatography than did poly(L-alanine) and poly(L-glutamate).     

Enhancement of molecular-shape selectivity in high-performance liquid chromatography through multi-anchoring of comb-shaped polymer on silica

Poly(octadecylacrylate) having plural trimethoxysilyl groups in the side chain (co-ODA(n)) was newly synthesized and immobilized onto silica through these groups. The liquid chromatographic behavior of silica-supported co-ODA(n) (Sil-co-ODA(n)) was investigated and compared with that of Sil-ODA(n), in which poly(octadecylacrylate) was immobilized through a terminal trimethoxy group at one side of the polymer main chain. Sil-co-ODA(n) showed higher selectivity for molecular shape, especially molecular planarity of PAHs than Sil-ODA(n).