A modified steepest descent method with applications to maximizing likelihood functions

In maximizing a non-linear function G(), it is well known that the steepest descent method has a slow convergence rate. Here we propose a systematic procedure to obtain a 1–1 transformation on the variables , so that in the space of the transformed variables, the steepest descent method produces the solution faster. The final solution in the original space is obtained by taking the inverse transformation. We apply the procedure in maximizing the likelihood functions of some generalized distributions which are widely used in modeling count data. It was shown that for these distributions, the steepest descent method via transformations produced the solutions very fast. It is also observed that the proposed procedure can be used to expedite the convergence rate of the first derivative based algorithms, such as Polak-Ribiere, Fletcher and Reeves conjugate gradient methods as well.     

PHYTOCHROME MEDIATED CAROTENOID SYNTHESIS IN THE FUNGUS VERTICILLIUM AGARZCZNUM

Abstract— Ten minutes of red irradiation (R) increased carotenogenesis in Verticillium agoricinum and this effect was reversed by 10min of far-red (FR) irradiation indicating that phytochrome is involved. A far-red minus red difference spectrum of a crude extract shows a peak at 670 nm and a dip at 750 nm wavelength, values slightly larger than higher plant phytochrome. indicating the presence of phytochrome.     

The dangers of using KBr,KI and CaI2 as mulling agents during the preparation of infrared discs of complexes

Tribochemical reactions of KBr, KI and CaI₂ with [Cu(L)Cl₂(EtOH)_3/2(H₂O)]1/2H₂O (L = formylhydrazine) give novel Cu^I and Cu^II complexes, which have been characterized by elemental analyses, spectral (i.r., u.v.–vis., ¹H-n.m.r.) and magnetic measurements. The i.r. spectra indicate that (L) behaves in a monodentate manner, coordinating via the azomethine nitrogen (C-N) group in the Cu^II complexes, but behaving as a bidentate ligand, via the carbonyl oxygen and NH₂ groups in the Cu^I complexes. KI and CaI₂ react with [Cu(L)Cl₂(EtOH)_3/2(H₂O)]-1/2H₂O in the solid state, accompanied by a colour change, substitution of the chloride by iodide ions, and reduction of Cu^II to Cu^I to give complexes with formulae [Cu(L)I(EtOH)_1/2] and [Cu_1.7(L)I_1.7(EtOH)_1/2]. On the other hand, the tribochemical reaction of KBr with [Cu(L)Cl₂(EtOH)_3/2(H₂O)]1/2H₂O is accompanied by a colour change; substitution of the chloride by bromide ions, but without reduction of Cu^II and yields a complex of formula [Cu(L)₂Br₂(EtOH)(H₂O)]1/2EtOH. The spectral and magnetic results suggest a distorted octahedral geometry for the Cu^II complexes while a tetrahedral geometry around the Cu^I ion. The non-stoichiometric structure of [Cu_1.7(L)I_1.7(EtOH)_1/2] is discussed.     

New stereoselective preparation of (Z)-3-perfluoroalkyl-3-magnesiated enoates by an iodine-magnesium exchange reaction

(Z)-Ethyl-3-perfluoroalkyl-3-magnesiated crotonates were prepared from (Z)-ethyl-3-perfluoroalkyl-3-iodo enoates by iodine-magnesium exchange reaction with isopropylmagnesium bromide in THF at -78 degrees C. These new reagents reacted with a range of electrophiles, leading to polyfunctional products bearing a perfluoroalkyl group.     

Indirect atomic absorption and atomic emission spectrometric determination of antazoline,hydralazine and amiloride hydrochlorides and quinine sulphate

Ion-association complexes of antazoline HCl [I], hydralazine HCl [II], amiloride HCl [III] and quinine sulphate [IV] with [Co(SCN)₄]^2– and [Co(NO₂)₆]^3– were precipitated and the excess unreacted cobalt complex was determined. A new method using atomic emission and atomic absorption spectrometry for the determination of the above drugs in pure solutions and pharmaceutical preparations is given. The drugs can be determined in the ranges 0.3–3.0, 0.19–1.96, 0.3–3.0, and 0.78–7.82 mg/25 ml solutions of I, II, III, and IV, respectively, with mean relative standard deviations of 0.65–2.03 % and recovery values of 95.76–101.2% indicating high precision and accuracy.     

Absorption spectra of 2-styryl-4-phenyl-thiazole ethiodides in organic solvents of varying polarities and determination of the formation constant of the charge transfer complex formed

The electronic absorption spectra of some 2-styryl-4-phenyl-thiazole ethiodides are studied in organic solvents of different polarities. The shorter wavelength band appearing in the visible region is assigned to an intramolecular charge transfer (CT)-transition originating from the phenyl moiety to the positively charged hetero ring, while the longer wavelength one is due to an intermolecular CT-transition from the iodide ion to the 2-styryl-4-phenyl-thiazolinium cation. These assignments are based on the nature of the aldehydic residue and effects of solvent, concentration, and temperature on both the position and absorptivity of the CT complex-band. It is concluded that the CT complex formed will be highly solvated inDMF, DMSO, ethanol and methanol relative to in CHCl₃, dioxane and acetone. The formation constant of the CT complex in solutions of different polarities is determined at different temperatures. Furthermore, the thermodynamic parameters H ^o, G ^o and S ^o for complex formation are calculated and discussed.

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Absorptionsspektren von 2-Styryl-4-phenyl-thiazol-ethiodiden in verschiedenen Lösungsmitteln und Bestimmung der Bildungskonstanten der Charge-Transfer-Komplexe

Zusammenfassung Die Elektronenanregungsspektren einiger substituierter 2-Styryl-4-phenyl-thiazol-ethiodide wurden in einigen Lösungsmitteln unterschiedlicher Polarität untersucht. Die Absorption bei kürzerer Wellenlänge wird einem intramolekularen Charge-Transfer (CT)-Übergang zugeordnet, die langwellige Bande einem intermolekularen CT-Übergang (Jodid—organ. Kation). Die Diskussion erfolgt basierend auf Substitutions-, Lösungsmittel-, Konzentrations-, und Temperatur-Effekten. Die Komplexbildungskonstanten und die thermodynamischen Parameter H ^o, G ^o und S ^o werden angegeben.

     

Enantioseparations by capillary electro-chromatography: differences exhibited by normal- and reversed-phase versions of polysaccharide stationary phases

The influence of using normal-phase and reversed-phase versions of four commercial polysaccharide stationary phases on chiral separations was investigated with capillary electrochromatography (CEC). Both versions of the stationary phases, Chiralcel OD, OJ, and Chiralpak AD, AS were tested for the separation of two basic, two acidic, a bifunctional, and a neutral compound. Different background electrolytes were used, two at low pH for the acid, bifunctional and neutral substances, and three at high pH for the basic, bifunctional and neutral ones. This setup allowed evaluating differences between both stationary-phase versions and between mobile-phase compositions on a chiral separation. Duplicate CEC columns of each stationary phase were in-house prepared and tested, giving information about the intercolumn reproducibility. In general, reversed-phase versions of the current commercial polysaccharide stationary phases are found to be best for reversed-phase CEC, even though at high pH no significant differences were seen between both versions. Most differences were observed at low pH. For acidic compounds, it was seen that an ammonium formate electrolyte performed best, which is also an excellent electrolyte if coupling with mass spectrometry is desired. For basic, bifunctional and neutral compounds, no significant differences between the three tested electrolytes were observed at high pH. Here, a phosphate buffer is preferred as electrolyte because of its buffering capacities. However, if coupling to mass spectrometry is wanted, the more volatile ammonium bicarbonate electrolyte can be used as an alternative.     

Divalent transition metal ion mixed ligand complexes with aliphatic dicarboxylic acids and imidazoles

Summary Mixed ligand metal complexes of Co^II, Ni^II and Cu^II with dicarboxylic aliphatic acids, H₂L (succinic, malic and tartaric) as primary ligands and with imidazoles, L (imidazole and 2-methylimidazole) as secondary ligands were prepared and characterized. MLL₂ and ML₄ molecular formulae were suggested for these complexes were Formation constants of the different complexes were determined pH-metrically at T = 25 ± 0.1°C and = 0.1 mol dm^–3 (NaClO₄). The stability of the mixed ligand complexes increased as the effective basicity of the dicarboxylic aliphatic acid anion increased, namely, tartarate < malate < succinate acid.     

Bis-(tetraethylammonium)[tetraazidocuprate(II)] and catena-di-μ-1,1-azido-[di-μ-1,1-azido-bis-(2,4-dimethylpyridine)dicopper(II)]

Two new copper(II) azido complexes, namely bis-(tetraethylammonium)[tetraazidocuprate(II)] (1) and catena-di--1,1-azido-[di--1,1-azido-bis-(2,4-dimethylpyridine)dicopper(II)] (2), have been prepared and characterized by spectroscopic and crystallographic methods. Complex (1) consists of isolated NEt⁺ ₄ cations and [Cu(N₃)₄]^2– anions. The site symmetry around the copper atom in the anion is 4/m. Complex (2) features a 1 D chain structure, five coordinated square pyramidal copper(II) atoms with both azides functioning as -1,1-bridges. The i.r. spectra reveal that both complexes contain asymmetric azido ligands. The solid and solution electronic spectra of (1) and (2) show very strong absorption bands in the visible region associated with N^– ₃ Cu^II charge-transfer transitions. The e.p.r. spectra of powder samples and solutions at room temperature were recorded and discussed.