Latin bitrades,dissections of equilateral triangles,and abelian groups

Let T=(T^*, T^?) be a spherical latin bitrade. With each a=(a₁, a₂, a₃)∈T^* associate a set of linear equations Eq(T, a) of the form b₁+b₂=b₃, where b=(b₁, b₂, b₃) runs through T^*\{a}. Assume a₁=0=a₂ and a₃=1. Then Eq(T,a) has in rational numbers a unique solution $b_{i}=\bar{b}_{i}Let T=(T^*, T^?) be a spherical latin bitrade. With each a=(a₁, a₂, a₃)∈T^* associate a set of linear equations Eq(T, a) of the form b₁+b₂=b₃, where b=(b₁, b₂, b₃) runs through T^*\{a}. Assume a₁=0=a₂ and a₃=1. Then Eq(T,a) has in rational numbers a unique solution $b_{i}=\bar{b}_{i}$. Suppose that $\bar{b}_{i}\not= \bar{c}_{i}$ for all b, c∈T^* such that $\bar{b}_{i}\not= \bar{c}_{i}$ and i∈{1, 2, 3}. We prove that then T^? can be interpreted as a dissection of an equilateral triangle. We also consider group modifications of latin bitrades and show that the methods for generating the dissections can be used for a proof that T^* can be embedded into the operational table of a finite abelian group, for every spherical latin bitrade T. © 2009 Wiley Periodicals, Inc. J Combin Designs 18: 1–24, 2010     

The thermodynamic dissociation constants of methotrexate by the nonlinear regression and factor analysis of multiwavelength spectrophotometric pH-titration data

The mixed dissociation constants of methotrexate — chemically (2S)-2-[(4-{[(2,4-diamino-7,8-dihydropteridin-6-yl)methyl] (methyl)amino}phenyl)formamido]pentanedioic acid (the cas number 59-05-2) at various ionic strengths I of range 0.01–0.4, and at temperatures of 25°C and 37°C, were determined with the use of two different multiwavelength and multivariate treatments of spectral data, SPECFIT32 and SQUAD(84) nonlinear regression analyses and INDICES factor analysis according to a general rule of first, determining the number of components, and then calculating the spectral responses and concentrations of the components. Concurrently, the experimental determination of the thermodynamic dissociation constants was in agreement with its computational prediction of the PALLAS programme based on knowledge of the chemical structures of the drug. The factor analysis in the INDICES programme predicts the correct number of light-absorbing components when the data quality is high and the instrumental error is known. Three thermodynamic dissociation constants were estimated by nonlinear regression of {pK _a , I} data: for methotrexate pK_a1^T= 2.895(13), pK_a2^T= 4.410(14), pK_a3^T= 5.726(15) at 25°C and pK_a1^T= 3.089(15), pK_a2^T= 4.392(12), pK_a3^T= 5.585(11) at 37°C, where the figure in brackets is the standard deviation in last significant digits. The reliability of the dissociation constants of the drug were proven by conducting goodness-of-fit tests of the multiwavelength spectrophotometric pH-titration data.      

Comparison of pressurised fluid and ultrasonic extraction methods for analysis of plant antioxidants and their antioxidant capacity

The analytical method based on the high-performance liquid chromatography coupled with UV detection (HPLC/UV) for determination of selected antioxidants (i.e., esculetin, scopoletin, 7-hydroxycoumarine, rutin, xanthotoxin, 5-methoxypsoralen and quercetin) in plant material was developed. Pressurised fluid extraction (PFE) and ultrasonic extraction (USE) methods for the isolation of these compounds from ten real plant samples were used. Both extraction methods were optimised and compared to each other. For the proposed HPLC/UV method the LOQ values (limit of quantification) in the range from 22.7 (xanthotoxin) to 97.2 ng mL⁻¹ (rutin) were obtained. For all extracts the antioxidant capacity based on the reduction of free 2,2-diphenyl-1-picrylhydrazyl radical (DPPH) was also determined. Results ranged from 82.04 to 94.43% of DPPH radical inhibition for PFE method and from 76.01 to 89.94% in the case of USE method.     

Nonlinear Models of Suspension Bridges: Discussion of the Results

In this paper we present several nonlinear models of suspension bridges; most of them have been introduced by Lazer and McKenna. We discuss some results which were obtained by the authors and other mathematicians for the boundary value problems and initial boundary value problems. Our intention is to point out the character of these results and to show which mathematical methods were used to prove them instead of giving precise proofs and statements.     

Catalytic effect of zinc oxide on the reduction of barium sulfate by methane

Reduction of barium sulfate by methane was investigated in this work. The thermogravimetric method was used to obtain kinetic parameters of the reaction in the temperature range of 900–975 °C at atmospheric pressure. The kinetics of the reaction has been studied both in the absence and presence of zinc oxide as a catalyst. The conversion–time data have been interpreted by using the grain model, and the effect of catalyst on the kinetic parameters has been elucidated. It was found that zinc oxide acted as fairly strong catalyst for the reaction, especially at higher temperatures. At about 975 °C the reaction rate constant was increased more than 7 times by using 2% of zinc oxide. This enhancement in the rate constant is valuable for industries.     

Homoclinic-Doubling Cascades

Cascades of period-doubling bifurcations have attracted much interest from researchers of dynamical systems in the past two decades as they are one of the routes to onset of chaos. In this paper we consider routes to onset of chaos involving homoclinic-doubling bifurcations. We show the existence of cascades of homoclinic-doubling bifurcations which occur persistently in two-parameter families of vector fields on ?³. The cascades are found in an unfolding of a codimension-three homoclinic bifurcation which occur an orbit-flip at resonant eigenvalues. We develop a continuation theory for homoclinic orbits in order to follow homoclinic orbits through infinitely many homoclinic-doubling bifurcations.     

C,N‐chelated triorganotin(IV) diesters of 4‐ketopimelic acid and their fungicidal activity

The set of four triorganotin(IV) diesters of 4‐ketopimelic acid containing {2‐[(CH₃)₂NCH₂]C₆H₄}‐ as a C,N‐chelating ligand was prepared. Their structures were studied by the help of IR, NMR and X‐ray crystallographic techniques in the case of {{2‐[(CH₃)₂NCH₂]C₆H₄}SnPh₂}₂[(OOCCH₂CH₂)₂C?]. All these compounds are monomeric both in solid state and solution with five‐coordinated tin atoms and medium strong intramolecular Sn? N connection. The antimycotical activity of these compound was studied and compared with the triorganotin(IV) derivatives of 4‐ketopimelic acid and antimycotical drugs in clinical use. Copyright © 2008 John Wiley & Sons, Ltd.     

Hydrolysis of C,N‐chelated diorganotin(IV) chlorides and catalysis of transesterification reactions

Diorganotin(IV) dichlorides of formula L^CNRSnCl₂ (where R is nBu or Ph) containing one L^CN chelating ligand were hydrolyzed with aqueous sodium hydroxide in benzene. The composition of the products is strongly dependent on the amount of hydroxide. The partially hydrolyzed compounds of composition (L^CNRSnCl)₂(µ‐O) were isolated as crystalline products. A hydrolysis where more than one molar equivalent of NaOH is employed gave only a mixture of unidentifiable products. The structure of (L^CNPhSnCl)₂(µ‐O) was determined by X‐ray diffraction techniques in the solid state. In solution there was a mixture of diastereoisomers found, where the tin atoms serve as a stereogenic centers. The catalytic activity of starting dichlorides as well as (L^CNPhSnCl)₂(µ‐O) in various transesterification processes was investigated. The activity is very low in the case of starting dichlorides. When two molar equivalents of NaH are added or (L^CNPhSnCl)₂(µ‐O) is employed in the catalytic experiments, the activity is comparable to the literature data. Copyright © 2009 John Wiley & Sons, Ltd.