Completeness of the Bethe Ansatz on Weyl Alcoves

We prove the completeness of the Bethe ansatz eigenfunctions of the Laplacian on a Weyl alcove with repulsive boundary condition at the walls. For the root system of type A this amounts to the result of Dorlas of the completeness of the Bethe ansatz eigenfunctions of the quantum Bose gas on the circle with repulsive delta-function interaction.     

Fractional wavelet analysis for the simultaneous quantitative analysis of lacidipine and its photodegradation product by continuous wavelet transform and multilinear regression calibration

Fractional wavelet transform (FWT) was applied to the original absorption spectra of lacidipine (LAC) and its photodegradation product (LACD), and the resulting FWT spectra were processed by continuous wavelet transform (CWT) and multilinear regression calibration (MLRC) for the simultaneous quantitative analysis of both products in their binary mixtures. These methods do not require any chemical separation step and chemical complex reaction to obtain a detectable signal for the degradation product. By using the Mexican hat function, 2 calibration functions for LAC and LACD were obtained by measuring the CWT transformed signals at 416.1 nm for LAC and 414.6 nm for LACD, after FWT processing of the original absorption spectra. The calibration graphs were linear in the concentration range of 5.08-40.64 microg/mL for LAC and 0.51-8.16 microg/mL for LACD. The limit of detection and the limit of quantitation were found to be 0.289 and 0.956 microg/mL for LAC and 0.036 and 0.118 microg/mL for LACD, respectively. For comparison, the MLRC algorithm was applied to the linear regression functions for the individual drug and its photoproduct. In this approach, a set of linear regression functions was obtained from the relationship between concentrations and FWT signals in the wavelength range 411.0-412.4 nm. Both methods were applied to the quantitative evaluation of LAC and LACD in laboratory and pharmaceutical samples, and produced very satisfactory results.     

A novel benzothiazole based azocalix[4]arene as a highly selective chromogenic chemosensor for Hg ion: A rapid test application in aqueous environment

A novel calix[4]arene derivative containing benzothiazole azo groups at the upper rim was synthesized as chromogenic chemosensor, and its binding and sensing properties with heavy metal ions (Pb²⁺, Hg²⁺, Ni²⁺, Cd²⁺, Cu²⁺, Zn²⁺, Co²⁺, Fe²⁺, Mn²⁺, Cr³⁺, Ag⁺) were investigated by UV-vis spectroscopy and voltammetric techniques. The results of spectroscopic and voltammetric experiments showed that the chromogenic chemosensor has high selectivity towards Hg²⁺ ion over the other heavy metal ions. Moreover, it was shown that the interaction between Hg²⁺ and the chromogenic chemosensor occurs by means of the benzothiazole azo groups at the upper rim by using differential pulse voltammetry. The stoichiometric ratio and the association constant were determined as 1:1 and (6.1 ± 0.3) × 10⁵ L mol⁻¹ for the complex between Hg²⁺ and the ionophore. Furthermore, we prepared a rapid test kit for early detection of Hg²⁺ in aqueous environment in the concentration range of 1 × 10⁻⁴ to 1 × 10⁻² M.     

On some qualitative behaviors of certain differential equations of fourth order with multiple retardations

In this paper, we give sufficient conditions to guarantee the asymptotic stability and boundedness of solutions to a kind of fourth-order functional differential equations with multiple retardations. By using the Lyapunov-Krasovskii functional approach, we establish two new results on the stability and boundedness of solutions, which include and improve some related results in the literature     

Determination of Naphthazarin Derivatives in 16 Alkanna Species by RP-LC Using UV and MS for Detection

As part of our ongoing studies, a new and validated method for analysis of isohexenyl-naphthazarines in Turkish Alkanna species was developed. By using reversed phase material (Synergi MAX RP) it was possible to determine four known isohexenylnaphthazarin-derivatives, namely alkannin, acetylalkannin, deoxyalkannin, and β,β-dimethylacrylalkannin within 25 min in n-hexane extracts of the roots. The quantification of these compounds in 16 Anatolian Alkanna species is described for the first time. In order to assure peak identity LC-MS experiments were performed. Quantitative results revealed that the most dominant compound in the extracts was β,β-dimethylacrylalkannin.     

On locally closedness and continuity

The aim of this paper is to introduce new classes of sets called δ-semi-generalized closed sets, locally δ-semi-generalized closed, lδsgc^*-sets, lδsgc^**-sets. Also, we introduce several forms of LδSGC-continuous functions. We discuss their properties and several examples are provided to illustrate the behaviour of these new types of sets and functions.     

Nonlinear experimental dye-doped nematic liquid crystal optical transmission spectra estimated by neural network empirical physical formulas

In this paper, two complementary objectives related to optical transmission spectra of nematic liquid crystals (NLCs) were achieved. First, at room temperature, for both pure and dye (DR9) doped E7 NLCs, the 10-250 W halogen lamp transmission spectra (wavelength 400-1200 nm) were measured at various bias voltages. Second, because the measured spectra were inherently highly nonlinear, it was difficult to construct explicit empirical physical formulas (EPFs) to employ as transmittance functions. To avoid this difficulty, layered feedforward neural networks (LFNNs) were used to construct explicit EPFs for these theoretically unknown nonlinear NLC transmittance functions. As we theoretically showed in a previous work, a LFNN, as an excellent nonlinear function approximator, is highly relevant to EPF construction. The LFNN-EPFs efficiently and consistently estimated both the measured and yet-to-be-measured nonlinear transmittance response values. The experimentally obtained doping ratio dependencies and applied bias voltage responses of transmittance were also confirmed by LFFN-EPFs. This clearly indicates that physical laws embedded in the physical data can be faithfully extracted by the suitable LFNNs. The extraordinary success achieved with LFNN here suggests two potential applications. First, although not attempted here, these LFNN-EPFs, by such mathematical operations as derivation, integration, minimization etc., can be used to obtain further transmittance related functions of NLCs. Second, for a given NLC response function, whose theoretical nonlinear functional form is yet unknown, a suitable experimental data based LFNN-EPF can be constructed to predict the yet-to-be-measured values.     

Mathematical algorithms applied to the multi-linear regression functions for the multicomponent determination of pharmaceutical dosage form containing three-component mixtures

In the presence of closely overlapping spectra, the quantitative multiresolution of ternary mixtures of three active compounds paracetamol (PAR), caffeine (CAF) and acetylsalycilic acid (ASP) in tablets, without using pretreatment such as separation step and graphical procedure of spectra was accomplished by the multivariate spectral calibration models, tri-linear regression calibration (TLRC), multi-linear regression calibration (MLRC) and Cramer's rule solution (CRS) of three linear equation functions in the matrix form. In the first two models, TLRC and MLRC are based on the use of the linear regression functions at selected wavelength sets in the spectral region of 210-300 nm. In the case of CRS model, A1(1) (1%, 1 cm) were used to obtain three linear equation functions and this linear equation system was resolved by the Cramer's rule for the prediction of PAR, CAF and ASP in samples. In the TLRC and CRS models, the selection of the appropriate wavelength set was performed by the Kaiser's technique. The algorithms of these mathematical calibration models were briefly described. The validation of TLRC, MLRC and CRS models was carried out by analyzing various synthetic ternary mixtures and by using the standard addition technique. These three calibration approaches were applied to the analysis of the real pharmaceutical tablets containing PAR, CAF and ASP. The obtained results were statistically compared with each other by using experimental and statistical tests. In the comparison of TLRC and MLRC models to the classical approach, CRS technique, the successful assay results were observed for the quantitative multiresolution of ternary mixture of the subject active compounds.     

Determination of trace cadmium in waters by flame atomic absorption spectrophotometry after preconcentration with 1-nitroso-2-naphthol-3,6-disulfonic acid on Ambersorb 572

A procedure for the determination of trace amount of cadmium after adsorption of its 1-nitroso-2-naphthol-3,6-disulfonic acid chelate on Ambersorb 572 has been proposed. This chelate is adsorbed on the adsorbent in the pH range 3-8 from large volumes of aqueous solution of water samples with a preconcentration factor of 200. After being sorbed, cadmium was eluted by 5 mL of 2.0 mol L(-1) nitric acid solution and determined directly by flame atomic absorption spectrophotometery (FAAS). The detection limit (3sigma) of cadmium was 0.32 microg L(-1). The precision of the proposed procedure, calculated as the relative standard deviation of recovery in sample solution (100 mL) containing 5 microg of cadmium was satisfactory (1.9%). The adsorption of cadmium onto adsorbent can formally be described by a Langmuir equation with a maximum adsorption capacity of 19.6 mg g(-1) and a binding constant of 6.5 x 10(-3) L mg(-1). Various parameters, such as the effect of pH and the interference of a number of metal ions on the determination of cadmium, have been studied in detail to optimize the conditions for the preconcentration and determination of cadmium in water samples. This procedure was applied to the determination of cadmium in tap and river water samples.     

Spectrophotometric multicomponent determination of sunset yellow, tartrazine and allura red in soft drink powder by double divisor-ratio spectra derivative, inverse least-squares and principal component regression methods

Double divisor-ratio spectra derivative (graphical method), classical least-squares and principal component regression (two numerical methods) methods were developed for the spectrophotometric multicomponent analysis of soft drink powders and synthetic mixtures containing three colorants without any chemical separation. The graphical method is based on the use of derivative signals of the ratio spectra using double divisor. In this method, the linear determination ranges were 2-8 mug ml(-1) sunset yellow, 4-18 mug ml(-1) tartrazine and 2-8 mug ml(-1) allura red in 0.1 M HCl. In the numerical methods, a training set was randomly prepared by using 18 samples containing between 0 and 8 mug ml(-1) of sunset yellow, 0-18 mug ml(-1) of tartrazine and 0-8 mug ml(-1) of allura red. The chemometric calibrations were calculated by using the prepared training set and its absorbances at seven points (from 375.0 to 550.0 nm) in the spectral region 325-584 nm. The proposed methods were validated by using synthetic ternary mixtures and applied to the simultaneous determination of three colorants in soft drink powders. The obtained results were statistically compared with each other.