Three-way Resolution of the Overlapping Ultrahigh-performance Liquid Spectrochromatograms for the Analysis of a Quaternary Mixture Using Parallel Factor Analysis

This paper presents a new application of three-way parallel factor analysis (3W-PARAFAC) model to the coeluting spectrochromatograms for the quantitative resolution of a quaternary mixture system consisting of paracetamol, propyphenazone, and caffeine with aspirin as an internal standard. Spectrochromatograms of calibration standards, validation sets, and unknown samples were recorded as a function of retention time and wavelength in the range of 0.0–2.5?min and 200–400?nm, respectively, using ultra-performance liquid chromatography with photodiode array detection (UPLC-PDA). Three-way UPLC-PDA data array X (retention time?×?wavelength?×?sample) was obtained from the data matrices of the spectrochromatograms. 3W-PARAFAC decomposition of three-way UPLC-PDA data array provided three loading matrices corresponding to chromatographic mode, spectral mode, and relative concentration mode. Quantitative estimation of paracetamol, propyphenazone, and caffeine in analyzed samples was accomplished using the relative concentration mode obtained by the deconvolution of the UPLC-PDA data set. The validity and ability of 3W-PARAFAC model were checked by analyzing independent test samples. It was observed from analyses that 3W-PARAFAC method has potential to uniquely resolve strongly overlapping peaks of analyzed compounds in a spectrochromatogram, which was obtained under experimental conditions consisting of the lower flow rate, short run time, and simple mobile phase composition. The proposed three-way chemometric approach was successfully applied to the simultaneous quantification of paracetamol, propyphenazone, and caffeine in tablets. Experiments showed that the determination results were in good agreement with label amount in commercial pharmaceutical preparation.     

Antimicrobial activities and absorption properties of disazo dyes containing imidazole and pyrazole moieties

The newly synthesized thirteen disazo dyes containing imidazole and pyrazole cycles (3a-3m) were carried out by diazotization reaction of 5-amino-4-arylazo-3-methyl-1H-pyrazoles (2a-2m) and coupling reaction with 1-methyl imidazole. Structures of synthesized azo dyes were characterized by UV–Vis, FT-IR, ¹H-NMR, elemental analysis and their solvatochromic properties were studied in DMSO, DMF, methanol, acetic acid and chloroform. In addition, the antimicrobial activities of dyes against twelve pathogenic bacteria were examined in detail and all dyes showed antimicrobial activity against different bacterial strains.     

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.     

The Semi-Infinite q-Boson System with Boundary Interaction

Upon introducing a one-parameter quadratic deformation of the q-boson algebra and a diagonal perturbation at the end point, we arrive at a semi-infinite q-boson system with a two-parameter boundary interaction. The eigenfunctions are shown to be given by Macdonald’s hyperoctahedral Hall–Littlewood functions of type BC. It follows that the n-particle spectrum is bounded and absolutely continuous and that the corresponding scattering matrix factorizes as a product of two-particle bulk and one-particle boundary scattering matrices.     

Two-stage linear decision rules for multi-stage stochastic programming

Multi-stage stochastic linear programs (MSLPs) are notoriously hard to solve in general. Linear decision rules (LDRs) yield an approximation of an MSLP by restricting the decisions at each stage to be an affine function of the observed uncertain parameters. Finding an optimal LDR is a static optimization problem that provides an upper bound on the optimal value of the MSLP, and, under certain assumptions, can be formulated as an explicit linear program. Similarly, as proposed by Kuhn et al. (Math Program 130(1):177–209, 2011) a lower bound for an MSLP can be obtained by restricting decisions in the dual of the MSLP to follow an LDR. We propose a new approximation approach for MSLPs, two-stage LDRs. The idea is to require only the state variables in an MSLP to follow an LDR, which is sufficient to obtain an approximation of an MSLP that is a two-stage stochastic linear program (2SLP). We similarly propose to apply LDR only to a subset of the variables in the dual of the MSLP, which yields a 2SLP approximation of the dual that provides a lower bound on the optimal value of the MSLP. Although solving the corresponding 2SLP approximations exactly is intractable in general, we investigate how approximate solution approaches that have been developed for solving 2SLP can be applied to solve these approximation problems, and derive statistical upper and lower bounds on the optimal value of the MSLP. In addition to potentially yielding better policies and bounds, this approach requires many fewer assumptions than are required to obtain an explicit reformulation when using the standard static LDR approach. A computational study on two example problems demonstrates that using a two-stage LDR can yield significantly better primal policies and modestly better dual policies than using policies based on a static LDR.

     

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.     

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     

An approach to best proximity points results via simulation functions

In this paper, we investigate of the existence of the best proximity points of certain mapping defined via simulation functions in the frame of complete metric spaces. We consider the uniqueness criteria for such mappings. The obtained results unify a number of the existing results on the topic in the literature.     

Systematic Encoding and Shortening of PAC Codes

Polarization adjusted convolutional (PAC) codes are a class of codes that combine channel polarization with convolutional coding. PAC codes are of interest for their high performance. This paper presents a systematic encoding and shortening method for PAC codes. Systematic encoding is important for lowering the bit-error rate (BER) of PAC codes. Shortening is important for adjusting the block length of PAC codes. It is shown that systematic encoding and shortening of PAC codes can be carried out in a unified framework.