Finite Eulerian posets which are binomial, Sheffer or triangular

In this paper we study finite Eulerian posets which are binomial, Sheffer or triangular. These important classes of posets are related to the theory of generating functions and to geometry. The results of this paper are organized as follows:

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We completely determine the structure of Eulerian binomial posets and, as a conclusion, we are able to classify factorial functions of Eulerian binomial posets.

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We give an almost complete classification of factorial functions of Eulerian Sheffer posets by dividing the original question into several cases.

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In most cases above, we completely determine the structure of Eulerian Sheffer posets, a result stronger than just classifying factorial functions of these Eulerian Sheffer posets.

We also study Eulerian triangular posets. This paper answers questions posed by R. Ehrenborg and M. Readdy. This research is also motivated by the work of R. Stanley about recognizing the boolean lattice by looking at smaller intervals.     

pH-Responsive Biocompatible Fluorescent Core-Shell Nanogel for Intracellular Imaging and Control Drug Release

This study reports a fluorescence iron core-carbonized biocompatible hybrid poly(ethylene glycol) (PEG)-oriented nanogel (Fe₂O₃@C@PEG-COOH nanogel). The fluorescence Fe₂O₃@C@PEG-COOH nanogel is prepared using a facile one-pot polycondensation reaction without organic solvents or catalysts. The properties of the fluorescenceFe₂O₃@C@PEG-COOH nanogel are investigated by fluorescence spectroscopy, transmission electron microscopy, X-ray diffraction, and thermogravimetric analysis. A change in pH as a stimulus can trigger the release of loaded doxorubicin (DOX). Under acidic conditions, the nanogel releases the highly loaded drug slowly compared to the neutral and basic conditions, which is important for cancer treatment. The synthesized fluorescenceFe₂O₃@C@PEG-COOH nanogel is well dispersed in water and shows fluorescence with high photostability, good biocompatibility with a paramagnetic nature. Furthermore, the nanogel can act as a potential fluorescent probe for cell imaging.     

Potentiometric ion-selective electrodes for determination of cyclopentolate hydrochloride and phenylephrine hydrochloride in their challenging ophthalmic formulation

Introduction of potentiometric ion-selective electrodes (ISEs) opened a new bright area in pharmaceutical analysis acknowledged as being an eco-friendly, simple, and energy-saving technique that is well-suited with microfabrication. In this contribution, potentiometric ISEs were employed as an alternative green analytical tool with the crucial goal of expanding the effective application of the potentiometric sensors in different disciplines of drug-stability studies and quality-control investigations. Four novel cyclopentolate hydrochloride and phenylephrine hydrochloride selective membrane sensors were constructed and evaluated. Sensors’ fabrication was achieved using potassium tetrakis (4-chlorophenyl) borate, a cationic exchanger, in a polyvinyl chloride polymeric matrix plasticized with 2-nitrophenyl octyl ether and using 2-hydroxy propyl-β-cyclodextrin as an ionophore. A comparative potentiometric study was implemented using two designs of ISEs; a conventional liquid inner contact and a glassy carbon solid-contact one. Using solid-contact ISEs, detection limit was substantially decreased and the discriminative ability in the presence of the most interfering substances was enhanced. This permits simultaneous estimation of both drugs, in spite of their similar ionic characteristics, abolishing the need for any pretreatment or separation steps in their challenging combined ophthalmic formulation as well as in rabbit aqueous humor and in the presence of their degradation products.     

Spectrophotometric study of the reaction mechanism between DDQ Pi- and iodine sigma-acceptors and chloroquine and pyrimethamine drugs and their determination in pure and in dosage forms

Two simple and accurate spectrophotometric methods are presented for the determination of anti-malarial drugs, chloroquine phosphate (CQP) and pyrimethamine (PYM), in pure and in different pharmaceutical preparations. The charge transphere (CT) reactions between CQP and PYM as electron donors and 2,3-dichloro-5,6-dicyano-p-benzoquinone (DDQ) pi-acceptor and iodine sigma-acceptor reagents to give highly coloured complex species have been spectrophotometrically studied. The optimum experimental conditions have been studied carefully. Beer' law is obeyed over the concentration range of 1.0-15 microg ml(-1) for CQP and 1.0-40 microg ml(-1) for PYM using I(2) and at 5.0-53 microg ml(-1) for CQP and 1.0-46 microg ml(-1) for PYM using DDQ reagents, respectively. For more accurate results, Ringbom optimum concentration range is calculated and found to be 10-53 and 8-46 microg ml(-1) for CQP and PYM using DDQ, respectively and 5-15 and 8-40 microg ml(-1) for CQP and PYM using iodine, respectively. The Sandell sensitivity is found to be 0.038 and 0.046 g cm(-2) for DDQ method and 0.0078 and 0.056 g cm(-2) for I(2) method for CQP and PYM, respectively which indicates the high sensitivity of both methods. Standard deviation (S.D.=0.012-0.014 and 0.013-0.015) and relative standard deviation (R.S.D.=0.09-1.4 and 1.3-1.5%) (n=5) for DDQ and I(2) methods respectively, refer to the high accuracy and precision of the proposed methods. These results are also confirmed by between day precision of percent recovery of 99-100.6%, and 98-101% for CQP and PYM by DDQ method and 99-102% and 99.2-101.4% for CQP and PYM by I(2) method respectively. These data are comparable to those obtained by British and American pharmacopoeias assay for the determination of CQP and PYM in raw materials and in pharmaceutical preparations.     

Spectrophotometric determination of verapamil hydrochloride in drug formulations with chloramine-T as oxidant

A new spectrophotometric method is described for the determination of verapamil hydrochloride, based on its oxidation with chloramine-T in hydrochloric acid medium. It produces a yellow colored compound with maximum absorbance at 425 nm. Beer's law was obeyed in the concentration range 0-340 micro g mL(-1) with molar absorptivity 2 x 10(3) L mol(-1) cm(-1) and RSD 0.3-0.82%. All variables were studied to optimize the reaction conditions. No interferences were observed from the common excipients present in the formulations. The method has been applied successfully to the determination of the drug in pharmaceutical preparations. Statistical comparison of the results with those from the reference method reveals excellent agreement and confirms that accuracy and precision are not significantly different.     

Equilibrium and kinetic study of novel methyltrimethoxysilane magnetic titanium dioxide nanocomposite for methylene blue adsorption from aqueous media

Novel magnetic titanium dioxide nanoparticles decorated with methyltrimethoxysilane (Fe₃O₄@TiO₂‐MTMOS) were successfully fabricated via a sol–gel method at room temperature. The synthesized material was characterized using Fourier transform infrared spectroscopy, X‐ray diffraction, scanning electron microscopy, energy‐dispersive X‐ray spectroscopy, thermogravimetric analysis and vibrating sample magnetometry. The removal efficiency of the adsorbent was evaluated through the adsorption of methylene blue (MB) dye from water samples. The adsorption isotherm and kinetics were evaluated using various models. The Langmuir model indicated a high adsorption capacity (11.5 mg g^?1) of Fe₃O₄@TiO₂‐MTMOS. The nanocomposite exhibited high removal efficiency (96%) and good regeneration (10 times) compared to Fe₃O₄ and Fe₃O₄@TiO₂ at pH = 9.0. Based on the adsorption mechanism, electrostatic interaction plays a main role in adsorption since MB dye is cationic in nature at pH = 9, whereas the adsorbent acquired an anionic nature. The newly synthesized Fe₃O₄@TiO₂‐MTMOS can be used as a promising material for efficient removal of MB dye from aqueous media.     

An expeditious synthesis of isoxazoline using cetyltrimethylammonium cerium nitrate: A phase transferring oxidative 1, 3-diplor cycloaddition

An expeditious and effective method for synthesis of isoxazoline from aldoximes and activated alkenes using cetyltrimethylammonium cerium nitrate at room temperature is described. Reaction was completed within short time period in high yields at room temperature.