Physicochemical Investigation of HDDP Azomethine Dye as Turn-On Fluorescent Chemosensor for High Selectivity and Sensitivity of Al<Superscript>3+</Superscript> Ions

4-[(2-Hydroxy-naphthalen-1-ylmethylene)-amino]-1,5-dimethyl-2-phenyl-1,2-dihydro-pyrazol-3-one (HDDP) was synthesized by the reaction of 4-amino-1,5-dimethyl-2-phenyl-1,2-dihydro-3H-pyrazol-3-one with 2-hydroxy-l-naphthaldehyde. The structure was confirmed by the IR, ¹H-NMR, ¹³C-NMR, and EI-MS spectra and elemental analysis. Physicochemical parameters of the HDDP such as extinction coefficient, oscillator strength, transition dipole moment, Stokes shift, and fluorescence quantum yield in different solvents were studied on the basis of polarities. The interactions of various metal ions with HDDP were also studied using steady state fluorescence measurements. The emission profile reveals that it acts as off–on type fluorescent chemosensor for selective and sensitive detection of Al³⁺ ions. Complexation stoichiometry and mechanism of enhancement were determined from a Benesi–Hildebrand plot.     

Kramer’s Sampling Theorem With Discontinuous Kernels

Kramer’s sampling theorem provides an algorithm for reconstructing a function ?, in the form $$ f(t)=\int_{a}^{b}\ F(x)K(x,t)dx,\qquad {\rm for\ some}\ F\ \in\ L^{2}(a,b), $$ from its values at a discrete set of points. In all the known examples, the kernel of the transform, K(x,t) is continuous in x and entire in t, even though the proof of the theorem shows that the continuity in x is not essential. This raises the question of whether it is possible to find an example of Kramer’s theorem with a discontinuous kernel. The aim of the paper is to answer this question in the affirmative. We show how one can construct a family of discontinuous kernels for which Kramer’s theorem holds and, in addition, each member of this family arises from a Sturm-Liouville problem, but with discontinuous initial conditions.     

Continuous catalytic Friedel-Crafts acylation in the biphasic medium of an ionic liquid and supercritical carbon dioxide

Immobilisation of catalytically-active metal salts in ionic liquids, with extraction by supercritical carbon dioxide, affords continuous Friedel-Crafts acylation, with in situ-recycling of the catalyst.     

Rapid micellar HPLC analysis of loratadine and its major metabolite desloratadine in nano-concentration range using monolithic column and fluorometric detection: application to pharmaceuticals and biological fluids

Background

Loratadine is a commonly used selective non-sedating antihistaminic drug. Desloratadine is the active metabolite of loratadine and, in addition, a potential impurity in loratadine bulk powder stated by the United States Pharmacopeia as a related substance of loratadine. Published methods for the determination of both analytes suffer from limited throughput due to the time-consuming steps and tedious extraction procedures needed for the analysis of biological samples. Therefore, there is a strong demand to develop a simple rapid and sensitive analytical method that can detect and quantitate both analytes in pharmaceutical preparations and biological fluids without prior sample extraction steps.

Results

A highly-sensitive and time-saving micellar liquid chromatographic method is developed for the simultaneous determination of loratadine and desloratadine. The proposed method is the first analytical method for the determination of this mixture using a monolithic column with a mobile phase composed of 0.15 M sodium dodecyl sulfate, 10% n-Butanol and 0.3% triethylamine in 0.02 M phosphoric acid, adjusted to pH 3.5 and pumped at a flow rate of 1.2 mL/min. The eluted analytes are monitored with fluorescence detection at 440 nm after excitation at 280 nm. The developed method is linear over the concentration range of 20.0–200.0 ng/mL for both analytes. The method detection limits are 15.0 and 13.0 ng/mL and the limits of quantification are 20.0 and 18.0 ng/mL for loratadine and desloratadine, respectively. Validation of the developed method reveals an accuracy of higher than 97% and intra- and inter-day precisions with relative standard deviations not exceeding 2%.

Conclusions

The method can be successfully applied to the determination of both analytes in various matrices including pharmaceutical preparations, human urine, plasma and breast milk samples with a run-time of less than 5 min and without prior extraction procedures. The method is ideally suited for use in quality control laboratories. Moreover, it could be a simple time-saving alternative to the official pharmacopeial method for testing desloratadine as a potential impurity in loratadine bulk powder.

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Graphical abstract Typical chromatogram of loratadine and its major metabolite desloratadine using the proposed micellar HPLC method

     

Some oscillation criteria for second order nonlinear functional ordinary differential equations

The main objective of this article is to study the oscillatory behavior of the solutions of the following nonlinear functional differential equations (a(t)x'(t))' δ1p(t)x'(t) δ2q(t)f(x(g(t))) = 0,for 0 ≤ t0 ≤ t, where δ1 = ±1 and δ2 = ±1. The functions p,q,g : [t0, ∞) → R, f :R → R are continuous, a(t) ＞ 0, p(t) ≥ 0,q(t) ≥ 0 for t ≥ t0, limt→∞ g(t) = ∞, and q is not identically zero on any subinterval of [t0, ∞). Moreover, the functions q(t),g(t), and a(t) are continuously differentiable.     

A generalization of the prolate spheroidal wave functions

Many systems of orthogonal polynomials and functions are bases of a variety of function spaces, such as the Hermite and Laguerre functions which are orthogonal bases of and and the Jacobi polynomials which are an orthogonal basis of a weighted The associated Legendre functions, and more generally, the spheroidal wave functions are also an orthogonal basis of

The prolate spheroidal wave functions, which are a special case of the spheroidal wave functions, possess a very surprising and unique property. They are an orthogonal basis of both and a subspace of known as the Paley-Wiener space of bandlimited functions. They also satisfy a discrete orthogonality relation. No other system of classical orthogonal functions is known to possess this strange property. This raises the question of whether there are other systems possessing this property.

The aim of the article is to answer this question in the affirmative by providing an algorithm to generate such systems and then demonstrating the algorithm by a new example.

     

Photoluminescence properties of thenardite activated with Eu

Na₂SO₄:Eu phosphors were prepared by heating pure natural thenardite with EuF₃ at 900 °C for 20 min in air. The photoluminescence (PL) and excitation spectra of as-prepared and γ-ray-irradiated phosphors were observed at 300 K. The PL spectrum under 394 nm excitation consisted of strong narrow bands with peaks at 579, 592, 616, 652, 697 and 741 nm, assigned to the ⁵D₀→⁷F_J (J=0, 1, 2, …, 5) transitions, respectively, within Eu³⁺. The PL spectrum under 340 nm excitation consisted of a broad Eu²⁺ band with a peak at 435 nm. The excitation spectrum obtained by monitoring the violet luminescence consisted of a weak band with a peak at approximately 261 nm and a broad Eu²⁺ band with a peak at approximately 338 nm. The relative efficiency of the violet luminescence of the γ-ray-irradiated phosphor at the exposure of 46 kGy increased up to 3.0 times that of the unirradiated phosphor. The enhancement of violet luminescence by γ-ray irradiation was ascribed to the conversion of Eu³⁺ to Eu²⁺ in Na₂SO₄.     

Abundant Exact Traveling Wave Solutions of Generalized Bretherton Equation via Improved (G′/G)-Expansion Method

In this article, we construct abundant exact traveling wave solutions involving free parameters to the generalized Bretherton equation via the improved (G′/G)-expansion method. The traveling wave solutions are presented in terms of the trigonometric, the hyperbolic, and rational functions. When the parameters take special values, the solitary waves are derived from the traveling waves.     

On the Theta Semigroup

In this paper we consider a semigroup on trigonometric expansions ${\{{\mathcal T}_t: t \geq 0\}}$ that will be called the Theta semigroup since its kernel is a multiple of ?? ₃(x, q), the third Jacobi theta function. We study properties of this semigroup and prove that it is a positive diffusion semigroup. We also obtain that its subordinated semigroup is the classical Poisson semigroup. The extensions to higher dimensions and to periodic ultra distributions are also considered.