Novel four-component route to the synthesis of spiro[indoline-3,4′-pyridine]-3′-carboxylate derivatives

An effective route to spiro[indoline-3,4′-pyridine]-3′-carboxylate derivatives is described. This involves reaction of isatin, 1-phenyl-2-(1,1,1-triphenyl-λ⁵-phosphanylidene)-1-ethanone, and benzylamine derivatives or aliphatic amines in the presence of alkyl acetoacetate (1,3-dicarbonyl compounds) in dry methanol under reflux conditions. The reactive 1:1 enaminone, which is obtained from the addition of the amine to 1,3-dicarbonyl compound, adds to the α,β-unsaturated ketone, which is formed from the reaction of isatin and 1-phenyl-2-(1,1,1-triphenyl-λ⁵-phosphanylidene)-1-ethanone, to produce the alkyl 1′-benzyl-2′-methyl-2-oxo-6′-phenyl-1′H-spiro[indoline-3,4′-pyridine]-3′-carboxylate derivatives in excellent yields.     

Bilinear optimality constraints for the cone of positive polynomials

For a proper cone \({{\mathcal K}\subset\mathbb{R}^n}\) and its dual cone \({{\mathcal K}^*}\) the complementary slackness condition \({\langle{\rm {\bf x}},{\rm {\bf s}}\rangle=0}\) defines an n-dimensional manifold \({C({\mathcal K})}\) in the space \({{\mathbb R}^{2n}}\) . When \({{\mathcal K}}\) is a symmetric cone, points in \({C({\mathcal K})}\) must satisfy at least n linearly independent bilinear identities. This fact proves to be useful when optimizing over such cones, therefore it is natural to look for similar bilinear relations for non-symmetric cones. In this paper we define the bilinearity rank of a cone, which is the number of linearly independent bilinear identities valid for points in \({C({\mathcal K})}\) . We examine several well-known cones, in particular the cone of positive polynomials \({{\mathcal P}_{2n+1}}\) and its dual, and show that there are exactly four linearly independent bilinear identities which hold for all \({({\rm {\bf x}},{\rm {\bf s}})\in C({\mathcal P}_{2n+1})}\), regardless of the dimension of the cones. For nonnegative polynomials over an interval or half-line there are only two linearly independent bilinear identities. These results are extended to trigonometric and exponential polynomials. We prove similar results for Müntz polynomials.     

A new solid phase micro extraction for simultaneous head space extraction of ultra traces of polar and non-polar compounds

The results of the innovative study on a new stationary phase with high efficiency based on ZnO nano and micro rod coating on fused silica are reported in this paper. ZnO nanorods with a diameter in the range of 70–300 nm and the length of about 500 nm, have been grown on fused silica fibers using a hydrothermal process. The extraction properties of the fiber were investigated using headspace solid-phase microextraction (HS-SPME) mode coupled with gas chromatography–mass spectrometry detection (GC–MS) for 1,4-dichloro-nitrobenzene, biphenyl and acenaphthene. The calibration curves were linear up to 10²–10⁷ ng L⁻¹ (R² > 0.995) with detection limits of 10⁻³ ng L⁻¹ for biphenyl and acenaphthene and 10 ng L⁻¹ for 1,4-dichloro-nitrobenzene. The RSD for single fiber and fiber-to-fiber were less than 7.0 and 11.5%, respectively. The high stability of the ZnO coating is proved at relatively high temperatures (up to 300 °C) with a high extraction capacity and long lifespan (more than 100 times). Promising recoveries (91–102%) were obtained in environmental water samples analysis by applying the proposed technique.     

Rapid and Facile Access to Indeno[1,2‐d]imidazoles via a Tandem Addition?Cyclization Reaction

A novel and tandem synthesis of highly functionalized tetrahydroindeno[1,2‐d]imidazole is described. A one‐pot reaction between a primary amine, an aryl isothiocyanate, and ninhydrin leads to highly substituted indeno[1,2‐d]imidazoles under solvent‐free conditions in excellent yields (Scheme). Their structures were corroborated spectroscopically (IR, ¹H‐ and ¹³C‐NMR, and EI‐MS) and by elemental analyses.     

Study binding of Al-curcumin complex to ds-DNA, monitoring by multispectroscopic and voltammetric techniques

In this work a complex of Al3+ with curcumin ([Al(curcumin) (EtOH)2](NO3)2) was synthesized and characterized by UV-vis, FT-IR, elemental analysis and spectrophotometric titration techniques. The mole ratio plot revealed a 1:1 complex between Al3+ and curcumin in solution. For binding studies of this complex to calf thymus-DNA various methods such as: UV-vis, fluorescence, circular dichroism (CD), FT-IR spectroscopy and cyclic voltammetry were used. The intrinsic binding constant of ACC with DNA at 25°C was calculated by UV-vis and cyclic voltammetry as 2.1×10(4) and 2.6×10(4), respectively. The thermodynamic studies showed that the reaction is enthalpy and entropy favored. The CD results showed that only the Δ-ACC interacts with DNA and the Δ-ACC form has not any tendency to interact with DNA, also the pure curcumin has not any stereoselective interaction with CT-DNA. Fluorimetric studies showed that fluorescence enhancement was initiated by a static process in the ground state. The cyclic voltammetry showed that ACC interact with DNA with a binding site size of 2. From the FT-IR we concluded that the Δ-ACC interacts with DNA via partial electrostatic and minor groove binding. In comparison with previous works it was concluded that curcumin significantly reduced the affinity of Al3+ to the DNA.     

Monolayer-protected gold nanoparticle coalescence induced by photogenerated radicals

Acyl and alkyl radicals generated photochemically in a solution containing monolayer-protected gold nanoparticles are shown to efficiently liberate the alkylthiolate ligands into the solution as the thioacetyl or alkyl sulfide, respectively. This radical-induced reaction initiates a coalescence of the gold cores to facilitate an increase in core size. The photoinitiated radical reaction also liberates monolayers from two-dimensional gold surfaces.     

Equimatchable claw-free graphs

A graph is equimatchable if all of its maximal matchings have the same size. A graph is claw-free if it does not have a claw as an induced subgraph. In this paper, we provide the first characterization of claw-free equimatchable graphs by identifying the equimatchable claw-free graph families. This characterization implies an efficient recognition algorithm.     

Positive semidefinite indicator property for norm-numerical range

In this paper, using an elementary method, we prove that if norm-numerical range related to an absolute norm \(\Vert .\Vert \) on \(\mathbb {C}^n\) satisfies the positive semidefinite indicator property, then \(\Vert .\Vert \) will be a multiple of Euclidian norm.     

Shape-Constrained Estimation Using Nonnegative Splines

We consider the problem of nonparametric estimation of unknown smooth functions in the presence of restrictions on the shape of the estimator and on its support using polynomial splines. We provide a general computational framework that treats these estimation problems in a unified manner, without the limitations of the existing methods. Applications of our approach include computing optimal spline estimators for regression, density estimation, and arrival rate estimation problems in the presence of various shape constraints. Our approach can also handle multiple simultaneous shape constraints. The approach is based on a characterization of nonnegative polynomials that leads to semidefinite programming (SDP) and second-order cone programming (SOCP) formulations of the problems. These formulations extend and generalize a number of previous approaches in the literature, including those with piecewise linear and B-spline estimators. We also consider a simpler approach in which nonnegative splines are approximated by splines whose pieces are polynomials with nonnegative coefficients in a nonnegative basis. A condition is presented to test whether a given nonnegative basis gives rise to a spline cone that is dense in the space of nonnegative continuous functions. The optimization models formulated in the article are solvable with minimal running time using off-the-shelf software. We provide numerical illustrations for density estimation and regression problems. These examples show that the proposed approach requires minimal computational time, and that the estimators obtained using our approach often match and frequently outperform kernel methods and spline smoothing without shape constraints. Supplementary materials for this article are provided online.     

Numerical analysis of the internal flow and the mixing chamber length effects on the liquid film thickness exiting from the effervescent atomizer

Journal of Thermal Analysis and Calorimetry - Two-phase flow was simulated within the effervescent atomizer by the volume of fluid interface tracing model. Different gas-to-liquid mass ratios...