On existence and multiplicity of similarity solutions to a nonlinear differential equation arising in magnetohydrodynamic Falkner–Skan flow for decelerated flows

Previously, existence and uniqueness of a class of monotone similarity solutions for a nonlinear differential equation arising in magnetohydrodynamic Falkner–Skan flow were considered in the case of accelerating flows. It was shown that a solution satisfying certain monotonicity properties exists and is unique for the case of accelerated flows and some decelerated flows. In this paper, we show that solutions to the problem can exist for decelerated flows even when the monotonicity conditions do not hold. In particular, these types of solutions have nonmonotone second derivatives and are, hence, a distinct type of solution from those studied previously. By virtue of this result, the present paper demonstrates the existence of an important type of solution for decelerated flows. Importantly, we show that multiple solutions can exist for the case of strongly decelerated flows, and this occurs because of the fact that the solutions do not satisfy the aforementioned monotonicity requirements. Copyright © 2015 John Wiley & Sons, Ltd.     

Fredholm boundary value problems for perturbed systems of dynamic equations on time scales

This paper offers conditions ensuring the existence of solutions of linear boundary value problems for systems of dynamic equations on time scales. Utilizing a method of Moore–Penrose pseudo‐inverse matrices leads to an analytical form of a criterion for the existence of solutions in a relevant space and, moreover, to the construction of a family of linearly independent solutions of such problems in a general case with the number of boundary conditions (defined by a linear vector functional) not coinciding with the number of unknowns of a system of dynamic equations. As an example of an application of the presented results, the problem of bifurcation of solutions of boundary value problems for systems of dynamic equations on time scales with a small parameter is considered.     

A turn-on and reversible fluorescence sensor with high affinity to Zn in aqueous solution

A new simple receptor 1 based on aminosalicylimine was prepared. It exhibited an ‘off–on fluorescence type’ mode with high sensitivity in the presence of Zn²⁺. In particular, this chemosensor could clearly distinguish Zn²⁺ from Cd²⁺. Also, it could be a reusable chemosensor because the addition of EDTA quenched the fluorescence of the Zn²⁺-2·1 complex. Furthermore, receptor 1 had a sufficiently low detection limit (68 nM) in aqueous solutions, which implies that 1 could sense the nanomolar concentration of Zn²⁺. Therefore, this sensor has the ability to be a practical system for the monitoring of Zn²⁺ concentrations in aqueous samples.     

Mild method for the synthesis of 1H-indazoles through oxime-phosphonium ion intermediate

The synthesis of 1H-indazoles from o-aminobenzoximes is achieved via N–N bond formation using triphenylphosphine, I₂, and imidazole. Selective formation of oxime-phosphonium ion intermediate in the presence of the amino group is the driving force for this reaction. The nucleophilicity of the arylamino group and electrophilicity toward the N–O bond of oxime also control the reaction. The reaction proceeds at a faster rate with good to excellent yield under this mild reaction condition and is amenable to scale-up.     

An elegant protocol for the synthesis of N-substituted pyrroles through C–N cross coupling/aromatization process using CuFe2O4 nanoparticles as catalyst under ligand-free conditions

A simple and efficient, ligand-free C–N cross-coupling of aryl halides/benzyl bromides with trans-4-hydroxy-l-proline has been developed to produce aromatized N-substituted pyrroles, using a catalytic amount of magnetically separable and recyclable CuFe₂O₄ nanoparticles, in the presence of Cs₂CO₃ in DMSO at 100 °C.     

Using LR-HSQMBC to observe long-range H–N correlations

The recently reported LR-HSQMBC experiment has been optimized for ¹H–¹⁵N long-range heteronuclear couplings. Several previously unreported four-bond correlations, consistent with the predicted by DFT calculations (0.2–0.3 Hz ⁴J_NH couplings), have been observed for strychnine using 2 Hz optimization of the LR-HSQMBC experiment. This experiment offers an advantage over accordion-optimized experiments such as IMPEACH and CIGAR for the observation of long-range ¹H–¹⁵N correlations in that the experiment is refocused and employs a CLIP pulse sequence element to bring the long-range correlations into phase, allowing broadband X-decoupling to be employed during acquisition.     

Two Aromatic Ester Organoimido Derivatives of Hexa­molybdate: Syntheses,Crystal Structures,and Spectroscopic Studies

Two alkylimido derivatives of hexamolybdate, (Bu₄N)₂[Mo₆O₁₈(≡N‐o‐COOCH₃C₆H₄)] ( 1 ) and (Bu₄N)₂[Mo₆O₁₈(≡N‐o‐COOCH₂CH₃C₆H₄)] ( 2 ), were synthesized in high purity and good yields by the reaction of [(C₄H₉)₄N]₄[α‐Mo₈O₂₆] and methyl anthranilate or ethyl‐o‐aminobenzoate hydrochloride with N,N′‐dicyclohexylcarbodiimide (DCC) as a dehydrating agent in dry acetonitrile solution, which were characterized by elemental analyses, IR, UV/Vis, and ¹H NMR spectroscopy as well as ESI‐MS, and single‐crystal X‐ray diffraction study. Compound 1 crystallizes in the monoclinic space group P2₁/n with one‐dimensional chain structure via intramolecular hydrogen bond. Compound 2 also crystallizes in the monoclinic space group P2₁/n with dimer structure by intramolecular hydrogen bonds and π–π interactions between the pairs of cluster anions.     

On the Solvent‐free Structure of a Jäger‐type Cobalt(II) N2O2‐Chelate Complex

A combined synchrotron X‐ray and density functional theory (DFT) study on the structure of a Jäger‐type N₂O₂ chelate complex was carried out. The ethoxy‐substituted bis(3‐oxo‐enaminato)cobalt(II) complex ( 1 ) was an original sample from the laboratory of the late Professor Ernst‐G. Jäger (University of Jena, Germany). Single‐crystal X‐ray analysis revealed essentially flat molecules of 1 , which are unsolvated and coordinatively unsaturated. The DFT calculations on the isolated molecule predict a planar structure for the non‐hydrogen atoms, which is a local minimum on the energy surface. The crystal packing is achieved through off‐set stacking (staircase arrangement), resulting in a herringbone pattern in the space group P2₁2₁2₁. The structure of 1 is compared to known structures of related bis(3‐oxo‐enaminato)cobalt(II) complexes ( 2 – 4 ). Original bulk material of 1 was investigated by scanning electron microscopy (SEM), powder X‐ray diffraction (PXRD), melting point determination, and infrared (IR) spectroscopy.