Exponential Dichotomy on the Real Line and Admissibility of Function Spaces

The purpose of this paper is to give characterizations for uniform exponential dichotomy of evolution families on the real line. We consider a general class of Banach function spaces denoted and we prove that if with and the pair is admissible for an evolution family then is uniformly exponentially dichotomic. By an example we show that the admissibility of the pair for an evolution family is not a sufficient condition for uniform exponential dichotomy. As applications, we deduce necessary and sufficient conditions for uniform exponential dichotomy of evolution families in terms of the admissibility of the pairs and with      

Exploring the Research Progress about the Applications of Cyclodextrins and Nanomaterials in Electroanalysis

Cyclodextrins and nanomaterials are widely used in the achievement of powerful platforms in supramolecular chemistry and nanotechnology. The relatively hydrophobic internal cavity of the CDs selectively retains molecules having the proper geometry, while the hydrophilic exterior allows CDs to improve the dispersibility and molecular recognition. The nanomaterials provide higher surface area, good conductivity, and electrocatalytic effect. The use of nanomaterials and CDs in electrochemical sensors’ design allows the development of a large variety of devices, explaining the increasing number of papers in the last years that are discussed in this review.     

Simultaneous Determination of Some Analgesic Drugs Using Mixed Mode Stationary Phase

A new HPLC method based on a mixed mode stationary phase Hypersil Duet C18/SAX was developed and applied for the simultaneous determination of acetaminophen, acetylsalicylic acid and codeine. Parameters, such as the composition of the mobile phase, the nature of the organic modifier, the buffer type and the flow rate were investigated to optimize the separation. The results obtained show that the new HPLC method is rapid, highly efficient and selective. The studied compounds are separated in 10 min, by means of a mobile phase containing phosphate buffer (pH 7.50) and methanol (65:35 v v^?1). The retention mechanisms of each analyte were investigated using both the linear solvent strength theory and stoichiometric displacement model. The method was fully validated and showed good linearity for each compound for a concentration ranging between 2.0 and 40 μg mL^?1. The limits of detection and quantification were determined and they are lower than 0.1 μg mL^?1. The precision (RSD) of the method does not exceed 2 % for all studied compounds. The method was successfully applied for the assay of acetaminophen, acetylsalicylic acid and codeine in pharmaceutical formulations.     

Extending strongly continuous functions between apartness spaces

A natural extension theorem for strongly continuous mappings, the morphisms in the category of apartness spaces, is proved constructively. The author thanks Douglas Bridges and the anonymous referee for their useful suggestions, and the FoRST New Zealand for supporting her as a Postdoctoral Research Fellow (contract number UOCX0215) during the writing of this paper.     

Input-output admissibility and exponential trichotomy of difference equations

We propose a new method for the study of the asymptotic behavior of difference equations in infinite-dimensional spaces, providing characterizations for the property of uniform exponential trichotomy. We deduce the structure of the stable, unstable and bounded subspace and prove the uniqueness of the projection families. We introduce a new admissibility concept with respect to a discrete input-output system and prove that this is a necessary and sufficient condition for the existence of uniform exponential trichotomy. Throughout the paper, there is no assumption on the coefficients and the obtained results are applicable to any class of difference equations.     

“Geländer” macrocycles: Synthesis,chirality and racemisation barriers

A new class of axially-chiral o,o′-bridged biphenyls containing etheroxime chains was obtained in good yields by the macrocyclisation reaction of o,o′-diformylbiphenyl dioxime with several ditosylated or dibrominated reagents. In all cases the enantiomers of the compounds were separated by HPLC using a chiral column (Chiralpack IC) and the stability of the enantiomers (barriers of racemisation) was investigated employing chiral HPLC or chiral Dynamic HPLC techniques. A slight influence on the barrier to rotation was noticed when the enantiomerisation was performed in the presence of suitable alkali cations.     

Synthesis,crystal structures,characterization and antitumor activities of two copper(II) complexes of a sulfonamide ligand

An N-sulfonamide (HL = N-(5-(4-methoxyph-enyl)-[1, 3, 4]–thiadiazole–2-yl)-naphtalenesulfonamide) and two of its Cu(II) complexes, [Cu(L)₂(py)₂] (C1) and [Cu(L)(phen)₂](L)1.25(MeOH) (C2), were synthesized. The X-ray crystal structures of the complexes have been determined. In complex C1, the copper atom is four-coordinated, forming a CuN₄ chromophore, while in complex C2, the copper atom is five-coordinated, forming a CuN₅ chromophore. The ligand acts as monodentate, coordinating the metal through a single thiadiazole N atom. The molecules from the reaction medium (pyridine and phenanthroline) are also involved in coordination to the copper atoms. The complexes have a square planar (C1) and slightly distorted square pyramidal (C2) geometries. The compounds were characterized by physicochemical and spectroscopic methods. Nuclease activity studies of the complexes confirm their capacity to cleave DNA. Both complexes also have SOD-like activity, but weaker than the native Cu₂Zn₂SOD activity. Cytotoxicity studies were carried out on melanoma cell line B16F10 and on normal retinal epithelial cell line (D407) and confirmed that C2 inhibits the growth of B16F10 cells, in a dose-dependent manner. Also, C2 displays a cytoselective profile, since it is not toxic to the D407 cell line. The results of the cell cytotoxicity studies are in concordance with the DNA cleavage and SOD mimetic activity studies and indicate that complex C2 has a high biological activity.     

Bis‐Sulfonyl O,C,O‐Chelated Metallylenes (Ge,Sn) as Adjustable Ligands for Iron and Tungsten Complexes

The synthesis and characterization of an E₂CE₂ bis‐sulfonyl aryl pincer ligand and its efficiency for the stabilization of compounds containing low‐valent Group 14 elements (Ge and Sn) are reported. Complexation reaction of these metallylenes with iron or tungsten complexes resulted in the modulation of the oxygen atoms of the sulfonyl groups implicated in the stabilization of the Group 14 elements, demonstrating the original adjustable character of the bis‐sulfonyl O₂S‐C‐SO₂ aryl pincer.