Multiplicatively and non-symmetric multiplicatively norm-preserving maps

Let A and B be Banach function algebras on compact Hausdorff spaces X and Y and let ‖.‖ _X and ‖.‖ _Y denote the supremum norms on X and Y, respectively. We first establish a result concerning a surjective map T between particular subsets of the uniform closures of A and B, preserving multiplicatively the norm, i.e. ‖Tf Tg‖ _Y = ‖fg‖ _X , for certain elements f and g in the domain. Then we show that if α ∈ ℂ {0} and T: A → B is a surjective, not necessarily linear, map satisfying ‖fg + α‖ _X = ‖Tf Tg + α‖ _Y , f,g ∈ A, then T is injective and there exist a homeomorphism φ: c(B) → c(A) between the Choquet boundaries of B and A, an invertible element η ∈ B with η(Y) ⊆ {1, −1} and a clopen subset K of c(B) such that for each f ∈ A,

Reactions of platinum complexes with 4,7-phenanthroline: crystal structures of mono- and binuclear platinum(II) complexes containing 4,7-phenanthroline

The reaction of a mixture of cis and trans-[PtCl₂(SMe₂)₂] with 4,7-phen (4,7-phen = 4,7-phenanthroline) in a molar ratio of 1 : 1 or 2 : 1 resulted in the formation of mono and binuclear complexes trans-[PtCl₂(SMe₂)(4,7-phen)] (1) and trans-[Pt₂Cl₄(SMe₂)₂(μ-4,7-phen)] (2), respectively. The products have been fully characterized by elemental analysis, ¹H, ¹³C{¹H}, HHCOSY, HSQC, HMBC, and DEPT-135 NMR spectroscopy. The crystal structure of 1 reveals that platinum has a slightly distorted square planar geometry. Both chlorides are trans with a deviation from linearity 177.66(3)°, while the N–Pt–S angle is 175.53(6)°. Similarly, the reaction of a mixture of cis and trans-[PtBr₂(SMe₂)₂] with 4,7-phen in a 1 : 1 or 2 : 1 mole ratio afforded the mono or binuclear complexes trans-[PtBr₂(SMe₂)(4,7-phen)] (3) and trans-[Pt₂Br₄(SMe₂)₂(μ-4,7-phen)] (4), respectively. The crystal structure of trans-[Pt₂Br₄(SMe₂)₂(μ-4,7-phen)].C₆H₆ reveals that 4,7-phen bridges between two platinum centers in a slightly distorted square planar arrangement of the platinum. In this structure, both bromides are trans, while the PtBr₂(SMe₂) moieties are syn to each other. NMR data of mono and binuclear complexes of platinum 1–4 show that the binuclear complexes exist in solution as a minor product, while the mononuclear complexes are major products.     

Computational design and multivariate optimization of an electrochemical metoprolol sensor based on molecular imprinting in combination with carbon nanotubes

This work describes the development of an electrochemical sensor based on a new molecularly imprinted polymer for detection of metoprolol (MTP) at ultra-trace level. The polypyrrole (PPy) was electrochemically synthesized on the tip of a pencil graphite electrode (PGE) which modified whit functionalized multi-walled carbon nanotubes (MWCNTs). The fabrication process of the sensor was characterized by cyclic voltammetry (CV) and the measurement process was carried out by differential pulse voltammetry (DPV). A computational approach was used to screening functional monomers and polymerization solvent for rational design of molecularly imprinted polymer (MIP). Based on computational results, pyrrole and water were selected as functional monomer and polymerization solvent, respectively. Several significant parameters controlling the performance of the MIP sensor were examined and optimized using multivariate optimization methods such as Plackett–Burman design (PBD) and central composite design (CCD). Under the selected optimal conditions, MIP sensor was showed a linear range from 0.06 to 490 μmol L⁻¹ MTP, a limit of detection of 2.88 nmol L⁻¹, a highly reproducible response (RSD 3.9%) and a good selectivity in the presence of structurally related molecules. Furthermore, the applicability of the method was successfully tested with determination of MTP in real samples (tablet, and serum).     

Multicomponent reaction of amine,carbon disulfide,and fluoronitrobenzene via nucleophilic attack on the fluorinated carbon for the synthesis of nitrophenyl methylcarbamodithioates

In this paper, multicomponent reaction of amine, carbon disulfide and fluoronitrobenzene is reported for the synthesis of nitrophenyl methylcarbamodithioate derivatives. The method is based on the nucleophilic attack of the activated methylcarbamodithioate salt to fluoronitrobenzene. Several starting materials are tested and successfully produced the corresponding nitrophenyl methylcarbamodithioate. A possible mechanism for the reaction is suggested.     

Application of Heteropolyacids as Heterogeneous and Recyclable Catalysts for One-Pot Synthesis of 3-Cyanopyridine Derivatives

A simple, clean and environmentally benign route to the synthesis of 3-cyanopyridines is described via a one-pot multi-component reaction of 3,4-dimethoxyacetophenone, malonitrile or ethylcyanoacetate, aldehyde and ammonium acetate using heteropolyacids as heterogeneous and recyclable catalysts in very good yields.     

Von Neumann entropy in a Rashba-Dresselhaus nanodot; dynamical electronic spin-orbit entanglement

The main purpose of the present article is to report the characteristics of von Neumann entropy, thereby, the electronic hybrid entanglement, in the heterojunction of two semiconductors, with due attention to the Rashba and Dresselhaus spin-orbit interactions. To this end, we cast the von Neumann entropy in terms of spin polarization and compute its time evolution; with a vast span of applications. It is assumed that gate potentials are applied to the heterojunction, providing a two dimensional parabolic confining potential (forming an isotropic nanodot at the junction), as well as means of controlling the spin-orbit couplings. The spin degeneracy is also removed, even at electronic zero momentum, by the presence of an external magnetic field which, in turn, leads to the appearance of Landau states. We then proceed by computing the time evolution of the corresponding von Neumann entropy from a separable (spin-polarized) initial state. The von Neumann entropy, as we show, indicates that electronic hybrid entanglement does occur between spin and two-dimensional Landau levels. Our results also show that von Neumann entropy, as well as the degree of spin-orbit entanglement, periodically collapses and revives. The characteristics of such behavior; period, amplitude, etc., are shown to be determined from the controllable external agents. Moreover, it is demonstrated that the phenomenon of collapse-revivals’ in the behavior of von Neumann entropy, equivalently, electronic hybrid entanglement, is accompanied by plateaus (of great importance in quantum computation schemes) whose durations are, again, controlled by the external elements. Along these lines, we also make a comparison between effects of the two spin-orbit couplings on the entanglement (von Neumann entropy) characteristics. The finer details of the electronic hybrid entanglement, which may be easily verified through spin polarization measurements, are also accreted and discussed. The novel results of the present article, with potent applications in the field of quantum information processing, provide a deeper understanding of the electronic von Neumann entropy and hybrid entanglement that occurs in two-dimensional nanodots.     

Spectroscopic analysis,docking and molecular dynamics simulation of the interaction of cinnamaldehyde with human serum albumin

Azobenzene derivatives due to their photo- and electroactive properties are an important group of compounds finding applications in diverse fields. Due to the possibility of controlling the trans–cis isomerization, azo-bearing structures are ideal building blocks for development of e.g. nanomaterials, smart polymers, molecular containers, photoswitches, and sensors. Important role play also macrocyclic compounds well known for their interesting binding properties. In this article selected macrocyclic compounds bearing azo group(s) are comprehensively described. Here, the relationship between compounds’ structure and their properties (as e.g. ability to guest complexation, supramolecular structure formation, switching and motion) is reviewed.     

Multilinear isometries on spaces of vector-valued continuous functions

In this paper we study multilinear isometries defined on certain subspaces of vector-valued continuous functions. We provide conditions under which such maps can be properly represented. Our results contain all known results concerning linear and bilinear isometries defined between spaces of continuous functions. The key result is a vector-valued version of the additive Bishop’s Lemma, which we think has interest in itself.