Practical Synthesis of 4-Benzylidene-2-phenyl-5(4H)-oxazolones

A simple and alternative method has been developed for the synthesis of 4-benzylidene-2-phenyl-5(4H)-oxazolones via reactions of hippuric acid with various aldehydes in the presence of 2-chloro-4,6-dimethoxy-1,3,5-triazine/N-methylmorpholine at 75 °C.

Supplemental materials are available for this article. Go to the publisher's online edition of Synthetic Communications® to view the free supplemental file.     

Real-time monitoring of protein complexes reveals their quaternary organization and dynamics

The dynamics of protein complexes are crucial for their function yet are challenging to study. Here, we present a nanoelectrospray (nESI) mass spectrometry (MS) approach capable of simultaneously providing structural and dynamical information for protein complexes. We investigate the properties of two small heat shock proteins (sHSPs) and find that these proteins exist as dodecamers composed of dimeric building blocks. Moreover, we show that these proteins exchange dimers on the timescale of minutes, with the rate of exchange being strongly temperature dependent. Because these proteins are expressed in the same cellular compartment, we anticipate that this dynamical behavior is crucial to their function in vivo. Furthermore, we propose that the approach used here is applicable to a range of nonequilibrium systems and is capable of providing both structural and dynamical information necessary for functional genomics.     

Best proximity point theorems

Let us assume that A and B are non-empty subsets of a metric space. In view of the fact that a non-self mapping T:A?B does not necessarily have a fixed point, it is of considerable significance to explore the existence of an element x that is as close to Tx as possible. In other words, when the fixed point equation Tx=x has no solution, then it is attempted to determine an approximate solution x such that the error d(x,Tx) is minimum. Indeed, best proximity point theorems investigate the existence of such optimal approximate solutions, known as best proximity points, of the fixed point equation Tx=x when there is no solution. Because d(x,Tx) is at least d(A,B), a best proximity point theorem ascertains an absolute minimum of the error d(x,Tx) by stipulating an approximate solution x of the fixed point equation Tx=x to satisfy the condition that d(x,Tx)=d(A,B). This article establishes best proximity point theorems for proximal contractions, thereby extending Banach’s contraction principle to the case of non-self mappings.     

Common Best Proximity Points: Global Optimal Solutions

Let S:A→B and T:A→B be given non-self mappings, where A and B are non-empty subsets of a metric space. As S and T are non-self mappings, the equations Sx=x and Tx=x do not necessarily have a common solution, called a common fixed point of the mappings S and T. Therefore, in such cases of non-existence of a common solution, it is attempted to find an element x that is closest to both Sx and Tx in some sense. Indeed, common best proximity point theorems explore the existence of such optimal solutions, known as common best proximity points, to the equations Sx=x and Tx=x when there is no common solution. It is remarked that the functions x→d(x,Sx) and x→d(x,Tx) gauge the error involved for an approximate solution of the equations Sx=x and Tx=x. In view of the fact that, for any element x in A, the distance between x and Sx, and the distance between x and Tx are at least the distance between the sets A and B, a common best proximity point theorem achieves global minimum of both functions x→d(x,Sx) and x→d(x,Tx) by stipulating a common approximate solution of the equations Sx=x and Tx=x to fulfill the condition that d(x,Sx)=d(x,Tx)=d(A,B). The purpose of this article is to elicit common best proximity point theorems for pairs of contractive non-self mappings and for pairs of contraction non-self mappings, yielding common optimal approximate solutions of certain fixed point equations. Besides establishing the existence of common best proximity points, iterative algorithms are also furnished to determine such optimal approximate solutions.     

Spectroscopic and dielectric properties of a lithia-containing glass

Glass of the composition 65SiO₂-20CaO-15Li₂O (mol %) was prepared and subjected to heat treatment. The obtained samples were characterized before and after heat treatment by DTA, TG, XRD, SEM, IR and dielectric spectroscopy. DTA showed an endothermic peak at 954 °C, accompanied by a pronounced change in the microstructure, as revealed by SEM. XRD showed that metasilicate predominates on heat treatment at 726 °C, while on heat treatment at 726 °C, then at 954 °C, disilicate crystallizes as the main phase. The IR spectra of the heat-treated glasses revealed that the vibrations of O-H groups are drastically decreased, while those due to non-bridging oxygens Si-O⁻ are increased. The dielectric constant (ε′), the loss tangent (tan δ) and the ac conductivity (σ_ac) for the prepared glasses were investigated before and after heat treatment over a moderately wide range of frequency and temperature. The activation energy of the dielectric relaxation process was found to depend on the techniques of sample preparation. A drop of dielectric constant values was observed for the heat-treated sample, which can be attributed to the ordering of the induced crystalline phases. The conductivity behavior suggests a hopping mechanism responsible for conduction.     

Best proximity point theorems: unriddling a special nonlinear programming problem

This paper addresses the non-linear programming problem of globally minimizing the real valued function x?d(x,Sx) where S is a generalized proximal contraction in the setting of a metric space. Eventually, one can obtain optimal approximate solutions to some fixed-point equations in the event that they have no solution.     

Best proximity point theorems: exposition of a significant non-linear programming problem

The primary goal of this work is to address the non-linear programming problem of globally minimizing the real valued function x → d(x, Tx) where T is presumed to be a non-self mapping that is a generalized proximal contraction in the setting of a metric space. Indeed, an iterative algorithm is presented to determine a solution of the preceding non-linear programming problem that focuses on global optimization. As a sequel, one can compute optimal approximate solutions to some fixed point equations and optimal solutions to some unconstrained non-linear programming problems.     

Application of a Double Aza-Michael Reaction in a 'Click, Click, Cy-Click' Strategy: From Bench to Flow

The development of a 'click, click, cy-click' process utilizing a double aza-Michael reaction to generate functionalized 1,2,5-thiadiazepane 1,1-dioxides is reported. Optimization in flow, followed by scale out of the inter-/intramolecular double aza-Michael addition has also been realized using a microwave-assisted, continuous flow organic synthesis platform (MACOS). In addition, a facile one-pot, sequential strategy employing in situ Huisgen cycloaddition post-double aza-Michael has been accomplished, and is applicable to library synthesis.     

New Charge Transfer Complexes of K+-Channel-Blocker Drug (Amifampridine; AMFP) for Sensitive Detection; Solution Investigations and DFT Studies

UV–Vis spectroscopy was used to investigate two new charge transfer (CT) complexes formed between the K⁺-channel-blocker amifampridine (AMFP) drug and the two π-acceptors 2,3-dichloro-5,6-dicyano-p-benzoquinone (DDQ) and tetracyanoethylene (TCNE) in different solvents. The molecular composition of the new CT complexes was estimated using the continuous variations method and found to be 1:1 for both complexes. The formed CT complexes’ electronic spectra data were further employed for calculating the formation constants (K_CT), molar extinction coefficients (ε_CT), and physical parameters at various temperatures, and the results demonstrated the high stability of both complexes. In addition, sensitive spectrophotometric methods for quantifying AMFP in its pure form were proposed and statistically validated. Furthermore, DFT calculations were used to predict the molecular structures of AMFP–DDQ and AMFP–TCNE complexes in CHCl₃. TD-DFT calculations were also used to predict the electronic spectra of both complexes. A CT-based transition band (exp. 399 and 417 nm) for the AMFP–TCNE complex was calculated at 411.5 nm (f = 0.105, HOMO-1 → LUMO). The two absorption bands at 459 nm (calc. 426.9 nm, f = 0.054) and 584 nm (calc. 628.1 nm, f = 0.111) of the AMFP–DDQ complex were theoretically assigned to HOMO-1 → LUMO and HOMO → LUMO excitations, respectively.