Norm Retrievable Frames and Their Perturbation in Finite Dimensional Complex Hilbert Spaces

In this article, we study the property of norm retrievability of spanning vectors in a finite dimensional complex Hilbert space ?. Using the set of zero trace operators on ? and two sets of self-adjoint operators on ? denoted by 𝒮^1,0 and 𝒮^1,1, we present some equivalent conditions to the norm retrievable frames in ?. We will also show that the property of norm retrievability for n-dimensional complex Hilbert space ? with n≠2 is stable under enough small perturbation of the frame set only for phase retrievable frames.     

Graphite/Methanesulfonic Acid (GMA) as a New Reagent for Sulfonylation of Phenols and Thia‐Fries Rearrangement of Aryl Sulfonates to Sulfonylphenols

A new facile method for direct sulfonylation of phenols was developed. Graphite in methanesulfonic acid (GMA) was used to prepare sulfonylphenols by sulfonylation of phenol and naphthalene derivatives with p‐toluenesulfonic acid (=4‐methylbenzenesulfonic acid) (Table 1) and the thia‐Fries rearrangement of aryl sulfonates (Table 4). Mechanistic studies showed that the sulfonylation reaction of phenols in GMA occurred through an initial sulfonate formation followed by a thia‐Fries rearrangement of the aryl sulfonate by an intermolecular mechanism (Scheme 3).     

Silica sulfuric acid: an efficient and reusable catalyst for the one-pot synthesis of 3,4-dihydropyrimidin-2(1H)-ones

Silica sulfuric acid efficiently catalyzes the three-component Biginelli reaction between an aldehyde, a β-dicarbonyl compound and urea or thiourea in refluxing ethanol to afford the corresponding dihydropyrimidinones in high yields. The catalyst is reusable and can be applied several times without any decrease in the yield of the reactions.     

Deuterium isotope effect and oxidation of labelled alcohols

Oxidation of alcoholsR-CHD-OH by CrO₃/pyridine gave the aldehydesR-CDO with a relatively small loss of D thus indicating a pronounced isotope effect.     

Solar dryers as a promising drying technology: a comprehensive review

Journal of Thermal Analysis and Calorimetry - Dryers are utilized in food industry and agriculture in order to extend the useful lifespan of corps. Thermal energy is required for water removal in...     

Control releasing 5-aminosalicylic acid using pH-sensitive hydrogel with novel albumin cross-linker

Intelligent drug delivery systems are growing and changing too fast, these systems usually show a proper response at the proper time to one or several environmental factors. In the current research a biodegradable drug delivery system (pectin-g-PMA-co-PAAm) was designed and synthesized to release 5 aminosalicylic acid (5-ASA). The synthesized hydrogel is based on natural pectin and is in the form of simultaneous graft copolymerization of synthesized acryl-acid and acryl-amid. Using vinylized bovine serum albumin (VBSA) as cross linker agent is amongst important characteristics of this hydrogel. VBSA was synthesized through BSA modification with methylene-bis-acrylamide (MBA). In addition to having high water absorption, this hydrogel is pH-sensitive. In vitro tests under acid and base conditions of stomach show that this hydrogel is an appropriate option to release drugs through mouth. SEM analysis images show that synthesized hydrogel has a porous surface composed of nano and micro cavities.     

An efficient synthesis of 5‐benzoyloxazolines by regio‐ and stereo‐controlled reaction of N‐substituted 2‐benzoylaziridines under microwave irradiation

Several N‐acyl‐2‐benzoylaziridines were prepared conveniently in good to high yields (71‐93%) and used in the preparation of 5‐benzoyloxazolines (76‐91%) by a regio‐ and stereo‐controlled reaction in the presence of Nal as an efficient catalyst under microwave irradiation in short reaction times (5‐10 mins). The structure of the regioisomeric product was confirmed by X‐ray analysis.     

Analytic study of sixth-order thin-film equation by tan(<Emphasis Type="BoldItalic">ϕ</Emphasis>/2)-expansion method

A improvement of the expansion methods, namely, the improved \(\tan (\phi (\xi )/2)\)-expansion method for solving the sixth-order thin-film equation is proposed. As a result, many new and more general exact traveling wave solutions are obtained including singular kink-type solutions. We obtained the further solutions comparing with other methods as Flitton and King (Eur J Appl Math 15:713–754, 2004) and Taha et al. (J King Saud Univ Sci 26:75–78, 2014). Recently this method is developed for searching exact traveling wave solutions of nonlinear partial differential equations. Abundant exact traveling wave solutions including kink and rational solutions have been found. These solutions might play important role in engineering and physics fields. Also the results demonstrate that the introduced method is powerful tools for solving the nonlinear partial differential equations.     

Study of complex formation between La+3, Ce+3 and Y3+ cations with some 18-membered crown ethers in methanol–water and methanol–acetonitrile binary mixtures

The complexation reactions between some rare earth metal cations (Ln; Y³⁺, La³⁺ and Ce³⁺) with 18-crown-6 (18C6), dicyclohexyl-18-crown-6 (DC18C6), benzo-18-crown-6 (B18C6) and decyl-18-crown-6 (Dec18C6), have been studied in methanol–acetonitrile (MeOH–AN) and methanol–water (MeOH–H₂O) binary mixtures using a competitive spectrophotometric method. 2-(2-thiazolylazo)-4-methyl phenol (TAC or L) was used as colorimetric complexant. It was found that the selectivity order of TAC for Ln cations is highly changed with changing the composition of the mixed solvents. Moreover, as the concentration of acetonitrile increases in MeOH–AN binary mixture, the stability of Ln–TAC complexes increases and passes through a maximum at a certain mole fraction of acetonitrile. In addition, the stability of Ln–crown ether complexes increases with increasing the concentration of methanol in MeOH–H₂O and acetonitrile in MeOH–AN binary solutions. A non linear behaviour was observed for variation of stability constants of all complexes versus the composition of the mixed solvents. The results show that 18C6 generally forms more stable complexes with La³⁺ and Ce³⁺ cations than DC18C6 in methanol and MeOH–H₂O binary mixtures, while this sequence is reversed in the methanol-acetonitrile binary mixtures which are rich with respect to acetonitrile.     

A Simple and Efficient Procedure for Synthesis of Optically Active 1,2,4‐Triazolo‐[3,4‐b]‐1,3,4‐Thiadiazole Derivatives Containing l‐Amino Acid Moieties

Some new and optically active 1,2,4‐triazolo thiadiazoles bearing N‐phthaloyl‐l ‐amino acids were synthesized by reaction of 4‐amino‐5‐(3‐ or 4‐)pyridyl‐3‐mercapto‐(4H)‐1,2,4‐triazoles with N‐phthaloyl‐l ‐amino acids in the presence of phosphorus oxychloride. All the newly synthesized compounds were confirmed by IR, ¹H NMR, ¹³C NMR and elemental analysis.