Λ-strongly summable sequence spaces in n-normed spaces defined by ideal convergence and an Orlicz function

In this paper we introduce some certain new sequence spaces via ideal convergence, λ-sequence and an Orlicz function in n-normed spaces and study different properties of these spaces and also establish some inclusion results among them.     

Supramolecular solvent-based liquid phase microextraction of malachite green at trace level from water samples for its UV–vis spectrophotometric detection

A simple and fast microextraction procedure based on supramolecular solvent extraction of malachite green from water samples has been established in the presented work. The effective analytical parameters including pH, solvent volume, sample volume etc. on the quantitative recoveries of the malachite green were optimised. Matrix effects were also investigated. The preconcentration factor was found as 50. The limit of detection and limit of quantification were 16.3 and 54.5 µg L^?1, respectively. The relative standard deviation percentage was below 7%. The presented procedure was applied to the determination of malachite green content of natural water samples from fish farm and tap water etc.     

A novel approach to produce monodisperse hollow pure silica spheres

In this work, we report an efficient method to produce pure hollow silica spheres (HSS) using phenyltrimethoxysilane (PTMS) compound. The production of HSS was carried out via hydrolysis of PTMS in the aqueous media and followed by a condensation reaction to form silica spheres with phenyl groups. The product was then calcined to remove phenyl groups and obtain pure silica spheres with >95% fine structure. The chemical nature of pure silica was confirmed by Fourier transforms infrared spectroscopy. The calcined HSS were stable beyond the temperature of 900 °C as confirmed by thermal gravimetric analysis (TGA). The calcined spheres preserved their spherical appearance and hollow core as shown by SEM and TEM micrographs. Interestingly, the average size of the spheres was reduced significantly after calcination from 760 to 510 nm, confirming further the removal of phenyl groups. The calcined HSS offered much higher surface area (A_s) when analysed by BET; A_s for calcined product was ～406 and mere ～4.8 m²/g for uncalcined HSS. Finally, drug release study of cisplatin/HSS showed over 45% of steady cumulative release for 72 h. The prepared HSS can be dispersed in water opening the possibility of many novel bio/non-bio applications.     

The nonlinear refraction and nonlinear absorption in 4-(4,6-diaminopyrimidin-2-ylthio) substituted double-decker Lu(III) phthalocyanine

A 4-(4,6-diaminopyrimidin-2-ylthio) substituted double-decker Lu(III) phthalocyanines (4) have been prepared and characterized by elemental analysis, IR, UV-vis and ¹H NMR spectroscopies. The nonlinear refractive index, nonlinear absorption and the optical limiting (OL) performance of the compound 4 in a 0.5 mm spectroscopic cell in DMF solution were investigated by using 4 ns pulse laser at 532 nm. Z-scan experiments have been conducted between 0.24 and 2.39 GW/cm² peak intensities for 10 Hz repetition rate and also between 2.39 and 23.89 GW/cm² peak intensities for 1 Hz repetition rate. The thermal effect contributes to the nonlinear response of the material higher than 0.72 GW/cm² peak intensity at 10 Hz. We measured the effective nonlinear refractive index of the material as 1.2×10⁻¹¹ esu at 3.5×10⁻⁴ M concentration with the peak intensity less than 0.72 GW/cm² and we found that nonlinear absorption was very small. On the other hand, when concentration is increased to 2.4×10⁻³ M material's nonlinear absorption becomes dominant mechanism for the nonlinear response and the compound 4 indicates OL behavior at 2.4×10⁻³ M concentration.     

Synthesis of chiral acetoxy lactones via the Baeyer-Villiger oxidation of cyclic aromatic acetoxy ketones

The α-acetoxylation of indanones and tetralones by using Mn(OAc)₃ followed by the enzyme catalyzed kinetic resolution of acetoxy ketones furnished both of the enantiomers of α-acetoxy ketones in good chemical and optical yields. The Baeyer-Villiger oxidation of α-acetoxy ketones with m-CPBA, CF₃SO₃H, and CH₂Cl₂, at rt gives the corresponding lactones without racemization. The acetoxy ketone moiety migrates selectively in order to form lactones. The mild hydrolysis of lactones affords phenolic α-hydroxycarboxylic acid derivatives.     

Pre-service Teachers’ Developing Conceptions about the Nature and Pedagogy of Mathematical Modeling in the Context of a Mathematical Modeling Course

Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers’ developing conceptions about (a) the nature of mathematical modeling in simulations of “real life” problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike other studies that have focused on single-topic and lesson-sized research sites, a course-sized research site was used in this study. Having been through several iterations over three teaching semesters, the 15-week long course was implemented with 25 pre-service secondary mathematics teachers. Findings revealed that pre-service teachers developed ideas about the nature of mathematical modeling involving what mathematical modeling is, the relationship between mathematical modeling and meaningful understanding, and the nature of mathematical modeling tasks. They also realized the changing roles of teachers during modeling implementations and diversity in students’ ways of thinking. The researchers’ conceptual development, on the other hand, involved realizing the critical aspect of the “teacher role” played by the instructor during modeling implementations, and the need for more experience of modeling implementations for pre-service teachers.     

Synthesis, molecular structure, spectroscopic studies and second-order nonlinear optical behaviour of N,N'-(2-hydroxy-propane-1,3-diyl)-bis(5-nitrosalicylaldiminato-N,O)-copper(II)

N,N'-(2-Hydroxy-propane-1,3-diyl)-bis(5-nitrosalicylaldiminato-N,O)-copper(II) has been synthesized. The crystal structure has been determined by X-ray diffraction analysis, and linear optical characterization has been determined by UV-vis spectroscopy. It was found that the molecule under investigation has solvatochromic behaviour in the UV region, implying non-zero microscopic first hyperpolarizability. To reveal the microscopic nonlinear optical (NLO) properties, the static first hyperpolarizabilities (beta) and the electric dipole moments (mu) were evaluated by using the ab initio finite field (FF) method. According to the results of the FF calculations, the synthesized compound exhibits non-zero beta values, and it might have microscopic NLO behaviour.     

Addition of trifluoromethyltrimethylsilane to acyl phosphonates: synthesis of TMS-protected 1-alkyl-1-trifluoromethyl-1-hydroxyphosphonates and 1-aryldifluoroethenyl phosphates

Addition reactions of nucleophilic CF3TMS to acyl phosphonates were investigated. Various acyl phosphonates reacted readily with CF3TMS in the presence of K2CO3 in DMF at rt to give 1-alkyl-2,2,2-trifluoro-1-trimethylsilyloxyethylphosphonate in 70-90% yields. When benzoyl phosphonates were used as starting material, after addition of CF3, the formed alcoholate undergoes phosphonate-phosphate rearrangement to form the acyl anion, followed by elimination of F- to give 1-aryldifluoroethenyl phosphates in 87-97% yields. As a representative example, vinylphosphate 6a was converted into 2,2-difluoro-1-phenylethanone 7 with 6 N HCl/EtOH/reflux or CAN/NaOH/MeOH/0 degrees C in 82-90% yields.     

Modelling of Swelling Phenomena in Charged Hydrated Porous Media

Biological tissues like articular cartilage and geomaterials like clay have a multicomponent microstructure. The charged solid is saturated by a viscous fluid, which itself is composed of several components: the liquid solvent and the dissolved ions, namely, water, anions and cations. These charged multiphase materials exhibit a swelling behaviour under varying chemical conditions. The model describing such materials combines electrochemical and mechanical effects like osmosis and electrostatics within a macroscopic formulation. Starting from the Theory of Porous Media (TPM), a four component model is presented, wherein all constituents are materially incompressible and mass exchanges are excluded. This isothermal model leads to a set of equations which consists of three primary variables: the solid displacement u _S, the pore‐pressure p and the molar ion concentration c_m, since the ion concentrations always depend on each other because of the electroneutrality condition. For the numerical treatment, the weak formulations of governing equations are implemented in the FE tool PANDAS, wherein Taylor‐Hood elements are used for the spatial discretization. Finally, a simulation of a 3‐d swelling experiment is shown. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)