On Non-M-Cosingular Completely ⊕-Supplemented Modules

In this paper, it is shown that any non--cosingular -supplemented module is if and only if has the summand intersection property. Let be any module such that has a coclosure in . Then we prove that is (completely) -supplemented if and only if for some submodule of such that and both are (completely) -supplemented.     

Fractal interpolation on the Sierpinski Gasket

We prove for the Sierpinski Gasket (SG) an analogue of the fractal interpolation theorem of Barnsley. Let V₀={p₁,p₂,p₃} be the set of vertices of SG and the three contractions of the plane, of which the SG is the attractor. Fix a number n and consider the iterations uw=uw₁uw₂?uwn for any sequence w=(w₁,w₂,…,wn)∈n{1,2,3}. The union of the images of V₀ under these iterations is the set of nth stage vertices Vn of SG. Let F:Vn→R be any function. Given any numbers αw(w∈n{1,2,3}) with 0<|αw|<1, there exists a unique continuous extension of F, such that

f(uw(x))=αwf(x)+hw(x)     

Electrochemical Analysis of Liposome-encapsulated Colistimethate Sodium

In this study, the neutral and cationic liposomal formulations of Colistimethate sodium (CMS), an antibiotic for multi-drug resistant gram-negative bacteria, were prepared and electrochemical quantification of CMS from these liposomes were achieved. This is the first study of the electrochemical detection of CMS released from liposomes. First, the electrochemical properties of CMS were analysed, then the encapsulation efficiency, and the release kinetic of CMS from liposomes were determined with Differential Pulse Voltammetry (DPV) measurements. In addition, Cyclic Voltammetry were applied to determine oxidation signal of CMS. A higher encapsulation efficiency was found in the cationic liposome compared to the neutral liposome. Moreover, CMS was controlled released from liposomes with zero-order drug release kinetics.     

Novel and enantioselective syntheses of (R)- and (S)-3-hydroxy-4-(2,4,5-trifluorophenyl)butanoic acid: a synthon for sitagliptin and its derivatives

A new synthetic strategy for (R)- and (S)-3-hydroxy-4-(2,4,5-trifluorophenyl)butanoic acid, a building block in the preparation of sitagliptin and its derivatives, was developed. Pd(OAc)₂ catalyzed coupling of 2,4,5-trifluoro-1-iodobenzene with allyl alcohol gave 3-(2,4,5-trifluorophenyl)propanal in a yield of 95%. l-Proline catalyzed reaction of the 3-phenylpropanal (in only 1.2 molar equiv) with nitrosobenzene followed by reduction with NaBH₄ and Pd/C catalyzed hydrogenation gave (R)-3-(2,4,5-trifluorophenyl)propane-1,2-diol with >99% ee and 65% yield. Selective tosylation of primary hydroxyl group of the 1,2-propandiol unit followed by cyanide displacement afforded (R)-3-hydroxy-4-(2,4,5-trifluorophenyl)butanenitrile (80%). The nitrile was converted to the title β-hydroxy acid under basic hydrolysis in a yield of 90%. Thus, (R)-3-hydroxy-4-(2,4,5-trifluorophenyl)butanoic acid was prepared enantioselectively from the starting material in four steps and 45% overall yield. The reaction sequence was repeated with d-proline as the catalyst to give (S)-3-hydroxy-4-(2,4,5-trifluorophenyl)butanoic acid in 45% overall yield and >99% enantiomeric excess.     

Surface spin disorder and spin-glass-like behaviour in manganese-substituted cobalt ferrite nanoparticles

Due to the increasing use of silver nanoparticles (AgNPs) in consumer products, it is essential to understand how variables, such as light exposure, may change the physical and chemical characteristics of AgNP suspensions. To this end, the effect of 300?nm ultraviolet (UV) light on (20, 40, 60 and 80)?nm citrate-capped AgNP suspensions has been investigated. As a consequence of irradiation, the initial yellow hue of the AgNP suspensions is transformed towards a near colorless solution due to the loss of the surface plasmon resonance (SPR) absorbance. The decrease in SPR absorbance followed a first-order decay process for all particle sizes with a rate constant that increased linearly with the AgNP specific surface area and non-linearly with light intensity. The rate of loss of the SPR absorbance decreased with increasing citrate concentration, suggesting a surface-mediated transformation. Absorbance, atomic force microscopy, and dynamic light scattering results all indicated that AgNP photolysis was accompanied by a diameter decrease and occasional aggregation. Furthermore, in situ transmission electron microscopy imaging using a specialized liquid cell also showed a decrease in the particle size and the formation of a core?Cshell structure in UV-exposed AgNPs. X-ray photoelectron spectroscopy analysis suggested that this shell consisted of oxidized silver. The SPR in UV-exposed AgNP suspensions could be regenerated by addition of a strong reducing agent (NaBH₄), supporting the idea that oxidized silver is present after photolysis. Evidence for UV-enhanced dissolution and the production of silver ions was obtained with the Donnan membrane technique. This study reveals that the physico-chemical properties of aqueous AgNP suspensions will change significantly upon exposure to UV light, with implications for environmental health and safety risk assessments.     

Development of All‐solid‐state Antidiabetic Drug Metformin‐selective Microsensor and its Electrochemical Applications

In this study, all‐solid‐state type potentiometric PVC membrane selective microsensor was developed for Metformin (MET) which is an antidiabetic drug active substance. Metformin‐tetraphenylborate (MET‐TPB) ion‐pair was used as an ionophore in the structure of the sensor membrane. It was determined that the sensor membrane at the ratio of 69 % o‐nitrophenyl octyl ether, 27 % polyvinyl chloride and 4 % MET‐TPB performed the best potentiometric performance. In a wide concentration range (1×10^?5–1×10^?1 mol/L), the slope, detection limit, response time, pH range, and life‐time of the sensor were determined as 55.9±1.6 mV (R²=0.996), 3.35×10^?6 mol/L, 8–10 s, pH: 3–8, and ～10 weeks, respectively. The voltammetric performances of the sensor were also investigated. The prepared microsensor was successfully utilized for the determination of Metformin in a pharmaceutical drug sample by potentiometry and voltammetry. It was observed that the obtained results were in agreement with the results obtained by the UV spectroscopy method at 95 % confidence level.     

A simple spectrophotometric procedure for determination of valaciclovir in dosage forms and biological fluids

A simple and selective spectrophotometric procedure for the determination of Valaciclovir (VALA) is proposed and applied to determine the substance in tablets and biological fluids. This procedure is proposed for the determination of VALA in Britton-Robinson (BR) buffer at pH 6.0, which allows quantification over the 4 × 10^?6 to 6 × 10^?5 M range for spectrophotometric measurements. The repeatability and reproducibilty of the procedure for serum and breast milk samples are estimated. Precision and accuracy are also checked. The standard additions method is used for biological fluids. The proposed produce was verified for the determination of VALA in real human serum, breast milk samples; the selectivity over the metabolites was found to be quite satisfactory.     

How well prepared are the teachers of tomorrow? An examination of prospective mathematics teachers' pedagogical content knowledge

There is a growing emphasis in the teaching profession on pedagogical content knowledge (PCK) as an important knowledge component. The study reported in this article investigates Turkish prospective mathematics teachers’ mathematics teaching knowledge in the numbers content domain. A series of 10 open-ended scenario-type questions were adopted to challenge 83 prospective mathematics teachers’ knowledge of the learner and presentation of content in the context of PCK. The participants’ responses were analysed by means of rubrics and scoring guides developed by the researchers. The results showed that many of the future teachers performed well in determining what misconceptions students might express in the given scenarios. However, a majority of the participants performed poorly on presentation of content in terms of instructional strategies. In line with these results, the authors offer some suggestions for teacher training programmes.     

Determination of gallium at trace levels using a spectrofluorimetric method in synthetic U–Ga and Ga–As solutions

A simple, easy to use and selective spectrofluorimetric method for the determination of trace levels of gallium has been developed. A new Schiff base, N-o-vanillidine-2-amino-p-cresol (OVAC) was synthesized and its fluorescence activity with gallium investigated. Based on this chelation reaction, a spectrofluorimetric method has been developed for the determination of gallium in synthetically prepared Ga–U and Ga–As samples buffered at pH 4.0 using acetic acid–sodium acetate. The chelation reaction between Ga(III) and N-o-vanillidine-2-amino-p-cresol was very fast, requiring only 30 min at room temperature to complex completely. The limit of detection (LOD) (3σ) for Ga(III) was 7.17 nM (0.50 μg L^?1), determined from the analysis of 11 different solutions of 20 μg L^?1 Ga(III).