Parallel and k-out-of-n: G systems with nonidentical components and their mean residual life functions

A system with n independent components which has a k-out-of-n: G structure operates if at least k components operate. Parallel systems are 1-out-of-n: G systems, that is, the system goes out of service when all of its components fail. This paper investigates the mean residual life function of systems with independent and nonidentically distributed components. Some examples related to some lifetime distribution functions are given. We present a numerical example for evaluating the relationship between the mean residual life of the k-out-of-n: G system and that of its components.     

A brief history of mathematics education in Turkey: K-12 mathematics curricula

In this study, we survey the history of mathematics education in Turkey starting with its historical roots in the foundation of the republic. The changes in mathematics education in Turkey over the last century are investigated through an analysis of changes in curricular documents for K-12 schools. We consider the factors and reasons affecting curriculum developments, changes in philosophy and structure in terms of standards, objective and instructions. This article utilizes archival research techniques by examining original sources and illustrates the nature of the changes benefiting from a historical perspective. As a result of such analysis of the aforesaid sources, we have seen that the main reasons for changing mathematics curricula are: to build up a modern civilization in Turkey; the reports of John Dewey and the recommendations of Kate Wofford, William C. Varaceus and Watson Dickerman; the desire to become a member of the European Union; international factors and political situations.     

Elliptic function solutions for some nonlinear pdes in mathematical physics

In this work, we have constructed various types of soliton solutions of the generalized regularized long wave and generalized nonlinear Klein-Gordon equations by the using of the extended trial equation method. Some of the obtained exact traveling wave solutions to these nonlinear problems are the rational function, 1-soliton, singular, the elliptic integral functions $F, E, \Pi$ and the Jacobi elliptic function sn solutions. Also, all of the solutions are compared with the exact solutions in literature, and it is seen that some of the solutions computed in this paper are new wave solutions.     

Synthesis,Spectrothermal Behaviour and Molecular Structure of Aquaorotatotriethanolaminenickel(II) Monohydrate

The aquaorotatotriethanolaminenickel(II) monohydrate, [Ni(HOr)(H₂O)(tea)]·H₂O ( 1 ), was synthesized and characterized by means of elementel analysis, IR and UV‐Vis, spectroscopy, magnetic susceptibility, thermal analysis and X‐ray diffraction techniques. The nickel ion in [Ni(C₅H₂N₂O₄)(H₂O)(N(C₂H₄OH)₃)] is chelated to the deprotonated N3 pyrimidine atom and to the carboxylate oxygen atom of the bidentate orotate dianion, and to the one nitrogen and two oxygen atoms of the tridentate triethanolamine molecule and its octahedral geometry is completed by an aqua ligand. It crystallizes in the monoclinic system, space group P2₁/c with lattice parameters a = 7.1528(5) Å, b = 19.4903(14) Å, c = 11.8085(8) Å, β = 106.237(5)°, V = 1580.55(19) ų, Z = 4. An extensive three dimensional network of O_w‐H…O, N‐H…O and O‐H…O hydrogen bonds, π‐π and π‐ring interactions are responsible for crystal stabilization. The decomposition reaction take places in the temperature range 20‐1000 °C in the static air atmosphere. Thermal decomposition of 1 proceeds in three stages.     

Speciation of Cr(III) and Cr(VI) in Environmental Samples after Solid Phase Extraction on Amberlite XAD–2000

A method for speciation of Cr(III) and Cr(VI) in real samples has been developed. Cr(VI) has been separated from Cr(III) and preconcentrated as its pyrrolidinedithiocarbamate (APDC) complex by using a column containing Amberlite XAD–2000 resin and determined by FAAS. Total chromium has also been determined by FAAS after conversion of Cr(III) to Cr(VI) by oxidation with KMnO₄. Cr(III) has been calculated by subtracting Cr(VI) from the total. The effect of pH, flow‐rate, adsorption and batch capacity and effect of various metal cations and salt anions on the sorption onto the resin were investigated. The adsorption is quantitative in the pH range of 1.5–2.5, and Cr(VI) ion was desorbed by using H₂SO₄ in acetone. The recovery of Cr(VI) was 97 ± 4 at a 95% confidence level. The highest preconcentration factor was 80 for a 200 mL sample volume. The adsorption and batch capacity of sorbent were 7.4 and 8.0 mg g^?1 Cr(VI), respectively, and loading half time was 5.0 min. The detection limit of Cr(VI) is 0.6 μg/L. The procedure has been applied to the determination and speciation of chromium in stream water, tap water, mineral spring water and spring water. Also, the proposed method was applied to total chromium preconcentration in microwave digested moss and rock samples with satisfactory results. The developed method was validated with CRM‐TMDW‐500 (Certified Reference Material Trace Metals in Drinking Water) and BCR‐CRM 144R s (Certified Reference Material Sewage Sludge, Domestic Origin) and the results obtained were in good agreement with the certified values. The relative standard deviations were below 6%.     

The Synthesis of Novel Crown Ethers. Part IV. Coumarin Derivatives of [18]crown-6 and Cation Binding from Fluorescence Spectra

4-H, 4-methyl and 4-phenyl-1-benzopyran-2-one derivatives of [18]crown-6 derivatives were synthesised from 6,7- and 7,8-dihydroxy-1-benzopyran-2-one reacting with pentaethylene glycol ditosylate in K₂CO₃/DMF/water. The products were identified by elemental analysis, EI-GC-mass spectra and ₁H-NMR spectroscopy. The Na⁺ association constants of some coumarin derivatives were determined with an ion selective electrode in water. The Na⁺ , K⁺, Ba²⁺ and Sr²⁺ binding role of such compounds were particularly observed as remarkable alterations in acetonitrile. The 1 : 1 associations constants of K⁺ and Na⁺ with some coumarin-[18]crown-6 derivatives estimated by this way in acetonitrile exhibited the utility of complexing enhanced quenching fluorescence spectra for the ion binding power of the such macrocycles.     

Comparative Methodology for Isolation of Flavonoid Glycosides from Clusia criuva Cambess

The family Guttiferae belongs to the superorder Theiflorae, order Theales and according to Dahlgren's system of classification, it is equivalent to Hypericaceae (=Clusiaceae) [1]. This family consists of 49 genera encompassing over 1000 species of wide distribution in the tropics as shrubs and trees [2]. Plants of the genus Clusia have been used in folk medicine for the treatment of different kind of illness such as: febrifuge, anti rheumatic, purgative, for stomach problems and, in Brazil, they are very commonly used to heal wounds [3]. The key of any study of material from natural sources is the availability of suitable separation methods for the isolation of pure products [4–6]. Tentatives for separations using chomatography on solid support phases were not very efficients in the fractionation of Clusia criuva Cambess methanolic/ethyl acetate extracts. However, the use of counter-current chromatography, an all liquid technique, showed advantages in comparison with the more traditional liquid-solid separation methods and even with HPLC. In this sense it was possible to isolate flavonoid glycosides from ethyl acetate extract of Clusia criuva, in a very short operation time.     

Optical solitons and modulation instability analysis of the (1+1)-dimensional coupled nonlinear Schrödinger equation

This study successfully reveals the dark, singular solitons, periodic wave and singular periodic wave solutions of the (1+1)-dimensional coupled nonlinear Schrödinger equation by using the extended rational sine-cosine and rational sinh-cosh methods. The modulation instability analysis of the governing model is presented. By using the suitable values of the parameters involved, the 2-, 3-dimensional and the contour graphs of some of the reported solutions are plotted.     

Some difference sequence spaces defined by a sequence of <Emphasis Type="Italic">ϕ</Emphasis> -functions

Abstract  In this paper, we introduce new difference sequence spaces combining with de la Vallee-Poussin mean using by a sequence of modulus functions and ϕ -functions. We also studied connections between statistically convergence related with this space. Keywords Difference sequence, Modulus function, ϕ -function, De la Vallee-Poussin means, Statistical convergence Mathematics Subject Classification (2000) 46A45, 40F05, 46A80