New soliton solutions of Davey–Stewartson equation with power-law nonlinearity

This study is related to new soliton solutions of Davey–Stewartson equation (DSE) with power-law nonlinearity. The generalized Kudryashov method which is one of the analytical methods has been used for finding exact solutions of this equation. By using this method, dark soliton solutions of DSE have been found. Also, by using Mathematica Release 9, some graphical representations have been done to analyze the motion of these solutions.     

Aqua­di­chloro­(di‐2‐pyridyl­di­azene)copper(II) monohydrate

The crystal structure of the mononuclear title complex, [CuCl₂(C₁₀H₈N₄)(H₂O)]·H₂O, shows an s‐cis/E/s‐trans‐configured di‐2‐pyridyl­diazene ligand, with the square‐pyramidal Cu^II ion coordinated to one pyridyl and one diazene N atom together with two Cl atoms and one aqua ligand. The crystal packing involves both hydrogen‐bonding and π–π interactions. The solvent water mol­ecule links three monomers to one another through hydrogen‐bonding interactions in which two monomers are linked via chloro ligands and the third via the aqua ligand. Face‐to‐face and weak slipped π–π interactions also occur between di‐2‐pyridyl­diazene moieties, and these interactions are responsible for the interchain packing.     

Derivatizable novel β-tetra 7-oxycoumarin-3-carboxylate substituted metallophthalocyanines: Synthesis and characterization

In this study, a novel phthalonitrile, ethyl 7-(3,4-dicyanophenoxy)coumarin-3-carboxylate (1), was prepared and characterized. The metallophthalocyanines (3–6) were prepared by cyclotetramerization of 1 with the corresponding metal salts {Zn(OAc)₂·2H₂O, Co(OAc)₂·4H₂O, Cu(OAc)₂, Ni(OAc)₂·4H₂O} in 2-chloronaphthalene. Reaction of 3 with aqueous hydrochloric acid gave the coumarino-zincphthalocyanine (3a) carrying carboxyl groups at the 3-position of all the coumarin moieties. Treatment of compound 3a with aqueous NaOH_./AgNO₃ or aqueous NaOH in N,N-dimethylformamide (DMF) gave the expected silver (3c) or sodium (3d) salts, respectively. The four carboxylic groups in coumarino-zincphthalocyanine (3a) and the four carboxylate groups in 3d make the compounds have good solubility in water. Heating of the acyl chloride derivative of 3 with morpholine in DMF yielded the corresponding 3-carboxymorpholinamide (3b). The newly prepared compounds, phthalonitrile and metallophthalocyanines, have been characterized by FT-IR, UV–Vis, MALDI-TOF and ¹H NMR spectroscopies.     

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.     

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.