Properties of eigenvalues and spectral singularities for impulsive quadratic pencil of difference operators

In this paper, we investigate the spectral analysis of impulsive quadratic pencil of difference operators. We first present a boundary value problem consisting one interior impulsive point on the whole axis corresponding to the above mentioned operator. After introducing the solutions of impulsive quadratic pencil of difference equation, we obtain the asymptotic equation of the function related to the Wronskian of these solutions to be helpful for further works, then we determine resolvent operator and continuous spectrum. Finally, we provide sufficient conditions guarenteeing finiteness of eigenvalues and spectral singularities by means of uniqueness theorems of analytic functions. The main aim of this paper is demonstrating the impulsive quadratic pencil of difference operator is of finite number of eigenvalues and spectral singularities with finite multiplicities which is an uninvestigated problem proposed in the literature.     

Multidetermination of thiamine HCl and pyridoxine HCl in their mixture using continuous daubechies and biorthogonal wavelet analysis

A new graphical method based on the one-dimensional wavelet transform (WT) was proposed and tested on mixture of thiamine hydrochloride (THI) and pyridoxine hydrochloride (PYR) in the presence of strongly overlapping signals. We selected from the data of the UV-VIS absorption spectra a signal consisting of 1150 points corresponding to the concentration range 8-32 mg ml⁻¹ for each vitamin and we subjected it to Daubechies8 (DAUB8) and Biorthogonal6.8 (BIOR6.8) wavelet transforms. Since the peaks of the transformed signals were bigger than original ones a zero crossing method was applied to obtain the calibration graphs. In addition, the validity of Beer-Lambert law was assumed for the transformed signals. An appropriate scale setting was choosing to obtain an alternative calibration for each method. Matlab 6.5 software was used for one-dimensional wavelet analysis and the basic concepts about wavelet method were given. The obtained results were successfully compared among each other as well as with those obtained by other literature methods. The method developed in this paper is rapid, easy to apply, not expensive and it is suitable for analyzing of the overlapping signals of compounds in their mixtures without any chemical pre-treatment.     

Synthesis and characterization of mononuclear cadmium(II) and dinuclear uranyl(VI) complexes with <Emphasis Type="Italic">vic</Emphasis>-dioximes

In this study, the mononuclear complexes of cadmium(II) and dinuclear complexes of uranyl(VI) with five vic-dioximes have been obtained. Cadmium(II) forms, with ligands, complexes [(L ^xH)(Cl)(H₂O)(Cd)] with x=1–5. Mononuclear complexes with a metal: ligand ratio of 1:1 were obtained for cadmium(II) with the ligands, and a chloride ion and a water molecule are also coordinated to the cadmium(II) ions. Uranyl(VI) complexes of these ligands are a dinuclear structure with μ-hydroxo-bridges. Uranyl(VI) forms, with ligands, complexes [(L^xH)₂(OH)₂(UO₂)₂] with x=1–5, which have a 2:2 metal:ligand ratio. The structures of the complexes were identified by elemental analysis, i.r., and ¹H-n.m.r. spectra, u.v.–vis. spectroscopy, magnetic susceptibility measurements, conductivity measurements and thermogravimetric analysis (t.g.a.).     

Optimization of a new resin, Amberlyst 36, as a solid-phase extractor and determination of copper(II) in drinking water and tea samples by flame atomic absorption spectrometry

A new simple and reliable method has been developed to separate and preconcentrate trace copper ion in drinking water and tea samples for subsequent measurement by flame atomic absorption spectrometry (FAAS). The copper ions are adsorbed quantitatively during passage of aqueous solutions through Amberlyst 36 cation exchange resin. After the separation and preconcentration stage, the analyte was eluted with a potassium cyanide solution and determined by FAAS. Different factors including pH of sample solution, sample volume, amount of resin, flow rate of aqueous solution, volume and concentration of eluent, and matrix effects for preconcentration were examined. The analytical figures of merit for the determination of copper are as follows: analytical detection limit (3 sigma), 0.26 microg/L; precision (RSD), 3.1% for 100 microg/L; enrichment factor, 200 (using 1000 mL of sample solution and 5 mL of eluent); time of analysis, 3.5 h (for obtaining enrichment factor of 200); capacity of resin, 125 mg/g. The method was applied for copper determination by FAAS in tap water, commercial natural spring water, commercial treated drinking water, and commercial tea bag sample. The accuracy of the method is confirmed by analyzing tea leaves (GBW 07605). The results demonstrated good agreement with the certified values.     

Synthesis and Characterization of Two vic-Dioximes Containing the 1,3-Dioxolane Ring and 1,4-Diaminobutane and Their Cobalt(II), Nickel(II), Copper(II) and Zinc(II) Metal Complexes

Two new vic-dioxime ligands, (E,E)-N-{4-[(1,4-dioxaspiro[4.4]non-2-ylmethyl)amino]butyl}-N-hydroxy-2-(hydroxyimino)ethanimidamide (L¹H₂) and (E,E)-N-{4-[(1,4-dioxaspiro[4.5]dec-2-ylmethyl)amino]butyl}-N-hydroxy-2-(hydroxyimino)ethanimidamide (L²H₂) containing two different heteroatoms (N,O) have been prepared from anti-chloroglyoxime, N-(1,4-dioxaspiro[4.4]non-2-ylmethyl)butane-1,4-diamine (3) and N-(1,4-dioxaspiro[4.5]dec-2-ylmethyl)butane-1,4-diamine (4). Co^II, Ni^II and Cu^II complexes of the ligands have a metal:ligand ratio of 1:2 and the ligands coordinate through the two N atoms, as do most of the vic-dioximes. However, Zn^II complexes of the ligands have a metal:ligand ratio of 1:1 and the ligands are coordinated only by the N, O atoms of the vic-dioximes. In the Co^II complexes two water molecules, and in the Zn^II complexes a chloride ion and a water molecule, are also coordinated to the metal ion. The structures of the compounds were determined by a combination of elemental analysis, magnetic moments, molar conductances, thermogravimetric analysis (t.g.a.) and spectroscopic (u.v.–vis., i.r., ¹H- and ¹³C-n.m.r.) data.     

Indoloquinazoline Alkaloids from Araliopsis tabouensis

Three new indoloquinazolidine‐type alkaloids, 8,13‐dihydro‐2‐methoxyindolo[2′,3′: 3,4]pyrido[2,1‐b]quinazolin‐5(7H)‐one ( 1 ), 8,13‐dihydro‐2‐methoxy‐13‐methylindolo[2′,3′: 3,4]pyrido[2,1‐b]quinazolin‐5(7H)‐one ( 2 ), and 5,8,13,14‐tetrahydro‐2‐methoxy‐14‐methyl‐5‐oxo‐7H‐indolo[2′,3′: 3,4]pyrido[2,1‐b]quinazolim‐6‐iun chloride ( 3 ) were isolated from Araliopsis tabouensis, together with three known compounds. The structures of the new compounds were determined primarily from 1D‐ and 2D‐NMR analysis. The antimalarial activities of compounds 1 – 5 were evaluated against Plasmodium falciparum D6 and W2 clones. The IC₅₀ values in antimalarial bioassay for compounds 2 – 5 varied from 1.8 to 4.7 μg/ml.     

On almost πgp-continuous functions

We introduce the notion of almost πgp-continuous functions. The characterizations of almost πgp-continuous functions and preservations theorems are obtained. Also, the implications between all related forms of continuities and almost πgp-continuity are discussed.     

Hybrid finite element/volume method for 3D incompressible flows with heat transfer

An implicit hybrid finite element (FE)/volume solver has been extended to incompressible flows coupled with the energy equation. The solver is based on the segregated pressure correction or projection method on staggered unstructured hybrid meshes. An intermediate velocity field is first obtained by solving the momentum equations with the matrix-free implicit cell-centred finite volume (FV) method. The pressure Poisson equation is solved by the node-based Galerkin FE method for an auxiliary variable. The auxiliary variable is used to update the velocity field and the pressure field. The pressure field is carefully updated by taking into account the velocity divergence field. Our current staggered-mesh scheme is distinct from other conventional ones in that we store the velocity components at cell centres and the auxiliary variable at vertices. The Generalized Minimal Residual (GMRES) matrix-free strategy is adapted to solve the governing equations in both FE and FV methods. The presented 2D and 3D numerical examples show the robustness and accuracy of the numerical method.     

Mehmet Nadir: An amateur mathematician in Ottoman Turkey

This note summarizes the results of a recent survey of all the mathematical work of Mehmet Nadir, a Turkish amateur mathematician and professional educator who lived from 1856 to 1927 during the last years of the Ottoman Empire and the first years of the Turkish Republic. It is shown that, although working in isolated and adverse conditions, Nadir was able to establish a continuous correspondence with mathematicians in western Europe and, through his studies in number theory, obtained some results of lasting value.