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Finite Dimensional Attractors For A Class Of Semilinear Wave Equations, A. Eden, V. Kalantarov
Finite Dimensional Attractors For A Class Of Semilinear Wave Equations, A. Eden, V. Kalantarov
Turkish Journal of Mathematics
In this paper we give a self-contained survey of results related with the global attractors for a class of nonlinear wave equations with damping or viscosity terms. In particular, we prove the existence of a finite dimensional attractor and estimate its fractal dimension by imbedding it in an exponential attractor. Some results on global stability, existence of finite dimensional attractors were already partially discussed in Kalantarov [44] and in Eden et. al. [25], however we simplify the framework by introducing a unified approach to both the existence of attractors through \alpha-contractions and the construction of exponential attractors via some Lipschitzianity …
Comparison Of Invariants For Triples Of Hilbert Spaces, P. A. Chalov
Comparison Of Invariants For Triples Of Hilbert Spaces, P. A. Chalov
Turkish Journal of Mathematics
In [2,3] the sequence of invariant characteristics (\mu_{m}) for the finite families of Hilbert spaces were considered. Here we make a comparison of these invariants among themselves. We construct some examples of triples of Hilbert spaces, which show that each system of the first r+1 characteristics is stronger than the system of the first r of them. Moreover we show that there exist triples of Hilbert spaces which on the one hand are not quasidiagonally isomorphic, but on the other hand they cannot be distinguished by any function \mu_{m},\,\, m\in\,\, \Bbb N.
An Extension Of The Binomial Theorem With Application To Stability Theory, Z. Zahreddinea
An Extension Of The Binomial Theorem With Application To Stability Theory, Z. Zahreddinea
Turkish Journal of Mathematics
We show how it is possible to put different stability types such as Routh-Hurwitz and Schur-Cohn on common grounds by establishing direct links between them. In the process, we obtain natural and elegant extensions of both Pascal's rule and the binomial theorem, which prove useful in establishing our main results. A M S subject classification: Primary 34D, Secondary 93D.
The Inverse Nonstationary Scattering Problem For A Hyperbolic System Of Equations On Semi-Axis, N. Sh. Iskenderov, A. Yildiz
The Inverse Nonstationary Scattering Problem For A Hyperbolic System Of Equations On Semi-Axis, N. Sh. Iskenderov, A. Yildiz
Turkish Journal of Mathematics
In this paper, the direct and inverse nonstationary scattering problem for a hyperbolic system of n equations (n>3) on a semi-axis is studied. The coefficients of the system are uniquely determined according to scattering operator. The solution of the problem is generalized for an arbitrary natural number n applying the properties of separation of factors by means of operator transformations to some elements of the scattering operator and its inverse as well as reducing the scattering problem given on a semi-axis to the scattering problem on the whole-axis.
Some Applications Of Fractional Calculus Operators To A Certain Subclass Of Analytic Functions With Negative Coefficients, Nak Eun Cho, M. K. Aouf
Some Applications Of Fractional Calculus Operators To A Certain Subclass Of Analytic Functions With Negative Coefficients, Nak Eun Cho, M. K. Aouf
Turkish Journal of Mathematics
The object of the present paper is to prove various distortion theorems for the fractional calculus of functions in the class T_{n}\left(\lambda,\alpha\right) consisting of analytic and univalent functions with negative coefficients. Furthermore, a distortion theorem for a fractional integral operator of functions in the class T_{n}\left(\lambda,\alpha\right) is shown.
On A Differential Sequence In Geometry, E. Ortaçgi̇l
On A Differential Sequence In Geometry, E. Ortaçgi̇l
Turkish Journal of Mathematics
We construct an exact differential sequence which indicates certain relations between curvature, local flatness, torsion and simplicity of higher order connections. Our formulas are expressed explicity in terms of the Christoffel symbols of dual \varepsilon-connections.
On The \Ell_{P} Norms Of Almost Cauchy-Toeplitz Matrices, D. Bozkurt
On The \Ell_{P} Norms Of Almost Cauchy-Toeplitz Matrices, D. Bozkurt
Turkish Journal of Mathematics
In this study, we have given the definition of almost Cauchy-Toeplitz matrix. i.e. its elements are t_{ij}= a(i=j) and t_{ij}=1/(i-j)\, (i\neq j) such that a is a real number. We have found a lower and upper bounds for the \ell_{p} norm of this matrix. Furthermore, we have done the proof of the conjecture that were given by myself for the spectral norm of this matrix.
On (\Sigma,\Tau) Derivations With Module Values, M. Soytürk
On (\Sigma,\Tau) Derivations With Module Values, M. Soytürk
Turkish Journal of Mathematics
Let R be a ring, X\neq (0) an R-bi-module, d: R\ra X a(\sigma,\tau)- derivation with module value such that d\sigma=\sigma d, d\tau=\tau d and U\neq (0) an ideal of R. Furthermore the following properties are also satisfied. \begin{eqnarray*} && \mbox{For }x\in X, a\in R\quad x Ra=0 \mbox{ implies } x=0 \mbox{ or } a=0 \ldots\ldots (G_{1})\\ && \mbox{For }a\in R, x\in X \quad a Rx=0 \mbox{ implies } a=0 \mbox{ or } x=0 \ldots\ldots (G_{2}) \end{eqnarray*} \noindent In this paper we have proved the following results; (1) If (G_{1}) (or (G_{2})) is satisfied and for a \in R, d(U) a=0 …
The Investigation Of Aluminum Sulfate-Potassium Chloride Solid Phase Reaction, İ. Ayhan Şengi̇l
The Investigation Of Aluminum Sulfate-Potassium Chloride Solid Phase Reaction, İ. Ayhan Şengi̇l
Turkish Journal of Chemistry
It was found that aluminum sulfate reacts with potassium chloride to produce K_{2}SO_{4}, Al_{2}O_{3}, and Cl_{2} in the solid phase at 700 ^{\circ}C. This reaction was investigated with thermal analysis under air and nitrogen atmosphere. By changing temperature and time parameters, the actual yield of conversion in question was examined analytically and the optimum temperature and time were found for the reaction. The rate expression of the solid phase reaction was also investigated and the rate equation was obtained.
Analysis Of Retention In Supercritical Fluid Chromatography And Its Relation To Solubility, Z. Şermin Gönenç, Uğur Akman, Aydın K. Sunol
Analysis Of Retention In Supercritical Fluid Chromatography And Its Relation To Solubility, Z. Şermin Gönenç, Uğur Akman, Aydın K. Sunol
Turkish Journal of Chemistry
The effects of temperature, pressure and supercritical fluid density on the solubility-retention relationship of solutes in supercritical fluid chromatography are investigated. New retention data for naphthalene, phenanthrene, benzoic acid and 2-methoxy-naphthalene is obtained as a function of pressure at different temperatures. The bulk of the data is taken near the critical region of the mobile gas where the anomalities are expected. This data is used to compare two approaches for thermodynamic modeling of pressure dependence of solute retention. In these approaches, mobile-phase partial molar volumes of the solutes are determined either from bulk solubility data or from infinite-dilution fugacity coefficients. …
Quantum-Chemical Investigations On The Functionalized 1h-Pyrimidines, İsmail Yildirim, Makbule Tezcan, Yahya Güzel, Emin Saripinar, Yunus Akçamur
Quantum-Chemical Investigations On The Functionalized 1h-Pyrimidines, İsmail Yildirim, Makbule Tezcan, Yahya Güzel, Emin Saripinar, Yunus Akçamur
Turkish Journal of Chemistry
Conformational analysis and quantum-chemical calculations were carried out by means of the methods MMP2 and SCF MO LCAO in the CNDO/2 and MNDO approximation for the series of compounds being functionalized 1H- pyrimidines. The analysis of the electron density distribution depending on the substituents' nature was done on the basis of the data obtained.
Investigation Of Acid Sites On V_{2}O_{5}/Tio_{2}(A) Catalysts By Ftir With Adsorption Of Pyridine, Ahmet Akbaş, Holger Mi̇tzel, Dieter Höni̇ce
Investigation Of Acid Sites On V_{2}O_{5}/Tio_{2}(A) Catalysts By Ftir With Adsorption Of Pyridine, Ahmet Akbaş, Holger Mi̇tzel, Dieter Höni̇ce
Turkish Journal of Chemistry
The V_{2}O_{5}/TiO_{2}(A) catalysts were prepared by the grafting and their Br\"{o}nsted and Lewis acid sites were investigated with pyridine adsorption by using FTIR Spectroscopy. The results obtained showed that monolayer or less coverage of the surface of the support, TiO_{2}(A), took place up to V_{2}O_{5} content of 11.88 \%. When V_{2}O_{5} amount was higher then 11.88 \%, the support was covered as multilayer. Pyridine adsorption studies showed that the number of the Lewis acid sites of the V_{2}O_{5}/TiO_{2}(A) catalysts decreased with increasing of V_{2} O_{5} amount. The number of the Br\"{o}nsted acid sites increased with increasing V_{2}O_{5} content, reached a …
Poly (D,L-Lactic Acid) Homopolymers: Synthesis And Characterization, Xu Kaitian, Ahmet Kozluca, Emir B. Denkbaş, Erhan Pi̇şki̇n
Poly (D,L-Lactic Acid) Homopolymers: Synthesis And Characterization, Xu Kaitian, Ahmet Kozluca, Emir B. Denkbaş, Erhan Pi̇şki̇n
Turkish Journal of Chemistry
In this study, poly(D,L-lactic acid or D,L-lactide) (PDLLA) homopolymers were synthesized with different molecular weights. Low molecular weight PDLLAs (MW_n: 500-2300) were synthesized by direct polycondensation of DL-lactic acid without using any catalyst, while high molecular weight PDLLAs ( MW_n: 8x10^3-150x10^3) were produced by ring-opening polymerization of DL-lactide with stannous chloride as catalyst (initiator). Average molecular weights of PDLLAs were determined by end-group analysis, by viscosimetric measurements and by HPLC. PDLLA homopolymers were characterized by FTIR, NMR and DSC. In the production of PDLLAs by direct polymerization, molecular weights of the PDLLAs increased with the increase in the polymerization time …
Catalysis Of Autoxidation Of 2,6-Di-Tert-Butylphenol In Water By Metallophthalocyanine Tetrasulfonates Bound To Polyelectrolyte Supports, Yasemin Tura Kopkalli, Hayrettin Türk
Catalysis Of Autoxidation Of 2,6-Di-Tert-Butylphenol In Water By Metallophthalocyanine Tetrasulfonates Bound To Polyelectrolyte Supports, Yasemin Tura Kopkalli, Hayrettin Türk
Turkish Journal of Chemistry
2,6-and 2,10-Ionenes and soluble poly(vinylbenzyl)trimethylammonium chloride polyelectrolytes were synthesized and used as catalyst supports for cobalt-, iron- and copper-phthalocyanine tetrasulfonates on the autoxidation of 2,6-di-{\it tert}-butylphenol in water by molecular oxygen. Polyelectrolyte supported cobalt-phthalocyanine tetrasulfonate showed the highest activity in comparison with the supported analogous of iron- and copper-phthalocyanine tetrasulfonates. The supported metallophthalocyanine tetrasulfonates had better catalytic activities than the unsupported analogous for the reaction. The reaction yielded 3,3',5,5'-tetra-tert-butyl- 4,4'-diphenoquinone as the only oxidation product of 2,6-di-tert-butylphenol. The extent of the reaction was affected by time, temperature, pH, the types and concentrations of supports and metallophthalocyanine tetrasulfonates.
A Kinetic Study Of Homogeneous Bulk Polymerization Of Ethyl Methacrylate Initiated By Benzoyl Peroxide And An N, N^{\Prime} -Dimethylaniline Redox Pair, Serap Şenel, Belma Işik-Yürüksoy, Olgun Güven
A Kinetic Study Of Homogeneous Bulk Polymerization Of Ethyl Methacrylate Initiated By Benzoyl Peroxide And An N, N^{\Prime} -Dimethylaniline Redox Pair, Serap Şenel, Belma Işik-Yürüksoy, Olgun Güven
Turkish Journal of Chemistry
The homogenous bulk polymerization of ethyl methacrylate (EMA) was studied using benzoyl peroxide (BPO) and an N,N^{\prime}-dimethylaniline (DMA) redox pair with the dilatometric method. The half-order dependence of the polymerization rate upon both the BPO and DMA concentrations was obtained. The overall activation energy of the polymerization was found to be between 32.3-55.3 kJ/mole for different initial molar ratios of the redox pair. A retaring effect was observed at lower polymerization temperatures for low concentrations of BPO. The formation of reddish colored polymers at higher DMA concentrations was explained by the adsorption of adduct formed between DMA radicals.
Crystal Structure Of Tris(2-Hydroxyethyl)Ammonium Bromide, Veysel T. Yilmaz, Hasan İçbudak, Halis Ölmez, R. Alan Howie
Crystal Structure Of Tris(2-Hydroxyethyl)Ammonium Bromide, Veysel T. Yilmaz, Hasan İçbudak, Halis Ölmez, R. Alan Howie
Turkish Journal of Chemistry
The crystal structure of tris(2-hydroxyethyl)ammonium bromide, [HN(CH_{2}CH_{2}OH)_{3}]Br, was determined as rhombohedral by single crystal X-ray diffractometer. The final R value was found to be 0.032 for 576 observed reflections. The crystal consists of layers of hydrogen-bonded cations, [HN(CH_{2}CH_{2}OH)_{3}]^{+} and anions, Br^{-}. Within a layer every cation donates and every anion accepts three hydrogen bonds. In the cation, trifurcated intramolecular hydrogen bonds are formed due to the surrounding of the hydrogen atom bonded to the N atom by the 2-hydroxyethyl groups.
Chelate Ring-Closure Kinetics Of Cr(Co)_5 (Dppm) Studied By ^{31}P-Nmr Spectroscopy, Saim Özkar, Ceyhan Kayran, Ayşin Tekkaya
Chelate Ring-Closure Kinetics Of Cr(Co)_5 (Dppm) Studied By ^{31}P-Nmr Spectroscopy, Saim Özkar, Ceyhan Kayran, Ayşin Tekkaya
Turkish Journal of Chemistry
^{31}P-NMR spectroscopy was used to study the kinetics of the chelate ring-closure reaction in CR(CO)_5 (DPPM) where DPPM is bis (diphenylphosphino) methane. DPPM is potentially a bidentate ligand, but in this complex it is coordinated to the transition metal in a monodentate fashion and therefore can undergo chelation. The thermal chelate ring-closure reaction was carried out in an NMR sample tube at a constant temperature and the course of the reaction was quantitatively followed by taking ^{31}P-NMR spectra in appropriate time intervals. Kinetic results have shown that the chelate ring-closure reaction of Cr(CO)_5 DPPM is of zero-order. Activation parameters were …
The Effects Of Polyacrylic Acid/Polypyrrole Composite Coating On Photocorrosion And Photoactivity Of Pyrite Electrodes, A. Sezai Saraç, Belkıs Ustamehmetoğlu, Esma Sezer, Candan Erbi̇l
The Effects Of Polyacrylic Acid/Polypyrrole Composite Coating On Photocorrosion And Photoactivity Of Pyrite Electrodes, A. Sezai Saraç, Belkıs Ustamehmetoğlu, Esma Sezer, Candan Erbi̇l
Turkish Journal of Chemistry
Electrically conducting polyacrylic acid (PAA)/Polypyrrole (PPy) composite films were prepared by electrochemical polymerization of pyrrole on PAA which was electrocheimically adsorbed on natural and synthetic pyrite ( FeS_{2}) electrodes. The application of such polymer coating on pyrite, which is one of the semiconducting materials for solar applications, shows almost total protection against corrosion and can improve the photoactive character of the electrode. Addition of Ce(IV) ammonium nitrate into this system improved the photoactivity of the PAA/PPy composite. The composite polymer has higher photoconductivity than the pure PPy, because of the doping effect of anions on the PPA/PPy composite.
Validity Of A Linear Estimator For The Total \Pi-Electron Energy Of Alternant Hydrocarbons, Lemi Türker
Validity Of A Linear Estimator For The Total \Pi-Electron Energy Of Alternant Hydrocarbons, Lemi Türker
Turkish Journal of Chemistry
The validity of a linear topological estimator formula which possesses a slope k such that 0