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Articles 136051 - 136080 of 304320

Full-Text Articles in Physical Sciences and Mathematics

Gorenstein Homological Dimensions Of Modules Over Triangular Matrix Rings, Rongmin Zhu, Zhongkui Liu, Zhanping Wang Jan 2016

Gorenstein Homological Dimensions Of Modules Over Triangular Matrix Rings, Rongmin Zhu, Zhongkui Liu, Zhanping Wang

Turkish Journal of Mathematics

Let $A$ and $B$ be rings, $U$ a $(B, A)$-bimodule, and $T=\left(\begin{smallmatrix} A & 0 \\ U & B \\\end{smallmatrix}\right)$ the triangular matrix ring. In this paper, we characterize the Gorenstein homological dimensions of modules over $T$, and discuss when a left $T$-module is a strongly Gorenstein projective or strongly Gorenstein injective module.

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Quenching Behavior Of A Semilinear Reaction-Diffusion System With Singularboundary Condition, Burhan Selçuk Jan 2016

Quenching Behavior Of A Semilinear Reaction-Diffusion System With Singularboundary Condition, Burhan Selçuk

Turkish Journal of Mathematics

In this paper, we study the quenching behavior of the solution of a semilinear reaction-diffusion system with singular boundary condition. We first get a local exisence result. Then we prove that the solution quenches only on the right boundary in finite time and the time derivative blows up at the quenching time under certain conditions. Finally, we get lower bounds and upper bounds for quenching time.

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Zero-Divisor Graph Of Matrix Rings And Hurwitz Rings, Ci̇hat Abdi̇oğlu Jan 2016

Zero-Divisor Graph Of Matrix Rings And Hurwitz Rings, Ci̇hat Abdi̇oğlu

Turkish Journal of Mathematics

Let $R$ be ring a with identity $1\neq 0$, $S_n(R)$ be a subring of the ring $T_n(R)$ of $n\times n$ upper triangular matrices over $R$, and $H_n(R)$ be the ring defined in the next section using $HR$, the ring of the Hurwitz series over $R$. In this paper, we introduce the zero-divisor graph $\overset{\rightarrow}{\Gamma}(S_n(R))$ and its underlying undirected graph $\Gamma(S_n(R))$ of $S_n(R)$. We give some basic graph theory properties of $\overset{\rightarrow}{\Gamma}(S_n(R))$. Moreover, we obtain some results of the zero-divisor directed graph of $\overset{\rightarrow}{\Gamma}(H_n(R))$.

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A Presentation And Some Finiteness Conditions For A New Version Of The Schützenberger Product Of Monoids, Eylem Güzel Karpuz, Firat Ateş, Ahmet Si̇nan Çevi̇k, İsmai̇l Naci̇ Cangül Jan 2016

A Presentation And Some Finiteness Conditions For A New Version Of The Schützenberger Product Of Monoids, Eylem Güzel Karpuz, Firat Ateş, Ahmet Si̇nan Çevi̇k, İsmai̇l Naci̇ Cangül

Turkish Journal of Mathematics

In this paper we first define a \textit{new version} of the Sch\"{u}tzenberger product for any two monoids $A$ and $B$, and then, by defining a generating and relator set, we present some finite and infinite consequences of the main result. In the final part of this paper, we give necessary and sufficient conditions for this new version to be periodic and locally finite.

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A New Security Relation Between Information Rate And State Size Of A Keystream Generator, Orhun Kara, İmran Ergüler, Emi̇n Anarim Jan 2016

A New Security Relation Between Information Rate And State Size Of A Keystream Generator, Orhun Kara, İmran Ergüler, Emi̇n Anarim

Turkish Journal of Electrical Engineering and Computer Sciences

Wireless communication in near field applications is becoming widespread. Most of the devices such as sensor networks or RFID applications are operated in constraint environments and some of these prevalent technologies require security applications. As one conclusion, the design and analysis of lightweight cryptographic algorithms has been one of the favorite research subjects over the last decade. We have seen that mostly lightweight block ciphers have been designed as symmetric encryption algorithms. The main reason is that stream ciphers are supposed to have large internal states due to the strict requirement related to their resistance against tradeoff attacks (time--memory--data tradeoff …

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The Dual Generalized Chernoff Inequality For Star-Shaped Curves, Deyan Zhang, Yunlong Yang Jan 2016

The Dual Generalized Chernoff Inequality For Star-Shaped Curves, Deyan Zhang, Yunlong Yang

Turkish Journal of Mathematics

In this paper, we first introduce the $k$-order radial function $\rho_k(\theta)$ for star-shaped curves in $\mathbb{R}^2$ and then prove a geometric inequality involving $\rho_k(\theta)$ and the area $A$ enclosed by a star-shaped curve, which can be looked upon as the dual Chernoff--Ou--Pan inequality. As a by-product, we get a new proof of the classical dual isoperimetric inequality. We also prove that $\frac{C^2}{k^2}\leq A

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Construction Of Biorthogonal Wavelet Packets On Local Fields Of Positive Characteristic, Firdous Ahmad Shah, Mohammad Younus Bhat Jan 2016

Construction Of Biorthogonal Wavelet Packets On Local Fields Of Positive Characteristic, Firdous Ahmad Shah, Mohammad Younus Bhat

Turkish Journal of Mathematics

Orthogonal wavelet packets lack symmetry, which is a much desired property in image and signal processing. The biorthogonal wavelet packets achieve symmetry where the orthogonality is replaced by biorthogonality. In the present paper, we construct biorthogonal wavelet packets on local fields of positive characteristic and investigate their properties by means of Fourier transforms. We also show how to obtain several new Riesz bases of the space $L^2(K)$ by constructing a series of subspaces of these wavelet packets. Finally, we provide algorithms for the decomposition and reconstruction using these biorthogonal wavelet packets.

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A Slotted Aloha-Based Cognitive Radio Network Under Capture Effect In Rayleigh Fading Channels, Muhammed Enes Bayrakdar, Sedat Atmaca, Alper Karahan Jan 2016

A Slotted Aloha-Based Cognitive Radio Network Under Capture Effect In Rayleigh Fading Channels, Muhammed Enes Bayrakdar, Sedat Atmaca, Alper Karahan

Turkish Journal of Electrical Engineering and Computer Sciences

In this paper, a slotted ALOHA-based cognitive radio (CR) network is proposed and the throughput performance of the proposed CR network model under Rayleigh fading channels is examined. Our CR network contains two special groups of users, primary users (PUs) and CR users (CRUs), and they are considered to be sharing a time-slotted-based common communication channel. While PUs can access the channel at any time owing to their legal right, CRUs can only access the channel when it is not occupied by the PUs. In the network model developed, PUs access the channel utilizing time division multiple access as a …

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On $Le$-Semigroups, Niovi Kehayopulu Jan 2016

On $Le$-Semigroups, Niovi Kehayopulu

Turkish Journal of Mathematics

We characterize the idempotent ideal elements of the $le$-semigroups in terms of semisimple elements and we prove, among others, that the ideal elements of an $le$-semigroup $S$ are prime (resp. weakly prime) if and only if they form a chain and $S$ is intraregular (resp. semisimple). The corresponding results on semigroups (without order) can be also obtained as an application of the results of this paper. The study of $poe$-semigroups plays an essential role in the theory of fuzzy semigroups and the theory of hypersemigroups.

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$\V\W$-Gorenstein Categories, Guoqiang Zhao, Juxiang Sun Jan 2016

$\V\W$-Gorenstein Categories, Guoqiang Zhao, Juxiang Sun

Turkish Journal of Mathematics

Let $\A$ be an abelian category, and $\V$,$\W$ two additive full subcategories of $\A$. We introduce and study the $\V\W$-Gorenstein subcategory of $\A$, which unifies many known notions, such as the Gorenstein category and the category consisting of $G_C$-projective (injective) modules, although they were defined in a different way. We also prove that the Bass class with respect to a semidualizing module is one kind of $\V\W$-Gorenstein category. The connections between $\V\W$-Gorenstein categories and Gorenstein categories are discussed. Some applications are given.

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On The Extended Zero Divisor Graph Of Commutative Rings, Driss Bennis, Jilali Mikram, Fouad Taraza Jan 2016

On The Extended Zero Divisor Graph Of Commutative Rings, Driss Bennis, Jilali Mikram, Fouad Taraza

Turkish Journal of Mathematics

In this paper we present a new graph that is closely related to the classical zero-divisor graph. In our case two nonzero distinct zero divisors $x$ and $y$ of a commutative ring $R$ are adjacent whenever there exist two nonnegative integers $n$ and $m$ such that $x^ny^m=0$ with $x^n\neq 0$ and $y^m\neq 0$. This yields an extension of the classical zero divisor graph $\Gamma(R)$ of $R$, which will be denoted by $\overline{\Gamma}(R)$. First we distinguish when $\overline{\Gamma}(R)$ and $\Gamma(R)$ coincide. Various examples in this context are given. We show that if $\overline{\Gamma}(R) \not=\Gamma(R)$, then $\overline{\Gamma}(R)$ must contain a cycle. We …

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The M[--] And --[M] Functors And Five Short Lemma In $H_V$-Modules, Yaser Vaziri, Mansour Ghadiri, Bijan Davvaz Jan 2016

The M[--] And --[M] Functors And Five Short Lemma In $H_V$-Modules, Yaser Vaziri, Mansour Ghadiri, Bijan Davvaz

Turkish Journal of Mathematics

The largest class of multivalued systems satisfying the module-like axioms are the $H_v$-modules. The main tools concerning the class of $H_v$-modules with the ordinary modules are the fundamental relations. Based on the relation $\varepsilon^*$, exact sequences in $H_v$-modules are defined. In this paper, we introduce the $H_v$-module $M[A]$ and determine its heart and the connection between equivalence relations $\varepsilon^*_{M[A]}$ and $\varepsilon^*_A$. Moreover, we define the $M[-]$ and $-[M]$ functors and investigate the exactness and some concepts related to them. Finally, we prove the five short lemma in $H_v$-modules.

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Some Results And Examples On Difference Cordial Graphs, Mohammed Seoud, Shakir Salman Jan 2016

Some Results And Examples On Difference Cordial Graphs, Mohammed Seoud, Shakir Salman

Turkish Journal of Mathematics

In this paper we introduce some results on difference cordial graphs and describe the difference cordial labeling for some families of graphs.

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Quadraticeigenparameter-Dependent Quantum Difference Equations, Yelda Aygar Küçükevci̇li̇oğlu Jan 2016

Quadraticeigenparameter-Dependent Quantum Difference Equations, Yelda Aygar Küçükevci̇li̇oğlu

Turkish Journal of Mathematics

The main aim of this paper is to construct quantum extension of the discrete Sturm--Liouville equation consisting of second-order difference equation and boundary conditions that depend on a quadratic eigenvalue parameter. We consider a boundary value problem (BVP) consisting of a second-order quantum difference equation and boundary conditions that depend on the quadratic eigenvalue parameter. We present a condition that guarantees that this BVP has a finite number of eigenvalues and spectral singularities with finite multiplicities.

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G-Frames For Operators In Hilbert $C^{\Ast}$-Modules, Zhongqi Xiang, Yongming Li Jan 2016

G-Frames For Operators In Hilbert $C^{\Ast}$-Modules, Zhongqi Xiang, Yongming Li

Turkish Journal of Mathematics

We present a generalization of g-frames related to an adjointable operator $K$ on a Hilbert $C^{\ast}$-module, which we call $K$-g-frames. We obtain several characterizations of $K$-g-frames and we also give conditions under which the removal of an element from a $K$-g-frame leaves again a $K$-g-frame. In addition, we define a concept of dual, and using it we study the relation between a $K$-g-frame and a g-Bessel sequence with respect to different sequences of Hilbert $C^{\ast}$-modules.

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On A Question About Almost Prime Ideals, Esmaeil Rostami, Reza Nekooei Jan 2016

On A Question About Almost Prime Ideals, Esmaeil Rostami, Reza Nekooei

Turkish Journal of Mathematics

In this paper, by giving an example we answer positively the question ``Does there exist a $P$-primary ideal $I$ in a Noetherian domain $R$ such that $PI = I^2$, but $I$ is not almost prime?", asked by S. M. Bhatwadekar and P. K. Sharma. We also investigated conditions under which the answer to the above mentioned question is negative.

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Lagrangian Description, Symplectization, And Eulerian Dynamics Of Incompressible Fluids, Hasan Gümral Jan 2016

Lagrangian Description, Symplectization, And Eulerian Dynamics Of Incompressible Fluids, Hasan Gümral

Turkish Journal of Mathematics

Eulerian dynamical equations in a three-dimensional domain are used to construct a formal symplectic structure on time-extended space. Symmetries, invariants, and conservation laws are related to this geometric structure. The symplectic structure incorporates dynamics of helicities as identities. The generator of the infinitesimal dilation for symplectic two-form can be interpreted as a current vector for helicity. Symplectic dilation implies the existence of contact hypersurfaces. In particular, these include contact structures on the space of streamlines and on the Bernoulli surfaces.

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Multiple Positive Solutions Of Nonlinear $M$-Point Dynamic Equations For $P$-Laplacian On Time Scales, Abdülkadi̇r Doğan Jan 2016

Multiple Positive Solutions Of Nonlinear $M$-Point Dynamic Equations For $P$-Laplacian On Time Scales, Abdülkadi̇r Doğan

Turkish Journal of Mathematics

In this paper, we study the existence of positive solutions of a nonlinear $ m $-point $p$-Laplacian dynamic equation $$(\phi_p(x^\Delta(t)))^\nabla+w(t)f(t,x(t),x^\Delta(t))=0,\hspace{2cm} t_1< t 1.$ Sufficient conditions for the existence of at least three positive solutions of the problem are obtained by using a fixed point theorem. The interesting point is the nonlinear term $f$ is involved with the first order derivative explicitly. As an application, an example is given to illustrate the result.

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Projective Crossed Modules Of Algebras And Cyclic Homology, Eli̇f Ilgaz Jan 2016

Projective Crossed Modules Of Algebras And Cyclic Homology, Eli̇f Ilgaz

Turkish Journal of Mathematics

In this work, we give a characterization of free crossed modules and also get a relation between projective crossed modules and the cyclic homology of associative algebras by using Hopf-type formulas.

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$Q$-Riordan Array For $Q$-Pascal Matrix And Its Inverse Matrix, Nai̇m Tuğlu, Fatma Yeşi̇l, Maciej Dziemianczuk, E. Gökçen Koçer Jan 2016

$Q$-Riordan Array For $Q$-Pascal Matrix And Its Inverse Matrix, Nai̇m Tuğlu, Fatma Yeşi̇l, Maciej Dziemianczuk, E. Gökçen Koçer

Turkish Journal of Mathematics

In this paper, we prove the $q$-analogue of the fundamental theorem of Riordan arrays. In particular, by defining two new binary operations $\ast_{q} $ and $\ast _{1/q}$, we obtain a $q$-analogue of the Riordan representation of the $q$-Pascal matrix. In addition, by aid of the $q$-Lagrange expansion formula we get $q$-Riordan representation for its inverse matrix.

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Existence Of Positive Solutions For Difference Systems Coming From A Model For Burglary, Tianlan Chen, Ruyun Ma Jan 2016

Existence Of Positive Solutions For Difference Systems Coming From A Model For Burglary, Tianlan Chen, Ruyun Ma

Turkish Journal of Mathematics

In this paper, we use the Brouwer degree to prove existence results of positive solutions for the following difference systems: $$\aligned &{D}_k\Delta^2(A_{k-1}-A^0_{k-1})-(A_{k}-A^0_{k})+N_kf(k, A_{k})=0,\ \ k\in[2, n-1]_\mathbb{Z},\\ &\Delta^2N_{k-1}+\Delta[g(k, A_{k}, \Delta A_{k-1})N_k]-w^2(N_k-1)=0,\ \ k\in[2, n-1]_\mathbb{Z},\\ &\Delta A_{1}=0=\Delta A_{n-1},\ \ \Delta N_{1}=0=\Delta N_{n-1}, \endaligned\eqno $$ where the assumptions on $w,\ D_k, A_k^0, f$, and $g$ are motivated by some mathematical models for the burglary of houses.

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A Characterization Of Derivations On Uniformly Mean Value Banach Algebras, Amin Hosseini Jan 2016

A Characterization Of Derivations On Uniformly Mean Value Banach Algebras, Amin Hosseini

Turkish Journal of Mathematics

In this paper, a uniformly mean value Banach algebra (briefly UMV-Banach algebra) is defined as a new class of Banach algebras, and we characterize derivations on this class of Banach algebras. Indeed, it is proved that if $\mathcal{A}$ is a unital UMV-Banach algebra such that either $a = 0$ or $b = 0$ whenever $ab = 0$ in $\mathcal{A}$, and if $\delta:\mathcal{A} \rightarrow \mathcal{A}$ is a derivation such that $a \delta(a) = \delta(a)a$ for all $a \in \mathcal{A}$, then the following assertions are equivalent:\\ (i) $\delta$ is continuous; \\(ii) $\delta(e^a) = e^a\delta(a)$ for all $a \in \mathcal{A}$; \\(iii) $\delta$ is …

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On The Solvability Of The Riemann Boundary Value Problem In Morrey--Hardy Classes, Bilal Bilalov, Telman Gasymov, Aida Guliyeva Jan 2016

On The Solvability Of The Riemann Boundary Value Problem In Morrey--Hardy Classes, Bilal Bilalov, Telman Gasymov, Aida Guliyeva

Turkish Journal of Mathematics

This work considers the Riemann boundary value problem with the piecewise continuous coefficient in Morrey-Hardy classes. Under some conditions on the coefficient, the Fredholmness of this problem is studied and the general solution of homogeneous and nonhomogeneous problems in Morrey-Hardy classes is constructed.

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Isometric $N$-Jordan Weighted Shift Operators, Saeed Yarmahmoodi, Karim Hedayatian Jan 2016

Isometric $N$-Jordan Weighted Shift Operators, Saeed Yarmahmoodi, Karim Hedayatian

Turkish Journal of Mathematics

A bounded linear operator $T$ on a Hilbert space is an isometric $N$-Jordan operator if it can be written as $A+Q$, where $A$ is an isometry and $Q$ is a nilpotent of order $N$ such that $AQ= QA$. In this paper, we will show that the only isometric $N$-Jordan weighted shift operators are isometries. This answers a question recently raised.

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Pseudospectral Operational Matrix For Numerical Solution Of Single And Multiterm Time Fractional Diffusion Equation, Saeid Gholami, Esmail Babolian, Mohammad Javidi Jan 2016

Pseudospectral Operational Matrix For Numerical Solution Of Single And Multiterm Time Fractional Diffusion Equation, Saeid Gholami, Esmail Babolian, Mohammad Javidi

Turkish Journal of Mathematics

This paper presents a new numerical approach to solve single and multiterm time fractional diffusion equations. In this work, the space dimension is discretized to the Gauss$-$Lobatto points. We use the normalized Grunwald approximation for the time dimension and a pseudospectral successive integration matrix for the space dimension. This approach shows that with fewer numbers of points, we can approximate the solution with more accuracy. Some examples with numerical results in tables and figures displayed.

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High-Order Uniformly Convergent Method For Nonlinear Singularly Perturbed Delay Differential Equations With Small Shifts, Abdelhay Salama, Dirhem Al-Amery Jan 2016

High-Order Uniformly Convergent Method For Nonlinear Singularly Perturbed Delay Differential Equations With Small Shifts, Abdelhay Salama, Dirhem Al-Amery

Turkish Journal of Mathematics

In this paper, we propose and analyze a high-order uniform method for solving boundary value problems (BVPs) for singularly perturbed nonlinear delay differential equations with small shifts (delay and advance). Such types of BVPs play an important role in the modeling of various real life phenomena, such as the variational problem in control theory and in the determination of the expected time for the generation of action potentials in nerve cells. To obtain parameter-uniform convergence, the present method is constructed on a piecewise-uniform Shishkin mesh. The error estimate is discussed and it is shown that the method is uniformly convergent …

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Forensic Investigation Of Cyberstalking Cases Using Behavioural Evidence Analysis, Noora Al Mutawa, Joanne Bryce, Virginia N.L. Franqueira, Andrew Marrington Jan 2016

Forensic Investigation Of Cyberstalking Cases Using Behavioural Evidence Analysis, Noora Al Mutawa, Joanne Bryce, Virginia N.L. Franqueira, Andrew Marrington

All Works

Behavioural Evidence Analysis (BEA) is, in theory, useful in developing an understanding of the offender, the victim, the crime scene, and the dynamics of the crime. It can add meaning to the evidence obtained through digital forensic techniques and assist investigators with reconstruction of a crime. There is, however, little empirical research examining the application of BEA to actual criminal cases, particularly cyberstalking cases. This study addresses this gap by examining the utility of BEA for such cases in terms of understanding the behavioural and motivational dimensions of offending, and the way in which digital evidence can be interpreted. It …

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Mixed Modulus Of Continuity In The Lebesgue Spaces With Muckenhouptweights And Their Properties, Ramazan Akgün Jan 2016

Mixed Modulus Of Continuity In The Lebesgue Spaces With Muckenhouptweights And Their Properties, Ramazan Akgün

Turkish Journal of Mathematics

Main properties of the mixed modulus of continuity in the Lebesgue spaces with Muckenhoupt weights are investigated. We use the mixed modulus of continuity to obtain Potapov type direct and inverse estimates of angular trigonometric approximation of functions in these spaces. We prove an equivalence between the mixed modulus of continuity and K -functional and realization functional.

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On Hermite-Hadamard Type Inequalities Via Generalized Fractional Integrals, Mohamed Jleli, Donal O'Regan, Bessem Samet Jan 2016

On Hermite-Hadamard Type Inequalities Via Generalized Fractional Integrals, Mohamed Jleli, Donal O'Regan, Bessem Samet

Turkish Journal of Mathematics

New Hermite-Hadamard type inequalities are obtained for convex functions via generalized fractional integrals. The results presented here are generalizations of those obtained in earlier works.

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New Approach Of Modifying The Anatase To Rutile Transition Temperature In Tio2 Photocatalysts, Ciara Byrne, Rachel Fagan, Steven Hinder, Declan Mccormack, Suresh Pillai Jan 2016

New Approach Of Modifying The Anatase To Rutile Transition Temperature In Tio2 Photocatalysts, Ciara Byrne, Rachel Fagan, Steven Hinder, Declan Mccormack, Suresh Pillai

Articles

In pure synthetic titanium dioxide, the anatase to rutile phase transition usually occurs between the temperatures of 600 °C and 700 °C. The phase transition temperature can be altered by various methods, including modifying the precursor or by adding dopant or modifier to the TiO2 sample. In an attempt to investigate the phase transition using aromatic carboxylic acids, the current study examines the impact of increasing concentrations of benzoic acid (1 : 0, 1 : 1, 1 : 4 and 1 : 8 molar ratio TiO2 : benzoic acid) on anatase to rutile transition. The samples were characterised using Raman …

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