WoS İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8653

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Citation - WoS: 389
Citation - Scopus: 428
Anomalous Diffusion Expressed Through Fractional Order Differential Operators in the Bloch-Torrey Equation
(Academic Press inc Elsevier Science, 2008) Abdullah, Osama; Baleanu, Dumitru; Zhou, Xiaohong Joe; Magin, Richard L.
Diffusion weighted MRI is used clinically to detect and characterize neurodegenerative, malignant and ischemic diseases. The correlation between developing pathology and localized diffusion relies on d iffusi on -weighted pulse sequences to probe biophysical models of molecular diffusion-typically exp[-(bD)]-where D is the apparent diffusion coefficient (turn (2)/s) and b depends on the specific gradient pulse sequence parameters. Several recent studies have investigated the so-called anomalous diffusion stretched exponential model-exp[-(bD)(alpha)], where alpha is a measure of tissue complexity that can be derived from fractal models of tissue structure. In this paper we propose an alternative derivation for the stretched exponential model using fractional order space and time derivatives. First, we consider the case where the spatial Laplacian in the Bloch-Torrey equation is generalized to incorporate a fractional order Brownian model of diffusivity. Second, we consider the case where the time derivative in the Bloch-Torrey equation is replaced by a Riemann-Liouville fractional order time derivative expressed in the Caputo form. Both cases revert to the classical results for integer order operations. Fractional order dynamics derived for the first case were observed to fit the signal attenuation in diffusion-weighted images obtained from Sephadex gels, human articular cartilage and human brain. Future developments of this approach may be useful for classifying anomalous diffusion in tissues with developing pathology. (c) 2007 Elsevier Inc. All rights reserved.
Citation - WoS: 9
Citation - Scopus: 13
The Convolution of Functions and Distributions
(Academic Press inc Elsevier Science, 2005) Tas, K; Fisher, B
The non-commutative convolution f * g of two distributions f and g in V is defined to be the limit of the sequence {(f tau(n)) * g}, provided the limit exists, where {tau(n)} is a certain sequence of functions in D converging to 1. It is proved that vertical bar x vertical bar(lambda) * (sgnx vertical bar x vertical bar(mu)) = 2 sin(lambda pi/2)cos(mu pi/2)/sin[(lambda+mu)pi/2] B(lambda+1, mu+1) sgn x vertical bar x vertical bar(lambda+mu+1), for -1 < lambda + mu < 0 and lambda, mu not equal -1, -2,..., where B denotes the Beta function. (c) 2005 Elsevier Inc. All rights reserved.
Citation - WoS: 2
Citation - Scopus: 2
Correlation Meets Causality: a Holistic Measure of Financial Contagion
(Academic Press inc Elsevier Science, 2024) Atasoy, Burak Sencer; Ozkan, Brahim
This study introduces a new measure of financial contagion. We argue that a rapid increase in correlations between two series is necessary but not sufficient for contagion to occur, and develop a contagion test that combines dynamic conditional correlations with time-varying Granger causality. We empirically illustrate our new approach using systemic risk data covering the period 1996 - 2023. We show that there are periods when correlations increase rapidly without causality, as well as periods when causality is present but correlations do not increase. The proposed test enables data-driven detection of contagion episodes and provides a clear distinction between interconnectedness and contagion.
Decoupling Structure of the Principal Sigma Model-Maxwell Interactions
(Academic Press inc Elsevier Science, 2008) Yilmaz, Nejat T.
The principal sigma model and Abelian gauge fields coupling is studied. By expressing the first-order formulation of the gauge field equations an implicit on-shell scalar-gauge field decoupling structure is revealed. It is also shown that due to this decoupling structure the scalars of the theory belong to the pure sigma model and the gauge fields sector consists of a number of coupled Maxwell theories with currents partially induced by the scalars. (C) 2008 Elsevier Inc. All rights reserved.
Citation - WoS: 3
Citation - Scopus: 3
Estimates of Entropy for Multiplier Operators of Systems of Orthonormal Functions
(Academic Press inc Elsevier Science, 2023) Milare, J.; Kushpel, A. K.; Tozoni, S. A.
We obtain upper and lower estimates for epsilon-entropy and entropy numbers of multiplier operators of systems of orthonormal functions bounded from Lp to Lq. Upper estimates in our study require that a Marcinkiewicz-type multiplier theorem is available for the system. As application we obtain estimates for epsilon-entropy and entropy numbers of the multiplier operators associated with the sequences (k-gamma (lnk)-xi)infinity k=2 and (e-gamma kr )infinity k=0 where gamma > 0, xi >= 0 and 0 < r < 1. Some of these estimates are order sharp. We verify that the trigonometric system on the circle, the Vilenkin system and the Walsh system satisfy the conditions of our study. We also study analogous results for the Haar system and the Walsh systems on spheres.(c) 2022 Elsevier Inc. All rights reserved.
Citation - WoS: 165
Citation - Scopus: 189
The Hamilton Formalism With Fractional Derivatives
(Academic Press inc Elsevier Science, 2007) Nawafleh, Khaled I.; Hijjawi, Raed S.; Muslih, Sami I.; Baleanu, Dumitru; Rabei, Eqab M.
Recently the traditional calculus of variations has been extended to be applicable for systems containing fractional derivatives. In this paper the passage from the Lagrangian containing fractional derivatives to the Hamiltonian is achieved. The Hamilton's equations of motion are obtained in a similar manner to the usual mechanics. In addition, the classical fields with fractional derivatives are investigated using Hamiltonian formalism. Two discrete problems and one continuous are considered to demonstrate the application of the formalism, the results are obtained to be in exact agreement with Agrawal's formalism. (c) 2006 Elsevier Inc. All rights reserved.
Citation - WoS: 157
Citation - Scopus: 180
Hamiltonian Formulation of Systems With Linear Velocities Within Riemann-Liouville Fractional Derivatives
(Academic Press inc Elsevier Science, 2005) Muslih, SI; Baleanu, D
The link between the treatments of constrained systems with fractional derivatives by using both Hamiltonian and Lagrangian formulations is studied. It is shown that both treatments for systems with linear velocities are equivalent. (c) 2004 Elsevier Inc. All rights reserved.
Citation - WoS: 290
Citation - Scopus: 332
The Impact of the Russia-Ukraine Conflict on the Connectedness of Financial Markets
(Academic Press inc Elsevier Science, 2022) Umar, Zaghum; Polat, Onur; Choi, Sun-Yong; Teplova, Tamara
We investigate the impact of geopolitical risks caused by the Russian-Ukrainian conflict on Russia, European financial markets, and the global commodity markets. We measure the dynamic connectedness among them using time- and frequency-based time-varying parameter vector autoregression (TVP-VAR) approaches. The empirical findings indicate that (i) their relationship has changed due to the conflict; (ii) European equities and Russian bonds are the net transmitters of shocks; and (iii) the conflict affects returns and volatility connectedness among them in terms of short-and long-term frequencies, respectively.
Citation - WoS: 3
Citation - Scopus: 3
Lower Bounds of Cowidths and Widths of Multiplier Operators
(Academic Press inc Elsevier Science, 2022) Kushpel, Alexander
The main objective of this article is to present new results on optimal reconstruction of function classes on probability spaces (Omega, A, nu) in the standard L-q spaces. We consider the problem of optimal reconstruction in the sense of the respective cowidths of standard function classes Lambda U-p generated by multiplier or pseudo differential operators Lambda : L-p -> L-q, 1 <= p, q <= infinity. Our approach is based on the estimates of volumes of John-Lowner ellipsoids and expectations of norms induced by orthonormal systems on (Omega, A, nu). It is shown that the results obtained are order sharp in many cases. In particular, we obtain sharp orders of entropy of Sobolev classes W-infinity(gamma), gamma > 0 in L-1 and n-widths of Lambda U-p in L-q, 1 < q <= p < infinity in the case of two-point homogeneous spaces and torus. (C) 2021 Elsevier Inc. All rights reserved.
Citation - WoS: 1
Citation - Scopus: 1
A New Hamiltonian System
(Academic Press inc Elsevier Science, 2020) Ugurlu, Ekin
This paper aims to share a new first-order differential equation that contains the continuous analogous of the orthogonal polynomials on the unit-circle. We introduce some basic results on the system and solutions of the system. Using nested-circle approach we introduce the possible number of square-integrable solutions of the system. At the end of the paper we share a limit-point criteria for the two-dimensional system of equations. (C) 2020 Elsevier Inc. All rights reserved.
Citation - WoS: 67
Citation - Scopus: 69
Numerical Approximation of Higher-Order Time-Fractional Telegraph Equation by Using a Combination of a Geometric Approach and Method of Line
(Academic Press inc Elsevier Science, 2016) Baleanu, D.; Hashemi, M. S.
We propose a simple and accurate numerical scheme for solving the time fractional telegraph (TFT) equation within Caputo type fractional derivative. A fictitious coordinate v is imposed onto the problem in order to transform the dependent variable u(x, t) into a new variable with an extra dimension. In the new space with the added fictitious dimension, a combination of method of line and group preserving scheme (GPS) is proposed to find the approximate solutions. This method preserves the geometric structure of the problem. Power and accuracy of this method has been illustrated through some examples of TFT equation. (C) 2016 Elsevier Inc. All rights reserved.
Citation - WoS: 22
Citation - Scopus: 27
On Multiplication in Finite Fields
(Academic Press inc Elsevier Science, 2010) Ozbudak, Ferruh; Cenk, Murat
We present a method for multiplication in finite fields which gives multiplication algorithms with improved or best known bilinear complexities for certain finite fields. Our method generalizes some earlier methods and combines them with the recently introduced complexity notion (M) over cap (q)(l), which denotes the minimum number of multiplications needed in F-q in order to obtain the coefficients of the product of two arbitrary l-term polynomials modulo x(l) in F-q[x]. We study our method for the finite fields F(q)n, where 2 <= n <= 18 and q = 2, 3,4 and we improve or reach the currently best known bilinear complexities. We also give some applications in cryptography. (C) 2010 Published by Elsevier Inc.
Citation - WoS: 2
On Oscillatory Solutions of Certain Forced Emden-Fowler Like Equations
(Academic Press inc Elsevier Science, 2008) Mustafa, Octavian G.
We give a constructive proof of existence to oscillatory solutions for the differential equations x ''(t) + a(t)vertical bar x(t)vertical bar lambda sign[x(t)] = e(t), where t >= t(0) >= 1 and lambda > 1, that decay to 0 when t -> infinity as 0(t(-mu)) for mu > 0 as close as desired to the "critical quantity" mu* = 2/lambda-1 For this class of equations, we have lim(t ->+infinity) E(t) = 0, where E(t) 0 and E ''(t) e(t) throughout [t(0) + infinity). We also establish that for any mu > mu* and any negative-valued E(t) = 0(t(-mu)) as t ->+infinity the differential equation has a negative-valued solution decaying to 0 at +infinity as o(t(-mu)). In this way, we are not in the reach of any of the developments from the recent paper [C.H Ou, J.S.W. Wong, Forced oscillation of nth-order functional differential equations, J. Math. Anal. Appl. 262 (2001) 722-732]. (C) 2008 Elsevier Inc. All rights reserved.
Citation - WoS: 4
Citation - Scopus: 4
On the Optimality of the Trigonometric System
(Academic Press inc Elsevier Science, 2020) Jarad, Fahd; Kushpel, A.; Tas, K.
We study a new phenomenon of the behaviour of widths with respect to the optimality of trigonometric system. It is shown that the trigonometric system is optimal in the sense of Kolmogorov widths in the case of "super-high" and "super-small" smoothness but is not optimal in the intermediate cases. Bernstein's widths behave differently when compared with Kolmogorov in the case of "super-small" smoothness. However, in the case of "super-high" smoothness Kolmogorov and Bernstein widths behave similarly, i.e. are realized by trigonometric polynomials. (C) 2019 Elsevier Inc. All rights reserved.
Citation - WoS: 1
Citation - Scopus: 1
Optimal Recovery and Volume Estimates
(Academic Press inc Elsevier Science, 2023) Kushpel, Alexander
We study volumes of sections of convex origin-symmetric bodies in Rn induced by orthonormal systems on probability spaces. The approach is based on volume estimates of John-Lowner ellipsoids and expectations of norms induced by the respective systems. The estimates obtained allow us to establish lower bounds for the radii of sections which gives lower bounds for Gelfand widths (or linear cowidths). As an application we offer a new method of evaluation of Gelfand and Kolmogorov widths of multiplier operators. In particular, we establish sharp orders of widths of standard Sobolev classes Wp & gamma;, & gamma; > 0 in Lq on two-point homogeneous spaces in the difficult case, i.e. if 1 < q < p < oo.& COPY; 2023 Elsevier Inc. All rights reserved.
Citation - WoS: 6
Citation - Scopus: 16
Parallel Wavecluster: a Linear Scaling Parallel Clustering Algorithm Implementation With Application To Very Large Datasets
(Academic Press inc Elsevier Science, 2011) Ozdogan, Cem; Yildirim, Ahmet Artu
A linear scaling parallel clustering algorithm implementation and its application to very large datasets for cluster analysis is reported. WaveCluster is a novel clustering approach based on wavelet transforms. Despite this approach has an ability to detect clusters of arbitrary shapes in an efficient way, it requires considerable amount of time to collect results for large sizes of multi-dimensional datasets. We propose the parallel implementation of the WaveCluster algorithm based on the message passing model for a distributed-memory multiprocessor system. In the proposed method, communication among processors and memory requirements are kept at minimum to achieve high efficiency. We have conducted the experiments on a dense dataset and a sparse dataset to measure the algorithm behavior appropriately. Our results obtained from performed experiments demonstrate that developed parallel WaveCluster algorithm exposes high speedup and scales linearly with the increasing number of processors. (C) 2011 Elsevier Inc. All rights reserved.
Citation - WoS: 8
Citation - Scopus: 8
Quantum Eye: Lattice Plasmon Effect on Quantum Fluctuations and Photon Detection
(Academic Press inc Elsevier Science, 2018) Salmanogli, Ahmad; Gecim, H. Selcuk
In this work, arrays of plasmonic nanoparticles coupled to a detector are designed and considered as a quantum eye. In the designed system, the plasmonic nanoparticles have a role like an ommatidium in the artificial compound eye; however, the quantum eye ommatidium acts with different functionality. To better understand this system, we analyze it with the full quantum theory, quantize lattice plasmon generated by the array of plasmonic nanoparticles, and finally derive bosonic operators using Heisenberg-Langevin equations. Moreover, we theoretically derive the radiative and non-radiative losses introduced by this system and examine lattice plasmon effect on spontaneous emission of the quantum dot (Purcell factor). The main goal of this article is to investigate the quantum eye's quantum properties such as quantum fluctuations, which is modeled and analyzed by studying the second-order correlation function. This function exhibits a significant bunching as a function of lattice plasmon optical properties. We can easily manipulate and improve the lattice plasmon optical properties, which dramatically depend on the array geometry. Finally, we study the quantum eye photon detection by a quantum measuring approach and show that the lattice plasmon has a strong effect on quantum properties after the one-count process. (C) 2018 Elsevier Inc. All rights reserved.
The Quaternion Group Has Ghost Number Three
(Academic Press inc Elsevier Science, 2017) Aksu, Fatma Altunbulak; Green, David J.
We prove that the group algebra of the quaternion group Q(8) over any field of characteristic two has ghost number three. (C) 2016 Elsevier Inc. All rights reserved.
Citation - WoS: 6
Citation - Scopus: 6
The Radii of Sections of Origin-Symmetric Convex Bodies and Their Applications
(Academic Press inc Elsevier Science, 2021) Tas, Kenan; Kushpel, Alexander
Let V and W be any convex and origin-symmetric bodies in R-n . Assume that for some A is an element of L (R-n -> R-n), det A not equal 0, V is contained in the ellipsoid A(-1)B((2))(n), where B-(2)(n) is the unit Euclidean ball. We give a lower bound for the W-radius of sections of A(-1) V in terms of the spectral radius of AA and the expectations of parallel to . parallel to(V) and parallel to . parallel to(W)0 with respect to Haar measure on Sn-1 subset of R-n. It is shown that the respective expectations are bounded as n -> infinity in many important cases. As an application we offer a new method of evaluation of n-widths of multiplier operators. As an example we establish sharp orders of n-widths of multiplier operators Lambda : L-p (M-d) -> L-q (M-d), 1 < q <= 2 <= p < infinity on compact homogeneous Riemannian manifolds M-d. Also, we apply these results to prove the existence of flat polynomials on M-d. (c) 2020 Elsevier Inc. All rights reserved.
Citation - WoS: 5
Retracted: on the Composition of the Distributions X+^λ and X+^μ (Retracted Article. See Vol. 330, Pg. 1494 2007)
(Academic Press inc Elsevier Science, 2006) Tas, K; Fisher, B
Let F be a distribution and let f be a locally summable function. The distribution F(f) is defined as the neutrix limit of the sequence {F-n(f)}, where F-n(x) = F(x) * delta(n)(x) and {delta(n)(x)) is a certain sequence of infinitely differentiable functions converging to the Dirac delta-function delta(x). The distributions (x(+)(mu) )(+)(lambda) are evaluated for lambda < 0, mu > 0 and lambda, lambda mu not equal -1, -2.... (c) 2005 Elsevier Inc. All rights reserved.

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