Bildiri Koleksiyonu | Matematik Bölümü

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https://hdl.handle.net/11729/5142

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On pseudo-umbilical rotational surfaces with pointwise 1-type gauss map in E-2(4)
(Istanbul Technical Univ, 2017-01-01) Bektaş, Burcu; Canfes, Elif Özkara; Dursun, Uğur
In this work, we study two families of rotational surfaces in the pseudo Euclidean space 1E4 with profile curves lying in 2 dimensional planes. First, we obtain a classification of pseudo umbilical spacelike surfaces and timelike surfaces in these families. Then, we show that in this classification there exists no a pseudo umbilical rotational surface in 1E4 with pointwise 1 type Gauss map of second kind. Finally, we determine such pseudo umbilical rotational surfaces in 1E4 having pointwise 1 type Gauss map of first kind.
Matching of cocycle extensions for second tangent groups
(American Institute of Physics Inc., 2022-11-07) Uçgun, Filiz Çağatay; Esen, Oğul; Sütlü, Serkan
We present the second-order tangent group of a Lie group as a cocycle extension of the first-order tangent group. We exhibit matching of the second-order tangent groups of two mutually interacting Lie groups. We examine the cocycle extension character of the matched second-order group and arrive at that matched pair of cocycle extensions is a cocycle extension by itself.
Nonlinear waves in a stenosed elastic tube filled with viscous fluid: Forced perturbed korteweg-de vries equation
(Springer Science and Business Media, LLC, 2008) Tay, Kim Gaik; Demiray, Hilmi; Tiong, Ong Chee
In the present work, treating the artery as a prestressed thin-walled and long circularly cylindrical elastic tube with a mild symmetrical stenosis and the blood as an incompressible Newtonian fluid, we have studied the propagation of weakly nonlinear waves in such a composite medium, in the long wave approximation, by use of the reductive perturbation method. By introducing a set of stretched coordinates suitable for the boundary value type of problems and expanding the field variables into asymptotic series of the smallness parameter of nonlinearity and dispersion, we obtained a set of nonlinear differential equations governing the terms at various order. By solving these nonlinear differential equations, we obtained the forced perturbed Korteweg-de Vries equation with variable coefficient as the nonlinear evolution equation. By use of the coordinate transformation, it is shown that this type of nonlinear evolution equation admits a progressive wave solution with variable wave speed.
On complex solutions of the eikonal equation
(IEEE, 2007) Hasanoğlu, Elman
In this paper a new approach of complex rays in an inhomogeneous medium is presented. Complex rays are complex solutions of the eikonal equation, the main equation of the geometical optics. It is shown that solving the eikonal equation by using the characteristic method naturally leads to the pseudoriemann and Minkowski geometries. In framework of these geometries complex rays , like the real ones, can be drawn in real space and they may have caustics, and caustics also can be drawn in real space.
Beam tracing theory in Minkowski space
(IEEE, 2011) Hasanoğlu, Elman
This paper provides a novel approach to beam theory in homogeneous lossless mediun. The main idea is to interpret the classic eikonal equation in three dimensional Minkowski space.
“International conference on vibration problems” ICOVP-2007 and a short history
(Springer Science and Business Media, LLC, 2008) İnan, Esin
[No abstract available]
Nonlinear wave modulation in a prestressed thin elastic tube filled with an inviscid fluid
(Wit Press, 2002) Bakırtaş, İlkay; Demiray, Hilmi
In the present work, employing the nonlinear equations of an incompressible, isotropic and elastic thin tube and the approximate equations of an incompressible inviscid fluid and then utilizing the reductive perturbation technique, the amplitude modulation of weakly nonlinear waves is examined. It is shown that, the amplitude modulation of these waves is governed by a nonlinear Schrödinger (NLS) equation. The result is compared with some previous works on the same subject. The modulational instability of the monochromatic wave solution is discussed for some elastic materials and initial deformations. It is shown that the amplitude modulation of weakly nonlinear waves near the marginal state is governed by the Generalized Nonlinear Schrödinger equation (GNLS).
Variable coefficient Korteweg-deVries equation in fluid-filled elastic tubes
(Technical University Liberec, 2011-09-05) Demiray, Hilmi
In the present work, treating the arteries as a prestressed thin elastic tube with a stenosis and the blood as an inviscid fluid, we have studied the propagation of weakly nonlinear waves in such a medium by use of the reductive perturbation method and obtained the variable coefficient Korteweg-deVries (KdV) equation as the evolution equation. A progressive wave type of solution to this evolution equation, in the sense of distribution, is presented and the result is discussed.
Cross-sectional thermoacoustic imaging using multi-layer cylindrical media
(IEEE, 2017-11-10) Elmas, Demet; Ünalmış Uzun, Banu; İdemen, Mehmet Mithat; Karaman, Mustafa
For cross-sectional two-dimensional thermoacustic imaging of breast and brain, we explored solution of the wave equation using layered tissue model consisting of concentric annular layers on a cylindrical cross-section. To obtain the forward and inverse solutions of the thermoacoustic wave equation, we derived the Green's function involving Bessel and Hankel functions by employing the geometrical and acoustic parameters (densities and velocities) of layered media together with temporal initial condition, radiation conditions and continuity conditions on the layers' boundaries. The image reconstruction based on this approach involves the layer parameters as the apriori information which can be estimated from the acquired thermoacoustic data. To test and compare our layered solution with conventional solution based on homogeneous medium assumption, we performed simulations using numerical test phantoms consisting of sources distributed in the layered structure.
Thermoacoustic image reconstruction based on layered tissue model
(SPIE-Int Soc Optical Engineering, 2017) Bayıntır, Hazel; İdemen, Mehmet Mithat; Ünalmış Uzun, Banu; Karaman, Mustafa; Elmas, Demet
We derived analytical forward and inverse solution of thermoacoustic wave equation for inhomogeneous multi layered planar and cylindrical mediums with the source distribution existing in all layers. These solutions are applicable for imaging of organs such as breast and brain, whose structures are suitable for multi-layer modelling. For qualitative testing and comparison of the point-spread-functions associated with the homogeneous and layered solutions, we performed numerical simulations. Our simulation results show that the conventional inverse solution based on homogeneous medium assumption, as expected, produces incorrect locations of point sources and significantly increased side lobes, whereas our inverse solution involving the multi-layered medium produces point sources at the correct locations with lower side lobes.
Çok katmanlı silindirik yapılar için termoakustik dalga denkleminin ters çözümü
(IEEE, 2017-06-27) Elmas, Demet; Ünalmış Uzun, Banu; İdemen, Mehmet Mithat; Karaman, Mustafa
Termoakustik görüntüleme, elektromanyetik enerji uyarımı ile ultrason dalgaları oluşumunu sağlayan yeni bir yöntemdir. Bu sistemin görüntüleme işlemi termoakustik dalga denkleminin ters çözümüne dayanmaktadır. Ters çözümde görüntülenecek dokunun homojen yapıda olduğu varsayımı, görüntü kalitesinin azalmasına neden olur. Bu çalışmada, meme ve beyinin görüntülemesinde uygulanabilecek üç boyutlu eş merkezli silindirik çok katmanlı yapılar için termoakustik dalga denkleminin analitik ters çözümü elde edilmiştir. Çözümü sayısal olarak test etmek için, noktasal kaynaklar içeren üç katmanlı fantom kullanılarak numerik simulasyonlar elde edilmiştir.
Çok katmanlı düzlemsel ortam için termoakustik dalga denkleminin çözümü
(IEEE, 2017-06-27) Bayıntır, Hazel; Ünalmış Uzun, Banu; İdemen, Mehmet Mithat; Karaman, Mustafa
Bu çalışmada, farklı akustik parametrelere sahip çok katmanlı düzlemsel ortam için tüm katmanlarda kaynak dağılımı olduğu varsayımı altında termoakustik dalga denkleminin analitik olarak düz ve ters çözümü elde edilmiştir. Çok katmanlı düzlemsel ortam için elde edilen analitik çözüm katmanlı düzlemsel green fonksiyonlarına dayanmaktadır. Çok katmanlı düzlemsel modelleme meme, deri ve karın bölgesi görüntülemelerine uygun bir modellemedir. Elde edilen analitik çözüm ile literatürde var olan homojen ortam varsayımına dayanan çözüm her katmanda noktasal kaynak alınarak sayısal olarak karşılaştırılmıştır.
A method for calculating profiles of a dielectric thick lenses
(IEEE, 2001) Hasanoğlu, Elman
Hasanov and Polat (see International Journal of Electronics and Communications (AEO), vol.54, no.2, p.109-113, 2000) investigated the transformation of a plane wavefront to another plane wavefront after passing through a thick lens and described the class of optical mappings realizable by means of such lenses. However, it is desirable to describe the class of optical mappings and calculate the lens profiles for a more general case when incoming and outgoing wavefronts have arbitrary shapes. For two reflecting surfaces a similar problem has been solved by Gasanov (1991). The aim of this paper is to provide a method for calculating the profiles of symmetric thick lenses which realize an a priori given optical mapping between spherical and plane wavefronts. It is shown that this mapping may be chosen freely and be used for various purposes such as satisfying Abbe's sine law or Herscel's condition exactly. We have shown, that calculating the profiles of lenses can be reduced to solving two first-order differential equations which can be solved separately. It is also shown that the geometry of the problem provides a natural condition to control the accuracy for the numerical solution of the obtained differential equations
Two reflector non symmetric shaped antenna systems
(IEEE, 2000) Hasanoğlu, Elman
Two reflector antenna systems with non symmetric reflecting surfaces under GO approximation are investigated. It is shown, that the problem of forming desired far field pattern leades to solving the system of partial differential equations with respect to mapping functions between wave fronts. One of these equations is non linear and expresses energy conversation law. It is shown that this equation can be solved separetly in the class of non smooth functions which has a discontinuty of first kind along a given curve.
Complex and real rays in three dimensional Minkowski space
(IEEE, 2002) Hasanoğlu, Elman
A new approach to the theory of complex rays is proposed. It is shown that the Minkowski space is more appropriate for describing these rays than the usual, Euclidian spaces. Some illustrative examples are represented.
A function of direction in a Weyl subspace associated with a set of orthogonal vector fields
(World Scientific Publ Co Pte Ltd, 2003) Özdeğer, Abdülkadir
Let W-m be an m-dimensional subspace of an n-dimensional Weyl space W-n. Suppose that (1)v, (2)v,..., (m)v are mutually orthogonal smooth vector fields in W-m and that v is a non-tangential smooth vector field defined on W-m. Consider the (m + 1)-dimensional net delta defined by (1)v, (2)v, ..., (m)v, v. In this work, we obtain a function of direction associated with the net delta and define a class of curves on W-m in relation to this function of direction.
Nonlinear waves in fluid-filled elastic tubes: A model to large arteries
(Springer, 2007) Demiray, Hilmi
In the present work, by treating the arteries as a prestressed thin walled elastic tube of variable radius and the blood as an incompressible inviscid fluid, we have studied the propagation of weakly nonlinear waves in such a medium through the use of long wave approximation and the reductive perturbation method. The KdV equation with variable coefficient is obtained as the evolution equation. By seeking a progressive wave type of solution to this equation, we observed that the wave speed decreases with increasing inner radius while it increases with decreasing inner radius of the tube. Such a result is to be expected from physical considerations.
Travelling waves in a prestressed elastic tube filled with a fluid of variable viscosity
(Springer, 2008) Demiray, Hilmi; Gaik, Tay Kim
In this work, treating the artery as a prestressed thin elastic tube with variable radius and the blood as all incompressible Newtonian fluid with variable viscosity, the propagation of nonlinear waves ill Such a composite medium is studied, in the long wave approximation, through the use of the reductive perturbation method and the Forced Korteweg-de Vries-Burgers (FKdVB) equation with variable coefficients is obtained as the evolution equation. A progressive wave type of solution is presented for this evolution equation and the result is discussed.
Quasiconformal harmonic mappings related to Janowski alpha-spirallike functions
(Amer Inst Physics, 2014) Aydoğan, Seher Melike; Polatoğlu, Yaşar
Let f = h(z) + g(z) be a univalent sense-preserving harmonic mapping of the open unit disc D = {z/vertical bar z vertical bar < 1}. If f satisfies the condition vertical bar omega(z)vertical bar = vertical bar g'(z)/h'(z)vertical bar < k, 0 < k < 1 the f is called k-quasiconformal harmonic mapping in D. In the present paper we will give some properties of the class of k-quasiconformal mappings related to Janowski alpha-spirallike functions.
Bounded harmonic mappings related to starlike functions
(Amer Inst Physics, 2014-12-17) Varol, Dürdane; Aydoğan, Seher Melike; Polatoğlu, Yaşar
Let f = h(z) + <(g(z))over bar> be a sense-preserving harmonic mapping in the open unit disc D = {z vertical bar vertical bar z vertical bar < 1}. If f satisfies the condition vertical bar 1/b(1) g'(z)/h' (z) - M vertical bar < M, M > 1/2, then f is called bounded harmonic mapping. The main purpose of this paper is to give some properties of the class of bounded harmonic mapping.

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