Browsing by Subject "Matematik"
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Item Hedef ve doğrusal programlama(2005) Altay Uğur GÜLBu makalede doğrusal ve hedef (amaç) programlama model yapısı özet olarak tanıtılmış ve her iki model arasındaki benzerlikler ve farklılıklar belirtilmiştir. Dalın sonra; kavak fidanı üretimine ilişkin örnek bir problem için doğrusal ve hedef programlama modelleri geliştirilmiş ve DS for Windows yazılımı ile çözülmüştür. Her iki modelin çözüm sonuçları bağlamında doğrusal ve amaç programlama modelleri karşılaştırmıştır. Yine; hedef programlamada, özellikle hedef değerlerden sapma istenmemesi durumunda, amaç fonksiyonları ile birlikte kısıtların nasıl kullanılacağı gösterilmiştir.Item The cosine rule II for a spherical tringle on the dual unit sphere $\\tilde{S}^2$(2005) M. KAZAZ; A. ÖZDEMİR; H. H. UĞURLUIn this work, we proved the Cosine Rule II for a spherical triangle on the dual unit sphere $\\tilde{S}^2.Item Determination of the steady state response of EFEF/VFVF supported rectangular specially orthotropic plates(2006) Muhiddin BAĞCI; GÖKHAN ALTINTAŞDetermination of the Steady State Response Of EFEF / VFVF Supported Rectangular Specially Orthotropic Plates is presented. EFEF and VFVF plates, these are rectangular plates with two opposite edges elastically or viscoelastically supported and remaining others free. Using the energy based finite difference method, the problem is modelled by a kind of finite difference element. Due to the significiance of the fundamental frequency of the plate, its variation was investigated with respect to mechanical properties of plate material and translational spring coefficient of supports. The steady state response of viscoelastically supported plates was also investigated numerically for various damping coefficients. In the numerical examples, the natural frequency parameters and steady state responses to a sinusoidally varying force are assessed for the fundamental mode. Convergence studies are made. Many new results have been presented. Considered problems are solved within the frame work of Kirchhoff-Love hypothesis.Item A similarity solution of fin equation with variable thermal conductivity and heat transfer coefficient(2006) M. PAKDEMİRLİ; A. Z. ŞAHİNA nonlinear fin equation in which thermal conductivity is an arbitrary function of temperature and, heat transfer coefficient is an arbitrary function of spatial variable is considered. Scaling transformation is applied to the equations to determine the specific forms of these functions for which the equation admits such type of transformation. It is found that for arbitrary heat conduction function, scaling transformation exists for an inverse square heat transfer coefficient. Selecting also the conductivity as an exponential function, the partial differential equation is transferred to an ordinary differential equation via similarity transformations. The resulting equation is solved numerically and temperature distribution is determined for various heat conductivity parameters.Item On the stability of delay integro-differential equations(2007) Salih YANÇINBAŞ; ALI FUAT YENIÇERIOGLUSome new stability results are given for a delay integro-differential equation. A basis theorem on the behavior of solutions of delay integro-differential equations is established. As a consequence of this theorem, a stability criterion is obtained.Item Araştırmaya Dayalı Fen Laboratuvarlarında Bilimsel Süreç Becerilerini Geliştirmede Etkili Araçlar: Vee ve I Diyagramları(2007) FATMA ŞAŞMAZ ÖREN; Nilgün TATARBu çalışmada, Vee ve I diyagramlarının temel özellikleri tanımlanarak, bu araçların araştırmaya dayalı fen laboratuvarlarında bilimsel süreç becerilerini geliştirmede etkililikleri incelenmiştir. Bu amaçla; Vee diyagramı nedir?, I diyagramı nedir? Vee ve I diyagramları nasıl organize edilir? Benzerlikleri ve farklılıkları nelerdir? Eğitim alan yazınında bu araçların etkililiği üzerine yapılan çalışmalar ve bulguları nelerdir? Bu araçların fen eğitimi açısından doğurguları nelerdir? sorularına cevap verilmeye çalışılmıştır. Bu derleme çalışmasında, ulusal ve uluslararası düzeydeki araştırma bulguları analiz edilmiştir.Item Comparison of IBM-2 calculations with X(5) critical point symmetry for low-lying states in $^{144-154} Nd$(2008) İLYAS İNCİ; Davut OLGUN; Nurettin TÜRKAN; Sait İNANThe X(5) would take place when moving continously from the pure U(5) symmetry to the SU(3) symmetry and it implies a definite relations among the level energies and among the E2 transition strengths. It was recently shown that a signature of phase transition is observed in the chain of Sm, Mo and Nd isotopes, where $^{152}Sm,^{104}Mo$ and $^{150}Nd$ display the predicted features of the X(5) symmetry and mark therefore the critical point. However, more detailed studies and experiments are needed to get ideas about this signature. Without entering into detail we have firstly compared the results obtained in our previous study [15] of $^{144-154}Nd$ with that of the limits in X(5) symmetry and then given a clear descripton about the validity of the Hamiltonian parameters used in the study. At the end, we have concluded that some of Nd isotopes display X(5) symmetry features.Item Generalized statistical mechanics for nucleus(2008) Ramazan ATİCİ; Özhan KAYACAN; HALİL BABACANIn this study, we derived the grand partition function and some thermodynamical quantities of the nucleus in the high temperature limit by adopting the ideal Fermi gas partition function of generalized Tsallis thermostatistics. The behaviour of number of neutron and internal energy are depicted as a function of temperature. Sensitivity of q entropy index to the number neutron are also analyzed.Item A root-finding algorithm with fifth order derivatives(2008) H. BOYACI; H. A. YURTSEVER; M. PAKDEMİRLİPerturbation theory is used to generate a root finding algorithm with fifth order derivatives. The algorithm is called Quintuple-Correction-Term algorithm. The new algorithm is contrasted with the previous Quadruple-Correction-Term and Triple- Correction-Term algorithms in the literature. It is found that adding a fifth correction term in the algorithm does not improve the performance.Item A new perturbation algorithm with better convergence properties: Multiple scales lindstedt poincare method(2009) H. BOYACI; M. PAKDEMİRLİ; M. M. F. KARAHANA new perturbation algorithm combining the Method of Multiple Scales and Lindstedt-Poincare techniques is proposed for the first time. The algorithm combines the advantages of both methods. Convergence to real solutions with large perturbation parameters can be achieved for both constant amplitude and variable amplitude cases. Three problems are solved: Linear damped vibration equation, classical duffing equation and damped cubic nonlinear equation. Results of Multiple Scales, new method and numerical solutions are contrasted. The proposed new method produces better results for strong nonlinearities.Item A geometrical optimization problem associated with fruits of poppy flower(2009) Feyza Candan; Gözde DEĞER; Mehmet PAKDEMİRLİInspired from the poppy fruit (Papaver rhoeas L.), a geometrical optimization problem is posed. The aim is to minimize the surface area for a given volume. The poppy fruit geometry is selected as the optimization geometry. The mathematical problem is solved using calculus. The optimum solutions obtained from mathematical model are contrasted with measurements of the fruit. A good agreement with difference in areas less than 1% in most of the cases is observed between the results.Item Eksenel hareketli çok mesnetli sürekli ortamların nonlineer titreşimleri(2009) Murat BAĞDATLI; Ali Yurddaş; Erdoğan ÖZKAYA; Ahmet KESİMLİ; Saim KURAL; Halil Rıdvan ÖZ-Item Difüzyon mekanizması için yeni bir matematiksel model ve uygulaması(2009) Salim ŞAHİN; Özhan KAYACAN-Item Bifurcation and chaos of slightly curved pipes(2010) B. Gültekin SINIRNon-linear vibrations of slightly curved pipes conveying fluid with constant velocity are investigated. The curvature is taken as an arbitrary function of the spatial variable. The initial displacement is considered due to the geometry of the pipe itself. The ends of the curved pipe are assumed to be immovable simple supports. The equations of motion of pipes are derived using Hamilton's principle and solved by Galerkin method. The bifurcation diagrams are presented for various amplitudes of the curvature function and fluid velocity. The periodic and chaotic motions have been observed in the transverse vibrations of slightly curved pipe conveying fluid.Item E(5) behaviour of the Ge isotopes(2010) İsmail MARAŞ; Nureddin TURKANThe sufficient aspects of model leading to the E(5) symmetry have been proved by presenting E(5) characteristic of the transitional nuclei $^{64-80}Ge.$ The positive parity states of even-mass Ge nuclei within the framework of Interacting Boson Model have been calculated and compared with the Davidson potential predictions along with the experimental data. It can be said that the set of parameters used in an calculations is the best approximation that has been carried out so far. Hence, Interacting Boson Approximation (IBA) is fairly reliable for the calculation of spectra in such set of Ge isotopes.Item Legendre series solutions of Fredholm integral equations(2010) Salih YALÇINBAŞ; Müge AYNİGÜL; Tuğçe AKKAYAA matrix method for approximately solving linear Fredholm integral equations of the second kind is presented. The solution involves a truncated Legendre series approximation. The method is based on first taking the truncated Legendre series expansions of the functions in equation and then substituting their matrix forms into the equation. Thereby the equation reduces to a matrix equation, which corresponds to a linear system of algebraic equations with unknown Legendre coefficients. In addition, some equations considered by other authors are solved in terms of Legendre polynomials and the results are compared.Item Calculation of generalized level densities for nuclei in mass region 20 < A < 50(2010) O. KAYACAN; H. BABACANIn this study, a relation between generalized level density and standard level density is derived. Using this relation and Bethe formula of Fermi gas model for standart level density we obtained a generalized nuclear level density formula for nucleus. Generalized level densities were calculated for some nuclei in mass region between 20 and 50 for different q values close to 1 . Our results explain experimental data better than those of Gilbert-Cameron (GC) and Rohr, which are two of the leading compilations in evaluating nuclear level density.Item The investigation of even-even $^{114-120}Xe$ isotopes by the framework of IBA(2010) Ramazan GÜMÜŞ; İsmail MARAŞ; Nurettin TÜRKANIn this work, the ground state, quasi beta and quasi gamma band energies $of ^{114,116,118,120}$ Xe isotopes have been investigated by using the both (IBM-1 and IBM-2) versions of interacting boson model (IBM). In calculations, the theoretical energy levels have been obtained by using PHINT and NP-BOS program codes. The presented results are compared with the experimental data in respective tables and figures. At the end, it was seen that the obtained theoretical results are in good agreement with the experimental data.Item Effect of material properties on vibrations of nonsymmetrical axially loaded thin-walled Euler-Bernoulli beams(2010) GÖKHAN ALTINTAŞThis paper focuses on effect of material properties on free vibration characteristics of nonsymmetrical axially loaded thin-walled Euler-Bernoulli beams. Many scientists studied the vibration of coupled systems but adequate consideration has not been given to detailed and parametric studies on the effect of material properties on vibration properties. The current findings of this study show that there have been quite different effects of material properties on the systems without symmetry axis than on the systems with symmetry axis. Material properties are properties affecting the free vibration behavior. Moreover, effect of axial load on natural frequencies was also investigated in this study. Convergence work revealed that the current mathematical model simulated the problem with excellent accuracy.Item Hermite series solutions of linear Fredholm integral equations(2011) Salih YALÇINBAŞ; Müge AYNİGÜLA matrix method for approximately solving linear Fredholm integral equations of the second kind is presented. The solution involves a truncated Hermite series approximation. The method is based on first taking the truncated Hermite series expansions of the functions in equation and then substituting their matrix forms into the equation. Thereby the equation reduces to a matrix equation, which corresponds to a linear system of algebraic equations with unknown Hermite coefficients. In addition, some equations considered by other authors are solved in terms of Hermite polynomials and the results are compared.