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Permanent URI for this collectionhttps://hdl.handle.net/20.500.14288/3
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Publication Metadata only On sums over the mobius function and discrepancy of fractions(Academic Press Inc Elsevier Science, 2013) Department of Mathematics; N/A; Alkan, Emre; Göral, Haydar; Faculty Member; Master Student; Department of Mathematics; College of Sciences; Graduate School of Sciences and Engineering; 32803; 252019We obtain quantitative upper bounds on partial sums of the Mobius function over semigroups of integers in an arithmetic progression. Exploiting, the cancellation of such sums, we deduce upper bounds for the discrepancy of fractions in the unit interval [0, 1] whose denominators satisfy the same restrictions. In particular, the uniform distribution and approximation of discrete weighted averages over such fractions are established as a consequence.Publication Metadata only High-rate LDPC codes from partially balanced incomplete block designs(Springer, 2022) Donovan, Diane; Price, Aiden; Rao, Asha; N/A; Department of Mathematics; Üsküplü, Elif; Yazıcı, Emine Şule; PhD Student; Faculty Member; Department of Mathematics; Graduate School of Sciences and Engineering; College of Sciences; N/A; 27432This paper presents a combinatorial construction of low-density parity-check (LDPC) codes from partially balanced incomplete block designs. Since Gallager's construction of LDPC codes by randomly allocating bits in a sparse parity-check matrix, many researchers have used a variety of more structured combinatorial approaches. Many of these constructions start with the Galois field; however, this limits the choice of parameters of the constructed codes. Here we present a construction of LDPC codes of length 4n(2) - 2n for all n using the cyclic group of order 2n. These codes achieve high information rate (greater than 0.8) for n >= 8, have girth at least 6 and have minimum distance 6 for n odd. The results provide proof of concept and lay the groundwork for potential high performing codes.Publication Metadata only Trigonometric series and special values of L-functions(Academic Press Inc Elsevier Science, 2017) Department of Mathematics; N/A; Alkan, Emre; Göral, Haydar; Faculty Member; Master Student; Department of Mathematics; College of Sciences; Graduate School of Sciences and Engineering; 32803; 252019Inspired by representations of the class number of imaginary quadratic fields, in this paper, we give explicit evaluations of trigonometric series having generalized harmonic numbers as coefficients in terms of odd values of the Riemann zeta function and special values of L-functions subject to the parity obstruction. The coefficients that arise in these evaluations are shown to belong to certain cyclotomic extensions. Furthermore, using best polynomial approximation of smooth functions under uniform convergence due to Jackson and their log-sine integrals, we provide approximations of real numbers by combinations of special values of L-functions corresponding to the Legendre symbol. Our method for obtaining these results rests on a careful study of generating functions on the unit circle involving generalized harmonic numbers and the Legendre symbol, thereby relating them to values of polylogarithms and then finally extracting Fourier series of special functions that can be expressed in terms of Clausen functions.Publication Metadata only Explicit realization of pseudo-Hermitian and quasi-Hermitian quantum mechanics for two-level systems(TÜBİTAK , 2006) N/A; Department of Mathematics; N/A; Mostafazadeh, Ali; Özçelik, Seher; Faculty Member; Master Student; Department of Mathematics; College of Sciences; Graduate School of Sciences and Engineering; 4231; N/AWe give an explicit characterization of the most general quasi-Hermitian operator H, the associated metric operators η-, and η+-pseudo-Hermitian operators acting in ℂ2. The latter represent the physical observables of a model whose Hamiltonian and Hubert space are respectively H and ℂ2 endowed with the inner product defined by η+. Our calculations allows for a direct demonstration of the fact that the choice of an irreducible family of observables fixes the metric operator up to a multiplicative factor.Publication Metadata only Prediction of folding type of proteins using mixed-integer linear programming(Elsevier Science Bv, 2005) Department of Industrial Engineering; Department of Industrial Engineering; N/A; Türkay, Metin; Yüksektepe, Fadime Üney; Yılmaz, Özlem; Faculty Member; Researcher; Master Student; Department of Industrial Engineering; College of Engineering; College of Engineering; Graduate School of Sciences and Engineering; 24956; N/A; N/AProteins are classified into four main structural classes by considering their amino acid compositions. Traditional approaches that use hyperplanes to partition data sets into two groups perform poorly due to the existence of four classes. Therefore, a novel method that uses mixed-integer programming is developed to overcome difficulties and inconsistencies of these traditional approaches. Mixed-integer programming (MIP) allows the use of hyper-boxes in order to define the boundaries of the sets that include all or some of the points in that class. For this reason, the efficiency and accuracy of data classification with MIP approach can be improved dramatically compared to the traditional methods. The efficiency of the proposed approach is illustrated on a training set of 120 proteins (30 from each type). The prediction results and their validation are also examined.Publication Metadata only Nonsmooth algorithms for minimizing the largest eigenvalue with applications to inner numerical radius (vol 40, pg 2342, 2020)(Oxford Univ Press, 2020) N/A; N/A; Department of Mathematics; Kangal, Fatih; Mengi, Emre; PhD Student; Faculty Member; Department of Mathematics; Graduate School of Sciences and Engineering; College of Sciences; N/A; 113760N/APublication Metadata only Modeling cutting forces for five axis milling of sculptured surfaces(Trans Tech Publications Ltd, 2011) Erdim, H.; N/A; Department of Mechanical Engineering; Boz, Yaman; Lazoğlu, İsmail; Master Student; Faculty Member; Department of Mechanical Engineering; Manufacturing and Automation Research Center (MARC); Graduate School of Sciences and Engineering; College of Engineering; N/A; 1793915-axis ball-end milling processes are used in various industries such as aerospace, automotive, die-mold and biomedical industries. 5-axis machining provides reduced cycle times and more accurate machining via reduction in machining setups, use of shorter tools due to improved tool accessibility. However, desired machining productivity and precision can be obtained by physical modeling of machining processes via appropriate selection of process parameters. In response to this gap in the industry this paper presents a cutting force model for 5-axis ball-end milling cutting force prediction. Cutter-workpiece engagement is extracted via developed solid modeler based engagement model. Simultaneous 5-axis milling tests are conducted on A17075 workpiece material with a carbide cutting tool. Validation of the proposed model is performed for impeller hub roughing toolpaths. Validation test proves that presented model is computationally efficient and cutting forces can be predicted reasonably well. The result of validation test and detailed comparison with the simulation are also presented in the paper.Publication Metadata only Existence of an attractor and determining modes for structurally damped nonlinear wave equations(Elsevier Science Bv, 2018) N/A; Department of Mathematics; Bilgin, Bilgesu Arif; Kalantarov, Varga; PhD Student; Faculty Member; Department of Mathematics; Graduate School of Sciences and Engineering; College of Sciences; N/A; 117655The paper is devoted to the study of asymptotic behavior as t -> +infinity of solutions of initial boundary value problem for structurally damped semi-linear wave equation partial derivative(2)(t)u(x, t) - Delta u(x, t)+gamma(-Delta)(theta)partial derivative(t) u(x,t) + f(u) = g(x), theta is an element of(0, 1), x is an element of Omega, t > 0 under homogeneous Dirichlet's boundary condition in a bounded domain Omega subset of R-3. We proved that the asymptotic behavior as t -> infinity of solutions of this problem is completely determined by dynamics of the first N Fourier modes, when N is large enough. We also proved that the semigroup generated by this problem when theta is an element of(1/2, 1) possesses an exponential attractor. (C) 2017 Elsevier B.V. All rights reserved.Publication Metadata only Code notes: designing a low-cost tangible coding tool for/with children(Association for Computing Machinery (ACM), 2018) N/A; Department of Psychology; N/A; Department of Psychology; Sabuncuoğlu, Alpay; Erkaya, Merve; Buruk, Oğuz Turan; Göksun, Tilbe; PhD Student; Undergraduate Student; PhD Student; Faculty Member; Department of Psychology; KU Arçelik Research Center for Creative Industries (KUAR) / KU Arçelik Yaratıcı Endüstriler Uygulama ve Araştırma Merkezi (KUAR); Graduate School of Sciences and Engineering; College of Social Sciences and Humanities; Graduate School of Social Sciences and Humanities; College of Social Sciences and Humanities; N/A; N/A; N/A; 47278Programming has become an essential subject for today's education curriculum and as a result, the importance of creating the right environments to teach is increasing. For such environments, featuring tangible tools enhances creativity and collaboration. However, due to their high prices, current tangible tools are not reachable by most of the students. We developed Code Notes as a low-cost, attainable and tangible tool aimed to motivate children to support programming education. Code Notes is comprised of an Android app and code-cardboards to teach the basic concepts in programming. We continue to develop the platform with insights gained from children. This paper shares the design phases of Code Notes and observations from our two-month programming project. We also presented some future concepts of Code Notes that offer an active and embodied interaction with the teaching material.Publication Metadata only Faster simulation methods for the non-stationary random vibrations of non-linear mdof systems(A A Balkema, 1995) Department of Mathematics; Department of Mathematics; N/A; N/A; Aşkar, Attila; Köylüoğlu, Hasan Uğur; Çakmak, Ayşe Selin; Nielsen, Susanne Ramtung; Faculty Member; Teaching Faculty; Other; Other; Department of Mathematics; College of Sciences; College of Sciences; N/A; N/A; 178822 N/A; N/A; N/AN/A