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Permanent URI for this collectionhttps://hdl.handle.net/20.500.14288/3
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Publication Metadata only A support function based algorithm for optimization with eigenvalue constraints(Siam Publications, 2017) N/A; Department of Mathematics; Mengi, Emre; Faculty Member; Department of Mathematics; College of Sciences; 113760Optimization of convex functions subject to eigenvalue constraints is intriguing because of peculiar analytical properties of eigenvalue functions and is of practical interest because of a wide range of applications in fields such as structural design and control theory. Here we focus on the optimization of a linear objective subject to a constraint on the smallest eigenvalue of an analytic and Hermitian matrix-valued function. We propose a numerical approach based on quadratic support functions that overestimate the smallest eigenvalue function globally. the quadratic support functions are derived by employing variational properties of the smallest eigenvalue function over a set of Hermitian matrices. We establish the local convergence of the algorithm under mild assumptions and deduce a precise rate of convergence result by viewing the algorithm as a fixed point iteration. the convergence analysis reveals that the algorithm is immune to the nonsmooth nature of the smallest eigenvalue. We illustrate the practical applicability of the algorithm on the pseudospectral functions.Publication Metadata only On regular embedding of H-designs into G-designs(Utilitas Mathematica, 2013) Quattrocchi, Gaetano; Department of Mathematics; Department of Mathematics; Department of Mathematics; Küçükçifçi, Selda; Smith, Benjamin R.; Yazıcı, Emine Şule; Faculty Member; Researcher; Faculty Member; Department of Mathematics; College of Sciences; College of Sciences; College of Sciences; 105252; N/A; 27432The graph H is embedded in the graph G, if H is a subgraph of G. An H-design is a decomposition of a complete graph into edge disjoint copies of the graph H, called blocks. An H-i-design with k blocks, say H-1, H-2, ...H-k is embedded in a G-design if for every H-i, there exists a distinct block, say G(i), in the G-design that embeds H-i. If G(i) are all isomorphic for 1 <= i <= k then the embedding is called regular. This paper solves the problem of the regular embedding of H-designs into G-designs when G has at most four vertices and four edges.Publication Metadata only Decay and growth estimates for solutions of second-order and third-order differential-operator equations(Elsevier, 2013) Yilmaz, Y.; Department of Mathematics; Kalantarov, Varga; Faculty Member; Department of Mathematics; College of Sciences; 117655We obtained decay and growth estimates for solutions of second-order and third-order differential-operator equations in a Hilbert space. Applications to initial-boundary value problems for linear and nonlinear non-stationary partial differential equations modeling the strongly damped nonlinear improved Boussinesq equation, the dual-phase-lag heat conduction equations, the equation describing wave propagation in relaxing media, and the Moore-Gibson-Thompson equation are given.Publication Metadata only Anticyclotomic p-ordinary Iwasawa theory of elliptic modular forms(De Gruyter, 2018) Lei, Antonio; Department of Mathematics; Büyükboduk, Kazım; Faculty Member; Department of Mathematics; College of Sciences; N/AThis is the first in a series of articles where we will study the Iwasawa theory of an elliptic modular form f along the anticyclotomic Z(p)-tower of an imaginary quadratic field K where the prime p splits completely. Our goal in this portion is to prove the Iwasawa main conjecture for suitable twists of f assuming that f is p-ordinary, both in the definite and indefinite setups simultaneously, via an analysis of Beilinson-Flach elements.Publication Metadata only Explicit horizontal open books on some Seifert fibered 3-manifolds(Elsevier Science Bv, 2007) N/A; Department of Mathematics; Özbağcı, Burak; Faculty Member; Department of Mathematics; College of Sciences; 29746We describe explicit horizontal open books on some Seifert fibered 3-manifolds. We show that the contact structures compatible with these horizontal open books are Stein fillable and horizontal as well. Moreover we draw surgery diagrams for some of these contact structures.Publication Metadata only Symplectic fillings of lens spaces as Lefschetz fibrations(European Mathematical Society, 2016) Bhupal, M.; Department of Mathematics; Özbağcı, Burak; Faculty Member; Department of Mathematics; College of Sciences; 29746We construct a positive allowable Lefschetz fibration over the disk on any minimal (weak) symplectic filling of the canonical contact structure on a lens space. Using this construction we prove that any minimal symplectic filling of the canonical contact structure on a lens space is obtained by a sequence of rational blowdowns from the minimal resolution of the corresponding complex two-dimensional cyclic quotient singularity.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 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 The energy spectrum of stochastic eddies with gamma distribution(Natural Sciences Publishing, 2015) Kara, Rukiye; Department of Mathematics; Çağlar, Mine; Faculty Member; Department of Mathematics; College of Sciences; 105131Çinlar velocity field which is based on eddies of rotational form is a promising subgrid velocity model for its use in large eddy simulation (LES). This has been confirmed by data analysis of high frequency radar observations. The energy spectrum plays a central role for representing the subgrid scales in filtered Navier-Stokes equations used in LES. We consider a truncated Gamma distribution for eddy sizes to replicate the subgrid scale energy spectrum analytically. Kolmogorov proposed a form of the spectrum that extends to the inertial scale. Lundgren vortex has a spectrum involving an exponential function and has been used in LES. Çinlar velocity spectrum which is based on the truncated Gamma distribution indicates a good match with the spectrum estimated from real data. The results of this study can be used for designing a method for representing the small scale structures in LES by modeling the subgrid stress.Publication Metadata only Spectral singularities and CPA-Laser action in a weakly nonlinear PT-Symmetric bilayer slab(Wiley, 2014) NA; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231We study optical spectral singularities of a weakly nonlinear PT-symmetric bilinear planar slab of optically active material. In particular, we derive the lasing threshold condition and calculate the laser output intensity. These reveal the following unexpected features of the system: (1) for the case that the real part of the refractive index of the layers are equal to unity, the presence of the lossy layer decreases the threshold gain; (2) for the more commonly encountered situations when -1 is much larger than the magnitude of the imaginary part of the refractive index, the threshold gain coefficient is a function of that has a local minimum. The latter is in sharp contrast to the threshold gain coefficient of a homogeneous slab of gain material which is a decreasing function of . We use these results to comment on the effect of nonlinearity on the prospects of using this system as a coherence perfect absorption-laser.