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Publication Metadata only A differential integrability condition for two-dimensional Hamiltonian systems(Czech Technical Univ Prague, 2014) N/A; Department of Mathematics; Mostafazadeh, Ali; Faculty Member; Department of Mathematics; College of Sciences; 4231We review, restate, and prove a result due to Kaushal and Korsch [Phys. Lett. A 276, 47 (2000)] on the complete integrability of two-dimensional Hamiltonian systems whose Hamiltonian satisfies a set of four linear second order partial differential equations. In particular, we show that a two- dimensional Hamiltonian system is completely integrable, if the Hamiltonian has the form H = T + V where V and T are respectively harmonic functions of the generalized coordinates and the associated momenta.Publication Metadata only A fredholm alternative-like result on power bounded operators(Scientific Technical Research Council Turkey-Tubitak, 2011) Yavuz, Onur; Department of Mathematics; Ülger, Ali; Faculty Member; Department of Mathematics; College of Sciences; N/ALet X be a complex Banach space and T:X\rightarrow X be a power bounded operator, i.e., \sup_{n \geq 0}\ T^n\Publication Open Access A note on a strongly damped wave equation with fast growing nonlinearities(American Institute of Physics (AIP) Publishing, 2015) Zelik, Sergey; Department of Mathematics; Kalantarov, Varga; Faculty Member; Department of Mathematics; College of Sciences; 117655A strongly damped wave equation including the displacement depending nonlinear damping term and nonlinear interaction function is considered. The main aim of the note is to show that under the standard dissipativity restrictions on the nonlinearities involved, the initial boundary value problem for the considered equation is globally well-posed in the class of sufficiently regular solutions and the semigroup generated by the problem possesses a global attractor in the corresponding phase space. These results are obtained for the nonlinearities of an arbitrary polynomial growth and without the assumption that the considered problem has a global Lyapunov function. (C) 2015 AIP Publishing LLCPublication Metadata only A note on contact surgery diagrams(World Scientific Publishing, 2005) N/A; Department of Mathematics; Özbağcı, Burak; Faculty Member; Department of Mathematics; College of Sciences; 29746We prove that for any positive integer k, the stabilization of a 1/k-surgery curve in a k contact surgery diagram induces an overtwisted contact structure.Publication Metadata only A note on the kadison-singer problem(Theta Foundation, 2010) Akemann, Charles A.; Tanbay, Betül; Department of Mathematics; Ülger, Ali; Faculty Member; Department of Mathematics; College of Sciences; N/ALet H be a separable Hilbert space with a fixed orthonormal basis (e(n)) n >= 1 and B(H) be the full von Neumann algebra of the bounded linear operators T : H -> H. identifying l(infinity) = C(beta N) with the diagonal operators, we consider C(beta N) as a subalgebra of B(H). For each t is an element of beta N, let [delta(t)] be the set of the states of B(H) that extend the Dirac measure delta(t). Our main result shows that, for each t in beta N, the set [delta(t)] either lies in a finite dimensional subspace of B(H)* or else it must contain a homeomorphic copy of beta N.Publication Metadata only A universal formula for the j-invariant of the canonical lifting(Elsevier, 2015) Department of Mathematics; Erdoğan, Altan; Teaching Faculty; Department of Mathematics; College of Sciences; N/AWe study the j-invariant of the canonical lifting of an elliptic curve as a Witt vector. We prove that its Witt coordinates lie in an open affine subset of the j-line and deduce the existence of a universal formula for the j-invariant of the canonical lifting. The canonical lifting of the elliptic curves with j-invariant 0 and 1728 over any characteristic is also explicitly found. (C) 2015 Elsevier Inc. All rights reserved.Publication Metadata only Addendum to “On the mean square average of special values of L-functions” [J. Number Theory 131 (8) (2011) 1470–1485](Elsevier, 2011) Department of Mathematics; Alkan, Emre; Faculty Member; Department of Mathematics; College of Sciences; 32803Publication Metadata only Alternating direction implicit technique and quantum evolution within the hydrodynamical formulation of Schrodinger's equation(Elsevier, 1998) Rabitz, H; N/A; Department of Mathematics; Dey, Bijoy K.; Aşkar, Attila; N/A; Faculty Member; Department of Mathematics; N/A; College of Sciences; N/A; 178822An alternative method of quantum dynamics is presented. The method is based on the hydrodynamical formulation of the time-dependent Schrodinger equation originally given by David Bohm in his quest for establishing a hidden variable alternative to the quantum mechanics. A new alternating direction implicit technique has been employed to decouple many-dimensional hydrodynamical equations into a set of one-dimensional equations which have been solved numerically by adopting a recently developed flux corrected transport algorithm. We apply the method to describe the dynamics of a quantum particle in three spatial dimensions where analytical solutions are known. (C) 1998 Elsevier Science B.V. All rights reserved.Publication Metadata only An Abstract Cogalois Theory for profinite groups(Elsevier, 2005) Basarab, EA; Department of Mathematics; Albu, Toma; Faculty Member; Department of Mathematics; College of Sciences; N/AThe aim of this paper is to develop an abstract group theoretic framework for the Cogalois Theory of field extensions. (c) 2005 Elsevier B.V. All rights reserved.Publication Metadata only An extension property for banach spaces(Institute of Mathematics, Polish Academy of Sciences, 2002) Department of Mathematics; Freedman, Walden; Faculty Member; Department of Mathematics; College of Sciences; N/AA Banach space X has property (E) if every operator from X into c0 extends to an operator from X** into c0; X has property (L) if whenever K ⊆ X is limited in X**, then K is limited in X; X has property (G) if whenever K ⊆ X is Grothendieck in X**, then K is Grothendieck in X. In all of these, we consider X as canonically embedded in X**. We study these properties in connection with other geometric properties, such as the Phillips properties, the Gelfand-Phillips and weak Gelfand-Phillips properties, and the property of being a Grothendieck space. © 2002, Instytut Matematyczny. All rights reserved.