Research Outputs

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Now showing 1 - 10 of 97
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    Publication
    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/A
    Let X be a complex Banach space and T:X\rightarrow X be a power bounded operator, i.e., \sup_{n \geq 0}\ T^n\
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    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; 29746
    We 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.
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    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/A
    Let 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.
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    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/A
    We 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.
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    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; 32803
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    Almost all hyperharmonic numbers are not integers
    (Elsevier, 2017) Sertbaş, Doğa Can; N/A; Göral, Haydar; Master Student; Graduate School of Sciences and Engineering; 252019
    It is an open question asked by Mezo that there is no hyperharmonic integer except 1. So far it has been proved that all hyperharmonic numbers are not integers up to order r = 25. In this paper, we extend the current results for large orders. Our method will be based on three different approaches, namely analytic, combinatorial and algebraic. From analytic point of view, by exploiting primes in short intervals we prove that almost all hyperharmonic numbers are not integers. Then using combinatorial techniques, we show that if n is even or a prime power, or r is odd then the corresponding hyperharmonic number is not integer. Finally as algebraic methods, we relate the integerness property of hyperharmonic numbers with solutions of some polynomials in finite fields. (C) 2016 Elsevier Inc. All rights reserved.
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    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/A
    The 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.
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    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/A
    A 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.
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    PublicationOpen Access
    An uncountable Mackey-Zimmer theorem
    (Institute of Mathematics of the Polish Academy of Sciences, 2022) Tao, Terence; Department of Mathematics; Jamneshan, Asgar; Faculty Member; Department of Mathematics; College of Sciences; 332404
    The Mackey–Zimmer theorem classifies ergodic group extensions X of a measure-preserving system Y by a compact group K, by showing that such extensions are isomorphic to a group skew-product X?Y??H for some closed subgroup H of K. An analogous theorem is also available for ergodic homogeneous extensions X of Y, namely that they are isomorphic to a homogeneous skew-product Y??H/M. These theorems have many uses in ergodic theory, for instance playing a key role in the Host–Kra structural theory of characteristic factors of measure-preserving systems.The existing proofs of the Mackey–Zimmer theorem require various “countability”, “separability”, or “metrizability” hypotheses on the group ? that acts on the system, the base space Y, and the group K used to perform the extension. In this paper we generalize the Mackey–Zimmer theorem to “uncountable” settings in which these hypotheses are omitted, at the cost of making the notion of a measure-preserving system and a group extension more abstract. However, this abstraction is partially counteracted by the use of a “canonical model” for abstract measure-preserving systems developed in a companion paper. In subsequent work we will apply this theorem to also obtain uncountable versions of the Host–Kra structural theory.
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    Anomalies in the transcriptional regulatory network of the Yeast Saccharomyces cerevisiae
    (Elsevier, 2010) N/A; Department of Physics; Tuğrul, Murat; Kabakçıoğlu, Alkan; N/A; Faculty Member; Department of Physics; Graduate School of Sciences and Engineering; College of Sciences; N/A; 49854
    We investigate the structural and dynamical properties of the transcriptional regulatory network of the Yeast Saccharomyces cerevisiae and compare it with two "unbiased" ensembles: one obtained by reshuffling the edges and the other generated by mimicking the transcriptional regulation mechanism within the cell. Both ensembles reproduce the degree distributions (the first-by construction-exactly and the second approximately), degree-degree correlations and the k-core structure observed in Yeast. An exceptionally large dynamically relevant core network found in Yeast in comparison with the second ensemble points to a strong bias towards a collective organization which is achieved by subtle modifications in the network's degree distributions. We use a Boolean model of regulatory dynamics with various classes of update functions to represent in vivo regulatory interactions. We find that the Yeast's core network has a qualitatively different behavior, accommodating on average multiple attractors unlike typical members of both reference ensembles which converge to a single dominant attractor. Finally, we investigate the robustness of the networks and find that the stability depends strongly on the used function class. The robustness measure is squeezed into a narrower band around the order-chaos boundary when Boolean inputs are required to be nonredundant on each node. However, the difference between the reference models and the Yeast's core is marginal, suggesting that the dynamically stable network elements are located mostly on the peripherals of the regulatory network. Consistently, the statistically significant three-node motifs in the dynamical core of Yeast turn out to be different from and less stable than those found in the full transcriptional regulatory network.