Publications with Fulltext

Permanent URI for this collectionhttps://hdl.handle.net/20.500.14288/6

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Quartile: search.filters.quartile.Q2Subject: search.filters.subject.Mathematics

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Now showing 1 - 10 of 27
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    PublicationOpen Access
    Motivic cohomology of fat points in milnor range
    (Deutsche Mathematiker-Vereinigung (DMV), 2018) Park, Jinhyun; Department of Mathematics; Ünver, Sinan; Faculty Member; Department of Mathematics; College of Sciences; 177871
    We introduce a new algebraic-cycle model for the motivic cohomology theory of truncated polynomials k[t]/(t(m)) in one variable. This approach uses ideas from the deformation theory and non-archimedean analysis, and is distinct from the approaches via cycles with modulus. We prove that the groups in the Milnor range give the Milnor K-groups of k[t]I/(t(m)), when the base field is of characteristic 0. Its relative part is the sum of the absolute Kahler differential forms.
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    PublicationOpen Access
    Optimal obstacle placement with disambiguations
    (Institute of Mathematical Statistics (IMS), 2012) Aksakalli, Vural; Department of Mathematics; Ceyhan, Elvan; Undergraduate Student; Faculty Member; Department of Mathematics; College of Sciences
    We introduce the optimal obstacle placement with disambiguations problem wherein the goal is to place true obstacles in an environment cluttered with false obstacles so as to maximize the total traversal length of a navigating agent (NAVA). Prior to the traversal, the NAVA is given location information and probabilistic estimates of each disk-shaped hindrance (hereinafter referred to as disk) being a true obstacle. The NAVA can disambiguate a disk's status only when situated on its boundary. There exists an obstacle placing agent (OPA) that locates obstacles prior to the NAVA's traversal. The goal of the OPA is to place true obstacles in between the clutter in such a way that the NAVA's traversal length is maximized in a game-theoretic sense. We assume the OPA knows the clutter spatial distribution type, but not the exact locations of clutter disks. We analyze the traversal length using repeated measures analysis of variance for various obstacle number, obstacle placing scheme and clutter spatial distribution type combinations in order to identify the optimal combination. Our results indicate that as the clutter becomes more regular (clustered), the NAVA's traversal length gets longer (shorter). On the other hand, the traversal length tends to follow a concave-down trend as the number of obstacles increases. We also provide a case study on a real-world maritime minefield data set.
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    PublicationOpen Access
    On the regularity of the solution map of the Euler-Poisson system
    (TÜBİTAK, 2019) Department of Mathematics; İnci, Hasan; Department of Mathematics; College of Sciences; 274184
    In this paper we consider the Euler-Poisson system (describing a plasma consisting of positive ions with a negligible temperature and massless electrons in thermodynamical equilibrium) on the Sobolev spaces H-s(R-3) , s > 5/2. Using a geometric approach we show that for any time T > 0 the corresponding solution map, (rho(0), u(0)) bar right arrow (rho(T), u(T)) , is nowhere locally uniformly continuous. On the other hand it turns out that the trajectories of the ions are analytic curves in R-3.
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    PublicationOpen Access
    Censoring distances based on labeled cortical distance maps in cortical morphometry
    (Frontiers, 2013) Nishino, Tomoyuki; Alexopolous, Dimitrios; Todd, Richard D.; Botteron, Kelly N.; Miller, Michael I.; Ratnanather, J. Tilak; Department of Mathematics; Ceyhan, Elvan; Undergraduate Student; Faculty Member; Department of Mathematics; College of Sciences
    It has been demonstrated that shape differences in cortical structures may be manifested in neuropsychiatric disorders. Such morphometric differences can be measured by labeled cortical distance mapping (LCDM) which characterizes the morphometry of the laminar cortical mantle of cortical structures. LCDM data consist of signed/labeled distances of gray matter (GM) voxels with respect to GM/white matter (VW) surface. Volumes and other summary measures for each subject and the pooled distances can help determine the morphometric differences between diagnostic groups, however they do not reveal all the morphometric information contained in LCDM distances. To extract more information from LCDM data, censoring of the pooled distances is introduced for each diagnostic group where the range of LCDM distances is partitioned at a fixed increment size; and at each censoring step, the distances not exceeding the censoring distance are kept. Censored LCDM distances inherit the advantages of the pooled distances but also provide information about the location of morphometric differences which cannot be obtained from the pooled distances. However, at each step, the censored distances aggregate, which might confound the results. The influence of data aggregation is investigated with an extensive Monte Carlo simulation analysis and it is demonstrated that this influence is negligible. As an illustrative example, GM of ventral medial prefrontal cortices (VMPFCs) of subjects with major depressive disorder (MDD), subjects at high risk (HR) of MDD, and healthy control (Ctrl) subjects are used. A significant reduction in laminar thickness of the VMPFC in MDD and HR subjects is observed compared to Ctrl subjects. Moreover, the GM LCDM distances (i.e., locations with respect to the GM/WM surface) for which these differences start to occur are determined. The methodology is also applicable to LCDM-based morphometric measures of other cortical structures affected by disease.
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    PublicationOpen Access
    Number of Least area planes in gromov hyperbolic 3-spaces
    (American Mathematical Society (AMS), 2010) Department of Mathematics; Coşkunüzer, Barış; Faculty Member; Department of Mathematics; College of Sciences
    We show that for a generic simple closed curve Γ in the asymptotic boundary of a Gromov hyperbolic 3-space with cocompact metric X, there exists a unique least area plane Σ in X such that ∂∞Σ = Γ. This result has interesting topological applications for constructions of canonical 2-dimensional objects in Gromov hyperbolic 3-manifolds.
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    PublicationOpen Access
    A class of Banach algebras whose duals have the Schur property
    (TÜBİTAK, 1999) Mustafayev, H.; Department of Mathematics; Ülger, Ali; Faculty Member; Department of Mathematics; College of Sciences
    Call a commutative Banach algebra A a γ-algebra if it contains a bounded group Λ such that aco(Λ) contains a multiple of the unit ball of A. In this paper, first by exhibiting several concrete examples, we show that the class of γ-algebras is quite rich. Then, for a γ-algebra A, we prove that A* has the Schur property iff the Gelfand spectrum Σ of A is scattered iff A* = ap(A) iff A* = Span(Σ).
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    PublicationOpen Access
    Canonical contact structures on some singularity links
    (Oxford University Press (OUP), 2014) Bhupal, Mohan; Department of Mathematics; Özbağcı, Burak; Faculty Member; Department of Mathematics; College of Sciences; 29746
    We identify the canonical contact structure on the link of a simple elliptic or cusp singularity by drawing a Legendrian handlebody diagram of one of its Stein fillings. We also show that the canonical contact structure on the link of a numerically Gorenstein surface singularity is trivial considered as a real plane bundle.
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    PublicationOpen Access
    Embedded plateau problem
    (American Mathematical Society (AMS), 2012) Department of Mathematics; Coşkunüzer, Barış; Faculty Member; Department of Mathematics; College of Sciences
    We show that if Gamma is a simple closed curve bounding an embedded disk in a closed 3-manifold M, then there exists a disk Sigma in M with boundary Gamma such that Sigma minimizes the area among the embedded disks with boundary Gamma. Moreover, Sigma is smooth, minimal and embedded everywhere except where the boundary Gamma meets the interior of Sigma. The same result is also valid for homogeneously regular manifolds with sufficiently convex boundary.
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    PublicationOpen Access
    An uncountable ergodic Roth theorem and applications
    (American Institute of Mathematical Sciences, 2022) Schmid, Polona durcik; Greenfeld, Rachel; Iseli, Annina; Jamneshan; Madrid, Jose; Department of Mathematics; Jamneshan, Asgar; Faculty Member; Department of Mathematics; College of Sciences; 332404
    We establish an uncountable amenable ergodic Roth theorem, in which the acting group is not assumed to be countable and the space need not be separable. This generalizes a previous result of Bergelson, McCutcheon and Zhang, and complements a result of Zorin-Kranich. We establish the following two additional results: First, a combinatorial application about triangular patterns in certain subsets of the Cartesian square of arbitrary amenable groups, extending a result of Bergelson, McCutcheon and Zhang for countable amenable groups. Second, a new uniformity aspect in the double recurrence theorem for Gamma-systems for uniformly amenable groups Gamma. As a special case, we obtain this uniformity over all Z-systems, and our result seems to be novel already in this case. Our uncountable Roth theorem is crucial in the proof of both of these results.
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    PublicationOpen Access
    Milnor fillable contact structures are universally tight
    (International Press Institute (IPI), 2010) Lekili, Yanki; Department of Mathematics; Özbağcı, Burak; Faculty Member; Department of Mathematics; College of Sciences; 29746
    We show that the canonical contact structure on the link of a normal complex singularity is universally tight. As a corollary we show the existence of closed, oriented, atoroidal 3-manifolds with infinite fundamental groups which carry universally tight contact structures that are not deformations of taut (or Reebless) foliations. This answers two questions of Etnyre in [12].