Now showing items 1-20 of 49

    • The stability space of the derived category of holomorphic triples and further investigations 

      Rüffer, Arne (2021-04-14)
      In this thesis we give a complete description of the Bridgeland stability space for the bounded derived category of holomorphic triples over a smooth projective curve of genus one as a connected, four dimensional complex ...
    • Constructing isostatic frameworks for the l1 and l infinity plane 

      Clinch, Katie; Kitson, Derek (Electronic Journal of Combinatorics, 2020-06-12)
      We use a new coloured multi-graph constructive method to prove that if the edge-set of a graph G = (V,E) has a partition into two spanning trees T1 and T2 then there is a map p : V → R2, p(v) = (p(v)1,p(v)2), such that ...
    • Graph rigidity for unitarily invariant matrix norms 

      Kitson, Derek; Levene, Rupert H (Elsevier, 2020-11-15)
      A rigidity theory is developed for bar-joint frameworks in linear matrix spaces endowed with a unitarily invariant matrix norm. Analogues of Maxwell's counting criteria are obtained and minimally rigid matrix frameworks ...
    • Symbol functions for symmetric frameworks 

      Kitson, Derek; Kastis, Eleftherios; McCarthy, John E (Elsevier, 2021-05-15)
      We prove a variant of the well-known result that intertwiners for the bilateral shift on ℓ2(Z) are unitarily equivalent to multiplication operators on L2(T). This enables us to unify and extend fundamental aspects of ...
    • Symmetric frameworks in normed spaces 

      Kitson, Derek; Nixon, Anthony; Schulze, Bernd (Elsevier, 2020-12-15)
      We develop a combinatorial rigidity theory for symmetric bar-joint frameworks in a general finite dimensional normed space. In the case of rotational symmetry, matroidal Maxwell-type sparsity counts are identified for a ...
    • Symmetric powers of trace forms on symbol algebras 

      Flatley, Ronan (Université D'Artois, 2013)
    • Anomalies of the magnitude of the bias of the maximum likelihood estimator of the regression slope 

      O'Driscoll, Diarmuid; Ramirez, Donald E. (Athens Institute for Education and Research, 2015)
      The slope of the best-fit line y h x x 0 1  ( )    from minimizing a function of the squared vertical and horizontal errors is the root of a polynomial of degree four which has exactly two real roots, one positive and ...
    • An investigation of the performance of five different estimators in the measurement error regression model 

      O'Driscoll, Diarmuid; Ramirez, Donald E. (Athens Institute for Education and Research, 2015)
      In a comprehensive paper by Riggs et al.(1978) the authors analyse the performances of numerous estimators for the regression slope in the measurement error model with positive measurement error variances >0 0 for X and ...
    • On moduli stacks of G-bundles over a curve (Pre-published version) 

      Hoffmann, Norbert (Springer, 2010)
      Let C be a smooth projective curve over an algebraically closed eld k of arbitrary characteristic. Given a linear algebraic group G over k, let MG be the moduli stack of principal G-bundles on C. We determine the set of ...
    • Moduli stacks of vector bundles on curves and the King–Schofield rationality proof (Pre-published version) 

      Hoffmann, Norbert (Springer, 2010)
      Let C be a connected smooth projective curve of genus g ≥ 2 over an algebraically closed field k. Consider the coarse moduli scheme Bunr,d (resp. Bunr,L) of stable vector bundles on C with rank r and degree d ∈ Z (resp. ...
    • On semistable vector bundles over curves (Pre-published version) 

      Hoffmann, Norbert; Biswas, Indranil; Hein, Georg (Elsevier, 2008)
      Let X be a geometrically irreducible smooth projective curve de ned over a eld k, and let E be a vector bundle on X. Then E is semistable if and only if there is a vector bundle F on X such that Hi(X; F E) = 0 for i = 0; ...
    • Poincaré families and automorphisms of principal bundles on a curve (Pre-published version) 

      Hoffmann, Norbert; Biswas, Indranil (Elsevier, 2009)
      Let C be a smooth projective curve, and let G be a reductive algebraic group. We give a necessary condition, in terms of automorphism groups of principal G-bundles on C, for the existence of Poincaré families parameterized ...
    • Moment estimation of measurement errors 

      O'Driscoll, Diarmuid; Ramirez, Donald E. (NEDETAS, 2011)
      The slope of the best-fit line from minimizing a function of the squared vertical and horizontal errors is the root of a polynomial of degree four. We use second order and fourth order moment equations to estimate the ratio ...
    • Revisiting some design criteria 

      O'Driscoll, Diarmuid; Ramirez, Donald E. (Athens Institute for Education and Research, 2015)
      We address the problem that the A (trace) design criterion is not scale invariant and often is in disagreement with the D (determinant) design criterion. We consider the canonical moment matrix CM and use the trace of its ...
    • Limitations of the least squares estimators; a teaching perspective 

      O'Driscoll, Diarmuid; Ramirez, Donald E. (Athens Institute for Education and Research, 2016)
      The standard linear regression model can be written as Y = Xβ+ε with X a full rank n × p matrix and L(ε) = N(0, σ2In). The least squares estimator is = (X΄X)−1XY with variance-covariance matrix Coυ( ) = σ2(X΄X)−1, where ...
    • A note on the computation of symmetric powers of hyperbolic forms and of trace froms on symbol algebras 

      Flatley, Ronan (Scientific Advances Publishers, 2014)
      Let K be a field with characteristic different from 2 and let S be a symbol algebra over K. We compute the symmetric powers of hyperbolic quadratic forms over K. Also, we compute the symmetric powers of the quadratic trace ...
    • Generalized vector bundles on curves (Pre-published version) 

      Hoffmann, Norbert; Stuhler, Ulrich; Jahnel, Joerg (de Gruyter, 1998)
      In their paper [14] G. Harder and M.S. Narasimhan (and independently D. Quillen) have constructed a canonical flag of subbundles on any vector bundle on a complete smooth algebraic curve over a field. This flag measures ...
    • Moduli schemes of generically simple Azumaya modules 

      Hoffmann, Norbert; Stuhler, Ulrich (Documenta Mathematica, 2005)
      Let A be an Azumaya algebra over a smooth projective variety X or more generally, a torsion free coherent sheaf of algebras over X whose generic fiber is a central simple algebra. We show that generically simple torsion ...
    • Mitigating collinearity in linear regression models using ridge, surrogate and raised estimators 

      O'Driscoll, Diarmuid; Ramirez, Donald E. (Cogent OA, 2016)
      Collinearity in the design matrix is a frequent problem in linear regression models, for example, with economic or medical data. Previous standard procedures to mitigate the effects of collinearity included ridge regression ...
    • Response surface designs using the generalized variance inflation factors 

      O'Driscoll, Diarmuid; Ramirez, Donald E. (Cogent OA, 2015)
      We study response surface designs using the generalized variance inflation factors for subsets as an extension of the variance inflation factors.