Browsing Department of Mathematics and Computer Studies by Title
Now showing items 19-38 of 52
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Limitations of the least squares estimators; a teaching perspective
(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 ... -
The line on moduli stacks of principal bundles on a curve
(Documenta Mathematica, 2010)Let G be an affine reductive algebraic group over an algebraically closed field k. We determine the Picard group of the moduli stacks of principal G–bundles on any smooth projective curve over k. -
Markovianity and the Thompson monoid F+ (Pre-published version)
(Elsevier, 2023-03-13)We introduce a new distributional invariance principle, called `partial spreadability', which emerges from the representation theory of the Thompson monoid F+ in noncommutative probability spaces. We show that a partially ... -
Minimizing oblique errors for robust estimating
(Irish Mathematical Society, 2008)The slope of the best fit line from minimizing the sum of the squared oblique errors is shown to be the root of a polynomial of degree four. We introduce a median estimator for the slope and, using a case study, we show ... -
Mitigating collinearity in linear regression models using ridge, surrogate and raised estimators
(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 ... -
Moduli schemes of generically simple Azumaya modules
(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 ... -
The moduli stack of vector bundles on a curve (Pre-published Version)
(Ramanujan Mathematical Society, 2010)This expository text tries to explain brie y and not too technically the notions of stack and algebraic stack, emphasizing as an example the moduli stack of vector bundles on an algebraic curve. -
Moduli stacks of vector bundles on curves and the King–Schofield rationality proof (Pre-published version)
(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. ... -
Moishezon twistor spaces without effective divisors of degree one (pre-published version)
(Universität Kaiserslautern, 1995)We study simply connected compact twistor spaces Z of positive type. Assuming that the fundamental linear system j \Gamma 1 2 Kj is at least a pencil, we prove the following theorem: the existence of an irreducible curve ... -
Moment estimation of measurement errors
(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 ... -
New examples of stable bundles on Calabi-Yau threefolds (Pre-published Version)
(Oxford University Press, 2012)In this paper we present a construction of stable bundles on Calabi-Yau threefolds using the method of bundle extensions. This construction applies to any given Calabi-Yau threefold with h1 , 1 > 1. We give examples ... -
A note on the computation of symmetric powers of hyperbolic forms and of trace froms on symbol algebras
(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 ... -
On a relative Fourier-Mukai transform on genus one fibrations
(Springer, 2006)We study relative Fourier-Mukai transforms on genus one fibrations with section, allowing explicitly the total space of the fibration to be singular and non-projective. Grothendieck duality is used to prove a ... -
On moduli stacks of G-bundles over a curve (Pre-published version)
(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 ... -
On semistable vector bundles over curves (Pre-published version)
(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; ... -
The Picard group of a coarse moduli space of vector bundles in positive characteristic (Pre-published version)
(Versita, co-published with Springer Verlag., 2012)Let C be a smooth projective curve over an algebraically closed field of arbitrary characteristic. Let Mss r,L denote the projective coarse moduli scheme of semistable rank r vector bundles over C with fixed determinant ... -
Poincaré families and automorphisms of principal bundles on a curve (Pre-published version)
(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 ... -
Poincaré families of G-bundles on a curve (Pre-published version)
(Springer Verlag, 2012)Let G be a reductive group over an algebraically closed field k. Consider the moduli space of stable principal G-bundles on a smooth projective curve C over k. We give necessary and sufficient conditions for the existence of ... -
Pseudospectra of elements of reduced Banach algebras II (Pre-published version)
(Faculty of Sciences and Mathematics, University of Nis, Serbia, 2018-06)Let A be a Banach algebra with identity 1 and p ∈ A be a non-trivial idempotent. Then q = 1 − p is also an idempotent. The subalgebras pAp and qAq are Banach algebras, called reduced Banach algebras, with identities p and ... -
Rationality and Poincaré families for vector bundles with extra structure on a curve (Pre-published version)
(Oxford University Press, 2007)Iterated Grassmannian bundles over moduli stacks of vector bundles on a curve are shown to be birational to an affine space times a moduli stack of degree 0 vector bundles, following the method of King and Schofield. ...