Browsing Department of Mathematics and Computer Studies by Title
Now showing items 12-31 of 52
-
Generalized vector bundles on curves (Pre-published version)
(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 ... -
Geometric view of measurement errors
(Taylor and Francis, 2011)The slope of the best fit line from minimizing the sum of the squared oblique errors is the root of a polynomial of degree four. This geometric view of measurement errors is used to give insight into the performance of ... -
Graph rigidity for unitarily invariant matrix norms (Pre-published)
(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 ... -
Homological algebra with locally compact abelian groups (Pre-published Version)
(Elsevier, 2007)In this article we study locally compact abelian (LCA) groups from the viewpoint of derived categories, using that their category is quasi-abelian in the sense of J.-P. Schneiders. We define a well-behaved derived Hom-complex ... -
Independent parameters for special instanton bundles on P^{2n+1} (Pre-published Version)
(Elsevier, 2011)Motivated by Yang-Mills theory in 4n dimensions, and generalizing the notion due to Atiyah, Drinfeld, Hitchin and Manin for n = 1, Okonek, Spindler and Trautmann introduced instanton bundles and special instanton bundles ... -
An investigation of the performance of five different estimators in the measurement error regression model
(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 ... -
Ireland's participation in the 50th international mathematical olympiad
(Irish Mathematical Society, 2009)The 50th International Mathematical Olympiad (IMO) took place in Bremen (Germany) from 12th July until 22nd July 2009. With 565 participants (59 of whom were girls) from 104 countries, this was the IMO with the largest ... -
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 ...