Browsing Mathematics and Computer Studies (Peerreviewed publications) by Issue Date
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EinsteinHermitian connection on twisted Higgs bundles (Prepublished Version)
(Elsevier Masson, 2010)Let X be a smooth projective variety over C. We prove that a twisted Higgs vector bundle (E , θ) on X admits an Einstein–Hermitian connection if and only if (E , θ) is polystable. A similar result for twisted vector bundles ... 
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. 
The BelavinDrinfeld theorem on nondegenerate solutions of the classical YangBaxter equation
(IOP Publishing, 2010)We give a coordinate free proof of Belavin and Drinfeld's Theorem about the classi cation of nondegenerate solutions of the classical YangBaxter equation. The equivalence of different characterisations of nondegeneracy ... 
On moduli stacks of Gbundles over a curve (Prepublished 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 Gbundles on C. We determine the set of ... 
Moduli stacks of vector bundles on curves and the King–Schofield rationality proof (Prepublished 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. ... 
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 ... 
Independent parameters for special instanton bundles on P^{2n+1} (Prepublished Version)
(Elsevier, 2011)Motivated by YangMills 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 ... 
The Brauer group of moduli spaces of vector bundles over a real curve
(American Mathematical Society (AMS), 2011)Let X be a geometrically connected smooth projective curve of genus gX ≥ 2 over R. Let M(r, ξ) be the coarse moduli space of geometrically stable vector bundles E over X of rank r and determinant ξ, where ξ is a real point ... 
Trace forms of symbol algebras (Prepublished version)
(World Scientific Publishing Complany, 2012)Let S be a symbol algebra. The trace form of S is computed and it is shown how this form can be used to determine whether S is a division algebra or not. In addition, the exterior powers of the trace form of S are computed. 
The Picard group of a coarse moduli space of vector bundles in positive characteristic (Prepublished version)
(Versita, copublished 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 of Gbundles on a curve (Prepublished version)
(Springer Verlag, 2012)Let G be a reductive group over an algebraically closed ﬁeld k. Consider the moduli space of stable principal Gbundles on a smooth projective curve C over k. We give necessary and suﬃcient conditions for the existence of ... 
New examples of stable bundles on CalabiYau threefolds (Prepublished Version)
(Oxford University Press, 2012)In this paper we present a construction of stable bundles on CalabiYau threefolds using the method of bundle extensions. This construction applies to any given CalabiYau threefold with h1 , 1 > 1. We give examples ... 
SU(5) heterotic standard model bundles (Prepublished version)
(Springer Verlag, 2012)We construct a class of stable SU(5) bundles on an elliptically ﬁbered CalabiYau threefold with two sections, a variant of the ordinary Weierstrass ﬁbration, which admits a free involution. The bundles are invariant under ... 
Analytic moduli spaces of simple sheaves on families of integral curves (Preprint version)
(Wiley, 2013)We prove the existence of fine moduli spaces of simple coherent sheaves on families of irreducible curves. Our proof is based on the existence of a universal upper bound of the Castelnuovo–Mumford regularity of such sheaves, ... 
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 ... 
Response surface designs using the generalized variance inflation factors
(Cogent OA, 2015)We study response surface designs using the generalized variance inflation factors for subsets as an extension of the variance inflation factors. 
Anomalies of the magnitude of the bias of the maximum likelihood estimator of the regression slope
(Athens Institute for Education and Research, 2015)The slope of the bestfit 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
(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 ... 
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 ... 
Algebraic dimension of twistor spaces whose fundamental system is a pencil (prepublished version)
(London Mathematical Society, 2017)We show that the algebraic dimension of a twistor space over nℂℙ2 cannot be two if n>4 and the fundamental system (that is, the linear system associated to the half‐anti‐canonical bundle, which is available on any twistor ...