Discriminating Completions of Hyperbolic Groups

A group G is called an A-group, where A is a given Abelian group, if it comes equipped with an action of A on G which mimics the way in which Z acts on any group. This action is codified in terms of certain axioms, all but one of which were introduced some years ago by R. C. Lyndon. For every such G and A there exists an A-exponential group G ^A which is the A-completion of G. We prove here that if G is a torsion-free hyperbolic group and if A is a torsion-free Abelian group, then the Lyndon's type completion G ^A of G is G-discriminated by G. This implies various model-theoretic and algorithmic results about G ^A .     

Secant varieties of Grassmann varieties

We consider the dimensions of the higher secant varieties of the Grassmann varieties. We give new instances where these secant varieties have the expected dimension and also a new example where a higher secant variety does not.

     

Secant varieties of toric varieties

Let X_P be a smooth projective toric variety of dimension n embedded in P^r using all of the lattice points of the polytope P. We compute the dimension and degree of the secant variety . We also give explicit formulas in dimensions 2 and 3 and obtain partial results for the projective varieties X_A embedded using a set of lattice points A⊂P∩Zⁿ containing the vertices of P and their nearest neighbors.     

Conormal varieties and characteristic varieties

We show that the conormal variety of a quasihomogeneous hypersurface in , for , whose link is a -homology sphere is not the characteristic variety of any -module.

     

Discriminating efficient units using MAJ FDH

Free Disposal Hull (FDH) is one of the tools in the theoretical and empirical work on the measurement of productive efficiency. Excluding linear combinations of extremal observations to construct this reference technology entails that many of the observations belonging to an evaluated dataset are labeled efficient by this method. Few researchers have sought to improve the discrimination power of FDH. Van Puyenbroeck [H. Tulkens, On FDH efficiency analysis: some methodological issues and applications to retail, banking, courts and urban transit, Journal of Productivity Analysis 4 (1993) 183-210] modified standard FDH method by using Andersen and Petersen [N. Adler, L. Friedman, Z. Siunuany-Stern, Review of ranking methods in the data envelopment analysis context, European Journal of Operational Research, 140 (2002) 249-265], referred to A&P FDH. Jahanshahloo et al. [J. Doyle, R. Green, Efficiency and cross-efficiency in DEA: derivation, meanings and uses, Journal of Operational Research Society 45 (5) (1994) 567-578] used 0-1 linear programming (LP), referred to 0-1 LP FDH to find FDH-efficient units. The purpose of this paper is two-folds: to propose MAJ FDH, similar to in spirit as the ranking method in data envelopment analysis by Mehrabian et al. [S. Mehrabian, M.R. Alirezaee, G.R. Jahanshahloo, A complete efficiency ranking of decision making units in data envelopment analysis, Communicational Optimization and Applications 14 (1999) 261-266] that may thus be used to discriminate between FDH-efficient units and to examine the tie-breaking ability of A&P FDH, 0-1 LP FDH, and MAJ FDH by using three numerical examples. Results of the comparisons show: (i) as the number of DMU, input and output is small where all of input and output levels are positive, the A&P FDH can provide a full ranking; (ii) as the number of DMU, input and output is small where some of input and output levels are equal to zero, none of three extended FDH methods can provide a full ranking; and (iii) as the number of DMU, input and output are increased where all of input and output levels are positive, it seems that ranking by MAJ FDH is more precise than other FDH methods.     

On tangential varieties of rational homogeneous varieties

The sphericality of tangential varieties of rational homogeneousvarieties is determined. The homogeneous coordinate rings andrings of covariants of the tangential varieties of homogenouslyembedded compact Hermitian symmetric spaces (CHSS) are determined.Bounds on the degrees of generators of the ideals of tangentialvarieties of CHSS are given, and more explicit information isobtained about the ideals in certain cases.     

Efficient Computation of Bayesian Optimal Discriminating Designs

An efficient algorithm for the determination of Bayesian optimal discriminating designs for competing regression models is developed, where the main focus is on models with general distributional assumptions beyond the “classical” case of normally distributed homoscedastic errors. For this purpose, we consider a Bayesian version of the Kullback–Leibler (KL). Discretizing the prior distribution leads to local KL-optimal discriminating design problems for a large number of competing models. All currently available methods either require a large amount of computation time or fail to calculate the optimal discriminating design, because they can only deal efficiently with a few model comparisons. In this article, we develop a new algorithm for the determination of Bayesian optimal discriminating designs with respect to the Kullback–Leibler criterion. It is demonstrated that the new algorithm is able to calculate the optimal discriminating designs with reasonable accuracy and computational time in situations where all currently available procedures are either slow or fail.     

线性等距码的一个判别条件

本通过分析线性等距码的特点，利用投射几何的知识，给出了有限域Fq上的线性等距码的一个判别条件。     

Discriminating between the nature of radioactive contamination

Effective management of radioactive contamination necessitates the accurate classification of the polluting elements. In many cases, such a classification is not straightforward. The physics of radioactive contamination is complex, primarily due to the mixture of radionuclides, their migration, and the prevalent weather conditions. Consequently, application of classical techniques is inappropriate in modelling such an environment. However, adopting the tools of fractal geometry provides an improved insight and helps with the relevant classification. Several techniques are implemented to determine geometric aspects of contaminated fields and some of the latest findings are reported here.     

Chordal varieties of Veronese varieties and catalecticant matrices

It is proved that the chordal variety of the Veronese variety is projectively normal, arithmetically caulay, and its homogeneous ideal is generated by the 3×3 minors of two catalecticant matrices. Results are generalized to the catalecticant varieties Gor_≤(T) witht ₁=2. Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 56. Algebraic Geometry-9, 1998.     

Congruence semimodular varieties I: Locally finite varieties

Dedicated to Bjarni Jónsson on the occasion of his 70th birthday     

Higher order secant varieties and blown up varieties

Let π:X→Y be the blowing up of the projective varietyY at s general points. Here we study the higher order secant varieties of the linearly normal embeddings ofX andY into projective spaces. We give conditions on the embedding ofY which imply that the firstt secant varieties of a related embedding ofX have the expected dimension.     

Higher order secant varieties and blown up varieties

Let π:X→Y be the blowing up of the projective varietyY at s general points. Here we study the higher order secant varieties of the linearly normal embeddings ofX andY into projective spaces. We give conditions on the embedding ofY which imply that the firstt secant varieties of a related embedding ofX have the expected dimension.