One parameter family of indecomposable optimal entanglement witnesses arising from generalized Choi maps

In the recent paper [Chru\'{s}ci\'{n}ski and Wudarski, arXiv:1105.4821], it was conjectured that the entanglement witnesses arising from some generalized Choi maps are optimal. We show that this conjecture is true. Furthermore, we show that they provide a one parameter family of indecomposable optimal entanglement witnesses.Comment: 3 page

Orthogonality of linear combinations of two orthogonal polynomial sequences

14 pages, no figures.-- MSC2000 code: 33C45.MR#: MR1865881 (2002j:33009)Zbl#: Zbl 0990.42007We find necessary and sufficient conditions for some linear combinations of two sequences of orthogonal polynomials to be again orthogonal.The first author (K.H.K.) was partially supported by KOSEF(99-2-101-001-5). The work of the third author (F.M.) was supported by Dirección General de Enseñanza Superior (DGES) of Spain under grant PB96-0120-C03-01.Publicad

Optimality for indecomposable entanglement witnesses

We examine various notions related with the optimality for entanglement witnesses arising from Choi type positive linear maps. We found examples of optimal entanglement witnesses which are non-decomposable, but which are not `non-decomposable optimal entanglement witnesses' in the sense of [M. Lewenstein, B. Kraus, J. Cirac, and P. Horodecki, Phys. Rev. A 62, 052310 (2000)]. We suggest to use the term `PPTES witness' and `optimal PPTES witness' in the places of `non-decomposable entanglement witness' and `non-decomposable optimal entanglement witnesses' in order to avoid possible confusion. We also found examples of non-extremal optimal entanglement witnesses which are indecomposable.Comment: 5 pages, 1 figure, 1 tabl

Entanglement witnesses arising from Choi type positive linear maps

We construct optimal PPTES witnesses to detect $3\otimes 3$ PPT entangled edge states of type $(6,8)$ constructed recently \cite{kye_osaka}. To do this, we consider positive linear maps which are variants of the Choi type map involving complex numbers, and examine several notions related to optimality for those entanglement witnesses. Through the discussion, we suggest a method to check the optimality of entanglement witnesses without the spanning property.Comment: 18 pages, 4 figures, 1 tabl

Compatible pairs of orthogonal polynomials

19 pages, no figures.-- MSC1991 code: 33C45.MR#: MR1736624 (2001a:33009)Zbl#: Zbl 0944.33012We find necessary and sufficient conditions for an orthogonal polynomial system to be compatible with another orthogonal polynomial system. As applications, we find new characterizations of semi-classical and classical orthogonal polynomials.The work of D. H. Kim and K. H. Kwon was partially supported by KOSEF (98-0701-03-01-5) and GARC at Seoul National University. The work of F. Marcellán was partially supported by Dirección General de Enseñanza Superior (DGES) of Spain under grant PB96-0120-C03-0l.Publicad

Discrete-continuous symmetrized Sobolev inner products

23 pages, no figures.-- MSC2000 code: 42C05.MR#: MR2069523 (2005f:42053)Zbl#: Zbl 1048.42023^aThis paper deals with the bilinear symmetrization problem associated with Sobolev inner products. Let $\{Q_n\}_{n=0}^{\infty}$ be the sequence of monic polynomials orthogonal with respect to a Sobolev inner product of order 1 when one of the measures is discrete and the other one is a nondiscrete positive Borel measure. Furthermore, assume that the supports of such measures are symmetric with respect to the origin so that the corresponding odd moments vanish. We consider the orthogonality properties of the sequences of monic polynomials $\{P_n\}_{n=0}^{\infty}$ and $\{R_n\}_{n=0}^{\infty}$ such that $Q_{2n}(x)=P_n(x^2)$, $Q_{2n+1}(x)=xR_n(x^2)$. Moreover, recurrence relations for $\{P_n\}_{n=0}^{\infty}$ and $\{R_n\}_{n=0}^{\infty}$ are obtained as well as explicit algebraic relations between them.The work of the second author has been partially supported by KRF-2002-070-C00004. The work of the third author has been partially supported by Dirección General de Investigación (Ministerio de Ciencia y Tecnología) of Spain under grant BFM 2000-0206-C04-01 and INTAS project INTAS 2000-272.Publicad

Zeros of Jacobi-Sobolev orthogonal polynomials

10 pages, no figures.-- MSC2000 codes: 33C45.MR#: MR2027148 (2004m:33017)Zbl#: Zbl pre05376428We investigate zeros of Jacobi-Sobolev orthogonal polynomials with respect to \multline \langle f, g\rangle = \int_{-1}^1 f(x)g(x)(1-x)^{ \alpha }(1+x)^{\beta} dx\\ +\gamma \int_{-1}^1 f'(x)g'(x)(1-x)^{ \alpha +1}(1+x)^{ \beta } dx,\endmultline where $\alpha >-1,\ -1 0$.KHK and GJY were partially supported by KOSEF (98-0701-03-01-5) and Hwarangdae Research Institute. FM was partially supported by Dirección General de Investigación (MCYT) of Spain under grant BFM2000-0206-C04-01 and INTAS00-272.Publicad

Prediction of the Feed Values of Maize Silage by Near Infrared Reflectance Spectroscopy

Until recently, feed evaluation of silages in official laboratories and feed factories was based on cutting date, chemical composition and the ammonia fraction. However, in vitro techniques have been developed based on rumen fluid or commercial enzymes to replace laborious, time-consuming and expensive digestibility experiments with animals. In this study the possibility of using near infrared reflectance spectroscopy (NIRS) to predict the chemical composition and digestibility of maize silage was examined