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A new approach to the 2-variable Subnormal Completion Problem
Curto, R.E.,Lee, S.H.,Yoon, J. Academic Press 2010 Journal of mathematical analysis and applications Vol.370 No.1
We study the Subnormal Completion Problem (SCP) for 2-variable weighted shifts. We use tools and techniques from the theory of truncated moment problems to give a general strategy to solve SCP. We then show that when all quadratic moments are known (equivalently, when the initial segment of weights consists of five independent data points), the natural necessary conditions for the existence of a subnormal completion are also sufficient. To calculate explicitly the associated Berger measure, we compute the algebraic variety of the associated truncated moment problem; it turns out that this algebraic variety is precisely the support of the Berger measure of the subnormal completion.
The Division Algorithm in Sextic Truncated Moment Problems
Curto, Raú,l E.,Yoo, Seonguk Birkha@user 2017 Integral equations and operator theory Vol.87 No.4
<P>For a degree 2n finite sequence of real numbers beta beta((2n)) = {beta(00,) beta 10, beta 01,..., beta 2n, 0, beta 2n-1,1,.., beta 1,2n-1, beta 0,2n}to have a representing measure mu, it is necessary for the associated moment matrix M(n) to be positive semidefinite, and for the algebraic variety associated to beta, nu beta nu(M(n)),, to satisfy rank M(n) <= card nu(beta) as well as the following consistency condition: if a polynomial p(x,y) equivalent to Sigma(ij) a(ij) x(4) y(i) of degree at most 2n vanishes on V beta, then the Riesz functional Lambda(p) equivalent to p(beta) := Sigma(ij) a(ij) beta(ij)=0. Positive semidefiniteness, recursiveness, and the variety condition of a moment matrix are necessary and sufficient conditions to solve the quadratic (n=1) and quartic (n=2) moment problems. Also, positive semidefiniteness, combined with consistency, is a sufficient condition in the case of extremal moment problems, i.e., when the rank of the moment matrix (denoted by r) and the cardinality of the associated algebraic variety (denoted by v) are equal. For extremal sextic moment problems, verifying consistency amounts to having good representation theorems for sextic polynomials in two variables vanishing on the algebraic variety of the moment sequence. We obtain such representation theorems using the Division Algorithm from algebraic geometry. As a consequence, we are able to complete the analysis of extremal sextic moment problems.</P>
Hyponormality and subnormality of block Toeplitz operators
Curto, Raú,l E.,Hwang, In Sung,Lee, Woo Young Elsevier 2012 Advances in mathematics Vol.230 No.4
<P><B>Abstract</B></P><P>In this paper, we are concerned with hyponormality and subnormality of block Toeplitz operators acting on the vector-valued Hardy space H<SUP>Cn</SUP>2 of the unit circle.</P><P>First, we establish a tractable and explicit criterion on the hyponormality of block Toeplitz operators having bounded type symbols via the triangularization theorem for compressions of the shift operator.</P><P>Second, we consider the gap between hyponormality and subnormality for block Toeplitz operators. This is closely related to Halmos’s Problem 5: Is every subnormal Toeplitz operator either normal or analytic? We show that if Φ is a matrix-valued rational function whose co-analytic part has a coprime factorization then every hyponormal Toeplitz operator <SUB>TΦ</SUB> whose square is also hyponormal must be either normal or analytic.</P><P>Third, using the subnormal theory of block Toeplitz operators, we give an answer to the following “Toeplitz completion” problem: find the unspecified Toeplitz entries of the partial block Toeplitz matrix A≔[<SUP>U∗</SUP>??<SUP>U∗</SUP>] so that A becomes subnormal, where U is the unilateral shift on <SUP>H2</SUP>.</P>
Subnormal and quasinormal Toeplitz operators with matrix-valued rational symbols
Curto, R.E.,Hwang, I.S.,Kang, D.O.,Lee, W.Y. Academic Press ; Elsevier Science B.V. Amsterdam 2014 Advances in mathematics Vol.255 No.-
In this paper we deal with the subnormality and the quasinormality of Toeplitz operators with matrix-valued rational symbols. In particular, in view of Halmos's Problem 5, we focus on the question: Which subnormal Toeplitz operators are normal or analytic? We first prove: Let Φ@?L<SUB>M'n</SUB><SUP>~</SUP> be a matrix-valued rational function having a ''matrix pole'', i.e., there exists α@?D for which kerH<SUB>Φ</SUB>@?(z-α)H<SUB>C^n</SUB><SUP>2</SUP>, where H<SUB>Φ</SUB> denotes the Hankel operator with symbol Φ. If(i)T<SUB>Φ</SUB> is hyponormal; (ii)ker[T<SUB>Φ</SUB><SUP>@?</SUP>,T<SUB>Φ</SUB>] is invariant for T<SUB>Φ</SUB>, then T<SUB>Φ</SUB> is normal. Hence in particular, if T<SUB>Φ</SUB> is subnormal then T<SUB>Φ</SUB> is normal. Next, we show that every pure quasinormal Toeplitz operator with a matrix-valued rational symbol is unitarily equivalent to an analytic Toeplitz operator.
Maria Victoria Curto Hernandez 부산외국어대학교 지중해지역원 2022 The Mediterranean Review Vol.15 No.1
This article reflects on the need to improve the dissemination of the research activity carried out within universities. It is based on a specific and personal case: the author’s experience within the Visionarias Project (www.visionarias.es), which works to rescue the hagiographic and mystical literature of Castilian women between 1400 and 1550. The article is divided into five parts: the first part is devoted to the role of women in the dissemination of knowledge in late medieval Europe; the second part deals with the literary and cultural activity of two Castilian nuns: Juana de la Cruz and Maria de Santo Domingo; the third part briefly presents the Visionarias Project; the fourth reflects on the usefulness of performative studies and theatre in the study and dissemination of female texts; and the fifth part puts forward some ideas on how to use social networks in favour of true scientific dissemination.
Mattarucchi, Elia,Marsoni, Milena,Binelli, Giorgio,Passi, Alberto,Lo Curto, Francesco,Pasquali, Francesco,Porta, Giovanni Korean Society for Biochemistry and Molecular Biol 2005 Journal of biochemistry and molecular biology Vol.38 No.5
Single nucleotide polymorphisms (SNPs) are becoming the most common type of markers used in genetic analysis. In the present report a SNP has been chosen to test the applicability of Real Time PCR to discriminate and quantify SNPs alleles on DNA pools. Amplification Refractory Mutation System (ARMS) and Mismatch Amplification Mutation Assay (MAMA) has been applied. Each assay has been pre-validated testing specificity and performances (linearity, PCR efficiency, interference limit, limit of detection, limit of quantification, precision and accuracy). Both the approaches achieve a precise and accurate estimation of the allele frequencies on pooled DNA samples in the range from 5% to 95% and don't require standard curves or calibrators. The lowest measurement that could be significantly distinguished from the background noise has been determined around the 1% for both the approaches, allowing to extend the range of quantifications from 1% to 99%. Furthermore applicability of Real Time PCR assays for general diagnostic purposes is discussed.
STELLAR VARIABILITY OF THE EXOPLANET HOSTING STAR HD 63454
Kane, Stephen R.,Dragomir, Diana,Ciardi, David R.,Lee, Jae-Woo,Lo Curto, Gaspare,Lovis, Christophe,Naef, Dominique,Mahadevan, Suvrath,Pilyavsky, Genady,Udry, Stephane,Wang, Xuesong,Wright, Jason IOP Publishing 2011 The Astrophysical journal Vol.737 No.2
<P>Of the hundreds of exoplanets discovered using the radial velocity ( RV) technique, many are orbiting close to their host stars with periods less than 10 days. One of these, HD 63454, is a young active K dwarf which hosts a Jovian planet in a 2.82 day period orbit. The planet has a 14% transit probability and a predicted transit depth of 1.2%. Here we provide a re-analysis of the RV data to produce an accurate transit ephemeris. We further analyze 8 nights of time series data to search for stellar activity both intrinsic to the star and induced by possible interactions of the exoplanet with the stellar magnetospheres. We establish the photometric stability of the star at the 3 mmag level despite strong Ca II emission in the spectrum. Finally, we rule out photometric signatures of both star-planet magnetosphere interactions and planetary transit signatures. From this we are able to place constraints on both the orbital and physical properties of the planet.</P>