Search results for "determinant"
showing 10 items of 377 documents
Homological Projective Duality for Determinantal Varieties
2016
In this paper we prove Homological Projective Duality for crepant categorical resolutions of several classes of linear determinantal varieties. By this we mean varieties that are cut out by the minors of a given rank of a n x m matrix of linear forms on a given projective space. As applications, we obtain pairs of derived-equivalent Calabi-Yau manifolds, and address a question by A. Bondal asking whether the derived category of any smooth projective variety can be fully faithfully embedded in the derived category of a smooth Fano variety. Moreover we discuss the relation between rationality and categorical representability in codimension two for determinantal varieties.
Large-x Analysis of an Operator-Valued Riemann–Hilbert Problem
2015
International audience; The purpose of this paper is to push forward the theory of operator-valued Riemann-Hilbert problems and demonstrate their effectiveness in respect to the implementation of a non-linear steepest descent method a la Deift-Zhou. In this paper, we demonstrate that the operator-valued Riemann-Hilbert problem arising in the characterization of so-called c-shifted integrable integral operators allows one to extract the large-x asymptotics of the Fredholm determinant associated with such operators.
On stability of logarithmic tangent sheaves. Symmetric and generic determinants
2021
We prove stability of logarithmic tangent sheaves of singular hypersurfaces D of the projective space with constraints on the dimension and degree of the singularities of D. As main application, we prove that determinants and symmetric determinants have stable logarithmic tangent sheaves and we describe an open dense piece of the associated moduli space.
Riemann-Hilbert approach to the time-dependent generalized sine kernel
2011
We derive the leading asymptotic behavior and build a new series representation for the Fredholm determinant of integrable integral operators appearing in the representation of the time and distance dependent correlation functions of integrable models described by a six-vertex R-matrix. This series representation opens a systematic way for the computation of the long-time, long-distance asymptotic expansion for the correlation functions of the aforementioned integrable models away from their free fermion point. Our method builds on a Riemann–Hilbert based analysis.
Jacobian of weak limits of Sobolev homeomorphisms
2016
Abstract Let Ω be a domain in ℝ n {\mathbb{R}^{n}} , where n = 2 , 3 {n=2,3} . Suppose that a sequence of Sobolev homeomorphisms f k : Ω → ℝ n {f_{k}\colon\Omega\to\mathbb{R}^{n}} with positive Jacobian determinants, J ( x , f k ) > 0 {J(x,f_{k})>0} , converges weakly in W 1 , p ( Ω , ℝ n ) {W^{1,p}(\Omega,\mathbb{R}^{n})} , for some p ⩾ 1 {p\geqslant 1} , to a mapping f. We show that J ( x , f ) ⩾ 0 {J(x,f)\geqslant 0} a.e. in Ω. Generalizations to higher dimensions are also given.
On the accurate determination of nonisolated solutions of nonlinear equations
1981
A simple but efficient method to obtain accurate solutions of a system of nonlinear equations with a singular Jacobian at the solution is presented. This is achieved by enlarging the system to a higher dimensional one whose solution in question is isolated. Thus it can be computed e. g. by Newton's method, which is locally at least quadratically convergent and selfcorrecting, so that high accuracy is attainable.
Planar Mappings of Finite Distortion
2010
We review recent results on planar mappings of finite distortion. This class of mappings contains all analytic functions and quasiconformal mappings.
Socio-Demographic Factors Involved in a Low-Incidence Phase of SARS-CoV-2 Spread in Sicily, Italy
2021
Background: The present study analysed SARS-CoV-2 cases observed in Sicily and investigated social determinants that could have an impact on the virus spread. Methods: SARS-CoV-2 cases observed among Sicilian residents between the 1 February 2020 and 15 October 2020 have been included in the analyses. Age, sex, date of infection detection, residency, clinical outcomes, and exposure route have been evaluated. Each case has been linked to the census section of residency and its socio-demographic data. Results: A total of 10,114 patients (202.3 cases per 100,000 residents
Type A Behaviour as a Determinant of Participation in Physical Activity and Sport Among Adolescents
1998
As a part of an extensive research project 'Cardiovascular Risks in Young Finns ; this study examined the relationship between Type A behaviour and sports participation among adolescents. Subjects were 852 12- and 15-year-old boys and girls randomly selected from five Finnish university towns and their rural surroundings. Type A behaviour was categorized into two dimensions encompassing impatient- aggressive competitiveness (IAC) and responsible hard-driving (RHD). Level of participation in sport was measured by means of a short questionnaire. The results of the present study showed that active adolescents scored significantly higher on the RHD factor than passive adolescents in the four a…
A new bipartite matching approach for record linkage: the case of two big Italian databases
2022
In recent years, university student mobility in Italy has worsened the north-south economic divide. Therefore, studying this phenomenon and its determinants is necessary to provide helpful information to support socio-economic policies. Thus, this paper aims at integrating two big databases about university students in Italy: the first one is provided by the Ministry of University and Research, concerning the university careers of student cohorts; the second one is provided by the AlmaLaurea consortium, concerning the university experiences of graduates and their success in the labour market. Both databases contain socio-demographic information that complements each other. The proposed meth…