Search results for " Dual"

Conformal Killing forms on nearly Kähler manifolds

2020

Abstract We study conformal Killing forms on compact 6-dimensional nearly Kahler manifolds. Our main result concerns forms of degree 3. Here we give a classification showing that all conformal Killing 3-forms are linear combinations of dω and its Hodge dual ⁎ d ω , where ω is the fundamental 2-form of the nearly Kahler structure. The proof is based on a fundamental integrability condition for conformal Killing forms. We have partial results in the case of conformal Killing 2-forms. In particular we show the non-existence of J-anti-invariant Killing 2-forms.

Fenchel type theorems for submanifolds of S n

1996

A DUALITY APPROACH TO THE FRACTIONAL LAPLACIAN WITH MEASURE DATA

2011

We describe a duality method to prove both existence and uniqueness of solutions to nonlocal problems like $$(-\Delta)^s v = \mu \quad \text{in } \mathbb{R}^N,$$ ¶ with vanishing conditions at infinity. Here $\mu$ is a bounded Radon measure whose support is compactly contained in $\mathbb{R}^N$, $N\geq2$, and $-(\Delta)^s$ is the fractional Laplace operator of order $s\in (1/2,1)$.

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.

An Introduction to Hodge Structures

2015

We begin by introducing the concept of a Hodge structure and give some of its basic properties, including the Hodge and Lefschetz decompositions. We then define the period map, which relates families of Kahler manifolds to the families of Hodge structures defined on their cohomology, and discuss its properties. This will lead us to the more general definition of a variation of Hodge structure and the Gauss-Manin connection. We then review the basics about mixed Hodge structures with a view towards degenerations of Hodge structures; including the canonical extension of a vector bundle with connection, Schmid’s limiting mixed Hodge structure and Steenbrink’s work in the geometric setting. Fin…

The Radon-Nikodym Theorem. Duality

1998

The band in M( ℜ) generated by a particular real measure μ can be characterized in various ways.

Italy’s North-South Divide Yet Again: Some New Evidence from Firms, Sectors and Territories

2021

The recent literature on the North-South divide in Italy has refuted a homogeneous reading and treatment of the “Southern question” and has recalled the importance of deep intra-South disparities. This paper contributes to this line of research, offering some descriptions of intra-South disparities. We first make use of data at the firm level pertaining to the manufacturing sector between 2008 and 2019 to show how productive units differ within each macro-area according to their main balance-sheet indicators and to technical efficiency, both in terms of their average and variability. Secondly, we use different data available at the provincial level to assess the territorial disparities exis…

Representación escolar de los espacios rurales: una investigación didáctica mediante métodos mixtos

2021

Los espacios rurales son objeto de representación histórica desde un relato homogéneo que no ha sido cuestionado en la geografía escolar y afecta a las explicaciones que realiza el alumnado de Educación Secundaria y Bachillerato. La teoría de las representaciones sociales y su relación con el espacio subjetivo permiten comprender las concepciones escolares del alumnado de diez centros escolares de la provincia de Valencia (España) acerca de los espacios rurales. Mediante un enfoque dual (estructural y procesual) que se acompaña de técnicas cualitativas y cuantitativas aplicadas al campo de la didáctica de las ciencias sociales se pretende diagnosticar los elementos que forman la cosmovisión…

In Silico Design of New Dual Inhibitors of SARS-CoV-2 MPRO through Ligand- and Structure-Based Methods

2023

The viral main protease is one of the most attractive targets among all key enzymes involved in the life cycle of SARS-CoV-2. Considering its mechanism of action, both the catalytic and dimerization regions could represent crucial sites for modulating its activity. Dual-binding the SARS-CoV-2 main protease inhibitors could arrest the replication process of the virus by simultaneously preventing dimerization and proteolytic activity. To this aim, in the present work, we identified two series’ of small molecules with a significant affinity for SARS-CoV-2 MPRO, by a hybrid virtual screening protocol, combining ligand- and structure-based approaches with multivariate statistical analysis. The B…

Entanglement robustness via spatial deformation of identical particle wave functions

2021

We address the problem of entanglement protection against surrounding noise by a procedure suitably exploiting spatial indistinguishability of identical subsystems. To this purpose, we take two initially separated and entangled identical qubits interacting with two independent noisy environments. Three typical models of environments are considered: amplitude damping channel, phase damping channel and depolarizing channel. After the interaction, we deform the wave functions of the two qubits to make them spatially overlap before performing spatially localized operations and classical communication (sLOCC) and eventually computing the entanglement of the resulting state. This way, we show tha…