Search results for "TENSOR"

Nori’s Diagram Category

2017

We explain Nori’s construction of an abelian category attached to the representation of a diagram and establish some properties for it. The construction is completely formal. It mimics the standard construction of the Tannakian dual of a rigid tensor category with a fibre functor . Only, we do not have a tensor product or even a category but only what we should think of as the fibre functor.

Tensor products of Fréchet or (DF)-spaces with a Banach space

1992

Abstract The aim of the present article is to study the projective tensor product of a Frechet space and a Banach space and the injective tensor product of a (DF)-space and a Banach space. The main purpose is to analyze the connection of the good behaviour of the bounded subsets of the projective tensor product and of the locally convex structure of the injective tensor product with the local structure of the Banach space.

On distinguished polynomials and their projections

2012

We study projections and injections between projective tensor products spaces or spaces of polynomials and we show that the example of a polynomial constructed in (4), that is neither p-dominated nor compact, can be identified with the projection map of the symmetric tensor product onto the space. Also we give a characterization of the weak and quasi approximation properties on symmetric tensor products.

Sobolev Spaces and Quasiconformal Mappings on Metric Spaces

2001

Heinonen and I have recently established a theory of quasiconformal mappings on Ahlfors regular Loewner spaces. These spaces are metric spaces that have sufficiently many rectifiable curves in a sense of good estimates on moduli of curve families. The Loewner condition can be conveniently described in terms of Poincare inequalities for pairs of functions and upper gradients. Here an upper gradient plays the role that the length of the gradient of a smooth function has in the Euclidean setting. For example, the Euclidean spaces and Heisenberg groups and the more general Carnot groups admit the type of a Poincare inequality we need. We describe the basics and discuss the associated Sobolev sp…

THE BISHOP-PHELPS-BOLLOBAS PROPERTY FOR HERMITIAN FORMS ON HILBERT SPACES

2013

Influence of Dynamics on The Analysis of Solid-State NMR Data From Membrane-bound Peptides

2009

By isotope labeling of membrane-bound peptides, typically with 2H, 19F, or 15N, solid-state NMR experiments can yield data from which the orientation of peptides in a native membrane environment can be determined. Such an orientation is defined by a tilt angle and an azimuthal rotation angle.Here we show that to obtain correct values of the orientation angles, it is important to include dynamics in the analysis of the NMR data. Nevertheless the effects of dynamics are different depending on the type of isotope labeling and NMR experiment considered.To analyze the influence of dynamics in detail, we generated virtual NMR observables using a model peptide undergoing explicit Gaussian fluctuat…

Homopolymer adsorption on periodically structured surfaces in systems with incommensurable lengths

2013

Surface-induced selective adsorption of homopolymers on a generic level is numerically analyzed for freely jointed chains (with a fixed bond length) whose monomers are attracted by the sites of regular periodic patterns. In particular, the behavior of the specific heat, the gyration tensor, and the bond order tensor are investigated as functions of the temperature. The properties of the transition are related to the interplay of the characteristic lengths. The adsorption proceeds in two steps for certain incommensurabilities of the bond length and the lattice constant. The corresponding adsorption mechanisms are elucidated by looking at the evolution of the inter bond angle distribution upo…

A soft-quadrumer model for diblock copolymers

2010

We present a new soft-particle type model for diblock copolymers and compare its phase diagram to experimental data as well as to results of other models. To determine the phase diagram we suggest studying geometrical characteristics of the mesophases. Diblock copolymer mesophases differ by the number and geometrical form of clusters of the two components formed in the mesophase. The form of these clusters can be characterized by values of the principle components of their gyration tensor and shape invariants determined from them. Alternatively, it has been suggested to use Minkowski functionals to characterize the global morphology of the different mesophases. We will also discuss the prac…

Neutrinoless double beta decay and QCD running at low energy scales

2018

There is a common belief that the main uncertainties in the theoretical analysis of neutrinoless double beta ($0\nu\beta\beta$) decay originate from the nuclear matrix elements. Here, we uncover another previously overlooked source of potentially large uncertainties stemming from non-perturbative QCD effects. Recently perturbative QCD corrections have been calculated for all dimension 6 and 9 effective operators describing $0\nu\beta\beta$-decay and their importance for a reliable treatment of $0\nu\beta\beta$-decay has been demonstrated. However, these perturbative results are valid at energy scales above $\sim 1$ GeV, while the typical $0\nu\beta\beta$-scale is about $\sim 100$ MeV. In vi…

Antisymmetric tensors in holographic approaches to QCD

2010

We study real (massive) antisymmetric tensors of rank two in holographic models of QCD based on the gauge/string duality. Our aim is to understand in detail how the anti-de Sitter/conformal field theory correspondence describes correlators with tensor currents in QCD. To this end we study a set of bootstrapped correlators with spin-1 vector and tensor currents, imposing matching to QCD at the partonic level. We show that a consistent description of this set of correlators yields a very predictive picture. For instance, it imposes strong constraints on infrared boundary conditions and precludes the introduction of dilatonic backgrounds as a mechanism to achieve linear confinement. Additional…