The Structure of Inner Multipliers on Spaces with Complete Nevanlinna Pick Kernels

We establish some multivariate generalizations of the Beurling-Lax-Halmos theorem.Comment: 21 page

Particle motion and the modelling of strain response in magnetic fabrics

Quantitative correlations between the magnetic fabric (magnetic susceptibility or remanent magnetic anisotropies), single mineral anisotropy, and preferred mineral orientation is investigated using computer modelling. The influences of various initial fabric patterns and imposed strain on the magnetic fabric are simulated using multiparticle systems represented by their magnetic anisotropy tensor. Each single mineral is numerically reoriented under coaxial deformation conditions using the strain response models of March and Jeffery/Gay. The calculated strain In ( e i ) versus magnetic fabric M i = In [ k i l(k max · k int · k min ) 1/3 ] curves show the following characteristics: (1) for initial randomly oriented distributions a log-linear correlation exists for strain magnitudes below 200 per cent. (2) For higher strains the curves asymptotically approach the M i value defined by the particle anisotropy. (3) The slope a of the correlation lines is a function of the particle anisotropy, the ellipsoid shape, and the strain response model. (4) Due to the prolate shape of particles, the maximum susceptibility axes are more sensitive to strain for initially anisotropic fabrics than the minimum axes. (5) The relationship between magnetic fabric and strain in multiparticle systems with known initial preferred orientations and single particle anisotropy shows a similar behaviour. Depending on the pattern and orientation of the initial fabric, the maximum axes show either a log-linear correlation to strain with a characteristic slope a or a kinked curve, with two almost linear parts.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71422/1/j.1365-246X.1992.tb02085.x.pd

Zeros of Functions with Finite Dirichlet Integral

In this paper, we refine a result of Nagel, Rudin, and Shapiro (1982) concerning the zeros of holomorphic functions on the unit disk with finite Dirichlet integral

Longing

Title Onlyhttps://scholarsjunction.msstate.edu/cht-sheet-music/7461/thumbnail.jp

Linear graph transformations on spaces of analytic functions

Let H be a Hilbert space of analytic functions with multiplier algebra M(H), and let M = {(f, T(1)f, ... ,T(n-1)f) : f is an element of D} be an invariant graph subspace for M(H)((n)). Here n >= 2, D subset of H is a vector-subspace, T-i : D -> H are linear transformations that commute with each multiplication operator M-phi is an element of M(H), and M is closed in H-(n). In this paper we investigate the existence of non-trivial common invariant subspaces of operator algebras of the type A(M) = {A is an element of B(H) : AD subset of D : AT(i)f = T(i)Af for all f is an element of D}. In particular, for the Bergman space L-0,(2) we exhibit examples of invariant graph subspaces of fiber dimension 2 such that A(M) does not have any nontrivial invariant subspaces that are defined by linear relations of the graph transformations for M. (C) 2015 Elsevier Inc. All rights reserved

Repair in the Circular Economy: Towards a National Swedish Strategy

Extending the lifetime of products is seen as a key objective for realising the vision of a Circular Economy. One way to increase the lifespan of products is to enable more repair activities. However, consumers encounter a variety of barriers for repairs, prompting public authorities in Europe and the US to adopt or propose policies in support of consumer repairs. Sweden has recently adopted a circular economy action plan, where increasing the number of consumer repairs is a stated objective. However, Sweden has so far only adopted a few repair policies, most notably through the tax reliefs for the repair sector that were implemented in 2017. The aim of this contribution is to research how Sweden could develop a more comprehensive policy mix for promoting consumer repairs, also by taking into consideration initiatives from other countries and regions. The research is based on a literature review and semi-structured interviews with policymakers and other relevant actors in Sweden, Europe and the US. The study shows that a lot of interesting initiatives aiming at increasing repairs are currently being proposed. The new requirements related to repairs, developed within the European Union’s (EU) Ecodesign Directive, have been positively received but the process is cumbersome and it will take time before their full effect becomes evident. Initiatives, such as the French repairability index and the French repair fund will create incentives for the producers to design more repairable products and make it easier for consumers to repair. On the same track, the Repair Network of Vienna with its repair vouchers makes repairs cheaper and more trustworthy. Also, the US policy proposals on right-to-repair laws would help to create an open market for repairs for a lot of products. Sweden has the possibility to gain knowledge through the implementation of similar policies, and by considering new policies suggested in literature and by the interviewees. Thus there is potential for Sweden to be a front-runner in creating a more resource efficient society through increased repair activity. Concluding, some preliminary proposals for a future policy mix are presented