Hankel and Toeplitz transforms on H 1: continuity, compactness and Fredholm properties

We revisit the boundedness of Hankel and Toeplitz operators acting on the Hardy space H 1 and give a new proof of the old result stating that the Hankel operator H a is bounded if and only if a has bounded logarithmic mean oscillation. We also establish a sufficient and necessary condition for H a to be compact on H 1. The Fredholm properties of Toeplitz operators on H 1 are studied for symbols in a Banach algebra similar to C + H ∞ under mild additional conditions caused by the differences in the boundedness of Toeplitz operators acting on H 1 and H 2.

Reconstruction and prediction of variations in the open solar magnetic flux and interplanetary conditions

Historic geomagnetic activity observations have been used to reveal centennial variations in the open solar flux and the near-Earth heliospheric conditions (the interplanetary magnetic field and the solar wind speed). The various methods are in very good agreement for the past 135 years when there were sufficient reliable magnetic observatories in operation to eliminate problems due to site-specific errors and calibration drifts. This review underlines the physical principles that allow these reconstructions to be made, as well as the details of the various algorithms employed and the results obtained. Discussion is included of: the importance of the averaging timescale; the key differences between “range” and “interdiurnal variability” geomagnetic data; the need to distinguish source field sector structure from heliospherically-imposed field structure; the importance of ensuring that regressions used are statistically robust; and uncertainty analysis. The reconstructions are exceedingly useful as they provide calibration between the in-situ spacecraft measurements from the past five decades and the millennial records of heliospheric behaviour deduced from measured abundances of cosmogenic radionuclides found in terrestrial reservoirs. Continuity of open solar flux, using sunspot number to quantify the emergence rate, is the basis of a number of models that have been very successful in reproducing the variation derived from geomagnetic activity. These models allow us to extend the reconstructions back to before the development of the magnetometer and to cover the Maunder minimum. Allied to the radionuclide data, the models are revealing much about how the Sun and heliosphere behaved outside of grand solar maxima and are providing a means of predicting how solar activity is likely to evolve now that the recent grand maximum (that had prevailed throughout the space age) has come to an end.

On the continuity of pullback attractors for evolution processes

In this paper we give general results on the continuity of pullback attractors for nonlinear evolution processes. We then revisit results of [D. Li, P.E. Kloeden, Equi-attraction and the continuous dependence of pullback attractors on parameters, Stoch. Dyn. 4 (3) (2004) 373-384] which show that, under certain conditions, continuity is equivalent to uniformity of attraction over a range of parameters (""equi-attraction""): we are able to simplify their proofs and weaken the conditions required for this equivalence to hold. Generalizing a classical autonomous result [A.V. Babin, M.I. Vishik, Attractors of Evolution Equations, North Holland, Amsterdam, 1992] we give bounds on the rate of convergence of attractors when the family is uniformly exponentially attracting. To apply these results in a more concrete situation we show that a non-autonomous regular perturbation of a gradient-like system produces a family of pullback attractors that are uniformly exponentially attracting: these attractors are therefore continuous, and we can give an explicit bound on the distance between members of this family. (C) 2009 Elsevier Ltd. All rights reserved.

Continuity of attractors for parabolic problems with localized large diffusion

In this paper we study the continuity of asymptotics of semilinear parabolic problems of the form u(t) - div(p(x)del u) + lambda u =f(u) in a bounded smooth domain ohm subset of R `` with Dirichlet boundary conditions when the diffusion coefficient p becomes large in a subregion ohm(0) which is interior to the physical domain ohm. We prove, under suitable assumptions, that the family of attractors behave upper and lower semicontinuously as the diffusion blows up in ohm(0). (c) 2006 Elsevier Ltd. All rights reserved.

Dynamics in dumbbell domains I. Continuity of the set of equilibria

We analyze the dynamics of a reaction-diffusion equation with homogeneous Neumann boundary conditions in a dumbbell domain. We provide an appropriate functional setting to treat this problem and, as a first step, we show in this paper the continuity of the set of equilibria and of its linear unstable manifolds. (c) 2006 Elsevier B.V. All rights reserved.

Continuity of Lyapunov functions and of energy level for generalized gradient semigroup

The global attractor of a gradient-like semigroup has a Morse decomposition. Associated to this Morse decomposition there is a Lyapunov function (differentiable along solutions)-defined on the whole phase space- which proves relevant information on the structure of the attractor. In this paper we prove the continuity of these Lyapunov functions under perturbation. On the other hand, the attractor of a gradient-like semigroup also has an energy level decomposition which is again a Morse decomposition but with a total order between any two components. We claim that, from a dynamical point of view, this is the optimal decomposition of a global attractor; that is, if we start from the finest Morse decomposition, the energy level decomposition is the coarsest Morse decomposition that still produces a Lyapunov function which gives the same information about the structure of the attractor. We also establish sufficient conditions which ensure the stability of this kind of decomposition under perturbation. In particular, if connections between different isolated invariant sets inside the attractor remain under perturbation, we show the continuity of the energy level Morse decomposition. The class of Morse-Smale systems illustrates our results.

Relationships between gender, age, family conditions, physical and mental health, and social isolation of elderly caregivers

Background: In an aging population an increasing number of elderly caregivers will be called upon to provide care over a long period, during which time they will be burdened both by caregiving and by the physiological effects of their own aging. Among them there will be more aged male caregivers, who will probably be less prepared than women to become caregivers. The aim of this study was to investigate the relationship between caregivers' gender, age, family income, living arrangements and social support as independent variables, and depressive symptoms, comorbidities, level of frailty, grip strength, walking speed and social isolation, as dependent variables. Methods: 176 elderly people (123 women) were selected from a sample of a population-based study on frailty (n = 900), who had cared for a spouse (79.3%) and/or parents (31.4%) in the past five years (mean age = 71.8 +/- 4.86 years; mean monthly family income in minimum wages = 4.64 +/- 5.14). The study used questionnaires and self-report scales, grip strength and walking speed tests. Results: 65% of participants evaluated caregiving as being very stressful. Univariate analyses of regression showed low family income as a risk factor for depression; being female and low perceived social support as a risk for comorbidities; being 80 years of age and above for low grip strength; and being male for social isolation indicated by discontinuity of activities and social roles. In multivariate analyses of regression, poverty arose as a risk factor for depression and being female for comorbidities. Conclusions: Gender roles, age, income and social support interacted with physical and emotional health, and with the continuity of social participation of elderly caregivers. Special attention must be given to male caregivers.

Richness of Lichen Species, Especially of Threatened Ones, Is Promoted by Management Methods Furthering Stand Continuity

Lichens are a key component of forest biodiversity. However, a comprehensive study analyzing lichen species richness in relation to several management types, extending over different regions and forest stages and including information on site conditions is missing for temperate European forests. In three German regions (Schwäbische Alb, Hainich-Dün, Schorfheide-Chorin), the so-called Biodiversity Exploratories, we studied lichen species richness in 631 forest plots of 400 m2 comprising different management types (unmanaged, selection cutting, deciduous and coniferous age-class forests resulting from clear cutting or shelterwood logging), various stand ages, and site conditions, typical for large parts of temperate Europe. We analyzed how lichen species richness responds to management and habitat variables (standing biomass, cover of deadwood, cover of rocks). We found strong regional differences with highest lichen species richness in the Schwäbische Alb, probably driven by regional differences in former air pollution, and in precipitation and habitat variables. Overall, unmanaged forests harbored 22% more threatened lichen species than managed age-class forests. In general, total, corticolous, and threatened lichen species richness did not differ among management types of deciduous forests. However, in the Schwäbische-Alb region, deciduous forests had 61% more lichen species than coniferous forests and they had 279% more threatened and 76% more corticolous lichen species. Old deciduous age classes were richer in corticolous lichen species than young ones, while old coniferous age-classes were poorer than young ones. Overall, our findings highlight the importance of stand continuity for conservation. To increase total and threatened lichen species richness we suggest (1) conserving unmanaged forests, (2) promoting silvicultural methods assuring stand continuity, (3) conserving old trees in managed forests, (4) promoting stands of native deciduous tree species instead of coniferous plantations, and (5) increasing the amount of deadwood in forests.

Compactified N = 1 supersymmetric Yang-Mills theory on the lattice: continuity and the disappearance of the deconfinement transition

Fermion boundary conditions play a relevant role in revealing the confinement mechanism of N=1 supersymmetric Yang-Mills theory with one compactified space-time dimension. A deconfinement phase transition occurs for a sufficiently small compactification radius, equivalent to a high temperature in the thermal theory where antiperiodic fermion boundary conditions are applied. Periodic fermion boundary conditions, on the other hand, are related to the Witten index and confinement is expected to persist independently of the length of the compactified dimension. We study this aspect with lattice Monte Carlo simulations for different values of the fermion mass parameter that breaks supersymmetry softly. We find a deconfined region that shrinks when the fermion mass is lowered. Deconfinement takes place between two confined regions at large and small compactification radii, that would correspond to low and high temperatures in the thermal theory. At the smallest fermion masses we find no indication of a deconfinement transition. These results are a first signal for the predicted continuity in the compactification of supersymmetric Yang-Mills theory.

Implementing a structural continuity constraint and a halting method for the topology optimization of energy absorbers

This study investigates topology optimization of energy absorbing structures in which material damage is accounted for in the optimization process. The optimization objective is to design the lightest structures that are able to absorb the required mechanical energy. A structural continuity constraint check is introduced that is able to detect when no feasible load path remains in the finite element model, usually as a result of large scale fracture. This assures that designs do not fail when loaded under the conditions prescribed in the design requirements. This continuity constraint check is automated and requires no intervention from the analyst once the optimization process is initiated. Consequently, the optimization algorithm proceeds towards evolving an energy absorbing structure with the minimum structural mass that is not susceptible to global structural failure. A method is also introduced to determine when the optimization process should halt. The method identifies when the optimization method has plateaued and is no longer likely to provide improved designs if continued for further iterations. This provides the designer with a rational method to determine the necessary time to run the optimization and avoid wasting computational resources on unnecessary iterations. A case study is presented to demonstrate the use of this method.

Moving together – conditions for intercultural development at a highly diverse Swedish school

This thesis is a case study of a primary school in a highly diverse urban neighbourhood in Sweden. Basic pre-conditions for intercultural school development are studied by examining the overall organisation of teaching, learning and opportunities for collaboration in the investigated case. The study focuses on the targeted support measures to enhance learning for students with an immigrant background: Mother tongue instruction, Swedish as a Second Language, and tutoring in the mother tongue, as well as looking at pedagogical support provided by the school library. The latter has a mission to promote learning and inclusion, where non-native speakers of Swedish are a prioritised group. Communities of practice linked to the work organisation at a meso-level are investigated, and the collaborative relationships between professional groups at the school involved in the various support measures. Teacher relationships and categorisations implied by support measures impact the learning spaces that are shaped for students and the teaching spaces within which teachers work. Collaborative opportunities and convergence of concerns in the teaching spaces combine to shape the overall space for intercultural development. The raw data for the case study consists of interviews, national policy documents and additional information on local work organisation gained through documents and observations. Four articles resulted from the case study, each focusing a specific support measure. An overarching analysis is then made of findings from these articles and the other dimensions of the investigation. The analysis describes the organisation in terms of monocultural or intercultural school cultures, pointing to significant characteristics of the landscapes of practice, with respect to their overall implications for the spaces of school development. In the discussion, findings are considered in relation to research on professional development in education, collaboration, democracy and inclusive schooling. The relative positioning of languages and cultures is given particular attention, to ascertain if the school culture is monocultural or intercultural in the sense given by Lahdenperä (2008), and to what extent it could enable intercultural development. Such positioning plays a role interms of affordances for identity, participation and engagement discussed by Wenger (1998). This case study should be understood against the wider background of recent social developments in Europe linked to globalisation and technological changes. It is argued that looking at the concrete specifics which facilitate or obstruct school development, and simultaneously reflecting on how the different forms of teaching interrelate in the overall organisation and in policy may provide a useful vantage point from which structural changes can be contemplated.The discussion underlines the importance of the physical localisation of activities, continuity in personal contacts and time available for joint pedagogical reflection, as basic conditions for effective intercultural dialogue in the organisation. Finally, the impact of policy is considered, looking at connections between levels of policy, expressed in official steering documents, and conditions for teaching and learning at the level of an individual school.

Measure-valued mass evolution problems with flux boundary conditions and solution-dependent velocities

In this paper we prove well-posedness for a measure-valued continuity equation with solution-dependent velocity and flux boundary conditions, posed on a bounded one-dimensional domain. We generalize the results of an earlier paper [J. Differential Equations, 259 (2015), pp. 10681097] to settings where the dynamics are driven by interactions. In a forward-Euler-like approach, we construct a time-discretized version of the original problem and employ those results as a building block within each subinterval. A limit solution is obtained as the mesh size of the time discretization goes to zero. Moreover, the limit is independent of the specific way of partitioning the time interval [0, T]. This paper is partially based on results presented in Chapter 5 of [Evolution Equations for Systems Governed by Social Interactions, Ph.D. thesis, Eindhoven University of Technology, 2015], while a number of issues that were still open there are now resolved.

Hydrazine-hydrate intercalated halloysite under controlled-rate thermal analysis conditions

The thermal behaviour of halloysite fully expanded with hydrazine-hydrate has been investigated in nitrogen atmosphere under dynamic heating and at a constant, pre-set decomposition rate of 0.15 mg min-1. Under controlled-rate thermal analysis (CRTA) conditions it was possible to resolve the closely overlapping decomposition stages and to distinguish between adsorbed and bonded reagent. Three types of bonded reagent could be identified. The loosely bonded reagent amounting to 0.20 mol hydrazine-hydrate per mol inner surface hydroxyl is connected to the internal and external surfaces of the expanded mineral and is present as a space filler between the sheets of the delaminated mineral. The strongly bonded (intercalated) hydrazine-hydrate is connected to the kaolinite inner surface OH groups by the formation of hydrogen bonds. Based on the thermoanalytical results two different types of bonded reagent could be distinguished in the complex. Type 1 reagent (approx. 0.06 mol hydrazine-hydrate/mol inner surface OH) is liberated between 77 and 103°C. Type 2 reagent is lost between 103 and 227°C, corresponding to a quantity of 0.36 mol hydrazine/mol inner surface OH. When heating the complex to 77°C under CRTA conditions a new reflection appears in the XRD pattern with a d-value of 9.6 Å, in addition to the 10.2 Ĺ reflection. This new reflection disappears in contact with moist air and the complex re-expands to the original d-value of 10.2 Å in a few h. The appearance of the 9.6 Å reflection is interpreted as the expansion of kaolinite with hydrazine alone, while the 10.2 Å one is due to expansion with hydrazine-hydrate. FTIR (DRIFT) spectroscopic results showed that the treated mineral after intercalation/deintercalation and heat treatment to 300°C is slightly more ordered than the original (untreated) clay.