135 research outputs found
The discrete fragmentation equations : semigroups, compactness and asynchronous exponential growth
In this paper we present a class of fragmentation semigroups which are compact in a scale of spaces defined in terms of finite higher moments. We use this compactness result to analyse the long time behaviour of such semigroups and, in particular, to prove that they have the asynchronous growth property. We note that, despite compactness, this growth property is not automatic as the fragmentation semigroups are not irreducible
Key strategies for managing acid sulphate soil (ASS) problems on the southeastern coast of New South Wales, Australia
The acidification of Australian coastal waterways as a result of the oxidation of acid sulphate soil (ASS) containing appreciable quantities of sulphidic material (e.g. pyrite) has well recognised environmental, economic and social effects including the loss of fish, biodiversity and agricultural productivity as well as the corrosion of concrete and steel infrastructure by acidic drainage. Largescale artificial drainage and one-way floodgates in low-lying coastal floodplains has lowered the groundwater table, thus enhancing pyritic oxidation and increasing the distribution, magnitude and frequency of acid generation and release of toxic metals such as aluminium (Al3+) and iron (total Fe) from ASS. Engineering strategies implemented on the Shoalhaven Floodplain, southeast New South Wales, Australia have been designed to remediate ASS. These include: (1) fixed-level v-notch weirs, which raise the groundwater table above the pyritic layer and reduce the rate of discharge of acidic products from the groundwater into the drains; (2) modified two-way floodgates, which allow for tidal buffering of acidic drainage; (3) a subsurface alkaline horizontal impermeable lime-fly ash barrier, which prevents pyrite oxidation and neutralises acidic groundwater and (4) an alkaline permeable reactive barrier (PRB) using recycled materials, which significantly increases groundwater pH and reduces Al and Fe concentrations within and down-gradient of the PRB. A critical review of each of these strategies will outline their role in remediating ASS and their respective benefits and limitations
Coagulation and fragmentation processes with evolving size and shape profiles : a semigroup approach
We investigate a class of bivariate coagulation-fragmentation equations. These equations describe the evolution of a system of particles that are characterised not only by a discrete size variable but also by a shape variable which can be either discrete or continuous. Existence and uniqueness of strong solutions to the associated abstract Cauchy problems are established by using the theory of substochastic semigroups of operators
Integral representation of the linear Boltzmann operator for granular gas dynamics with applications
We investigate the properties of the collision operator associated to the
linear Boltzmann equation for dissipative hard-spheres arising in granular gas
dynamics. We establish that, as in the case of non-dissipative interactions,
the gain collision operator is an integral operator whose kernel is made
explicit. One deduces from this result a complete picture of the spectrum of
the collision operator in an Hilbert space setting, generalizing results from
T. Carleman to granular gases. In the same way, we obtain from this integral
representation of the gain operator that the semigroup in L^1(\R \times \R,\d
\x \otimes \d\v) associated to the linear Boltzmann equation for dissipative
hard spheres is honest generalizing known results from the first author.Comment: 19 pages, to appear in Journal of Statistical Physic
The Existence of Moments of Solutions to Transport Equations with Inelastic Scattering and their Application in the Asymptotic Analysis
Quantum Kinetic Evolution of Marginal Observables
We develop a rigorous formalism for the description of the evolution of
observables of quantum systems of particles in the mean-field scaling limit.
The corresponding asymptotics of a solution of the initial-value problem of the
dual quantum BBGKY hierarchy is constructed. Moreover, links of the evolution
of marginal observables and the evolution of quantum states described in terms
of a one-particle marginal density operator are established. Such approach
gives the alternative description of the kinetic evolution of quantum
many-particle systems to generally accepted approach on basis of kinetic
equations.Comment: 18 page
Nonlinear Neumann boundary stabilization of the wave equation using rotated multipliers
The rotated multipliers method is performed in the case of the boundary
stabilization by means of a(linear or non-linear) Neumann feedback. this method
leads to new geometrical cases concerning the "active" part of the boundary
where the feedback is apllied. Due to mixed boundary conditions, these cases
generate singularities. Under a simple geometrical conditon concerning the
orientation of boundary, we obtain a stabilization result in both cases.Comment: 17 pages, 9 figure
Distributionally chaotic families of operators on Fréchet spaces
This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Communications on Pure and Applied Analysis (CPAA) following peer review. The definitive publisher-authenticated version Conejero, J. A., Kostić, M., Miana, P. J., & Murillo-Arcila, M. (2016). Distributionally chaotic families of operators on Fréchet spaces.Communications on Pure and Applied Analysis, 2016, vol. 15, no 5, p. 1915-1939, is available online at: http://dx.doi.org/10.3934/cpaa.2016022The existence of distributional chaos and distributional irregular vectors has been recently considered in the study of linear dynamics of operators and C-0-semigroups. In this paper we extend some previous results on both notions to sequences of operators, C-0-semigroups, C-regularized semigroups, and alpha-timesintegrated semigroups on Frechet spaces. We also add a study of rescaled distributionally chaotic C-0-semigroups. Some examples are provided to illustrate all these results.The first and fourth authors are supported in part by MEC Project MTM2010-14909, MTM2013-47093-P, and Programa de Investigacion y Desarrollo de la UPV, Ref. SP20120700. The second author is partially supported by grant 174024 of Ministry of Science and Technological Development, Republic of Serbia. The third author has been partially supported by Project MTM2013-42105-P, DGI-FEDER, of the MCYTS; Project E-64, D.G. Aragon, and Project UZCUD2014-CIE-09, Universidad de Zaragoza. The fourth author is supported by a grant of the FPU Program of Ministry of education of Spain.Conejero, JA.; Kostic, M.; Miana Sanz, PJ.; Murillo Arcila, M. (2016). Distributionally chaotic families of operators on Fréchet spaces. Communications on Pure and Applied Analysis. 15(5):1915-1939. https://doi.org/10.3934/cpaa.2016022S1915193915
A pragmatic effectiveness study of 10-session cognitive behavioural therapy (CBT-T) for eating disorders: Targeting barriers to treatment provision
Objective
Ten‐session cognitive behavioural therapy (CBT‐T) for transdiagnostic eating disorders targets several barriers to treatment, including cost, therapist expertise, and lengthy wait lists.
Method
We used a case series design to investigate the effectiveness of CBT‐T delivered by trainee psychologists in a postgraduate training clinic. Participants were randomly allocated to commence treatment either immediately or after a 4‐week waitlist period. CBT‐T was delivered to 52 patients, by six different trainees under supervision. Measures of eating disorder cognitions and behaviours, quality of life, and general psychopathology were examined in completer and intention‐to‐treat analyses using multilevel modelling. Last observation carried forward was applied for abstinence, remission, and good outcome analyses to aid comparison with prior studies.
Results
Significant improvements, associated with medium to large effect sizes, were found for eating disorder cognitions, behaviours quality of life, and negative affect from baseline to posttreatment, and at 1‐ and 3‐month follow‐up. Attrition (38.5%) was comparable with other treatment studies.
Conclusion
Results provide evidence for the effectiveness of CBT‐T delivered by trainee psychologists for transdiagnostic eating disorder patients, thus tackling some important barriers for treatment. Longer follow‐up, randomised controlled trial designs, and moderator analyses will provide more robust evidence about which patients do best with a shorter therapy
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