ORCID Profile
0000-0002-0122-3789
Current Organisation
University of Sydney
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Publisher: Elsevier BV
Date: 2016
Publisher: Springer Science and Business Media LLC
Date: 06-06-2006
Publisher: Informa UK Limited
Date: 19-10-2022
Publisher: Elsevier BV
Date: 04-2006
Publisher: Informa UK Limited
Date: 12-2012
Publisher: Springer Science and Business Media LLC
Date: 26-03-2010
Publisher: Cambridge University Press (CUP)
Date: 08-2002
DOI: 10.1017/S0308210500001888
Abstract: It is proved that elliptic boundary-value problems have a global smoothing property in Lebesgue spaces, provided the underlying space of weak solutions admits a Sobolev-type inequality. The results apply to all standard boundary conditions, and a wide range of non-smooth domains, even if the classical estimates fail. The dependence on the data is explicit. In particular, this provides good control over the domain dependence, which is important for applications involving varying domains.
Publisher: Birkhäuser Basel
Date: 1999
Publisher: Cambridge University Press (CUP)
Date: 29-03-2017
DOI: 10.1017/S0004972717000260
Abstract: We carry out an in-depth study of some domination and smoothing properties of linear operators and of their role within the theory of eventually positive operator semigroups. On the one hand, we prove that, on many important function spaces, they imply compactness properties. On the other hand, we show that these conditions can be omitted in a number of Perron–Frobenius type spectral theorems. We furthermore prove a Kreĭn–Rutman type theorem on the existence of positive eigenvectors and eigenfunctionals under certain eventual positivity conditions.
Publisher: Elsevier BV
Date: 08-0012
Publisher: Springer Science and Business Media LLC
Date: 2009
Publisher: Wiley
Date: 02-2008
DOI: 10.1112/BLMS/BDM091
Publisher: Walter de Gruyter GmbH
Date: 10-03-2018
Abstract: We consider a parameter dependent parabolic logistic population model with diffusion and degenerate logistic term allowing for refuges for the population. The aim of the paper is to remove quite restrictive geometric and smoothness conditions on the refuge used in the existing literature. The key is a new simplified construction of a supersolution that does not make use of any regularity condition of the refuge. At the same time we also simplify other arguments commonly used in the literature.
Publisher: Elsevier BV
Date: 07-2016
Publisher: American Mathematical Society (AMS)
Date: 20-07-2009
Publisher: American Institute of Mathematical Sciences (AIMS)
Date: 2008
Publisher: Springer Science and Business Media LLC
Date: 24-08-2012
Publisher: Elsevier BV
Date: 03-2005
Publisher: Informa UK Limited
Date: 2013
Publisher: Springer Science and Business Media LLC
Date: 07-2021
DOI: 10.1038/S41598-021-92699-7
Abstract: We present mathematical simulations of shapes of red blood cells (RBCs) and their cytoskeleton when they are subjected to linear strain. The cell surface is described by a previously reported quartic equation in three dimensional (3D) Cartesian space. Using recently available functions in Mathematica to triangularize the surfaces we computed four types of curvature of the membrane. We also mapped changes in mesh-triangle area and curvatures as the RBCs were distorted. The highly deformable red blood cell (erythrocyte RBC) responds to mechanically imposed shape changes with enhanced glycolytic flux and cation transport. Such morphological changes are produced experimentally by suspending the cells in a gelatin gel, which is then elongated or compressed in a custom apparatus inside an NMR spectrometer. A key observation is the extent to which the maximum and minimum Principal Curvatures are localized symmetrically in patches at the poles or equators and distributed in rings around the main axis of the strained RBC. Changes on the nanometre to micro-meter scale of curvature, suggest activation of only a subset of the intrinsic mechanosensitive cation channels, Piezo1, during experiments carried out with controlled distortions, which persist for many hours. This finding is relevant to a proposal for non-uniform distribution of Piezo1 molecules around the RBC membrane. However, if the curvature that gates Piezo1 is at a very fine length scale, then membrane tension will determine local curvature so, curvatures as computed here (in contrast to much finer surface irregularities) may not influence Piezo1 activity. Nevertheless, our analytical methods can be extended address these new mechanistic proposals. The geometrical reorganization of the simulated cytoskeleton informs ideas about the mechanism of concerted metabolic and cation-flux responses of the RBC to mechanically imposed shape changes.
Publisher: Elsevier BV
Date: 09-1995
Publisher: American Mathematical Society (AMS)
Date: 21-03-2000
DOI: 10.1090/S0002-9947-00-02444-2
Abstract: We develop a theory of generalised solutions for elliptic boundary value problems subject to Robin boundary conditions on arbitrary domains, which resembles in many ways that of the Dirichlet problem. In particular, we establish L p L_p - L q L_q -estimates which turn out to be the best possible in that framework. We also discuss consequences to the spectrum of Robin boundary value problems. Finally, we apply the theory to parabolic equations.
Publisher: Cambridge University Press (CUP)
Date: 1995
DOI: 10.1017/S0308210500030389
Abstract: In this paper we analyse the change of stability of Schrödinger semigroups with indefinite potentials when a coupling parameter varies. Generically, the change of stability takes place at a principal eigenvalue associated with the problem. The uniqueness of the principal eigenvalue is shown for several classes of potentials.
Publisher: Informa UK Limited
Date: 17-07-2023
Publisher: Walter de Gruyter GmbH
Date: 02-2013
Abstract: We consider the principal eigenvalue of a cooperative system of elliptic boundary value problems as a parameter tends to infinity. The main aim is to introduce a new approach to deal with the limit problem by focusing on the resolvent operator corresponding to the system rather than the eigenvalue problem itself. This allows the consistent use of elementary properties of bilinear forms and the semi-groups they induce. At the same time we weaken assumptions in related work.
Publisher: Cambridge University Press (CUP)
Date: 14-02-2019
DOI: 10.1017/MAG.2019.4
Abstract: There is a long tradition of using geometry to solve problems from mechanics. Unfortunately this tradition is not practised much in schools and university any more. With this exposition we would like to demonstrate how elementary properties of ellipses can be used to solve a problem related to the conical pendulum. The problem of the conical pendulum is to consider a mass attached to one end of a light inextensible string of length with the other end attached at the top of a vertical rod. The mass is moving about the rod in uniform circular motion in a horizontal plane. Given the angular velocity of the mass, the question is to determine the angle the string makes with the rod.
Publisher: Springer Science and Business Media LLC
Date: 10-1994
DOI: 10.1007/BF02218853
Publisher: Informa UK Limited
Date: 2012
Publisher: Springer Science and Business Media LLC
Date: 10-1997
Publisher: Springer Science and Business Media LLC
Date: 26-06-2018
Publisher: Cambridge University Press (CUP)
Date: 14-05-2020
DOI: 10.1017/S1446788720000166
Abstract: We discuss an alternative approach to Fréchet derivatives on Banach spaces inspired by a characterisation of derivatives due to Carathéodory. The approach allows many questions of differentiability to be reduced to questions of continuity. We demonstrate how that simplifies the theory of differentiation, including the rules of differentiation and the Schwarz lemma on the symmetry of second-order derivatives. We also provide a short proof of the differentiable dependence of fixed points in the Banach fixed point theorem.
Publisher: Springer Science and Business Media LLC
Date: 17-06-2010
Publisher: Cambridge University Press (CUP)
Date: 1998
DOI: 10.1017/S0308210500027323
Abstract: We prove that a class of weighted semilinear reaction diffusion equations on R N generates gradient-like semiflows on the Banach space of bounded uniformly continuous functions on R N . If N = 1 we show convergence to a single equilibrium. The key for getting the result is to show the exponential decay of the stationary solutions, which is obtained by means of a decay estimate of the kernel of the underlying semigroup.
Publisher: Society for Industrial & Applied Mathematics (SIAM)
Date: 2008
DOI: 10.1137/060675629
Publisher: Elsevier
Date: 2008
Publisher: Springer Science and Business Media LLC
Date: 22-01-2011
Publisher: Wiley
Date: 20-12-2007
Abstract: Let Ω ⊂ ℝ N be (Wiener) regular. For λ 0 and f ∈ L ∞ (ℝ N ) there is a unique bounded, continuous function u : ℝ N → ℝ solving λu – Ω u = f in 𝔻(Ω)′, u = 0 on ℝ N \\ Ω. Given open sets Ω n we introduce the notion of regular convergence of Ω n to Ω as n → ∞. It implies that the solutions u n of ( P ) converge (locally) uniformly to u on ℝ N . Whereas L 2 ‐convergence has been treated in the literature, our criteria for uniform convergence are new. The notion of regular convergence is very general. For instance the sequence of open sets obtained by cutting into a ball converges regularly. Other ex les show that uniform convergence is possible even if the measure of Ω n \\ Ω stays larger than a positive constant for all n ∈ ℕ. Applications to spectral theory, parabolic equations and nonlinear equations are given. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Publisher: Elsevier BV
Date: 02-2023
Publisher: Informa UK Limited
Date: 15-10-2007
Publisher: Informa UK Limited
Date: 2015
Publisher: Elsevier BV
Date: 03-2003
Publisher: Elsevier BV
Date: 09-2016
Publisher: Springer Science and Business Media LLC
Date: 26-05-2014
Publisher: Khayyam Publishing, Inc
Date: 09-2023
No related grants have been discovered for Daniel Daners.