162 research outputs found
Hardy-Carleman Type Inequalities for Dirac Operators
General Hardy-Carleman type inequalities for Dirac operators are proved. New
inequalities are derived involving particular traditionally used weight
functions. In particular, a version of the Agmon inequality and Treve type
inequalities are established. The case of a Dirac particle in a (potential)
magnetic field is also considered. The methods used are direct and based on
quadratic form techniques
A study of blow-ups in the Keller-Segel model of chemotaxis
We study the Keller-Segel model of chemotaxis and develop a composite
particle-grid numerical method with adaptive time stepping which allows us to
accurately resolve singular solutions. The numerical findings (in two
dimensions) are then compared with analytical predictions regarding formation
and interaction of singularities obtained via analysis of the stochastic
differential equations associated with the Keller-Segel model
Sums of magnetic eigenvalues are maximal on rotationally symmetric domains
The sum of the first n energy levels of the planar Laplacian with constant
magnetic field of given total flux is shown to be maximal among triangles for
the equilateral triangle, under normalization of the ratio (moment of
inertia)/(area)^3 on the domain. The result holds for both Dirichlet and
Neumann boundary conditions, with an analogue for Robin (or de Gennes) boundary
conditions too. The square similarly maximizes the eigenvalue sum among
parallelograms, and the disk maximizes among ellipses. More generally, a domain
with rotational symmetry will maximize the magnetic eigenvalue sum among all
linear images of that domain. These results are new even for the ground state
energy (n=1).Comment: 19 pages, 1 figur
Assessment of needs, health-related quality of life, and satisfaction with care in breast cancer patients to better target supportive care
Background This study assessed whether breast cancer (BC) patients express similar levels of needs for equivalent severity of symptoms, functioning difficulties, or degrees of satisfaction with care aspects. BC patients who did (or not) report needs in spite of similar difficulties were identified among their sociodemographic or clinical characteristics. Patients and methods Three hundred and eighty-four (73% response rate) BC patients recruited in ambulatory or surgery hospital services completed the European Organisation for Research and Treatment of Cancer Quality of Life questionnaire (EORTC QLQ)-C30 quality of life [health-related quality of life (HRQOL)], the EORTC IN-PATSAT32 (in-patient) or OUT-PATSAT35 (out-patient) satisfaction with care, and the supportive care needs survey short form 34-item (SCNS-SF34) measures. Results HRQOL or satisfaction with care scale scores explained 41%, 45%, 40% and 22% of variance in, respectively, psychological, physical/daily living needs, information/health system, and care/support needs (P < 0.001). BC patients' education level, having children, hospital service attendance, and anxiety/depression levels significantly predicted differences in psychological needs relative to corresponding difficulties (adjusted R2 = 0.11). Medical history and anxiety/depression levels significantly predicted differences in information/health system needs relative to degrees of satisfaction with doctors, nurses, or radiotherapy technicians and general satisfaction (adjusted R2 = 0.12). Unmet needs were most prevalent in the psychological domains across hospital services. Conclusions Assessment of needs, HRQOL, and satisfaction with care highlights the subgroups of BC patients requiring better supportive care targetin
Critical dynamics of self-gravitating Langevin particles and bacterial populations
We study the critical dynamics of the generalized Smoluchowski-Poisson system
(for self-gravitating Langevin particles) or generalized Keller-Segel model
(for the chemotaxis of bacterial populations). These models [Chavanis & Sire,
PRE, 69, 016116 (2004)] are based on generalized stochastic processes leading
to the Tsallis statistics. The equilibrium states correspond to polytropic
configurations with index similar to polytropic stars in astrophysics. At
the critical index (where is the dimension of space),
there exists a critical temperature (for a given mass) or a
critical mass (for a given temperature). For or
the system tends to an incomplete polytrope confined by the box (in a
bounded domain) or evaporates (in an unbounded domain). For
or the system collapses and forms, in a finite time, a Dirac peak
containing a finite fraction of the total mass surrounded by a halo. This
study extends the critical dynamics of the ordinary Smoluchowski-Poisson system
and Keller-Segel model in corresponding to isothermal configurations with
. We also stress the analogy between the limiting mass of
white dwarf stars (Chandrasekhar's limit) and the critical mass of bacterial
populations in the generalized Keller-Segel model of chemotaxis
Asymptotic expansions of the solutions of the Cauchy problem for nonlinear parabolic equations
Let be a solution of the Cauchy problem for the nonlinear parabolic
equation and
assume that the solution behaves like the Gauss kernel as . In
this paper, under suitable assumptions of the reaction term and the initial
function , we establish the method of obtaining higher order
asymptotic expansions of the solution as . This paper is a
generalization of our previous paper, and our arguments are applicable to the
large class of nonlinear parabolic equations
Flat galaxies with dark matter halos - existence and stability
We consider a model for a flat, disk-like galaxy surrounded by a halo of dark
matter, namely a Vlasov-Poisson type system with two particle species, the
stars which are restricted to the galactic plane and the dark matter particles.
These constituents interact only through the gravitational potential which
stars and dark matter create collectively. Using a variational approach we
prove the existence of steady state solutions and their nonlinear stability
under suitably restricted perturbations.Comment: 39 page
Finite mass self-similar blowing-up solutions of a chemotaxis system with non-linear diffusion
For a specific choice of the diffusion, the parabolic-elliptic
Patlak-Keller-Segel system with non-linear diffusion (also referred to as the
quasi-linear Smoluchowski-Poisson equation) exhibits an interesting threshold
phenomenon: there is a critical mass such that all the solutions with
initial data of mass smaller or equal to exist globally while the
solution blows up in finite time for a large class of initial data with mass
greater than . Unlike in space dimension 2, finite mass self-similar
blowing-up solutions are shown to exist in space dimension
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