167 research outputs found
Asymptotic behavior of a free boundary problem for the growth of multi-layer tumors in necrotic phase
In this paper we study a free boundary problem for the growth of multi-layer
tumors in necrotic phase. The tumor region is strip-like and divided into
necrotic region and proliferating region with two free boundaries. The upper
free boundary is tumor surface and governed by a Stefan condition. The lower
free boundary is the interface separating necrotic region from proliferating
region, its evolution is implicit and intrinsically governed by an obstacle
problem. We prove that the problem has a unique flat stationary solution, and
there exists a positive constant , such that the flat stationary
solution is asymptotically stable for cell-to-cell adhesiveness
, and unstable for .Comment: 22 page
A lower bound on the fidelity between two states in terms of their Bures distance
Fidelity is a fundamental and ubiquitous concept in quantum information
theory. Fuchs-van de Graaf's inequalities deal with bounding fidelity from
above and below. In this paper, we give a lower bound on the quantum fidelity
between two states in terms of their Bures distance.Comment: 5 pages, LaTeX, we have corrected some errors appearing in the
original manuscript. We have partially fixed the gap in the proof of the
previous versions. A new method towards the conjectured inequality in the
present version is being expecte
Asymptotic Behavior of Solutions of a Free Boundary Problem Modelling the Growth of Tumors with Stokes Equations
We study a free boundary problem modelling the growth of non-necrotic tumors
with fluid-like tissues. The fluid velocity satisfies Stokes equations with a
source determined by the proliferation rate of tumor cells which depends on the
concentration of nutrients, subject to a boundary condition with stress tensor
effected by surface tension. It is easy to prove that this problem has a unique
radially symmetric stationary solution. By using a functional approach, we
prove that there exists a threshold value for the surface tension
coefficient , such that in the case this radially
symmetric stationary solution is asymptotically stable under small non-radial
perturbations, whereas in the opposite case it is unstable
Remarks on the Sequential Products
In this paper, we show that those sequential products which were proposed by
Liu and Shen and Wu in [J. Phys. A: Math. Theor. {\bf 42}, 185206 (2009), J.
Phys. A: Math. Theor. {\bf 42}, 345203 (2009)] are just unitary equivalent to
the sequential product
A generalized family of discrete PT-symmetric square wells
N-site-lattice Hamiltonians H are introduced and perceived as a set of
systematic discrete approximants of a certain PT-symmetric
square-well-potential model with the real spectrum and with a non-Hermiticity
which is localized near the boundaries of the interval. Its strength is
controlled by one, two or three parameters. The problem of the explicit
construction of a nontrivial metric which makes the theory unitary is then
addressed. It is proposed and demonstrated that due to the not too complicated
tridiagonal-matrix form of our input Hamiltonians the computation of the metric
is straightforward and that its matrix elements prove obtainable,
non-numerically, in elementary polynomial forms.Comment: 21 pages, 2 figure
Asymptotic Stability of Stationary Solutions of a Free Boundary Problem Modeling the Growth of Tumors with Fluid Tissues
This paper aims at proving asymptotic stability of the radial stationary
solution of a free boundary problem modeling the growth of nonnecrotic tumors
with fluid-like tissues. In a previous paper we considered the case where the
nutrient concentration satisfies the stationary diffusion equation
, and proved that there exists a threshold value
for the surface tension coefficient , such that the radial
stationary solution is asymptotically stable in case , while
unstable in case . In this paper we extend this result to the
case where satisfies the non-stationary diffusion equation
\epsln\partial_t\sigma=\Delta\sigma-f(\sigma). We prove that for the same
threshold value as above, for every there is a
corresponding constant \epsln_0(\gamma)>0 such that for any
0<\epsln<\epsln_0(\gamma) the radial stationary solution is asymptotically
stable with respect to small enough non-radial perturbations, while for
and \epsln sufficiently small it is unstable under
non-radial perturbations
A Survey of Dynamical Matrices Theory
In this note, we survey some elementary theorems and proofs concerning
dynamical matrices theory. Some mathematical concepts and results involved in
quantum information theory are reviewed. A little new result on the matrix
representation of quantum operation are obtained. And best separable
approximation for quantum operations is presented.Comment: 22 pages, LaTe
Samuel multiplicities and Browder Spectrum of Operator Matrices
we show that the definitions of some classes of semi-Fredholm operators,
which use the language of algebra and first introduced by X. Fang in [8], are
equivalent to that of some well-known operator classes. For example, the
concept of shift-like semi-Fredholm operator on Hilbert space coincide with
that of upper semi-Browder operator. For applications of Samuel multiplicities
we characterize the sets of and respectively, where M_{C}=({array}{cc}A&C 0&B
{array}) denotes a 2-by-2 upper triangular operator matrix acting on the
Hilbert space .Comment: 1
Unified (r,s)-relative entropy
In this paper, we introduce and study unified -relative entropy and
quantum unified -relative entropy, in particular, our main results of
quantum unified -relative entropy are established on the separable
complex Hilbert spaces. Moreover, the entanglement-measure of states due to the
quantum unified -relative entropy is considered, too. Our results
improved a uncorrect statement on the monotone property of entanglement-measure
function
A lower bound of quantum conditional mutual information
In this paper, a lower bound of quantum conditional mutual information is
obtained by employing the Peierls-Bogoliubov inequality and Golden Thompson
inequality. Comparison with the bounds obtained by other researchers indicates
that our result is independent of any measurements. It may give some new
insights over squashed entanglement and perturbations of Markov chain states.Comment: 11 pages, LaTeX, published version. The missed second author is also
adde
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