342 research outputs found
Norm discontinuity and spectral properties of Ornstein-Uhlenbeck semigroups
Let be a real Banach space. We study the Ornstein-Uhlenbeck semigroup
associated with the Ornstein-Uhlenbeck operator Here is a positive symmetric operator from
to and is the generator of a -semigroup on . Under
the assumption that admits an invariant measure we prove that if
is eventually compact and the spectrum of its generator is nonempty, then \n
P(t)-P(s)\n_{L^1(E,\mu)} = 2 for all with . This result
is new even when . We also study the behaviour of in the space
. We show that if there exists such that \n
P(t)-P(s)\n_{BUC(E)} = 2 for all with . Moreover,
under a nondegeneracy assumption or a strong Feller assumption, the following
dichotomy holds: either \n P(t)- P(s)\n_{BUC(E)} = 2 for all , \
, or is the direct sum of a nilpotent semigroup and a
finite-dimensional periodic semigroup. Finally we investigate the spectrum of
in the spaces and .Comment: 14 pages; to appear in J. Evolution Equation
Comparison of CT and chemical-shift MRI for differentiating thymoma from non-thymomatous conditions in myasthenia gravis: value of qualitative and quantitative assessment
Controllability and Qualitative properties of the solutions to SPDEs driven by boundary L\'evy noise
Let be the solution to the following stochastic evolution equation (1)
du(t,x)& = &A u(t,x) dt + B \sigma(u(t,x)) dL(t),\quad t>0; u(0,x) = x taking
values in an Hilbert space \HH, where is a \RR valued L\'evy process,
an infinitesimal generator of a strongly continuous semigroup,
\sigma:H\to \RR bounded from below and Lipschitz continuous, and B:\RR\to H
a possible unbounded operator. A typical example of such an equation is a
stochastic Partial differential equation with boundary L\'evy noise. Let
\CP=(\CP_t)_{t\ge 0} %{\CP_t:0\le t<\infty}T>0BAx\in H\CP_T^\star \delta_xH\HHLAB$ the solution of Equation [1] is
asymptotically strong Feller, respective, has a unique invariant measure. We
apply these results to the damped wave equation driven by L\'evy boundary
noise
Accuracy of CT-guided transthoracic needle biopsy of lung lesions: Factors affecting diagnostic yield
Diffusion-weighted magnetic resonance imaging: new perspectives in the diagnostic pathway of non-complicated acute pyelonephritis
Adjoint bi-continuous semigroups and semigroups on the space of measures
For a given bi-continuous semigroup T on a Banach space X we define its
adjoint on an appropriate closed subspace X^o of the norm dual X'. Under some
abstract conditions this adjoint semigroup is again bi-continuous with respect
to the weak topology (X^o,X). An application is the following: For K a Polish
space we consider operator semigroups on the space C(K) of bounded, continuous
functions (endowed with the compact-open topology) and on the space M(K) of
bounded Baire measures (endowed with the weak*-topology). We show that
bi-continuous semigroups on M(K) are precisely those that are adjoints of a
bi-continuous semigroups on C(K). We also prove that the class of bi-continuous
semigroups on C(K) with respect to the compact-open topology coincides with the
class of equicontinuous semigroups with respect to the strict topology. In
general, if K is not Polish space this is not the case
DEDALO: PHASE II STUDY OF DARATUMUMAB PLUS POMALIDOMIDE AND DEXAMETHASONE (DPD) IN PATIENTS WITH RELAPSED/REFRACTORY MULTIPLE MYELOMA AND 17P DELETION
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Linear Operator Inequality and Null Controllability with Vanishing Energy for unbounded control systems
We consider linear systems on a separable Hilbert space , which are null
controllable at some time under the action of a point or boundary
control. Parabolic and hyperbolic control systems usually studied in
applications are special cases. To every initial state we
associate the minimal "energy" needed to transfer to in a time ("energy" of a control being the square of its norm). We
give both necessary and sufficient conditions under which the minimal energy
converges to for . This extends to boundary control
systems the concept of null controllability with vanishing energy introduced by
Priola and Zabczyk (Siam J. Control Optim. 42 (2003)) for distributed systems.
The proofs in Priola-Zabczyk paper depend on properties of the associated
Riccati equation, which are not available in the present, general setting. Here
we base our results on new properties of the quadratic regulator problem with
stability and the Linear Operator Inequality.Comment: In this version we have also added a section on examples and
applications of our main results. This version is similar to the one which
will be published on "SIAM Journal on Control and Optimization" (SIAM
Exponential Ergodicity of stochastic Burgers equations driven by -stable processes
In this work, we prove the strong Feller property and the exponential
ergodicity of stochastic Burgers equations driven by -subordinated
cylindrical Brownian motions with . To prove the results, we
truncate the nonlinearity and use the derivative formula for SDEs driven by
-stable noises established in Zhang (arXiv:1204.2630v2).Comment: 17p
Anti-prion drug mPPIg5 inhibits PrP(C) conversion to PrP(Sc).
Prion diseases, also known as transmissible spongiform encephalopathies, are a group of fatal neurodegenerative diseases that include scrapie in sheep, bovine spongiform encephalopathy (BSE) in cattle and Creutzfeldt-Jakob disease (CJD) in humans. The 'protein only hypothesis' advocates that PrP(Sc), an abnormal isoform of the cellular protein PrP(C), is the main and possibly sole component of prion infectious agents. Currently, no effective therapy exists for these diseases at the symptomatic phase for either humans or animals, though a number of compounds have demonstrated the ability to eliminate PrPSc in cell culture models. Of particular interest are synthetic polymers known as dendrimers which possess the unique ability to eliminate PrP(Sc) in both an intracellular and in vitro setting. The efficacy and mode of action of the novel anti-prion dendrimer mPPIg5 was investigated through the creation of a number of innovative bio-assays based upon the scrapie cell assay. These assays were used to demonstrate that mPPIg5 is a highly effective anti-prion drug which acts, at least in part, through the inhibition of PrP(C) to PrP(Sc) conversion. Understanding how a drug works is a vital component in maximising its performance. By establishing the efficacy and method of action of mPPIg5, this study will help determine which drugs are most likely to enhance this effect and also aid the design of dendrimers with anti-prion capabilities for the future
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