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On Existence of -solutions for Coupled Boltzmann Transport Equation and Radiation Therapy Treatment Optimization
The paper considers a linear system of Boltzmann transport equations
modelling the evolution of three species of particles, photons, electrons and
positrons. The system is coupled because of the collision term (an integral
operator). The model is intended especially for dose calculation (forward
problem) in radiation therapy. It, however, does not apply to all relevant
interactions in its present form. We show under physically relevant assumptions
that the system has a unique solution in appropriate (-based) spaces and
that the solution is non-negative when the data (internal source and inflow
boundary source) is non-negative. In order to be self-contained as much as is
practically possible, many (basic) results and proofs have been reproduced in
the paper. Existence, uniqueness and non-negativity of solutions for the
related time-dependent coupled system are also proven. Moreover, we deal with
inverse radiation treatment planning problem (inverse problem) as an optimal
control problem both for external and internal therapy (in general
-spaces). Especially, in the case variational equations for an
optimal control related to an appropriate differentiable convex object function
are verified. Its solution can be used as an initial point for an actual
(global) optimization.Comment: Corrected typos. Added a new section 3. Revised the argument of
Example 7.
Rolling Manifolds: Intrinsic Formulation and Controllability
In this paper, we consider two cases of rolling of one smooth connected
complete Riemannian manifold onto another one (\hM,\hg) of equal
dimension . The rolling problem corresponds to the situation
where there is no relative spin (or twist) of one manifold with respect to the
other one. As for the rolling problem , there is no relative spin and also
no relative slip. Since the manifolds are not assumed to be embedded into an
Euclidean space, we provide an intrinsic description of the two constraints
"without spinning" and "without slipping" in terms of the Levi-Civita
connections and \nabla^{\hg}. For that purpose, we recast the
two rolling problems within the framework of geometric control and associate to
each of them a distribution and a control system. We then investigate the
relationships between the two control systems and we address for both of them
the issue of complete controllability. For the rolling , the reachable
set (from any point) can be described exactly in terms of the holonomy groups
of and (\hM,\hg) respectively, and thus we achieve a complete
understanding of the controllability properties of the corresponding control
system. As for the rolling , the problem turns out to be more delicate. We
first provide basic global properties for the reachable set and investigate the
associated Lie bracket structure. In particular, we point out the role played
by a curvature tensor defined on the state space, that we call the
\emph{rolling curvature}. In the case where one of the manifolds is a space
form (let say (\hM,\hg)), we show that it is enough to roll along loops of
and the resulting orbits carry a structure of principal bundle which
preserves the rolling distribution. In the zero curvature case, we deduce
that the rolling is completely controllable if and only if the holonomy
group of is equal to SO(n). In the nonzero curvature case, we prove
that the structure group of the principal bundle can be realized as the
holonomy group of a connection on , that we call the rolling
connection. We also show, in the case of positive (constant) curvature, that if
the rolling connection is reducible, then admits, as Riemannian
covering, the unit sphere with the metric induced from the Euclidean metric of
. When the two manifolds are three-dimensional, we provide a complete
local characterization of the reachable sets when the two manifolds are
three-dimensional and, in particular, we identify necessary and sufficient
conditions for the existence of a non open orbit. Besides the trivial case
where the manifolds and (\hM,\hg) are (locally) isometric, we show
that (local) non controllability occurs if and only if and (\hM,\hg)
are either warped products or contact manifolds with additional restrictions
that we precisely describe. Finally, we extend the two types of rolling to the
case where the manifolds have different dimensions
LĂĂKE â„ LAPSI : LÀÀkeoppaat leikki-ikĂ€iselle (1-6v.) lapselle ja hĂ€nen vanhemmilleen Lasten ja nuorten sairaalan SydĂ€nosastolle K4
LĂĂKE â„ LAPSI - LÀÀkeoppaat leikki-ikĂ€iselle (1-6v.) lapselle ja hĂ€nen vanhemmilleen Lasten ja nuorten sairaalan SydĂ€nosastolle K4
OpinnÀytetyö on työelÀmÀlÀhtöinen ja se tehtiin HUS:n Lasten ja nuorten sairaalan SydÀnosastolle K4. OpinnÀytetyö koostuu teoreettisesta ja toiminnallisesta osuudesta. OpinnÀytetyön tarkoituksena oli toteuttaa lÀÀkehoidon oppaat leikki-ikÀiselle sydÀnlapselle ja hÀnen vanhemmilleen.
OpinnÀytetyönÀ tehtyjen oppaiden tavoitteena on auttaa leikki-ikÀistÀ sydÀnlasta ymmÀrtÀmÀÀn lÀÀkityksen tarkoitus sekÀ vÀhentÀÀ lÀÀkkeiden antamiseen kohdistuvia pelkoja. Vanhemmille pyritÀÀn antamaan tarvittavat tiedot ja apuvÀline, opas, jotta he voisivat tukea ja ohjata lasta lÀÀkehoidossa.
Teoreettisessa osuudessa kÀsitellÀÀn leikki-ikÀistÀ lasta, lasten lÀÀkehoidon erityispiirteitÀ, sydÀnsairaan lapsen lÀÀkehoitoa, leikki-ikÀisen lapsen pelkoja sekÀ leikki-ikÀisen lapsen ja vanhempien valmistamista lÀÀkehoitoon. Myös oppaan laatimisen teoriaa on kÀsitelty.
Toiminnallinen osuus koostuu kahdesta sydĂ€nlapsen lÀÀkehoitoa kĂ€sittelevĂ€stĂ€ oppaasta. SydĂ€nlapsen oma lÀÀkekirja on suunnattu leikki-ikĂ€iselle (1-6v.) lapselle. Lapsen opas on vĂ€rityskirjamuotoon tehty kuvakirja, jossa lyhyiden tekstien avulla kerrotaan lapselle lÀÀkehoidosta. Lapsen oppaasta tehtiin myös valmiiksi vĂ€ritetty versio. SydĂ€nlapsen lÀÀkitys - Vanhempien opas on leikki-ikĂ€isen lapsen vanhemmille suunnattu âtietopakettiâ sydĂ€nlapsen lÀÀkehoidosta.MEDICINE â„ CHILD - Medicine guides for play-aged (1-6-year old) child and parents at the Cardiac Ward K4 of the Hospital for Children and Adolescents
This thesis is based on working life needs and it was made for Children's Hospital Cardiac Ward K4. The thesis consists of a theoretical and a functional section. The purpose of this thesis was to produce medical guides for a play-aged child with heart defects and her/his parents.
The aim of the guides made for this thesis is to help play-aged children with heart defects to understand the purpose of the medication and to decrease the fears being aimed at administering medicine. Parents are about to be given the knowledge and instrument, the guide, that are needed so that they can support and instruct their child in medical care.
The theoretical section examines the play-aged child, special characteristics of childrenâs medical care, medical treatment of a child with heart disease, play-aged childâs fears, and preparing a play-aged child and parents for medical care. Also theory of creating a guide has been handled.
The functional section consists of two medical guides dealing with medical care of a child with heart defects. Medicine guide for a child with heart defects is directional for a play-aged (1-6-year old) child. The childâs guide is made as a coloring book formed picture book with short texts about medical care. An already colored version of the child's guide was also made. Parentsâ guide is written as âinformational packageâ about medical care of a child with heart defects
Rolling Manifolds of Different Dimensions
If and (\hM,\hg) are two smooth connected complete oriented
Riemannian manifolds of dimensions and \hn respectively, we model the
rolling of onto (\hM,\hg) as a driftless control affine systems
describing two possible constraints of motion: the first rolling motion
captures the no-spinning condition only and the second rolling
motion corresponds to rolling without spinning nor slipping. Two
distributions of dimensions (n + \hn) and , respectively, are then
associated to the rolling motions and respectively.
This generalizes the rolling problems considered in \cite{ChitourKokkonen1}
where both manifolds had the same dimension. The controllability issue is then
addressed for both and and completely solved for
. As regards to , basic properties for the reachable
sets are provided as well as the complete study of the case (n,\hn)=(3,2) and
some sufficient conditions for non-controllability
Energy and protein nutrition of dairy cows during the dry period and early lactation : Production performance and adaptation from pregnancy to lactation
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