1,057 research outputs found
Linear orthogonality preservers of Hilbert bundles
Due to the corresponding fact concerning Hilbert spaces, it is natural to ask
if the linearity and the orthogonality structure of a Hilbert -module
determine its -algebra-valued inner product. We verify this in the case
when the -algebra is commutative (or equivalently, we consider a Hilbert
bundle over a locally compact Hausdorff space). More precisely, a
-linear map (not assumed to be bounded) between two
Hilbert -modules is said to be "orthogonality preserving" if
\left =0 whenever \left =0. We prove
that if is an orthogonality preserving map from a full Hilbert
-module into another Hilbert -module that
satisfies a weaker notion of -linearity (known as "localness"),
then is bounded and there exists such that
\left\ =\ \phi\cdot\left, \quad \forall
x,y \in E. On the other hand, if is a full Hilbert -module over
another commutative -algebra , we show that a
"bi-orthogonality preserving" bijective map with some "local-type
property" will be bounded and satisfy \left\ =\
\phi\cdot\left\circ\sigma, \quad \forall x,y \in E where and is a homeomorphism
Linear orthogonality preservers of Hilbert -modules over general -algebras
As a partial generalisation of the Uhlhorn theorem to Hilbert -modules,
we show in this article that the module structure and the orthogonality
structure of a Hilbert -module determine its Hilbert -module
structure. In fact, we have a more general result as follows. Let be a
-algebra, and be Hilbert -modules, and be the ideal of
generated by . If is an
-module map, not assumed to be bounded but satisfying then there exists a unique central positive multiplier such
that As a consequence, is automatically bounded, the induced
map is adjointable, and
is isomorphic to as Hilbert -modules. If, in addition,
is bijective, then is isomorphic to .Comment: 15 page
Analysis Of The Suspension Beam In Accelerometer For Stiffness Constant And Resonant Frequency By Using Analytical And Numerical Investigation
Mikro-meterpecut yang digunakan dalam pelbagai penerapan hanya akan tercapai dengan jayanya sekiranya keperluan frekuensi resonans dan kepekaan dapat dipenuhi dan konsisten.
A successful and consistent performance of micro-accelerometer which has been applied in various applications can only be achieved when the resonant frequency and the sensitivity requirement are fulfilled
Analysis Of The Suspension Beam In Accelerometer For Stiffness Constant And Resonant Frequency By Using Analytical And Numerical Investigation [TL589.2.A3 W872 2007 f rb].
Mikro-meterpecut yang digunakan dalam pelbagai penerapan hanya akan tercapai dengan jayanya sekiranya keperluan frekuensi resonans dan kepekaan dapat dipenuhi dan konsisten. Berdasarkan syarat-syarat tersebut, analisis struktur pada pekali kekukuhan and frekuensi resonans bagi rasuk ampaian dalam meter pecut dan seterusnya pengoptimuman kepada kepekaan haruslah dilakukan.
A successful and consistent performance of micro-accelerometer which has been applied in various applications can only be achieved when the resonant frequency and the sensitivity requirement are fulfilled. In view of this, structural analysis on stiffness constant and resonant frequency for the suspension beam in accelerometer, and subsequently optimization design of accelerometer with respect to sensitivity in term of displacement against acceleration must be performed
Promoting social-emotional learning in Chinese schools : a feasibility study of PATHS implementation in Hong Kong
This paper describes a pilot study of a reduced version of the PATHS Curriculum, a USdeveloped evidence-based SEL program, among schools in Hong Kong SAR (China).
Three hundred and sixteen 12th grade students in three elementary schools participated
in the study. A limited number of first grade PATHS lessons were adapted and translated
into Chinese. Twelve teachers learned and adopted these lessons in their teaching.
Students in these classrooms learned about different emotions and practiced self-control.
The intervention lasted four months. After the intervention, students showed
improvement in emotion understanding, emotion regulation and prosocial behavior. No
change was observed in the level of children’s problem behaviors. Over 65% of the
teachers reported a high degree of satisfaction and willingness to adopt the intervention.
The effects of the intervention varied among schools, with variations in the level of
intervention and principal support, but not in the quality of implementation. Discussion
is focused on the factors that could shape the adoption and implementation of SEL
programs, especially the role of the difference in school systems between Hong Kong
and the United States.peer-reviewe
An ab initio Molecular Orbital Study of the Insertions of Difluorocarbene into Substituted Ethenes
Ab initio MO calculations predict the activation energies for the insertions of difluorocarbene into substituted ethenes C2H3X (X = F, Cl, Me) to be 61,68 and 52 kJ mol-1, respectively; these results indicate that the monosubstitution on the ethene has no significant effects on the activation energy of the reaction
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