165 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
Property (T) for non-unital C*-algebras
Inspired by the recent work of Bekka, we study two reasonable analogues of
property (T) for not necessarily unital C*-algebras. The stronger one of the
two is called ``property (T)'' and the weaker one is called ``property
(T_{e})''. It is shown that all non-unital C*-algebras do not have property (T)
(neither do their unitalizations). Moreover, all non-unital -unital
C*-algebras do not have property (T_e).Comment: 7 pages; to appear in J. Math. Anal. App
Effective Transfer of Pretrained Large Visual Model for Fabric Defect Segmentation via Specifc Knowledge Injection
Fabric defect segmentation is integral to textile quality control. Despite
this, the scarcity of high-quality annotated data and the diversity of fabric
defects present significant challenges to the application of deep learning in
this field. These factors limit the generalization and segmentation performance
of existing models, impeding their ability to handle the complexity of diverse
fabric types and defects. To overcome these obstacles, this study introduces an
innovative method to infuse specialized knowledge of fabric defects into the
Segment Anything Model (SAM), a large-scale visual model. By introducing and
training a unique set of fabric defect-related parameters, this approach
seamlessly integrates domain-specific knowledge into SAM without the need for
extensive modifications to the pre-existing model parameters. The revamped SAM
model leverages generalized image understanding learned from large-scale
natural image datasets while incorporating fabric defect-specific knowledge,
ensuring its proficiency in fabric defect segmentation tasks. The experimental
results reveal a significant improvement in the model's segmentation
performance, attributable to this novel amalgamation of generic and
fabric-specific knowledge. When benchmarking against popular existing
segmentation models across three datasets, our proposed model demonstrates a
substantial leap in performance. Its impressive results in cross-dataset
comparisons and few-shot learning experiments further demonstrate its potential
for practical applications in textile quality control.Comment: 13 pages,4 figures, 3 table
Cross-disciplinary collaboration through WuZhiQiao Project to foster cultural exchange and community engagement
In 2013, students of the Technological and Higher Education Institute of Hong Kong (THEi), with the support of WuZhiQiao (WZQ) Charitable Foundation, formed a core team of 11 students to organize and participate in social service projects to help the underprivileged in the Chinese mainland.
WuZhiQiao (WZQ) projects, the first cross-region social service engagement by THEi students, bring together students from Hong Kong and the Mainland. WZQ Charitable Foundation aims to help the Chinese traditional village in building Pedestrian Bridge and organizing community projects. Since there are Chinese villages facing flooding during rainy seasons, the local villagers will be trapped inside the village without the chance to go outside or wade outside the village. There are hundreds of such villages and they highly need our help.
Each project mainly involves two or three institutes from Hong Kong and the Mainland, and they organize the whole volunteer project including planning, investigation, design, promotion and operation. Through involvement in different states or provinces, WZQ projects provide good chance of communication and interaction between Hong Kong teams and the Mainland teams and advocate intercultural social services. The projects can foster the cultural exchange between Hong Kong and the Mainland.
Moreover, the majority of WZQ project members are coming from the fields of engineering, architecture and health care. We can practice our learning from lectures through the project implementation. Different parties are involved in the engineering projects including clients, consultants, contractors, surveyors, engineers and workers. Engineering students can gain good understanding of the holistic picture of a real-life engineering project. We visited the location village for investigation to learn more about the local culture, geometry and the people’s needs and discussed with the Mainland Team through online chatting tools in order to propose the optimal pedestrian building design and other community projects.
Having spent over six months in planning and preparation, THEi students will implement a bridge-building and community project in Chongqing in January 2015. Through engagement in this service-learning project, not only the undergraduates of THEi can benefit through personal development but the life quality of the disadvantaged can also be improved
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