Theta series and generalized special cycles on Hermitian locally symmetric manifolds

We study generalized special cycles on Hermitian locally symmetric spaces $\Gamma \backslash D$ associated to the groups $G=\mathrm{U}(p,q)$, $\mathrm{Sp}(2n,\mathbb{R})$ and $\mathrm{O}^*(2n)$. These cycles are (covered by) locally symmetric spaces associated to subgroups of $G$ which are of the same type. Using oscillator representation and a construction which essentially comes from the thesis of Greg Anderson, we show that Poincar\'e duals of these generalized special cycles can be viewed as Fourier coefficients of a theta series. This gives new cases of theta lifts from the cohomology of Hermtian locally symmetric manifolds associated to $G$ to vector valued automorphic forms associated to the groups $G'=\mathrm{U}(m,m)$, $\mathrm{O}(m,m)$ or $\mathrm{Sp}(m,m)$ which forms a reductive dual pair with $G$ in the sense of Howe

Special cycles on unitary Shimura varieties at ramified primes I

In this paper, we study special cycles on unitary Shimura varieties at the ramified primes of a imaginary quadratic number field ${\bf k}$ and special cycles on the corresponding Rapoport-Zink spaces. We write down the support of these special cycles and relate them by a uniformization theorem. We then compute their dimensions

Identification of the salmonid IL-17A/F1a/b, IL-17A/F2b, IL-17A/F3 and IL-17N genes and analysis of their expression following in vitro stimulation and infection

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The Kudla-Rapoport conjecture at a ramified prime for U(1,1)U(1, 1)

In this paper, we proved a local arithmetic Siegel-Weil formula for a $U(1, 1)$-Shimura variety at a ramified prime, a.k.a. a Kudla-Rapoport conjecture at a ramified case. The formula needs to be modified from the original Kudla-Rapoport conjecture. In the process, we also gives an explicit decomposition of the special divisors of the Rapoport-Zink space of unitary type $(1, 1)$ (Kr\"amer model). A key ingredient is to relate the Rapoport-Zink space to the Drinfeld upper plane.Comment: 34pp, final version, published in Transactions of the AM

Designing And Implementing An Online WebGIS-Based Decision Support System

This paper focuses on providing a market analysis solution through designing and implementing an online decision-support system (DSS) for businesses decision makers in Tobacco industry in China. The procedure makes use of data, information and software from Web based Geographical Information Systems (GIS) to generate online analysis, mapping and visualisation systems. These procedures are integrated and synchronised with market analysis techniques and customer relationship management (CRM) systems. By integrating these two techniques, a webGIS-based tobacco market information system is presented to demonstrate the significance of WebGIS in market analysis field. Specifically, to meet the needs of market practitioners (retailer, distributor and industry authority) in understanding the current market and sales performance, the system is designed and mainly consisted of four functional components: Communication and administration, Current market analysis, CRM (Client Relationship Management) and Sales/customer analysis, and Operational issues. From the system design and system usage perspectives, the illustration on the system architecture and the process of marketing information transmission reveals the benefits raised from this E-commerce tool to both the system users and service provider in marketing analysis. Based on this, the fusion of technology enhancement and marketing strategy in business process are called for and discussed

Locally symmetric spaces and the cohomology of the Weil representation

We study generalized special cycles on Hermitian locally symmetric spaces $\Gamma \backslash D$ associated to the groups $G=\mathrm{U}(p,q)$, $\mathrm{Sp}(2n,\R)$ and $\mathrm{O}^*(2n)$. These cycles are covered by symmetric spaces associated to subgroups of $G$ which are of the same type. Using the oscillator representation and the thesis of Greg Anderson (\cite{Anderson}), we show that Poincar\'e duals of these generalized special cycles can be viewed as Fourier coefficients of a theta series. This gives new cases of theta lifts from the cohomology of Hermitian locally symmetric manifolds associated to $G$ to vector-valued automorphic functions associated to the groups $G'=\mathrm{U}(m,m)$, $\mathrm{O}(m,m)$ or $\mathrm{Sp}(m,m)$ which are members of a dual pair with $G$ in the sense of Howe. The above three groups are all the groups that show up in real reductive dual pairs of type I whose symmetric spaces are of Hermitian type with the exception of $\mathrm{O}(p,2)$

A Simulation By Using Cohesive Zone Model For Indentation Test In Thin-Film/Substrate Systems

Master'sMASTER OF ENGINEERIN

Distinct response of immune gene expression in peripheral blood leucocytes modulated by bacterin vaccine candidates in rainbow trout Oncorhynchus mykiss : A potential in vitro screening and batch testing system for vaccine development in aquaculture

Acknowledgements Ahmed Attaya's PhD project was funded by the Newton Fund, the British Council, and the National Institute of Oceanography and Fisheries, Hurghada, Egypt. This research was also supported financially by a grant (BB/M013022/1) from the UK Biotechnology and Biological Sciences Research Council (BBSRC).Peer reviewedPostprin