Atomic decomposition of real-variable type for Bergman spaces in the unit ball of Cn\mathbb{C}^n

In this paper, we show that every (weighted) Bergman space $\mathcal{A}^p_{\alpha} (\mathbb{B}_n)$ in the complex ball admits an atomic decomposition of real-variable type for any $0 -1.$ More precisely, for each $f \in \mathcal{A}^p_{\alpha} (\mathbb{B}_n)$ there exist a sequence of real-variable (p, \8)_{\alpha}-atoms $a_k$ and a scalar sequence $\{\lambda_k \}$ with \sum_k | \lambda_k |^p < \8 such that $f = \sum_k \lambda_k P_{\alpha} (a_k),$ where $P_{\alpha}$ is the Bergman projection from $L^2_{\alpha} (\mathbb{B}_n)$ onto $\mathcal{A}^2_{\alpha} (\mathbb{B}_n).$ The proof is constructive, and our construction is based on some sharp estimates about Bergman metric and Bergman kernel functions in $\mathbb{B}_n.$Comment: 28 page

Well-Posedness Properties In Variational Analysis And Its Applications

This dissertation focuses on the study and applications of some significant properties in well-posedness and sensitivity analysis, among which the notions of uniform metric regularity , higher-order metric subregularity and its strong subregularity counterpart play an essential role in modern variational analysis. We derived verifiable sufficient conditions and necessary conditions for those notions in terms of appropriate generalized differential as well as geometric constructions of variational analysis. Concrete examples are provided to illustrate the behavior and compare the results. Optimality conditions of parametric variational systems (PVS) under equilibrium constraints are also investigated via the terms of coderivatives. We derived necessary optimality and suboptimality conditions for various problems of constrained optimization and equilibria such as MPECs with amenable/full rank potentials and EPECs with closed preferences in finite-dimensional spaces

Mutational Analysis of HIV-1 Nucleocapsid Protein and Methods Development for Aptamer Discovery

This dissertation focuses on structural and functional studies related to the interaction between proteins and nucleic acids and their applications. The work reported here includes two projects. The first part of the thesis is on the mutational and combinatorial analysis of HIV-1 nucleocapsid protein (NCp7). Sixteen mutants of NCp7 were constructed and over-expressed in E. coli . The dissociation constants (K d ) between the mutant proteins and the major packaging signal in HIV-1, SL3 RNA, were measured using tryptophan fluorescence titration assay and/or isothermal titration calorimetry (ITC) assay. Most mutants show tolerance of the mutation but some mutants, including F16A, I24A and K14E-E21K, suffered moderate to significant loss of affinity for SL3 RNA, indicating the roles of the affected residues in the interaction between NCp7 and SL3. The second part focuses on the development of methods for aptamer discovery. Two prototype platforms were set up to imitate the two main-stream next-generation sequencing (NGS) technologies, bridge amplification based and emulsion PCR based NGS technologies. Proof-of-principle experiments were carried out and optimized to evaluate the practicality of these platforms in high-throughput and multiplexed aptamer discovery

Performance Analysis of a Dual-Hop Cooperative Relay Network with Co-Channel Interference

This paper analyzes the performance of a dual-hop amplify-and-forward (AF) cooperative relay network in the presence of direct link between the source and destination and multiple co-channel interferences (CCIs) at the relay. Specifically, we derive the new analytical expressions for the moment generating function (MGF) of the output signal-to-interference-plus-noise ratio (SINR) and the average symbol error rate (ASER) of the relay network. Computer simulations are given to confirm the validity of the analytical results and show the effects of direct link and interference on the considered AF relay network