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- Approximation algorithms, consensus, regime-switching process, step size (1)
- Averaging principle, complexity comparison, Identification system, Large deviations, non-homogeneity, Two-time-scale system (1)
- Bott-stable (1)
- Eigenfunctions of Laplacian on smooth manifolds, existence of maximizers, geometric estimates of nodal sets and nodal domains, Hardy-Littlewood-Sobolev inequalities, Heisenberg group (1)
- General linear group of a Banach algebra (1)
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Articles 1 - 6 of 6
Full-Text Articles in Mathematics
Nodal Geometry Of Eigenfunctions On Smooth Manifolds And Hardy-Littlewood-Sobolev Inequalities On The Heisenberg Group, Xiaolong Han
Nodal Geometry Of Eigenfunctions On Smooth Manifolds And Hardy-Littlewood-Sobolev Inequalities On The Heisenberg Group, Xiaolong Han
Wayne State University Dissertations
Part I: Let (M,g) be a n dimensional smooth, compact, and connected Riemannian manifold without boundary, consider the partial differential equation on M:
-Δu=Λu,
in which Δ is the Laplace-Beltrami operator. That is, u is an eigenfunction with eigenvalue Λ. We analyze the asymptotic behavior of eigenfunctions as Λ go to ∞ (i.e., limit of high energy states) in terms of the following aspects.
(1) Local and global properties of eigenfunctions, including several crucial estimates for further investigation.
(2) Write the nodal set of u as N={u=0}, estimate the size of N using Hausdorff measure. Particularly, surrounding the conjecture that …
Spaces Of Sections Of Banach Algebra Bundles, Emmanuel Dror Farjoun, Claude Schochet
Spaces Of Sections Of Banach Algebra Bundles, Emmanuel Dror Farjoun, Claude Schochet
Mathematics Faculty Research Publications
Suppose that B is a G-Banach algebra over 𝔽 = ℝ or ℂ, X is a finite dimensional compact metric space, ζ : P → X is a standard principal G-bundle, and Aζ = Γ(X,P xG B) is the associated algebra of sections. We produce a spectral sequence which converges to π∗(GLoAζ) with
E_2p,q ≅ Ȟp(X ; πq(GLoB)).
A related spectral sequence converging to K∗+1(Aζ) (the real or complex topological …
S-Index: A Comprehensive Scholar Impact Index, Shlomo S. Sawilowsky
S-Index: A Comprehensive Scholar Impact Index, Shlomo S. Sawilowsky
Theoretical and Behavioral Foundations of Education Faculty Publications
Limitations of impact indices to compare scholars across disciplines and time based only the number of publications and citations are discussed. The S-index, based on more comprehensive scholar impact factors, is proposed.
Stabilization And Classification Of Poincare Duality Embeddings, John Whitson Peter
Stabilization And Classification Of Poincare Duality Embeddings, John Whitson Peter
Wayne State University Dissertations
We define a space E(K,X) of Poincare Duality embeddings and show that such spaces admit a highly connected stabilization map.
This serves as a tool for classifying Poincare Duality embeddings in terms of the homotopy types of their complements. In
particular, a Poincare embedding gives rise to a fiberwise duality
map in the category of retractive spaces over X. We use this construction to obtain a highly connected classification map with target a moduli space of unstable complements for Poincare embeddings. As consequences, we obtain stabilization and classication results for
smooth embeddings.
Large Deviations Of Stochastic Systems And Applications, Qi He
Large Deviations Of Stochastic Systems And Applications, Qi He
Wayne State University Dissertations
This dissertation focuses on large deviations of stochastic systems with applications to optimal control and system identification. It encompasses analysis of two-time-scale Markov processes and system identification with regular and quantized data. First, we develops large deviations principles for systems driven by continuous-time Markov chains with twotime scales and related optimal control problems. A distinct feature of our setup is that the Markov chain under consideration is time dependent or inhomogeneous. The use of two time-scale formulation stems from the effort of reducing computational complexity in a wide variety of applications in control, optimization, and systems theory. Starting with a …
Consensus-Type Stochastic Approximation Algorithms, Yu Sun
Consensus-Type Stochastic Approximation Algorithms, Yu Sun
Wayne State University Dissertations
This work is concerned with asymptotic properties of consensus-type algorithms for networked systems whose topologies switch randomly. The regime-switching process is modeled as a discrete-time Markov chain with a nite state space. The consensus control is achieved by designing stochastic approximation algorithms. In the setup, the regime-switching process (the Markov chain) contains a rate parameter
"Ε> 0 in the transition probability matrix that characterizes how frequently the topology switches. On the other hand, the consensus control algorithm uses a step-size Μ that denes how fast the network states are updated. Depending on their relative values, three distinct scenarios emerge. Under …