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Boundary Harnack principle and gradient estimates for fractional Laplacian perturbed by non-local operators
Harmonic function boundary Harnack principle gradient estimate
2016/1/20
Boundary Harnack principle and gradient estimates for fractional Laplacian perturbed by non-local operators.
Exact Solutions to the Six-Vertex Model with Domain Wall Boundary Conditions and Uniform Asymptotics of Discrete Orthogonal Polynomials on an Infinite Lattice
Statistical Mechanics Random Matrices Orthogonal Polynomials Asymptotics Riemann-Hilbert Problems
2015/1/19
In this dissertation the partition function, $Z_n$, for the six-vertex model with domain wall boundary conditions is solved in the thermodynamic limit in various regions of the phase diagram. In the f...
Determining electrical and heat transfer parameters using coupled boundary measurements
electrical impedance tomography heat transfer inverse problem
2011/1/21
Let ⊂ Rn, n ≥ 3, be a smooth bounded domain and consider a coupled system in consisting of a conductivity equation ∇ · (x)∇u(t, x) =0 and an anisotropic heat equation −1(x)@t...
Detection boundary in sparse regression
High-dimensional regression detection boundary sparse vectors sparsity minimax hypothesis testing
2010/12/1
We study the problem of detection of a p-dimensional sparse vector of parameters in the linear regression model with Gaussian noise. We establish the detection boundary, i.e., the necessary and suffic...