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A Discrete Weighted Helmholtz Decomposition and Applications to Non-overlapping Domain Decomposition for Saddle-point Maxwell Systems with Jumps in Coefficients
Maxwell's equations N秂d秂lec 痭ite elements weighted Helmholtz decom-position domain decomposition saddle-point system, preconditioners, condition number
2012/8/8
We shall establish a discrete weighted Helmholtz decomposition in edge element
spaces, which is stable uniformly with respect to the jumps in the discontinuous weight
function. The stable decomposit...
Several Pairs of Differential Operators and Their Applications in Variational Calculusof a General Third Order Energy
Di甧rential operator Euler-Lagrange equation Complete-variation Geo-metric energy functional Curvature
2012/8/8
Gradient, divergence and Laplace-Beltrami operators over surfaces have played im-
portant roles in many 痚lds related to geometry and analysis, such as di甧rential ge-
ometry, computational geometry a...
Computation and Applications of Centroidal Voronoi Tessellations
calculate Voronoi tessellation
2014/10/30
Centroidal Voronoi Tessellation (CVT) is a special Voronoi tessellation in which every site xicoincides withci, the centroid of its Voronoi cellVi,CVT (left) and its corresponding Delaunay triangulati...
Multidimensional Interleavings and Applications to Topological Inference
Multidimensional Interleavings Topological Inference Algebraic Topology
2012/6/27
This work concerns the theoretical foundations of persistence-based topological data analysis. We develop theory of topological inference in the multidimensional persistence setting, and directly at t...
Derivative Formula, Integration by Parts Formula and Applications for SDEs Driven by Fractional Brownian Motion
Derivative formula integration by parts formula Harnack inequality stochastic differential equation fractional Brownian motion
2012/6/21
In the paper, the Bismut derivative formula is established for multidimensional SDEs driven by additive fractional noise ($1/2and moreover the Harnack inequality is given. Through a Lamperti t...
Nullspaces of Conformally Invariant Operators. Applications to $Q_{k}$-curvature
Spectral geometry conformal geometry nodal sets Qk-curvature
2012/6/19
We study conformal invariants that arise from functions in the nullspace of conformally covariant differential operators. The invariants include nodal sets and the topology of nodal domains of eigenfu...
An improved geometric inequality via vanishing moments, with applications to singular Liouville equations
Geometric PDEs Variational Methods Min-max Schemes
2012/6/14
We consider a class of singular Liouville equations on compact surfaces motivated by the study of Electroweak and Self-Dual Chern-Simons theories, the Gaussian curvature prescription with conical sing...
The theory of Hahn meromorphic functions, a holomorphic Fredholm theorem and its applications
Hahn meromorphic functions holomorphic Fredholm theorem its applications Classical Analysis and ODEs
2012/5/9
We introduce a class of functions near zero on the logarithmic cover of the complex plane that have convergent expansions into generalized power series. These power series are general enough to cover ...
Modularity lifting results in parallel weight one and applications to the Artin conjecture: the tamely ramified case
Modularity lifting results parallel weight one Artin conjecture tamely ramified case Number Theory
2012/4/18
We extend the modularity lifting result of the arXiv:1111.2804 to allow Galois representations with some ramification at p. We also prove modularity mod 2 and 5 of certain Galois representations. We u...
A Structure Theorem for Poorly Anticoncentrated Gaussian Chaoses and Applications to the Study of Polynomial Threshold Functions
Structure Theorem Anticoncentrated Gaussian Chaoses Study of Polynomial Threshold Functions
2012/4/18
We prove a structural result for degree-$d$ polynomials. In particular, we show that any degree-$d$ polynomial, $p$ can be approximated by another polynomial, $p_0$, which can be decomposed as some fu...
Fundamental domain of invariant sets and applications
Fundamental domain partial hyperbolicity cocycle transitivity accessibility essential saturation
2012/4/18
Let $X$ be a compact metric space and $f:X\to X$ a homeomorphism on $X$. We construct a fundamental domain for the set with finite peaks for each cocycle induced by $\phi\in C(X,R)$. In particular we ...
Extremal Distribution for the Discrete 5-convex Stochastic Ordering and Applications
s-convex order moment space extremal distribution branching process Lundberg's coeffici
2011/11/9
In this paper, motivated by the idea from Courtois and Denuit et al.(2006), we derive extremal distribution for the discrete 5-convex stochastic ordering. As applications,We improve lower and upper bo...
Exponential convergence rates of second quantization semigroups and applications
Convergence rate tail norm entropy second quantization
2011/11/4
Exponentialconvergence rates in the L2-tail norm and entropy are characterized forthe second quantization semigroups by using the corresponding baseDirichlet form. This supplements the well known resu...
On an algebraic formula and applications to group action on manifolds
algebraic formula applications group action manifolds
2018/4/19
Inspired by a recent result of Cho-Kim-Park, we consider a purely algebraic result. Then given a circle or cyclic group of prime order action on a manifold, we will use it to estimate the lower bound ...
In this short note, we present certain generalized versions of the commutator formulas of some natural operators on manifolds, and give some applications.