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In the past two decades, starting with the pioneering work of Bourgain, Brezis, and Mironescu, there has been widespread interest in characterizing Sobolev and BV (bounded variation) functions by mean...
我们将介绍由Bar-Gauduchon-Moroianu给出的spin流形上Dirac算子在度量变化时一阶变分公式的证明。作为应用,我们将计算Dirac算子沿Ricci flow的一阶变分。
We consider general surface energies, which are weighted integrals over a closed surface with a weight function depending on the position, the unit normal and the total curvature of the surface. Ene...
We consider a family of high-order, weighted essentially non-oscillatory central schemes (CWENO) for approximating solutions of one-dimensional hyperbolic systems of conservation laws. We are interest...
We generalize the theorem of E. Cattani, P. Deligne, and A. Kaplan to admissible variations of mixed Hodge structure.
Copy number changes, the gains and losses of chromosome segments, are a common type of genetic variation among healthy individuals as well as an important feature in tumor genomes. Microarray techno...
We present an alternating augmented Lagrangian method for convex optimization problems where the cost function is the sum of two terms, one that is separable in the variable blocks, and a second that ...
This paper describes newly invented multiscale transforms known under the name of the ridgelet [6] and the curvelet transforms [9, 8]. These systems combine ideas of multiscale analysis and geometry. ...
Intellectual disability (ID) is a highly heritable mental disease. Especially, the underlying molecular mechanism of non-syndromic intellectual disability (NSID), a subtype of ID with no ...
A generalized complex manifold which satisfies the $\partial \overline{\partial}$-lemma admits a Hodge decomposition in twisted cohomology. Using a Courant algebroid theoretic approach we study the be...
We consider the functional regular variation in the space $\mathbb{D}$ of c\`adl\`ag functions of multivariate mixed moving average (MMA) processes of the type $X_t = \int\int f(A, t - s) \Lambda (d A...
Abstract: This paper is concerned with the numerical minimization of energy functionals in $BV(\Omega)$ (the space of bounded variation functions) involving total variation for gray-scale 1-dimensiona...
Abstract: We consider the dynamics of the Total Variation Flow (TVF) $u_t=\div(Du/|Du|)$ and of the Sign Fast Diffusion Equation (SFDE) $u_t=\Delta\sign(u)$ in one spatial dimension. We find the expli...
Abstract: We investigate the properties of absolutely continuous invariant probability measures (ACIPs) for piecewise area preserving maps (PAPs) on $\mathbb{R}^d$. This class of maps unifies piecewis...
Our purpose is to prove the uniqueness of the representation for G-martingales with finite variation.

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