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A class of nonlinear integrable PDEs admit non-smooth solitary wave solutions as certain special weak solutions. These solutions can be used to capture main attributes of solutions of these PDEs, e.g....
Whether the 3D incompressible Euler equations can develop a finite-time singularity from smooth initial data is an outstanding open problem. In this talk, we will first review recent progress in singu...
Nematic liquid crystals (NLCs) are anisotropic material intermediate that combine the fluidity of liquids with the orientational order of solids. NLCs are best known for their applications in the thri...
The moduli space of a smooth manifold X is defined to be the classifying space of its diffeomorphism group. Understanding the cohomology group of this space is important because elements in this group...
We show that for every nonelementary representation of a surface group into SL(2, C) there is a Riemann surface structure such that the Higgs bundle associated to the representation lies outside the d...
On representation varieties of Artin groups,projective arrangements and the fundamental groups of smooth complex algebraic varieties.
PIECEWISE SMOOTH PERTURBATIONS OF INTEGRABLE SYSTEMS     INTEGRABLE SYSTEMS  PERTURBATIONS       font style='font-size:12px;'> 2015/9/29
We review several recent results showing that small piecewise smooth perturbations of integrable systems may exhibit unstable behavior on the set of initial condition of large measure. We also presen...
A Smooth Multivariate Interpolation Algorithm     Interpolation Algorithm  Smooth       font style='font-size:12px;'> 2015/8/25
This brief paper introduces an algorithm for smooth interpolation of a multivariate function. The input data for the algorithm consists of a set of function values and derivatives up to order r on a...
We present a high-order boundary integral equation solver for 3D elliptic boundary value problems on domains with smooth boundaries. We use Nystro ¨m’s method for discretization, and combine it with s...
We nd it interesting that such a natural naive approach as we will describe actually works, and yields a desingularization with these nice properties.
The contractile activation of airway smooth muscle tissues stimulates actin polymerization and the inhibition of actin polymerization inhibits tension development. Actin depolymerizing factor (ADF) an...
Obesity increases cardiovascular disease risk and is associated with factors of the “metabolic syndrome” (MetS), a disorder including hypertension, hypercholesterolemia and/or impaired glucose toleran...
An ultrathin polymer sheet floating on a fluid forms a periodic pattern of parallel wrinkles when subjected to uniaxial compression. The wave number of the wrinkle pattern increases sharply near the f...
The aim of this study was to localize oxytocin receptor (OTR) in the stomach and to investigate the effect of OT on gastric motility in rats. Western blot and immunohistochemistry methods were used to...
We study the regularity of the solutions to initial-boundary value problems for N-systems of the p-Laplacian type, in $n\geq 3$ space variables, with square-integrable external forces in the space-tim...

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