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We investigate a one-dimensional model describing the motion of liquid drops sliding down an inclined plane (the so-called quasi-static approximation model). We prove existenceand uniqueness of a solu...
ON THE MODULI SPACE OF POLYGONS IN THE EUCLIDEAN PLANE.
We prove there are finitely many isometry classes of planar central configurations (also called relative equilibria) in the Newtonian 5-body problem, except perhaps if the 5-tuple of positive masses b...
We present a simple constructive proof of the Uniformization Theorem which works for plane domains. The proof is a combination of covering space theory and Koebe's constructive proof of the Riemann ma...
Characteristic numbers of families of maps of nodal curves to P2 are de ned as intersection of natural divisor classes. (This de nition agrees with the usual de nition for families of plane curves.)...
We will have two main characters in these notes: the maximum principle and the sliding method. The latter has a twin, the moving plane method–they are often so indistinguishable that we will count the...
Random Walks and Plane Arrangements in Three Dimensions.
Neighbour search (NS) is the core of any implementations of smoothed particle hydrodynamics (SPH). In this paper, we present an efficient O( N log N) neighbour search method based on the plane sweep (...
We define the disposition polynomial Rm(x1, x2,..., xn) as ∏k=0m-1(x1 + x2 + ... + xn + k). When m=n-1, this polynomial becomes the generating function of plane trees with respect to the number of you...
In the paper, an improved algorithm is presented for Delaunay triangulation of the point-set in the plain. Based on the original algorithm, we propose the notion of removing circle. During the process...
A numerical analysis has been carried out to study the problem of plane stagnation double-diffusive MHD convective flow with convective boundary condition in a porous media. The governing nonlinear pa...
The method of enhanced assumed strains (EAS) is a popular tool for avoiding locking phenomena, e.g., a remedy for shear locking in plane elasticity. We consider bending-dominated problems and prove ...
In this paper we extend the concept of Milnor fiber and Milnor number of a curve singularity allowing the ambient space to be a quotient surface singularity. A generalization of the local {\delta}-inv...
We consider planar solutions to certain quasilinear elliptic equations subject to the Dirichlet boundary conditions. We show that if the boundary data has finite number of relative maxima and minima t...
We isolate a general class of smooth rational cubic fourfolds containing a plane whose associated quadric surface bundle does not have a rational section. Equivalently, the Brauer class of the even Cl...

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