Edgebreaker and valence-driven approaches use split operations to separate the 3D model into two components. These algorithms raise some bottlenecks for spending increased overheads to record the displacement, or an extra operator is needed for identifying the branch. This study applies an edge-based compression strategy, and proposes using the J operator… (More)
Here we initiate the program for computing the Leray-Schauder topological degree for SU (3) Toda system. This program still contains a lot of challenging problems for analysts. The first step of our approach is to answer whether concentration phenomena holds or not. In this paper, we prove the concentration phenomena holds while ρ 1 crosses 4π, and ρ 2 / ∈… (More)
We give a new bound on the exponent for nonexistence of stable solutions to the biharmonic problem ∆ 2 u = u p , u > 0 in R n where p > 1, n ≥ 20.
SUMMARY This study proposes an edge-based single-resolution compression scheme for triangular mesh connectivity. The proposed method improves upon EdgeBreaker. Nearly all of these algorithms are either multiple traversals or operate in reverse order. Operating in reverse order should work only off-line in the EdgeBreaker decompression process. Many… (More)
We consider the stationary radial solution in the classical Gierer
We consider the following class of equations with exponential nonlinearities on a compact surface M :
The aim of this paper is to use a selection process and a careful study of the interaction of bubbling solutions to show a classification result for the blow-up values of the elliptic sinh-Gordon equation ∆u + h 1 e u − h 2 e −u = 0 in B 1 ⊂ R 2. In particular we show that the blow-up values are multiple of 8π. It generalizes the result of Jost, Wang, Ye… (More)
We develop gluing method for fourth order ODEs and construct infinitely many non-radial singular solutions for a bi-harmonic equation with supercritical exponent.
We consider the following nonlinear Neumann problem: ∆u − µu + u q = 0 in Ω, u > 0 in Ω, ∂u ∂ν = 0 on ∂Ω, where Ω ⊂ R n is a smooth and bounded domain, µ > 0 and ν denotes the outward unit normal vector of Ω. Lin and Ni (1986) conjectured that when q = n+2 n−2 , for µ small, all solutions are constants. We show that this conjecture is false for… (More)