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Some results on Chern's problem
minimal hypersurface pinching problem Clifford minimal hypersurface
2011/1/18
For a compact minimal hypersurface M in Sn+1 with the squared length of the second fundamental form S we confirm that there exists a positive constant (n) depending only on n, such that if n ≤ S ≤ n ...
On the Combinatorial Multi-Armed Bandit Problem with Markovian Rewards
Combinatorial Multi-Armed Bandit Problem Markovian Rewards
2011/1/21
We consider a combinatorial generalization of the classical multi-armed bandit problem that is defined as follows.There is a given bipartite graph of M users and N M resources.
Solution for the problem of the game heads or tails
Solution；problem of the game heads；tails
2011/1/17
In this paper, we describe the solution for a problem dealing with definite properties of binary sequences. This problem, proposed by Xavier Grandsart in the form of a mathematical contest [1], has be...
Relative Equilibria of the $(1+N)$-Vortex Problem
Relative Equilibria $(1+N)$-Vortex Problem
2011/1/18
We examine existence and stability of relative equilibria of the n-vortex problem specialized to the case where N vortices have small and equal circulation and one vortex has large circulation.
On the limit behavior of metrics in continuity method to Kahler-Einstein problem in toric Fano case
limit behavior of metrics continuity method Kahler-Einstein problem
2011/2/25
This is a continuation of paper [7]. On any toric Fano manifold, we discuss the behavior of limit metric of a sequence of metrics, which are solutions to a continuity family of complex Monge-Amp`ere e...
A new characterization of Carmichael numbers via a generalization of Lehmer's totient problem
new characterization Carmichael numbers generalization of Lehmer's totient problem
2011/1/20
Lehmer’s totient problem consists of determining the set of positive integers n such that '(n)|n − 1 where ' is Euler’s totient function. Any such composite number is a Carmichael number.
On a finite element approximation of the Stokes problem under leak or slip boundary conditions of friction type
Finite element method Stokes equations Boundary conditions of friction type
2011/2/25
A nite element approximation of the Stokes equations under a certain nonlinear boundary condition, namely, the slip or leak boundary con-dition of friction type, is considered. We propose an approxim...
Two phase Stefan-type problem: Regularization near initial data by phase dynamics
Two phase Stefan-type problem Regularization initial data phase dynamics
2011/1/18
In this paper we investigate the regularizing behavior of two-phase Stefan problem near initial data. The main step in the analysis is to establish that in any given scale, the scaled solution is very...