This paper proposes a stochastic dynamics model in which people who are endowed with different discount factors chose to buy the capital stock periodically with different periodicities and are exposed to randomness at...This paper proposes a stochastic dynamics model in which people who are endowed with different discount factors chose to buy the capital stock periodically with different periodicities and are exposed to randomness at arithmetic progression times. We prove that the realization of a stochastic equilibrium may render to the people quite unequal benefits. Its proof is based on Erdös Discrepancy Problem that an arithmetic progression sum of any sign sequence goes to infinity, which is recently solved by Terence Tao [1]. The result in this paper implies that in some cases, the sources of inequality come from pure luck.展开更多
Around 1994,Erdos et al.abstracted from their work the following problem:"Given ten points A<sub>ij</sub>,1≤i【j≤5,on a plane and no three of them being collinear,if there are five points A<sub&g...Around 1994,Erdos et al.abstracted from their work the following problem:"Given ten points A<sub>ij</sub>,1≤i【j≤5,on a plane and no three of them being collinear,if there are five points A<sub>k</sub>,1≤k≤5,on the plane,including points at infinity,with at least two points distinct, such that A<sub>i</sub>,A<sub>j</sub>,A<sub>ij</sub>are collinear,where 1≤i【j≤5,is it true that there are only finitely many such A<sub>k</sub>’s?"Erdos et al.obtained the result that generally there are at most 49 groups of such A<sub>k</sub>’s. In this paper,using Clifford algebra and Wu’s method,we obtain the result that generally there are at most 6 such groups of A<sub>k</sub>’s.展开更多
In this paper, we find two integers k0, m of 159 decimal digits such that if k ≡ k0 （mod m）, then none of five consecutive odd numbers k, k - 2, k - 4, k - 6 and k - 8 can be expressed in the form 2^n ± p^α, ...In this paper, we find two integers k0, m of 159 decimal digits such that if k ≡ k0 （mod m）, then none of five consecutive odd numbers k, k - 2, k - 4, k - 6 and k - 8 can be expressed in the form 2^n ± p^α, where p is a prime and n, α are nonnegative integers.展开更多
文摘This paper proposes a stochastic dynamics model in which people who are endowed with different discount factors chose to buy the capital stock periodically with different periodicities and are exposed to randomness at arithmetic progression times. We prove that the realization of a stochastic equilibrium may render to the people quite unequal benefits. Its proof is based on Erdös Discrepancy Problem that an arithmetic progression sum of any sign sequence goes to infinity, which is recently solved by Terence Tao [1]. The result in this paper implies that in some cases, the sources of inequality come from pure luck.
基金This paper is supported partially by the NNSF of China
文摘Around 1994,Erdos et al.abstracted from their work the following problem:"Given ten points A<sub>ij</sub>,1≤i【j≤5,on a plane and no three of them being collinear,if there are five points A<sub>k</sub>,1≤k≤5,on the plane,including points at infinity,with at least two points distinct, such that A<sub>i</sub>,A<sub>j</sub>,A<sub>ij</sub>are collinear,where 1≤i【j≤5,is it true that there are only finitely many such A<sub>k</sub>’s?"Erdos et al.obtained the result that generally there are at most 49 groups of such A<sub>k</sub>’s. In this paper,using Clifford algebra and Wu’s method,we obtain the result that generally there are at most 6 such groups of A<sub>k</sub>’s.
基金the National Natural Science Foundation of China,Grant No 10471064 and 10771103
文摘In this paper, we find two integers k0, m of 159 decimal digits such that if k ≡ k0 （mod m）, then none of five consecutive odd numbers k, k - 2, k - 4, k - 6 and k - 8 can be expressed in the form 2^n ± p^α, where p is a prime and n, α are nonnegative integers.
