在研究圆周上的van der Waerden数的过程中,将van der Waerden问题转化为矩阵形式的线性不等式组的求解问题,想通过解这个不等式组,来找出van der Waerden数Wh(n,n)的更好的上界.在p=nr±1这两种情况下,我们求得了关于x和bk的p个分...在研究圆周上的van der Waerden数的过程中,将van der Waerden问题转化为矩阵形式的线性不等式组的求解问题,想通过解这个不等式组,来找出van der Waerden数Wh(n,n)的更好的上界.在p=nr±1这两种情况下,我们求得了关于x和bk的p个分量的参数表达.展开更多
Abstract. Let H^n be the Heisenberg group and Q = 2n＋2 be its homogeneous dimen- sion. In this paper, we consider the Schr6dinger operator -△H^n ＋V, where △H^n is the sub-Laplacian and V is the nonnegative potenti...Abstract. Let H^n be the Heisenberg group and Q = 2n＋2 be its homogeneous dimen- sion. In this paper, we consider the Schr6dinger operator -△H^n ＋V, where △H^n is the sub-Laplacian and V is the nonnegative potential belonging to the reverse H61der class Bql for ql _〉 Q/2. We show that the operators T1 = V（-△H^n-In ＋V）-1 and T2 = V1/2（-△H^n-V）-1/2 are both bounded from 1 n HL^1（H^n ） into L1（H^n）. Our results are also valid on the stratified Lie group.展开更多
证明:若(xij)是一个元素不全为零的m×n非负矩阵,则当0<p<1时,有(m^(p-1)sum from i=1 to m ( ) r_i^p+n^(p-1) sum form j=1 to n ( ) c_j^p)/sum form to i=1 to m ( ) sum form to j=1 to n ( ) x_(ij)~p+(mn)^(p-1) sum ...证明:若(xij)是一个元素不全为零的m×n非负矩阵,则当0<p<1时,有(m^(p-1)sum from i=1 to m ( ) r_i^p+n^(p-1) sum form j=1 to n ( ) c_j^p)/sum form to i=1 to m ( ) sum form to j=1 to n ( ) x_(ij)~p+(mn)^(p-1) sum form to i=1 to m ( ) sum form to j=1 to n ( )x_(ij)~p ≤m^(p-1)+n^(p-1)/(mn)^(p-1)+min(m^(p-1)),n^(p-1).这一结果是对2002年Yang Xiaojing发表在Linear Algebra and its Application上的当p1时此不等式的反向不等式的一个补充,使整个不等式得以更加完整.展开更多
基金Supported by National Natural Science Foundation of China(10471048)Research Foundation of Hubei Education Committee(B20092809)Research Foundation of Xianning University(Bk0714)
文摘Abstract. Let H^n be the Heisenberg group and Q = 2n＋2 be its homogeneous dimen- sion. In this paper, we consider the Schr6dinger operator -△H^n ＋V, where △H^n is the sub-Laplacian and V is the nonnegative potential belonging to the reverse H61der class Bql for ql _〉 Q/2. We show that the operators T1 = V（-△H^n-In ＋V）-1 and T2 = V1/2（-△H^n-V）-1/2 are both bounded from 1 n HL^1（H^n ） into L1（H^n）. Our results are also valid on the stratified Lie group.
文摘证明:若(xij)是一个元素不全为零的m×n非负矩阵,则当0<p<1时,有(m^(p-1)sum from i=1 to m ( ) r_i^p+n^(p-1) sum form j=1 to n ( ) c_j^p)/sum form to i=1 to m ( ) sum form to j=1 to n ( ) x_(ij)~p+(mn)^(p-1) sum form to i=1 to m ( ) sum form to j=1 to n ( )x_(ij)~p ≤m^(p-1)+n^(p-1)/(mn)^(p-1)+min(m^(p-1)),n^(p-1).这一结果是对2002年Yang Xiaojing发表在Linear Algebra and its Application上的当p1时此不等式的反向不等式的一个补充,使整个不等式得以更加完整.
