It is shown that an arbitrary function from D Rn to Rm will become C0,a-continuous in almost every x∈ D after restriction to a certain subset with limit pointx. For n 〉 m differentiability can be obtained. Example...It is shown that an arbitrary function from D Rn to Rm will become C0,a-continuous in almost every x∈ D after restriction to a certain subset with limit pointx. For n 〉 m differentiability can be obtained. Examples show the Ho1der exponent a=min{1,n/m}is optimal.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
文摘It is shown that an arbitrary function from D Rn to Rm will become C0,a-continuous in almost every x∈ D after restriction to a certain subset with limit pointx. For n 〉 m differentiability can be obtained. Examples show the Ho1der exponent a=min{1,n/m}is optimal.
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.
