In this paper, we investigate the Hansdorff dimension of a class of exceptional sets occurring in Oppenheim series expansion. As an application, we get the exact Hansdorff dimension of the set in Liiroth series expans...In this paper, we investigate the Hansdorff dimension of a class of exceptional sets occurring in Oppenheim series expansion. As an application, we get the exact Hansdorff dimension of the set in Liiroth series expansion. Moreover, we give an estimate of such dimensional number.展开更多
For Oppenheim series epansions, the authors of [7] discussed the exceptional sets Bm={x∈（0,1]：1〈dj（x）/h（j-1）（d（j-1）（x））≤m for any j ≥2} In this paper, we investigate the Hausdorff dimension of a kind o...For Oppenheim series epansions, the authors of [7] discussed the exceptional sets Bm={x∈（0,1]：1〈dj（x）/h（j-1）（d（j-1）（x））≤m for any j ≥2} In this paper, we investigate the Hausdorff dimension of a kind of exceptional sets occurring in alternating Oppenheim series expansion. As an application, we get the exact Hausdorff dimension of the-set in Luroth series expansion, also we give an estimate of such dimensional number.展开更多
完全非负矩阵在Hadamard乘积意义下是不封闭的。对于两个三对角完全非负矩阵A=(a_(ij)),B=(b_(ij)),Markham证明了它们的Hadamard乘积的行列式满足Oppenheim不等式。我们应用完全非负矩阵的Hadamard中心的性质,改进了Markham的相应结果...完全非负矩阵在Hadamard乘积意义下是不封闭的。对于两个三对角完全非负矩阵A=(a_(ij)),B=(b_(ij)),Markham证明了它们的Hadamard乘积的行列式满足Oppenheim不等式。我们应用完全非负矩阵的Hadamard中心的性质,改进了Markham的相应结果,给出了新的下界(A_1为删去第一行的A的主子矩阵):det(AB)≥(multiply from i=1 to n b_(ii))detA+(multiply from i=1 to n a_(ii))detB-detAdetB+(detA)((multiply from i=2 to n a_(ii)/detA_1)-1)(b_(11)detB_1-detB)+(detB)((multiply from i=2 to n b_(ii)/detB_1)-1)(a_(11)detA_1-detA)。展开更多
文摘In this paper, we investigate the Hansdorff dimension of a class of exceptional sets occurring in Oppenheim series expansion. As an application, we get the exact Hansdorff dimension of the set in Liiroth series expansion. Moreover, we give an estimate of such dimensional number.
文摘For Oppenheim series epansions, the authors of [7] discussed the exceptional sets Bm={x∈（0,1]：1〈dj（x）/h（j-1）（d（j-1）（x））≤m for any j ≥2} In this paper, we investigate the Hausdorff dimension of a kind of exceptional sets occurring in alternating Oppenheim series expansion. As an application, we get the exact Hausdorff dimension of the-set in Luroth series expansion, also we give an estimate of such dimensional number.
基金Supported by the Science Foundation of Fujian Educational Department (JA03159) the Science ResearchFoundation of Putian University(2004Q003 2004Q002)
文摘完全非负矩阵在Hadamard乘积意义下是不封闭的。对于两个三对角完全非负矩阵A=(a_(ij)),B=(b_(ij)),Markham证明了它们的Hadamard乘积的行列式满足Oppenheim不等式。我们应用完全非负矩阵的Hadamard中心的性质,改进了Markham的相应结果,给出了新的下界(A_1为删去第一行的A的主子矩阵):det(AB)≥(multiply from i=1 to n b_(ii))detA+(multiply from i=1 to n a_(ii))detB-detAdetB+(detA)((multiply from i=2 to n a_(ii)/detA_1)-1)(b_(11)detB_1-detB)+(detB)((multiply from i=2 to n b_(ii)/detB_1)-1)(a_(11)detA_1-detA)。
