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与一类算术函数关联的矩阵的行列式的下界 被引量:1
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作者 洪绍方 263.net 《数学年刊(A辑)》 CSCD 北大核心 2000年第3期377-382,共6页
设f为一个算术函数,S={x1,…,xn}为一个n元正整数集合.称S为gcd-封闭的,如果对于任意1≤i,j≤n,均有(xi,xj)∈S.以S={y1,…,ym)表示包含S的最小gcd-封闭的正整数集合.设(f{xi,xj))表示一个n×n矩阵,其(i,j... 设f为一个算术函数,S={x1,…,xn}为一个n元正整数集合.称S为gcd-封闭的,如果对于任意1≤i,j≤n,均有(xi,xj)∈S.以S={y1,…,ym)表示包含S的最小gcd-封闭的正整数集合.设(f{xi,xj))表示一个n×n矩阵,其(i,j)项为f在xi与xj的最大公因子(xi,xj)处的值.设(f[xi,xj])表示一个n×n矩阵,其(i,j)项为f在xi与xj的最小公倍数[xi.xj]处的值.本文证明了。(i)如果f∈Cs={f:(f*μ)(d)>0,x∈S,d|x}这里f*μ表示f与μ的Dirichlet来积,μ表示Mobius函数,那么并且(1)取等号当且公当S=(ii)如果f为乘法函数,并且1/f∈Ca,那么并且(2)取等号当且仅当S=。不等式(1)和(2)分别改进了Bourque与Ligh在1993年和1995年所得到的结果。#且(1)$$95llttgS-g;(n)toilk#ffed数,#if}。C。,W4并且问取等号当且仅当S一S. 展开更多
关键词 算术函数 最大公因子 矩阵 行列工 下界
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30Gbit/s Parallel Optical Receiver Module
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作者 陈弘达 贾九春 +1 位作者 裴为华 唐君 《Journal of Semiconductors》 EI CAS CSCD 北大核心 2006年第4期696-699,共4页
A 30Gbit/s receptor module is developed with a CMOS integrated receiver chip(IC) and a GaAs-based 1 × 12 photo detector array of PIN-type. Parallel technology is adopted in this module to realize a high-speed r... A 30Gbit/s receptor module is developed with a CMOS integrated receiver chip(IC) and a GaAs-based 1 × 12 photo detector array of PIN-type. Parallel technology is adopted in this module to realize a high-speed receiver module with medium speed devices. A high-speed printed circuit board(PCB) is designed and produced. The IC chip and the PD array are packaged on the PCB by chip-on-board technology. Flip chip alignment is used for the PD array accurately assembled on the module so that a plug-type optical port is built. Test results show that the module can receive parallel signals at 30Gbit/s. The sensitivity of the module is - 13.6dBm for 10^-13 BER. 展开更多
关键词 receiver module PARALLEL PD array
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Theoretical Studies of Active Power/angle Sub-matrix in Power Flow Jacobian for Power System Analysis
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作者 曹国云 张卿 +1 位作者 钟德成 陈陈 《Journal of Shanghai Jiaotong university(Science)》 EI 2008年第5期562-567,共6页
Properties of the active power/angle sub-matrix in the power flow Jacobian for power system analysis are studied. The sub-matrix is a dominant and irreducible matrix under very general conditions of power systems, so ... Properties of the active power/angle sub-matrix in the power flow Jacobian for power system analysis are studied. The sub-matrix is a dominant and irreducible matrix under very general conditions of power systems, so that it is invertible. Also the necessary conditions for its singularity are given. These theoretical results can be used to clarify the ambiguous understanding of the sub-matrix in current literature, and also provide the theoretical foundations for the applications based on reduced power flow Jaeobian. Numerical simulation on the IEEE 118-bus power system is used to illustrate our results. 展开更多
关键词 dominant matrix irreducible matrix power flow Jacobian reduced power flow aacobian power system analysis V-Q sensitivity
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