Let Bn be the set of all n×n Boolean Matrices; R（A） denote the row space of A∈Bn, ｜R（A）｜ denote the cardinality of R（A）, m, n, k, l, t, i, γi be positive integers, Si, λi be non negative integers. In t...Let Bn be the set of all n×n Boolean Matrices; R（A） denote the row space of A∈Bn, ｜R（A）｜ denote the cardinality of R（A）, m, n, k, l, t, i, γi be positive integers, Si, λi be non negative integers. In this paper, we prove the following two results：（1）Let n≥13,n-3≥k〉Sl,Si＋〉Si,i=1,2…,l-1.if k＋l≤n,then for any m=2^k＋2^S1-l＋…＋2^S1,there exists A∈Bn,such that ｜R（A）｜=m.（2）Let n≥13,n-3≥k〉Sn-k-1〉Sn-k-2〉…S1〉λt〉λt-1〉…〉λ1,2≤t≤n-k.If exist γi（k＋1≤γi≤n-1,i=1,2…,t-1）γi〈γi＋1 and λt-λt-1≤k-Sn-γ1,λt-i-λt-i-1≤Sn-γi-Sn-γii＋1,i=1,2…,t-2,then for any m=2^k＋2^Sn-k-1＋2^Sn-k-1＋2^Sn-k-2＋…＋2^S1＋2^λt＋2^λt-1…＋2^λ1,there exists A∈Bn,as such that ｜R（A）｜=m.展开更多
In this paper, we introduce the concept of AK-property for the perfect ma-trix algebras ∑(λ) and give some characterizations of∑(λ)possessing AK-property.
The problem of fast computing the QR factorization of row or column symmetric matrix isconsidered. We address two new algorithms based on a correspondence of Q and R matrices between the rowor column symmetric matrix ...The problem of fast computing the QR factorization of row or column symmetric matrix isconsidered. We address two new algorithms based on a correspondence of Q and R matrices between the rowor column symmetric matrix and its mother matrix. Theoretical analysis and numerical evidence show that, fora class of row or column symmetric matrices, the QR factorization using the mother matrix rather than therow or column symmetric matrix per se can save dramatically the CPU time and memory without loss of anynumerical precision.展开更多
基金Foundation item： Supported by the Guangdong Provincial Natural Science Foundation of China（06029035）
文摘Let Bn be the set of all n×n Boolean Matrices; R（A） denote the row space of A∈Bn, ｜R（A）｜ denote the cardinality of R（A）, m, n, k, l, t, i, γi be positive integers, Si, λi be non negative integers. In this paper, we prove the following two results：（1）Let n≥13,n-3≥k〉Sl,Si＋〉Si,i=1,2…,l-1.if k＋l≤n,then for any m=2^k＋2^S1-l＋…＋2^S1,there exists A∈Bn,such that ｜R（A）｜=m.（2）Let n≥13,n-3≥k〉Sn-k-1〉Sn-k-2〉…S1〉λt〉λt-1〉…〉λ1,2≤t≤n-k.If exist γi（k＋1≤γi≤n-1,i=1,2…,t-1）γi〈γi＋1 and λt-λt-1≤k-Sn-γ1,λt-i-λt-i-1≤Sn-γi-Sn-γii＋1,i=1,2…,t-2,then for any m=2^k＋2^Sn-k-1＋2^Sn-k-1＋2^Sn-k-2＋…＋2^S1＋2^λt＋2^λt-1…＋2^λ1,there exists A∈Bn,as such that ｜R（A）｜=m.
文摘In this paper, we introduce the concept of AK-property for the perfect ma-trix algebras ∑(λ) and give some characterizations of∑(λ)possessing AK-property.
文摘三维超快成像是超声技术发展的重要方向.基于二维全采样阵列的传统三维成像方法需要较多成像阵元和采样通道,其紧密的阵元排列设计也客观上限制了阵列孔径大小和成像分辨率.行列寻址(row-column addressing,RCA)探头以行列检索的方式将通道数自N×N减少为N+N,从而极大地降低了阵列的硬件实现成本.本文仿真了中心频率为6MHz的128行+128列的RCA阵列,结合多角度平面波正交复合成像方法,通过延时叠加(delay and sum,DAS)波束合成、基于特征值分解(singular value decomposition,SVD)的杂波滤除和自相关多普勒速度求解算法,实现了血流仿体的多普勒成像,并分析了不同复合角度序列对成像效果的影响.定量分析表明,当角度数从5个增至33个时,-6 dB分辨率从0.986 mm提升至0.493 mm;当复合角度为17个时,功率多普勒图像的SNR可达30 dB,彩色多普勒沿直径方向的速度分布和真实值的平均误差约为26.0%.以上结果表明,基于RCA阵列的三维成像技术能够获得三维B-mode、功率多普勒和彩色多普勒图像,增大复合平面波角度数和角度范围可显著提高成像质量.本研究对于三维超快超声多普勒成像技术发展具有借鉴意义,相关方法有应用于血流血管成像,并进一步实现基于神经-血管耦合的组织功能监测与成像的潜力和前景.
基金This work was supported by the National Natural Science Foundation of China (Nos.60172026 & 60172005) the Basic Research Foundation of Tsinghua University (No. JC2001028)the Scientific Innovation Foundation of Ph.D. Candidates of Tsinghua Universit
文摘The problem of fast computing the QR factorization of row or column symmetric matrix isconsidered. We address two new algorithms based on a correspondence of Q and R matrices between the rowor column symmetric matrix and its mother matrix. Theoretical analysis and numerical evidence show that, fora class of row or column symmetric matrices, the QR factorization using the mother matrix rather than therow or column symmetric matrix per se can save dramatically the CPU time and memory without loss of anynumerical precision.
