Given a positive definite matrix measure Ω supported on the unit circle T, then main purpose of this paper is to study the asymptotic behavior of L n()L n(Ω) -1 and Φ n(z;)Φ n(z;Ω) -1 where(z)=Ω(z)+Mδ(z-w...Given a positive definite matrix measure Ω supported on the unit circle T, then main purpose of this paper is to study the asymptotic behavior of L n()L n(Ω) -1 and Φ n(z;)Φ n(z;Ω) -1 where(z)=Ω(z)+Mδ(z-w); |w|>1,M is a positive definite matrix and δ is the Dirac matrix measure. Here, L n(·) means the leading coefficient of the orthonormal matrix polynomials Φ n(z;·). Finally, we deduce the asymptotic behavior of Φ n(w;)Φ n(w;Ω)* in the case when M=I.展开更多
为有效控制输电塔的有害振动需要了解其振动特性,提出一种惯性测量数据矩阵模式的输电塔振动分析方法。将微惯性测量单元(Micro-Inertia-Measurement-Unit,MIMU)安装在输电塔上通过Kalman滤波预处理三轴原始数据,重构权重奇异值分解(Wei...为有效控制输电塔的有害振动需要了解其振动特性,提出一种惯性测量数据矩阵模式的输电塔振动分析方法。将微惯性测量单元(Micro-Inertia-Measurement-Unit,MIMU)安装在输电塔上通过Kalman滤波预处理三轴原始数据,重构权重奇异值分解(Weighted Singular Value Decomposition,WSVD)后的相干振动分量建立平动/扭动矩阵。提取矩阵序列中的变换矩阵,计算其Frobenius范数度量暂态振动间的变异度来估计幅值与频率。根据幅频参数计算振动耗能,观测输电塔各轴向以及整体的振动情况。最后设计振动台、转台实验验证振动数据处理方法的有效性,并对不同风荷载下的塔线模型与真型风振试验进行特性分析。结果表明输电塔振动以水平方向的平动形式为主,随风向夹角的增大其非线性效应逐渐增强,所提出的数据处理方法能够有效获得振动信息,可为控制有害振动的阻尼器的设计提供参考。展开更多
在图形处理器(GPU)上实现对角稀疏矩阵向量乘法(SpMV)可以充分利用GPU的并行计算能力,并加速矩阵向量乘法;然而,相关主流算法存在零元填充数据多、计算效率低的问题。针对上述问题,提出一种对角SpMV算法DIA-Dynamic(DIAgonal-Dynamic)...在图形处理器(GPU)上实现对角稀疏矩阵向量乘法(SpMV)可以充分利用GPU的并行计算能力,并加速矩阵向量乘法;然而,相关主流算法存在零元填充数据多、计算效率低的问题。针对上述问题,提出一种对角SpMV算法DIA-Dynamic(DIAgonal-Dynamic)。首先,设计一种全新的动态划分策略,根据矩阵的不同特征进行分块,在保证GPU高计算效率的同时大幅减少零元填充,去除冗余计算量;其次,提出一种对角稀疏矩阵存储格式BDIA(Block DIAgonal)存储分块数据,并调整数据布局,提高GPU上的访存性能;最后,基于GPU的底层进行条件分支优化,以减少分支判断,并使用动态共享内存解决向量的不规则访问问题。DIA-Dynamic与前沿Tile SpMV算法相比,平均加速比达到了1.88;与前沿BRCSD(Diagonal Compressed Storage based on Row-Blocks)-Ⅱ算法相比,平均零元填充减少了43%,平均加速比达到了1.70。实验结果表明,DIA-Dynamic能够有效提高GPU上对角SpMV的计算效率,缩短计算时间,提升程序性能。展开更多
This study introduces the representation of natural number sets as row vectors and pretends to offer a new perspective on the strong Goldbach conjecture. The natural numbers are restructured and expanded with the incl...This study introduces the representation of natural number sets as row vectors and pretends to offer a new perspective on the strong Goldbach conjecture. The natural numbers are restructured and expanded with the inclusion of the zero element as the source of a strong Goldbach conjecture reformulation. A prime Boolean vector is defined, pinpointing the positions of prime numbers within the odd number sequence. The natural unit primality is discussed in this context and transformed into a source of quantum-like indetermination. This approach allows for rephrasing the strong Goldbach conjecture, framed within a Boolean scalar product between the prime Boolean vector and its reverse. Throughout the discussion, other intriguing topics emerge and are thoroughly analyzed. A final description of two empirical algorithms is provided to prove the strong Goldbach conjecture.展开更多
文摘Given a positive definite matrix measure Ω supported on the unit circle T, then main purpose of this paper is to study the asymptotic behavior of L n()L n(Ω) -1 and Φ n(z;)Φ n(z;Ω) -1 where(z)=Ω(z)+Mδ(z-w); |w|>1,M is a positive definite matrix and δ is the Dirac matrix measure. Here, L n(·) means the leading coefficient of the orthonormal matrix polynomials Φ n(z;·). Finally, we deduce the asymptotic behavior of Φ n(w;)Φ n(w;Ω)* in the case when M=I.
文摘为有效控制输电塔的有害振动需要了解其振动特性,提出一种惯性测量数据矩阵模式的输电塔振动分析方法。将微惯性测量单元(Micro-Inertia-Measurement-Unit,MIMU)安装在输电塔上通过Kalman滤波预处理三轴原始数据,重构权重奇异值分解(Weighted Singular Value Decomposition,WSVD)后的相干振动分量建立平动/扭动矩阵。提取矩阵序列中的变换矩阵,计算其Frobenius范数度量暂态振动间的变异度来估计幅值与频率。根据幅频参数计算振动耗能,观测输电塔各轴向以及整体的振动情况。最后设计振动台、转台实验验证振动数据处理方法的有效性,并对不同风荷载下的塔线模型与真型风振试验进行特性分析。结果表明输电塔振动以水平方向的平动形式为主,随风向夹角的增大其非线性效应逐渐增强,所提出的数据处理方法能够有效获得振动信息,可为控制有害振动的阻尼器的设计提供参考。
文摘在图形处理器(GPU)上实现对角稀疏矩阵向量乘法(SpMV)可以充分利用GPU的并行计算能力,并加速矩阵向量乘法;然而,相关主流算法存在零元填充数据多、计算效率低的问题。针对上述问题,提出一种对角SpMV算法DIA-Dynamic(DIAgonal-Dynamic)。首先,设计一种全新的动态划分策略,根据矩阵的不同特征进行分块,在保证GPU高计算效率的同时大幅减少零元填充,去除冗余计算量;其次,提出一种对角稀疏矩阵存储格式BDIA(Block DIAgonal)存储分块数据,并调整数据布局,提高GPU上的访存性能;最后,基于GPU的底层进行条件分支优化,以减少分支判断,并使用动态共享内存解决向量的不规则访问问题。DIA-Dynamic与前沿Tile SpMV算法相比,平均加速比达到了1.88;与前沿BRCSD(Diagonal Compressed Storage based on Row-Blocks)-Ⅱ算法相比,平均零元填充减少了43%,平均加速比达到了1.70。实验结果表明,DIA-Dynamic能够有效提高GPU上对角SpMV的计算效率,缩短计算时间,提升程序性能。
文摘This study introduces the representation of natural number sets as row vectors and pretends to offer a new perspective on the strong Goldbach conjecture. The natural numbers are restructured and expanded with the inclusion of the zero element as the source of a strong Goldbach conjecture reformulation. A prime Boolean vector is defined, pinpointing the positions of prime numbers within the odd number sequence. The natural unit primality is discussed in this context and transformed into a source of quantum-like indetermination. This approach allows for rephrasing the strong Goldbach conjecture, framed within a Boolean scalar product between the prime Boolean vector and its reverse. Throughout the discussion, other intriguing topics emerge and are thoroughly analyzed. A final description of two empirical algorithms is provided to prove the strong Goldbach conjecture.
