In this paper,we study compressed data separation(CDS)problem,i.e.,sparse data separation from a few linear random measurements.We propose the nonconvex ℓ_(q)-split analysis with ℓ_(∞)-constraint and 0<q≤1.We cal...In this paper,we study compressed data separation(CDS)problem,i.e.,sparse data separation from a few linear random measurements.We propose the nonconvex ℓ_(q)-split analysis with ℓ_(∞)-constraint and 0<q≤1.We call the algorithm ℓ_(q)-split-analysis Dantzig selector(ℓ_(q)-split-analysis DS).We show that the two distinct subcomponents that are approximately sparse in terms of two different dictionaries could be stably approximated via the ℓ_(q)-split-analysis DS,provided that the measurement matrix satisfies either a classical D-RIP(Restricted Isometry Property with respect to Dictionaries and ℓ_(2) norm)or a relatively new(D,q)-RIP(RIP with respect to Dictionaries and ℓ_(q)-quasi norm)condition and the two different dictionaries satisfy a mutual coherence condition between them.For the Gaussian random measurements,the measurement number needed for the(D,q)-RIP condition is far less than those needed for the D-RIP condition and the(D,1)-RIP condition when q is small enough.展开更多
利用基于密度泛函理论(DFT)的Dmol^(3)程序广义梯度近似PBE泛函,研究了Co^(q)_(n)(n=1~5;q=0,+,-)团簇和原子氧吸附在团簇上的几何结构、稳定性、电子性质和吸附反应行为。结果表明:Co^(q)_(n)团簇的几何结构保持不变,阳离子型团簇(Co^(...利用基于密度泛函理论(DFT)的Dmol^(3)程序广义梯度近似PBE泛函,研究了Co^(q)_(n)(n=1~5;q=0,+,-)团簇和原子氧吸附在团簇上的几何结构、稳定性、电子性质和吸附反应行为。结果表明:Co^(q)_(n)团簇的几何结构保持不变,阳离子型团簇(Co^(+)_(n))的平均结合能远大于中性型(Co^(0)_(n))和阴离子型(Co^(-)_(n))团簇的平均结合能,这是因为团簇失去一个电子后可以显著增强该团簇的稳定性;原子氧在Co^(q)_(n)团簇顶位、桥位、空位的吸附稳定性、Co—O键长、原子氧的电荷转移都呈现出规律性变化,说明原子氧被活化;Co^(-)_(4) O B团簇的吸附能为-8.375 eV,轨道分析进一步表明其原子氧的2p轨道和钴的3d轨道杂化,相互作用为化学吸附。展开更多
Influenced by the fact that vorticity represents rotation for rigid body,people believe this idea also works for fluid flow.However,the vortex predictions by vorticity do not match experimental results,which drove sci...Influenced by the fact that vorticity represents rotation for rigid body,people believe this idea also works for fluid flow.However,the vortex predictions by vorticity do not match experimental results,which drove scientists to look for more appropriate methods to identify vortex.All vortex identification methods can be categorized into three generations.The vorticity-based method is classified as the first generation.Methods relying on eigenvalues of velocity gradient tensor are considered as the second generation.People still believe vorticity is vortex since vorticity theory looks correct in mathematics,but all other methods are only scalars and unable to indicate the swirl direction.Recently,a new vortex identification method called Liutex is innovated.It is regarded as the third-generation method,not only overcoming all previous methods’drawbacks but also having a clear physical meaning.The direction of Liutex represents the swirl axis of rotation,and its strength is equal to twice the angular speed.In this paper,we did a correlation analysis between vorticity,Q,λ_(ci),λ_(2)methods and Liutex based on a direct numerical simulation(DNS)case of boundary layer transition.The results show that the correlation between vorticity and Liutex is very small or even negative in strong shear regions,which demonstrates that using vorticity to detect vortex lacks scientific foundation and vorticity is not appropriate to represent vortex.The correlation analysis also shows that the second generation is contaminated too by shear and thus is not accurate to identify the vortex structure.展开更多
数独是一个难以求解的整数规划问题,可以通过实数编码的方式去除整数约束的限制,将整数规划模型转化为一个ℓ_(0)范数极小化模型.已有算法大多是求解松弛的ℓ1范数极小化模型,只能求解部分数独问题.本文证明对于数独这样一个特殊的问题,ℓ_...数独是一个难以求解的整数规划问题,可以通过实数编码的方式去除整数约束的限制,将整数规划模型转化为一个ℓ_(0)范数极小化模型.已有算法大多是求解松弛的ℓ1范数极小化模型,只能求解部分数独问题.本文证明对于数独这样一个特殊的问题,ℓ_(q)(0<q<1)范数极小化模型等价于ℓ_(0)范数极小化模型,同时用ℓ_(1/2)-SLP(sequential linear programming)算法求解ℓ_(1/2)范数极小化模型.数值实验表明该方法可以求解更多的数独问题,本文从时间和成功率两方面验证了算法的高效性.展开更多
基金Supported by the National Key Research and Development Program of China(Grant No.2021YFA1003500)the NSFC(Grant Nos.U21A20426,11971427,12071426 and 11901518)。
文摘In this paper,we study compressed data separation(CDS)problem,i.e.,sparse data separation from a few linear random measurements.We propose the nonconvex ℓ_(q)-split analysis with ℓ_(∞)-constraint and 0<q≤1.We call the algorithm ℓ_(q)-split-analysis Dantzig selector(ℓ_(q)-split-analysis DS).We show that the two distinct subcomponents that are approximately sparse in terms of two different dictionaries could be stably approximated via the ℓ_(q)-split-analysis DS,provided that the measurement matrix satisfies either a classical D-RIP(Restricted Isometry Property with respect to Dictionaries and ℓ_(2) norm)or a relatively new(D,q)-RIP(RIP with respect to Dictionaries and ℓ_(q)-quasi norm)condition and the two different dictionaries satisfy a mutual coherence condition between them.For the Gaussian random measurements,the measurement number needed for the(D,q)-RIP condition is far less than those needed for the D-RIP condition and the(D,1)-RIP condition when q is small enough.
文摘利用基于密度泛函理论(DFT)的Dmol^(3)程序广义梯度近似PBE泛函,研究了Co^(q)_(n)(n=1~5;q=0,+,-)团簇和原子氧吸附在团簇上的几何结构、稳定性、电子性质和吸附反应行为。结果表明:Co^(q)_(n)团簇的几何结构保持不变,阳离子型团簇(Co^(+)_(n))的平均结合能远大于中性型(Co^(0)_(n))和阴离子型(Co^(-)_(n))团簇的平均结合能,这是因为团簇失去一个电子后可以显著增强该团簇的稳定性;原子氧在Co^(q)_(n)团簇顶位、桥位、空位的吸附稳定性、Co—O键长、原子氧的电荷转移都呈现出规律性变化,说明原子氧被活化;Co^(-)_(4) O B团簇的吸附能为-8.375 eV,轨道分析进一步表明其原子氧的2p轨道和钴的3d轨道杂化,相互作用为化学吸附。
文摘Influenced by the fact that vorticity represents rotation for rigid body,people believe this idea also works for fluid flow.However,the vortex predictions by vorticity do not match experimental results,which drove scientists to look for more appropriate methods to identify vortex.All vortex identification methods can be categorized into three generations.The vorticity-based method is classified as the first generation.Methods relying on eigenvalues of velocity gradient tensor are considered as the second generation.People still believe vorticity is vortex since vorticity theory looks correct in mathematics,but all other methods are only scalars and unable to indicate the swirl direction.Recently,a new vortex identification method called Liutex is innovated.It is regarded as the third-generation method,not only overcoming all previous methods’drawbacks but also having a clear physical meaning.The direction of Liutex represents the swirl axis of rotation,and its strength is equal to twice the angular speed.In this paper,we did a correlation analysis between vorticity,Q,λ_(ci),λ_(2)methods and Liutex based on a direct numerical simulation(DNS)case of boundary layer transition.The results show that the correlation between vorticity and Liutex is very small or even negative in strong shear regions,which demonstrates that using vorticity to detect vortex lacks scientific foundation and vorticity is not appropriate to represent vortex.The correlation analysis also shows that the second generation is contaminated too by shear and thus is not accurate to identify the vortex structure.
文摘数独是一个难以求解的整数规划问题,可以通过实数编码的方式去除整数约束的限制,将整数规划模型转化为一个ℓ_(0)范数极小化模型.已有算法大多是求解松弛的ℓ1范数极小化模型,只能求解部分数独问题.本文证明对于数独这样一个特殊的问题,ℓ_(q)(0<q<1)范数极小化模型等价于ℓ_(0)范数极小化模型,同时用ℓ_(1/2)-SLP(sequential linear programming)算法求解ℓ_(1/2)范数极小化模型.数值实验表明该方法可以求解更多的数独问题,本文从时间和成功率两方面验证了算法的高效性.
