A left ideal I of a ring R is small in case for every proper left ideal K of R, K ＋ I ≠R. A ring R is called left PS-coherent if every principally small left ideal Ra is finitely presented. We develop, in this paper...A left ideal I of a ring R is small in case for every proper left ideal K of R, K ＋ I ≠R. A ring R is called left PS-coherent if every principally small left ideal Ra is finitely presented. We develop, in this paper, PS-coherent rings as a generalization of P-coherent rings and J-coherent rings. To characterize PS-coherent rings, we first introduce PS-injective and PS-flat modules, and discuss the relation between them over some spacial rings. Some properties of left PS-coherent rings are also studied.展开更多
In order to understand the mass transport and the dynamic genesis associated with a compressible vortex formation,a dynamic analysis of compressible vortex rings (CVRs) generated by shock tubes by using the framework ...In order to understand the mass transport and the dynamic genesis associated with a compressible vortex formation,a dynamic analysis of compressible vortex rings (CVRs) generated by shock tubes by using the framework of Lagrangiancoherent structures (LCSs) and finite-time Lyapunov exponents field (FTLE) is performed. Numerical calculation is performed to simulate the evolution of CVRs generated by shock tubes with 70 mm, 100 mm, and 165 mm of the driver sectionat the circumstances of pressure ratio = 3. The formation of CVRs is studied according to FTLE fields. The mass transportduring the formation is obviously seen by the material manifold reveled by FTLE fields. A non-universal formation numberfor the three CVRs is obtained. Then the elliptic LCSs is implemented on three CVRs. Fluid particles separated by ellipticLCSs and ridges of FTLE are traced back to t = 0 to identify the fluid that eventually forms the CVRs. The elliptic LCSsencompass around 60% fluid material of the advected bulk but contain the majority of the circulation of the ring. The otherparts of the ring carrying almost zero circulation advect along with the ring. Combining the ridges of FTLE and the ellipticLCS, the whole CVR can be divided into three distinct dynamic parts: vortex part, entrainment part, and advected part. Inaddition, a criterion based on the vortex part formation is suggested to identify the formation number of CVRs.展开更多
In [1], Saroj Jain Posed an open Problem: Is a right IF-ring left coherent? In this note, we discuss this problem and Prove that a two-sided IF-ring certainly is twosided coherent,
Coherent electronic dynamics are of great significance in photo-induced processes and molecular magnetism.We theoretically investigate electronic dynamics of triatomic molecule H_(3)^(2+) by circularly polarized pulse...Coherent electronic dynamics are of great significance in photo-induced processes and molecular magnetism.We theoretically investigate electronic dynamics of triatomic molecule H_(3)^(2+) by circularly polarized pulses,including electron density distributions,induced electronic currents,and ultrafast magnetic field generation.By comparing the results of the coherent resonant excitation and direct ionization,we found that for the coherent resonant excitation,the electron is localized and the coherent electron wave packet moves periodically between three protons,which can be attributed to the coherent superposition of the ground A′state and excited E+state.Whereas,for the direct single-photon ionization,the induced electronic currents mainly come from the free electron in the continuum state.It is found that there are differences in the intensity,phase,and frequency of the induced current and the generated magnetic field.The scheme allows one to control the induced electronic current and the ultrafast magnetic field generation.展开更多
Let R be a ring, n, d be fixed non-negative integers, Jn,d the class of （n, d）- injective left R-modules, and Fn,d the class of （n, d）-flat right R-modules. In this paper, we prove that if R is a left n-coherent r...Let R be a ring, n, d be fixed non-negative integers, Jn,d the class of （n, d）- injective left R-modules, and Fn,d the class of （n, d）-flat right R-modules. In this paper, we prove that if R is a left n-coherent ring and m ≥ 2, then gl-right-Jn,a-dimRM ≤ m if and only if gl-left-Jn,d-dimRM ≤ m -- 2, if and only if Extm＋k（M, N） = 0 for all left R-modules M, N and all k 〉 -1, if and only if Extm-l（M, N） = 0 for all left R-modules M, N. Meanwhile, we prove that if R is a left n-coherent ring, then - - is right balanced on MR ×RM by Fn,d × Jn,d, and investigate the global right Jn,d-dimension of RM and the global right Fn,d-dimension of MR by right derived functors of - -. Some known results are obtained as corollaries.展开更多
Optical coherence tomography(OCT)allows a direct and precise measurement of laser welding depth by coaxially measuring the keyhole depth and can be used for process monitoring and control.When OCT measurement was take...Optical coherence tomography(OCT)allows a direct and precise measurement of laser welding depth by coaxially measuring the keyhole depth and can be used for process monitoring and control.When OCT measurement was taken during single-beam laser welding,the keyhole instability of aluminum welding resulted in highly scattered OCT data and complicated the welding depth extraction methods.As a combination of an inner core beam and an outer ring beam,a novel adjustable ring mode(ARM)laser for producing a stable keyhole was applied to the OCT measurement.Different ARM laser power arrangements were conducted on aluminum and copper.The results indicated that the ring beam greatly improved the stability of the core beam-induced keyhole,and smooth welding depth can be extracted from the concentrated OCT data.展开更多
文摘A left ideal I of a ring R is small in case for every proper left ideal K of R, K ＋ I ≠R. A ring R is called left PS-coherent if every principally small left ideal Ra is finitely presented. We develop, in this paper, PS-coherent rings as a generalization of P-coherent rings and J-coherent rings. To characterize PS-coherent rings, we first introduce PS-injective and PS-flat modules, and discuss the relation between them over some spacial rings. Some properties of left PS-coherent rings are also studied.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.91441205 and 91941301)China Postdoctoral Science Foundation(Grant No.2018M642007).
文摘In order to understand the mass transport and the dynamic genesis associated with a compressible vortex formation,a dynamic analysis of compressible vortex rings (CVRs) generated by shock tubes by using the framework of Lagrangiancoherent structures (LCSs) and finite-time Lyapunov exponents field (FTLE) is performed. Numerical calculation is performed to simulate the evolution of CVRs generated by shock tubes with 70 mm, 100 mm, and 165 mm of the driver sectionat the circumstances of pressure ratio = 3. The formation of CVRs is studied according to FTLE fields. The mass transportduring the formation is obviously seen by the material manifold reveled by FTLE fields. A non-universal formation numberfor the three CVRs is obtained. Then the elliptic LCSs is implemented on three CVRs. Fluid particles separated by ellipticLCSs and ridges of FTLE are traced back to t = 0 to identify the fluid that eventually forms the CVRs. The elliptic LCSsencompass around 60% fluid material of the advected bulk but contain the majority of the circulation of the ring. The otherparts of the ring carrying almost zero circulation advect along with the ring. Combining the ridges of FTLE and the ellipticLCS, the whole CVR can be divided into three distinct dynamic parts: vortex part, entrainment part, and advected part. Inaddition, a criterion based on the vortex part formation is suggested to identify the formation number of CVRs.
文摘In [1], Saroj Jain Posed an open Problem: Is a right IF-ring left coherent? In this note, we discuss this problem and Prove that a two-sided IF-ring certainly is twosided coherent,
基金Project supported by the National Natural Science Foundation of China(Grant Nos.12074146 and 12074142)。
文摘Coherent electronic dynamics are of great significance in photo-induced processes and molecular magnetism.We theoretically investigate electronic dynamics of triatomic molecule H_(3)^(2+) by circularly polarized pulses,including electron density distributions,induced electronic currents,and ultrafast magnetic field generation.By comparing the results of the coherent resonant excitation and direct ionization,we found that for the coherent resonant excitation,the electron is localized and the coherent electron wave packet moves periodically between three protons,which can be attributed to the coherent superposition of the ground A′state and excited E+state.Whereas,for the direct single-photon ionization,the induced electronic currents mainly come from the free electron in the continuum state.It is found that there are differences in the intensity,phase,and frequency of the induced current and the generated magnetic field.The scheme allows one to control the induced electronic current and the ultrafast magnetic field generation.
文摘Let R be a ring, n, d be fixed non-negative integers, Jn,d the class of （n, d）- injective left R-modules, and Fn,d the class of （n, d）-flat right R-modules. In this paper, we prove that if R is a left n-coherent ring and m ≥ 2, then gl-right-Jn,a-dimRM ≤ m if and only if gl-left-Jn,d-dimRM ≤ m -- 2, if and only if Extm＋k（M, N） = 0 for all left R-modules M, N and all k 〉 -1, if and only if Extm-l（M, N） = 0 for all left R-modules M, N. Meanwhile, we prove that if R is a left n-coherent ring, then - - is right balanced on MR ×RM by Fn,d × Jn,d, and investigate the global right Jn,d-dimension of RM and the global right Fn,d-dimension of MR by right derived functors of - -. Some known results are obtained as corollaries.
基金supported by the National Natural Science Foundation of China(No.12002215)the China Postdoctoral Science Foundation(No.2022T150437)the National Key Research and Development Program of China(No.2019YFC1511102)。
文摘Optical coherence tomography(OCT)allows a direct and precise measurement of laser welding depth by coaxially measuring the keyhole depth and can be used for process monitoring and control.When OCT measurement was taken during single-beam laser welding,the keyhole instability of aluminum welding resulted in highly scattered OCT data and complicated the welding depth extraction methods.As a combination of an inner core beam and an outer ring beam,a novel adjustable ring mode(ARM)laser for producing a stable keyhole was applied to the OCT measurement.Different ARM laser power arrangements were conducted on aluminum and copper.The results indicated that the ring beam greatly improved the stability of the core beam-induced keyhole,and smooth welding depth can be extracted from the concentrated OCT data.
