A circular shaft is often used to access a working well for deep underground space utilization.As the depth of underground space increases,the excavation depth of the shaft increases.In this study,the deformation char...A circular shaft is often used to access a working well for deep underground space utilization.As the depth of underground space increases,the excavation depth of the shaft increases.In this study,the deformation characteristics of a circular shaft with a depth of 56.3 m were presented and analysed.The main monitoring contents included:(1)wall deflection;(2)vertical wall movement;(3)horizontal soil movement;(4)vertical surface movement;and(5)basal heave.Horizontally,the maximum wall deflection was only 7.7 mm.Compared with the wall deflection data collected for another 29 circular excavations,the ratio of maximum wall deflection to excavation depth of this shaft was smaller due to a smaller ratio of diameter to excavation depth.The wall deflection underwent two stages of deformation:the first stage was mainly circumferential compression caused by the mutual extrusion of joints between walls,and the second stage was typical vertical deflection deformation.The horizontal soil movement outside the shaft was greater than the wall deflection and the deep soil caused great horizontal movement because of dewatering at confined water layers.Vertically,a basal heave of 203.8 mm occurred in the pit centre near the bottom.Meanwhile,the shaft was uplifted over time and showed 3 stages of vertical movement.The surface outside the shaft exhibited settlement and uplift deformation at different locations due to different effects.The basal heave caused by excavation was the dominant factor,driving the vertical movement of the shaft as well as the surrounding surface.The correlation between the wall deflection and the surface settlement outside the shaft was weak.展开更多
Given any integers a,b,c, and d with a 〉 1, c ≥ 0, b ≥ a＋c, and d ≥ b ＋ c, the notion of （a, b, c, d）-Koszul algebra is introduced, which is another class of standard graded algebras with ＂nonpure＂ resolutio...Given any integers a,b,c, and d with a 〉 1, c ≥ 0, b ≥ a＋c, and d ≥ b ＋ c, the notion of （a, b, c, d）-Koszul algebra is introduced, which is another class of standard graded algebras with ＂nonpure＂ resolutions, and includes many Artin-Schelter regular algebras of low global dimension as specific examples. Some basic properties of （a, b, c, d）-Koszul algebras/modules are given, and several criteria for a standard graded algebra to be （a, b, c, d）- Koszul are provided.展开更多
An object that possesses chirality,that is,having its mirror image not overlayed on itself by rotation and translation,can provide a different optical response to a left-or right-handed circular polarized light.Chiral...An object that possesses chirality,that is,having its mirror image not overlayed on itself by rotation and translation,can provide a different optical response to a left-or right-handed circular polarized light.Chiral nanostructures may exhibit polarization-selective optical properties that can be controlled for micro-to-nano optical element engineering.An attractive way to induce such complex nanostructures in three-dimension in glass is femtosecond laser direct writing.However,the mechanism of femtosecond laser induced chirality remains to be unveiled due to complex physical and chemical processes occurring during the ultrashort light-matter interaction.Here,a phenomenological model is proposed and is built on two-layers phase shifters to account for this laser-induced optical chirality in an initially achiral material(silica glass).This model is based on the observation that femtosecond laser induced nanogratings own two principal contributions to its aggregate birefringent response:a form and a stress-related one.By refining this formalism,a multilayer approach is developed to imprint on demand optical rotation.Values up to+/-60°at 550 nm within an optimal 80μm thickness in silica glass are possible,corresponding to the highest value in a glass to date.These results provide new insights of circular-optical control in micro-nano optical manufacturing and open new opportunities for photonics applications.展开更多
Let(H,αH,βH,ψH,ωH,SH)be a BiHom-Hopf algebra and(A,αA,βA)be an(H,αH,βH,ψH,ωH)-BiHom-bimodule algebra,where the mapsαH,βH,ψH,ωH,αA,βA are bijective.We first prove the Maschke-type theorem for the BiHom-...Let(H,αH,βH,ψH,ωH,SH)be a BiHom-Hopf algebra and(A,αA,βA)be an(H,αH,βH,ψH,ωH)-BiHom-bimodule algebra,where the mapsαH,βH,ψH,ωH,αA,βA are bijective.We first prove the Maschke-type theorem for the BiHom-L-R smash product over a finite-dimensional semisimple BiHom-Hopf algebra.Next we give a Morita context between the BiHom-subalgebra A^(biH)and the BiHom-L-R smash product A#H.展开更多
Temporal and spatial resonant modes are always possessed in physical systems with energy oscillation.In ultrafast fiber lasers,enormous progress has been made toward controlling the interactions of many longitudinal m...Temporal and spatial resonant modes are always possessed in physical systems with energy oscillation.In ultrafast fiber lasers,enormous progress has been made toward controlling the interactions of many longitudinal modes,which results in temporally mode-locked pulses.Recently,optical vortex beams have been extensively investigated due to their quantized orbital angular momentum,spatially donut-like intensity,and spiral phase front.In this paper,we have demonstrated the first to our knowledge observation of optical vortex mode switching and their corresponding pulse evolution dynamics in a narrow-linewidth mode-locked fiber laser.The spatial mode switching is achieved by incorporating a dual-resonant acousto-optic mode converter in the vortex mode-locked fiber laser.The vortex mode-switching dynamics have four stages,including quiet-down,relaxation oscillation,quasi mode-locking,and energy recovery prior to the stable mode-locking of another vortex mode.The evolution dynamics of the wavelength shifting during the switching process are observed via the time-stretch dispersion Fourier transform method.The spatial mode competition through optical nonlinearity induces energy fluctuation on the time scale of ultrashort pulses,which plays an essential role in the mode-switching dynamic process.The results have great implications in the study of spatial mode-locking mechanisms and ultrashort laser applications.展开更多
Let R be a Noetherian semiperfect algebra. A necessary and sufficient condition for a finitely generated R-module to be quasi-d-Koszul is given, which improves one of the main results in [1]. The authors also give a n...Let R be a Noetherian semiperfect algebra. A necessary and sufficient condition for a finitely generated R-module to be quasi-d-Koszul is given, which improves one of the main results in [1]. The authors also give a necessary and sufficient condition for the Minimal Horseshoe Lemma holding in mod(R). As an application, it is proved that the "Minimal Horseshoe Lemma" is true in the category of quasi-d-Koszul modules under certain conditions.展开更多
基金the National Natural Science Foundation of China(Grant No.52090083)Shanghai Chenguang Program(Grant No.20CG26)Consulting project on Shanghai deep tunnel project.
文摘A circular shaft is often used to access a working well for deep underground space utilization.As the depth of underground space increases,the excavation depth of the shaft increases.In this study,the deformation characteristics of a circular shaft with a depth of 56.3 m were presented and analysed.The main monitoring contents included:(1)wall deflection;(2)vertical wall movement;(3)horizontal soil movement;(4)vertical surface movement;and(5)basal heave.Horizontally,the maximum wall deflection was only 7.7 mm.Compared with the wall deflection data collected for another 29 circular excavations,the ratio of maximum wall deflection to excavation depth of this shaft was smaller due to a smaller ratio of diameter to excavation depth.The wall deflection underwent two stages of deformation:the first stage was mainly circumferential compression caused by the mutual extrusion of joints between walls,and the second stage was typical vertical deflection deformation.The horizontal soil movement outside the shaft was greater than the wall deflection and the deep soil caused great horizontal movement because of dewatering at confined water layers.Vertically,a basal heave of 203.8 mm occurred in the pit centre near the bottom.Meanwhile,the shaft was uplifted over time and showed 3 stages of vertical movement.The surface outside the shaft exhibited settlement and uplift deformation at different locations due to different effects.The basal heave caused by excavation was the dominant factor,driving the vertical movement of the shaft as well as the surrounding surface.The correlation between the wall deflection and the surface settlement outside the shaft was weak.
基金This work was supported by the National Natural Science Foundation of China （Grant Nos. 11571316, 11001245） and the Natural Science Foundation of Zhejiang Province （Grant No. LY16A010003）.
文摘Given any integers a,b,c, and d with a 〉 1, c ≥ 0, b ≥ a＋c, and d ≥ b ＋ c, the notion of （a, b, c, d）-Koszul algebra is introduced, which is another class of standard graded algebras with ＂nonpure＂ resolutions, and includes many Artin-Schelter regular algebras of low global dimension as specific examples. Some basic properties of （a, b, c, d）-Koszul algebras/modules are given, and several criteria for a standard graded algebra to be （a, b, c, d）- Koszul are provided.
基金Agence Nationale pour la Recherche,FLAG-IR project,grant number ANR-18-CE08-0004-01d CNRS Défi Instrumentation aux Limites,UltraBragg project,Science and Technology Commission of Shanghai Municipality(20JC1415700)+1 种基金Jiafeng Lu acknowledges the China Scholarship Council(CSC)for the funding No.202006890077We greatly acknowledge Dr.Maxime Cavillon for valuable discussions.
文摘An object that possesses chirality,that is,having its mirror image not overlayed on itself by rotation and translation,can provide a different optical response to a left-or right-handed circular polarized light.Chiral nanostructures may exhibit polarization-selective optical properties that can be controlled for micro-to-nano optical element engineering.An attractive way to induce such complex nanostructures in three-dimension in glass is femtosecond laser direct writing.However,the mechanism of femtosecond laser induced chirality remains to be unveiled due to complex physical and chemical processes occurring during the ultrashort light-matter interaction.Here,a phenomenological model is proposed and is built on two-layers phase shifters to account for this laser-induced optical chirality in an initially achiral material(silica glass).This model is based on the observation that femtosecond laser induced nanogratings own two principal contributions to its aggregate birefringent response:a form and a stress-related one.By refining this formalism,a multilayer approach is developed to imprint on demand optical rotation.Values up to+/-60°at 550 nm within an optimal 80μm thickness in silica glass are possible,corresponding to the highest value in a glass to date.These results provide new insights of circular-optical control in micro-nano optical manufacturing and open new opportunities for photonics applications.
基金supported by the NSF of China(Nos.11801515,12071441)the Natural Science Foundation of Zhejiang Province(No.LY20A010003)the Foundation of Zhejiang Educational Committee(No.Y201942625).
文摘Let(H,αH,βH,ψH,ωH,SH)be a BiHom-Hopf algebra and(A,αA,βA)be an(H,αH,βH,ψH,ωH)-BiHom-bimodule algebra,where the mapsαH,βH,ψH,ωH,αA,βA are bijective.We first prove the Maschke-type theorem for the BiHom-L-R smash product over a finite-dimensional semisimple BiHom-Hopf algebra.Next we give a Morita context between the BiHom-subalgebra A^(biH)and the BiHom-L-R smash product A#H.
基金National Key Research and Development Program of China(2018YFB1801800)National Natural Science Foundation of China(91750108,61635006)111 Project(D20031)。
文摘Temporal and spatial resonant modes are always possessed in physical systems with energy oscillation.In ultrafast fiber lasers,enormous progress has been made toward controlling the interactions of many longitudinal modes,which results in temporally mode-locked pulses.Recently,optical vortex beams have been extensively investigated due to their quantized orbital angular momentum,spatially donut-like intensity,and spiral phase front.In this paper,we have demonstrated the first to our knowledge observation of optical vortex mode switching and their corresponding pulse evolution dynamics in a narrow-linewidth mode-locked fiber laser.The spatial mode switching is achieved by incorporating a dual-resonant acousto-optic mode converter in the vortex mode-locked fiber laser.The vortex mode-switching dynamics have four stages,including quiet-down,relaxation oscillation,quasi mode-locking,and energy recovery prior to the stable mode-locking of another vortex mode.The evolution dynamics of the wavelength shifting during the switching process are observed via the time-stretch dispersion Fourier transform method.The spatial mode competition through optical nonlinearity induces energy fluctuation on the time scale of ultrashort pulses,which plays an essential role in the mode-switching dynamic process.The results have great implications in the study of spatial mode-locking mechanisms and ultrashort laser applications.
基金supported by the Zhejiang Innovation Project(No.T200905)
文摘Let R be a Noetherian semiperfect algebra. A necessary and sufficient condition for a finitely generated R-module to be quasi-d-Koszul is given, which improves one of the main results in [1]. The authors also give a necessary and sufficient condition for the Minimal Horseshoe Lemma holding in mod(R). As an application, it is proved that the "Minimal Horseshoe Lemma" is true in the category of quasi-d-Koszul modules under certain conditions.
