In complete metric spaces, the common fixed point theorems for sequences of φ-type contraction set-valued mappings are established, and the corresponding random com- mon fixed point theorems for set-valued mappings a...In complete metric spaces, the common fixed point theorems for sequences of φ-type contraction set-valued mappings are established, and the corresponding random com- mon fixed point theorems for set-valued mappings are also obtained.展开更多
Borehole acoustic reflection logging can provide high resolution images of nearborehole geological structure. However, the conventional seismic migration and imaging methods are not effective because the reflected wav...Borehole acoustic reflection logging can provide high resolution images of nearborehole geological structure. However, the conventional seismic migration and imaging methods are not effective because the reflected waves are interfered with the dominant borehole-guided modes and there are only eight receiving channels per shot available for stacking. In this paper, we apply an equivalent offset migration method based on wave scattering theory to process the acoustic reflection imaging log data from both numerical modeling and recorded field data. The result shows that, compared with the routine post-stack depth migration method, the equivalent offset migration method results in higher stack fold and is more effective for near-borehole structural imaging with low SNR acoustic reflection log data.展开更多
The study delves into multiplicative contractions,exploring the existence and uniqueness of common fixed points for a weakly compatible pair of mappings.Those mappings adhere to specific multiplicative contraction con...The study delves into multiplicative contractions,exploring the existence and uniqueness of common fixed points for a weakly compatible pair of mappings.Those mappings adhere to specific multiplicative contraction conditions characterized by exponents expressed as fraction multiplicative metric spaces.It is noted that a metric can induce a multiplicative metric,and conversely,a multiplicative metric can give a rise to a metric on a nonempty set.As an application,another proof of the existence and uniqueness of the solution of a multiplicative initial problem is given.展开更多
The adaptive optics system for the second-generation Very Large Telescope-interferometer(VLTI)instrument GRAVITY consists of a novel cryogenic near-infrared wavefront sensor to be installed at each of the four unit te...The adaptive optics system for the second-generation Very Large Telescope-interferometer(VLTI)instrument GRAVITY consists of a novel cryogenic near-infrared wavefront sensor to be installed at each of the four unit telescopes of the Very Large Telescope(VLT).Feeding the GRAVITY wavefront sensor with light in the 1.4–2.4μm band,while suppressing laser light originating from the GRAVITY metrology system requires custom-built optical componets.In this paper,we present the development of a quantitative near-infraredpoint diffraction interferometric characterization technique,which allows measuring the transmitted wavefront error of the silicon entrance windows of the wavefront sensor cryostat.The technique can be readily applied to quantitative phase measurements in the near-infrared regime.Moreover,by employing a slightly off-axis optical setup,the proposed method can optimize the required spatial resolution and enable real time measurement capabilities.The feasibility of the proposed setup is demonstrated,followed by a theoretical analysis and experimental results.Our experimental results show that the phase error repeatability in the nanometer regime can be achieved.展开更多
In this work,a novel fluid-structure coupling method called the common node discrete element-smoothed particle hydrodynamics(DS-SPH)method is introduced.This framework combines the principles of the common node discre...In this work,a novel fluid-structure coupling method called the common node discrete element-smoothed particle hydrodynamics(DS-SPH)method is introduced.This framework combines the principles of the common node discrete element method(DEM)and smoothed particle hydrodynamics(SPH)to construct DEM-SPH particles situated on the same node.By doing so,the DEM particles can interact with the SPH particles within their support domain,enabling fluid-structure interaction(FSI).To determine the DEM microscopic parameters required for this method,uniaxial compression and three-point bending tests are conducted on sea ice.To verify the proposed model,we select the interaction between sea ice and structures as a case study.Through simulation,the model's capability of accurately depicting sea ice deformation and fracture has been demonstrated.The results indicate that the inclusion of SPH particles with fluid properties in the DEM model has minimal impact on the main mechanical parameters of sea ice.Additionally,it helps prevent the occurrence of particle splashing during cement failure.However,it is observed that the size of DEM particles and the friction between DEM particles and the structure significantly influence the macroscopic mechanical behavior of the common-node DEM-SPH model.Finally,we compare the fracture behavior of sea ice and the ice forces acting on structures obtained from the current model with on-site measured results.The agreement between the two sets of data is excellent,further validating the effectiveness of the proposed model in practical applications.展开更多
基金Foundation item： Supported by the Science Foundation from the Ministry of Education of Jiangsu Province（04KJD110168, 06KJBll0107）
文摘In complete metric spaces, the common fixed point theorems for sequences of φ-type contraction set-valued mappings are established, and the corresponding random com- mon fixed point theorems for set-valued mappings are also obtained.
基金supported by the National Natural Science Foundation of China (Grant No.50674098)the 863 Program (Grant No.2006AA06Z207 & 2006AA06Z213)the 973 Program (Grant No.2007CB209601)
文摘Borehole acoustic reflection logging can provide high resolution images of nearborehole geological structure. However, the conventional seismic migration and imaging methods are not effective because the reflected waves are interfered with the dominant borehole-guided modes and there are only eight receiving channels per shot available for stacking. In this paper, we apply an equivalent offset migration method based on wave scattering theory to process the acoustic reflection imaging log data from both numerical modeling and recorded field data. The result shows that, compared with the routine post-stack depth migration method, the equivalent offset migration method results in higher stack fold and is more effective for near-borehole structural imaging with low SNR acoustic reflection log data.
基金Supported by the General Project of Science and Technology Department of Sichuan Province(2018JY0256)the Scientific Research Fund of Leshan Normal University(DGZZ202024)。
文摘The study delves into multiplicative contractions,exploring the existence and uniqueness of common fixed points for a weakly compatible pair of mappings.Those mappings adhere to specific multiplicative contraction conditions characterized by exponents expressed as fraction multiplicative metric spaces.It is noted that a metric can induce a multiplicative metric,and conversely,a multiplicative metric can give a rise to a metric on a nonempty set.As an application,another proof of the existence and uniqueness of the solution of a multiplicative initial problem is given.
文摘The adaptive optics system for the second-generation Very Large Telescope-interferometer(VLTI)instrument GRAVITY consists of a novel cryogenic near-infrared wavefront sensor to be installed at each of the four unit telescopes of the Very Large Telescope(VLT).Feeding the GRAVITY wavefront sensor with light in the 1.4–2.4μm band,while suppressing laser light originating from the GRAVITY metrology system requires custom-built optical componets.In this paper,we present the development of a quantitative near-infraredpoint diffraction interferometric characterization technique,which allows measuring the transmitted wavefront error of the silicon entrance windows of the wavefront sensor cryostat.The technique can be readily applied to quantitative phase measurements in the near-infrared regime.Moreover,by employing a slightly off-axis optical setup,the proposed method can optimize the required spatial resolution and enable real time measurement capabilities.The feasibility of the proposed setup is demonstrated,followed by a theoretical analysis and experimental results.Our experimental results show that the phase error repeatability in the nanometer regime can be achieved.
基金financially supported by the National Natural Science Foundation of China (Grant No.52201323)。
文摘In this work,a novel fluid-structure coupling method called the common node discrete element-smoothed particle hydrodynamics(DS-SPH)method is introduced.This framework combines the principles of the common node discrete element method(DEM)and smoothed particle hydrodynamics(SPH)to construct DEM-SPH particles situated on the same node.By doing so,the DEM particles can interact with the SPH particles within their support domain,enabling fluid-structure interaction(FSI).To determine the DEM microscopic parameters required for this method,uniaxial compression and three-point bending tests are conducted on sea ice.To verify the proposed model,we select the interaction between sea ice and structures as a case study.Through simulation,the model's capability of accurately depicting sea ice deformation and fracture has been demonstrated.The results indicate that the inclusion of SPH particles with fluid properties in the DEM model has minimal impact on the main mechanical parameters of sea ice.Additionally,it helps prevent the occurrence of particle splashing during cement failure.However,it is observed that the size of DEM particles and the friction between DEM particles and the structure significantly influence the macroscopic mechanical behavior of the common-node DEM-SPH model.Finally,we compare the fracture behavior of sea ice and the ice forces acting on structures obtained from the current model with on-site measured results.The agreement between the two sets of data is excellent,further validating the effectiveness of the proposed model in practical applications.
