We take phase modulation to create discrete phase-controlled sources and realize the super-bunching effect by a phasecorrelated method. From theoretical and numerical simulations, we find the space translation invaria...We take phase modulation to create discrete phase-controlled sources and realize the super-bunching effect by a phasecorrelated method. From theoretical and numerical simulations, we find the space translation invariance of the bunching effect is a key point for the ghost imaging realization. Experimentally, we create the orderly phase-correlated discrete sources which can realize high-visibility second-order ghost imaging than the result with chaotic sources. Moreover, some factors affecting the visibility of ghost image are discussed in detail.展开更多
The basis functions of the translation invariant shell model are used to construct the ground state nuclear wave functions of <sup>3</sup>H. The used residual two-body interactions consist of central, tens...The basis functions of the translation invariant shell model are used to construct the ground state nuclear wave functions of <sup>3</sup>H. The used residual two-body interactions consist of central, tensor, spin orbit and quadratic spin orbit terms with Gaussian radial dependence. The parameters of these interactions are so chosen in such a way that they represent the long-range attraction and the short-range repulsion of the nucleon-nucleon interactions. These parameters are so chosen to reproduce good agreement between the calculated values of the binding energy, the root mean-square radius, the D-state probability, the magnetic dipole moment and the electric quadrupole moment of the deuteron nucleus. The variation method is then used to calculate the binding energy of triton by varying the oscillator parameter which exists in the nuclear wave function. The obtained nuclear wave functions are then used to calculate the root mean-square radius and the magnetic dipole moment of the triton.展开更多
We show that the matrix (or more generally tensor) product states in a finite translation invariant system can be accurately constructed from a same set of local matrices (or tensors) that are determined from an i...We show that the matrix (or more generally tensor) product states in a finite translation invariant system can be accurately constructed from a same set of local matrices (or tensors) that are determined from an infinite lattice system in one or higher dimensions. This provides an efficient approach for studying translation invariant tensor product states in finite lattice systems. Two methods are introduced to determine the size-independent local tensors.展开更多
A sparsifying transform for use in Compressed Sensing (CS) is a vital piece of image reconstruction for Magnetic Resonance Imaging (MRI). Previously, Translation Invariant Wavelet Transforms (TIWT) have been shown to ...A sparsifying transform for use in Compressed Sensing (CS) is a vital piece of image reconstruction for Magnetic Resonance Imaging (MRI). Previously, Translation Invariant Wavelet Transforms (TIWT) have been shown to perform exceedingly well in CS by reducing repetitive line pattern image artifacts that may be observed when using orthogonal wavelets. To further establish its validity as a good sparsifying transform, the TIWT is comprehensively investigated and compared with Total Variation (TV), using six under-sampling patterns through simulation. Both trajectory and random mask based under-sampling of MRI data are reconstructed to demonstrate a comprehensive coverage of tests. Notably, the TIWT in CS reconstruction performs well for all varieties of under-sampling patterns tested, even for cases where TV does not improve the mean squared error. This improved Image Quality (IQ) gives confidence in applying this transform to more CS applications which will contribute to an even greater speed-up of a CS MRI scan. High vs low resolution time of flight MRI CS re-constructions are also analyzed showing how partial Fourier acquisitions must be carefully addressed in CS to prevent loss of IQ. In the spirit of reproducible research, novel software is introduced here as FastTestCS. It is a helpful tool to quickly develop and perform tests with many CS customizations. Easy integration and testing for the TIWT and TV minimization are exemplified. Simulations of 3D MRI datasets are shown to be efficiently distributed as a scalable solution for large studies. Comparisons in reconstruction computation time are made between the Wavelab toolbox and Gnu Scientific Library in FastTestCS that show a significant time savings factor of 60×. The addition of FastTestCS is proven to be a fast, flexible, portable and reproducible simulation aid for CS research.展开更多
Numerical oscillation of the total energy can be observed when the Kohn-Sham equation is solved by real-space methods to simulate the translational move of an electronic system.Effectively remove or reduce the unphysi...Numerical oscillation of the total energy can be observed when the Kohn-Sham equation is solved by real-space methods to simulate the translational move of an electronic system.Effectively remove or reduce the unphysical oscillation is crucial not only for the optimization of the geometry of the electronic structure,but also for the study of molecular dynamics.In this paper,we study such unphysical oscillation based on the numerical framework in[G.Bao,G.H.Hu,and D.Liu,An h-adaptive fi-nite element solver for the calculations of the electronic structures,Journal of Computational Physics,Volume 231,Issue 14,Pages 4967-4979,2012],and deliver some numerical methods to constrain such unphysical effect for both pseudopotential and all-electron calculations,including a stabilized cubature strategy for Hamiltonian operator,and an a posteriori error estimator of the finite element methods for Kohn-Sham equation.The numerical results demonstrate the effectiveness of our method on restraining unphysical oscillation of the total energies.展开更多
The gravitational field h_(μν)with spin-2 is introduced naturally by the requirement that the Lagrangian is locally translation invariant in Minkowski spacetime.The interactions between the h_(μν)and spin-1/2,0,1 ...The gravitational field h_(μν)with spin-2 is introduced naturally by the requirement that the Lagrangian is locally translation invariant in Minkowski spacetime.The interactions between the h_(μν)and spin-1/2,0,1 matter fields are obtained along with the Lagrangian for the gravitational field including self-interactions.The deflection angle of light when it passes through the sun is calculated with different gauge conditions as an example.Our leading-order result is the same as that from general relativity,although the basic ideas are different.It is interesting that gravity can be described in a similar way to other fundamental interactions in Minkowski spacetime,and it may provide a new scenario for the Universe.展开更多
The structure of the set S of shiftable points of wavelet subspaces is researched in this paper.We prove that S=R or S=(1/q)Z where q ∈ N.The spectral and functional characterizations for the shiftability are given.F...The structure of the set S of shiftable points of wavelet subspaces is researched in this paper.We prove that S=R or S=(1/q)Z where q ∈ N.The spectral and functional characterizations for the shiftability are given.Furthermore,the nonharmonic wavelet bases are discussed.展开更多
This paper proposes a new set of 3D rotation scaling and translation invariants of 3D radially shifted Legendre moments. We aim to develop two kinds of transformed shifted Legendre moments: a 3D substituted radial sh...This paper proposes a new set of 3D rotation scaling and translation invariants of 3D radially shifted Legendre moments. We aim to develop two kinds of transformed shifted Legendre moments: a 3D substituted radial shifted Legendre moments (3DSRSLMs) and a 3D weighted radial one (3DWRSLMs). Both are centered on two types of polynomials. In the first case, a new 3D ra- dial complex moment is proposed. In the second case, new 3D substituted/weighted radial shifted Legendremoments (3DSRSLMs/3DWRSLMs) are introduced using a spherical representation of volumetric image. 3D invariants as derived from the sug- gested 3D radial shifted Legendre moments will appear in the third case. To confirm the proposed approach, we have resolved three is- sues. To confirm the proposed approach, we have resolved three issues: rotation, scaling and translation invariants. The result of experi- ments shows that the 3DSRSLMs and 3DWRSLMs have done better than the 3D radial complex moments with and without noise. Sim- ultaneously, the reconstruction converges rapidly to the original image using 3D radial 3DSRSLMs and 3DWRSLMs, and the test of 3D images are clearly recognized from a set of images that are available in Princeton shape benchmark (PSB) database for 3D image.展开更多
In this paper, among other things, the author studies the weak^*-closed left translation invariant complemented subspace of semigroup algebras and group algebras. Also, the author studies the relationships between pr...In this paper, among other things, the author studies the weak^*-closed left translation invariant complemented subspace of semigroup algebras and group algebras. Also, the author studies the relationships between projections and amenability.展开更多
We construct charged black hole solutions with hyperscaling violation in the infrared(IR) region in Einstein-Maxwell-Dilaton-Axion theory and investigate the temperature behavior of the ratio of holographic shear vi...We construct charged black hole solutions with hyperscaling violation in the infrared(IR) region in Einstein-Maxwell-Dilaton-Axion theory and investigate the temperature behavior of the ratio of holographic shear viscosity to the entropy density. When translational symmetry breaking is relevant in the IR, the power law of the ratio is verified numerically at low temperature T, namely, η/s ~ T^κ, where the values of exponent κ coincide with the analytical results. We also find that the exponent κ is not affected by irrelevant current, but is reduced by the relevant current.展开更多
In this article, we extend the well known Wendel's theorem to the context of vector-valued L1-spaces on hypergroups. In this regard, various cases have been studied.
All continuous translation invariant complex-valued valuations on Lebesgue measurable functions are completely classified.And all continuous rotation invariant complex-valued valuations on spherical Lebesgue measurabl...All continuous translation invariant complex-valued valuations on Lebesgue measurable functions are completely classified.And all continuous rotation invariant complex-valued valuations on spherical Lebesgue measurable functions are also completely classified.展开更多
This paper discuss band-limited scaling function, especially on the interval band case and three interval bands case, its relationship to oversampling property and weakly translation invariance are also studied. At th...This paper discuss band-limited scaling function, especially on the interval band case and three interval bands case, its relationship to oversampling property and weakly translation invariance are also studied. At the end, we propose an open problem.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant No.62105188)。
文摘We take phase modulation to create discrete phase-controlled sources and realize the super-bunching effect by a phasecorrelated method. From theoretical and numerical simulations, we find the space translation invariance of the bunching effect is a key point for the ghost imaging realization. Experimentally, we create the orderly phase-correlated discrete sources which can realize high-visibility second-order ghost imaging than the result with chaotic sources. Moreover, some factors affecting the visibility of ghost image are discussed in detail.
文摘The basis functions of the translation invariant shell model are used to construct the ground state nuclear wave functions of <sup>3</sup>H. The used residual two-body interactions consist of central, tensor, spin orbit and quadratic spin orbit terms with Gaussian radial dependence. The parameters of these interactions are so chosen in such a way that they represent the long-range attraction and the short-range repulsion of the nucleon-nucleon interactions. These parameters are so chosen to reproduce good agreement between the calculated values of the binding energy, the root mean-square radius, the D-state probability, the magnetic dipole moment and the electric quadrupole moment of the deuteron nucleus. The variation method is then used to calculate the binding energy of triton by varying the oscillator parameter which exists in the nuclear wave function. The obtained nuclear wave functions are then used to calculate the root mean-square radius and the magnetic dipole moment of the triton.
基金supported by the National Natural Science Foundation of Chinathe National Program for Basic Research of the Ministry of Science and Technology of China
文摘We show that the matrix (or more generally tensor) product states in a finite translation invariant system can be accurately constructed from a same set of local matrices (or tensors) that are determined from an infinite lattice system in one or higher dimensions. This provides an efficient approach for studying translation invariant tensor product states in finite lattice systems. Two methods are introduced to determine the size-independent local tensors.
文摘A sparsifying transform for use in Compressed Sensing (CS) is a vital piece of image reconstruction for Magnetic Resonance Imaging (MRI). Previously, Translation Invariant Wavelet Transforms (TIWT) have been shown to perform exceedingly well in CS by reducing repetitive line pattern image artifacts that may be observed when using orthogonal wavelets. To further establish its validity as a good sparsifying transform, the TIWT is comprehensively investigated and compared with Total Variation (TV), using six under-sampling patterns through simulation. Both trajectory and random mask based under-sampling of MRI data are reconstructed to demonstrate a comprehensive coverage of tests. Notably, the TIWT in CS reconstruction performs well for all varieties of under-sampling patterns tested, even for cases where TV does not improve the mean squared error. This improved Image Quality (IQ) gives confidence in applying this transform to more CS applications which will contribute to an even greater speed-up of a CS MRI scan. High vs low resolution time of flight MRI CS re-constructions are also analyzed showing how partial Fourier acquisitions must be carefully addressed in CS to prevent loss of IQ. In the spirit of reproducible research, novel software is introduced here as FastTestCS. It is a helpful tool to quickly develop and perform tests with many CS customizations. Easy integration and testing for the TIWT and TV minimization are exemplified. Simulations of 3D MRI datasets are shown to be efficiently distributed as a scalable solution for large studies. Comparisons in reconstruction computation time are made between the Wavelab toolbox and Gnu Scientific Library in FastTestCS that show a significant time savings factor of 60×. The addition of FastTestCS is proven to be a fast, flexible, portable and reproducible simulation aid for CS research.
基金Thework ofG.Baowas supported in part by the NSF grantsDMS-0968360,DMS-1211292the ONR grant N00014-12-1-0319+3 种基金a Key Project of the Major Research Plan of NSFC(No.91130004)a special research grant from Zhejiang UniversityThe research of G.H.Hu was supported in part by MYRG2014-00111-FST and MRG/016/HGH/2013/FST from University of Macao,085/2012/A3 from FDCT of Macao S.A.R.,and National Nat-ural Science Foundation of China(Grant No.11401608)The research of D.Liu was supported by NSF grants DMS-0968360 and NSF-DMS 1418959.
文摘Numerical oscillation of the total energy can be observed when the Kohn-Sham equation is solved by real-space methods to simulate the translational move of an electronic system.Effectively remove or reduce the unphysical oscillation is crucial not only for the optimization of the geometry of the electronic structure,but also for the study of molecular dynamics.In this paper,we study such unphysical oscillation based on the numerical framework in[G.Bao,G.H.Hu,and D.Liu,An h-adaptive fi-nite element solver for the calculations of the electronic structures,Journal of Computational Physics,Volume 231,Issue 14,Pages 4967-4979,2012],and deliver some numerical methods to constrain such unphysical effect for both pseudopotential and all-electron calculations,including a stabilized cubature strategy for Hamiltonian operator,and an a posteriori error estimator of the finite element methods for Kohn-Sham equation.The numerical results demonstrate the effectiveness of our method on restraining unphysical oscillation of the total energies.
基金Supported by the National Nature Science Foundation of China(NSFC,11975241)。
文摘The gravitational field h_(μν)with spin-2 is introduced naturally by the requirement that the Lagrangian is locally translation invariant in Minkowski spacetime.The interactions between the h_(μν)and spin-1/2,0,1 matter fields are obtained along with the Lagrangian for the gravitational field including self-interactions.The deflection angle of light when it passes through the sun is calculated with different gauge conditions as an example.Our leading-order result is the same as that from general relativity,although the basic ideas are different.It is interesting that gravity can be described in a similar way to other fundamental interactions in Minkowski spacetime,and it may provide a new scenario for the Universe.
基金This work is supported by Postdoctoral Research Fund of China,NSF of China under Grant 69772025Open Fund of National Laboratory for Machine Perception of Peking University
文摘The structure of the set S of shiftable points of wavelet subspaces is researched in this paper.We prove that S=R or S=(1/q)Z where q ∈ N.The spectral and functional characterizations for the shiftability are given.Furthermore,the nonharmonic wavelet bases are discussed.
文摘This paper proposes a new set of 3D rotation scaling and translation invariants of 3D radially shifted Legendre moments. We aim to develop two kinds of transformed shifted Legendre moments: a 3D substituted radial shifted Legendre moments (3DSRSLMs) and a 3D weighted radial one (3DWRSLMs). Both are centered on two types of polynomials. In the first case, a new 3D ra- dial complex moment is proposed. In the second case, new 3D substituted/weighted radial shifted Legendremoments (3DSRSLMs/3DWRSLMs) are introduced using a spherical representation of volumetric image. 3D invariants as derived from the sug- gested 3D radial shifted Legendre moments will appear in the third case. To confirm the proposed approach, we have resolved three is- sues. To confirm the proposed approach, we have resolved three issues: rotation, scaling and translation invariants. The result of experi- ments shows that the 3DSRSLMs and 3DWRSLMs have done better than the 3D radial complex moments with and without noise. Sim- ultaneously, the reconstruction converges rapidly to the original image using 3D radial 3DSRSLMs and 3DWRSLMs, and the test of 3D images are clearly recognized from a set of images that are available in Princeton shape benchmark (PSB) database for 3D image.
文摘In this paper, among other things, the author studies the weak^*-closed left translation invariant complemented subspace of semigroup algebras and group algebras. Also, the author studies the relationships between projections and amenability.
基金Supported by National Natural Science Foundation of China(11275208,11575195)Opening Project of Shanghai Key Laboratory of High Temperature Superconductors(14DZ2260700)Jiangxi Young Scientists(Jing Gang Star)Program and 555 Talent Project of Jiangxi Province
文摘We construct charged black hole solutions with hyperscaling violation in the infrared(IR) region in Einstein-Maxwell-Dilaton-Axion theory and investigate the temperature behavior of the ratio of holographic shear viscosity to the entropy density. When translational symmetry breaking is relevant in the IR, the power law of the ratio is verified numerically at low temperature T, namely, η/s ~ T^κ, where the values of exponent κ coincide with the analytical results. We also find that the exponent κ is not affected by irrelevant current, but is reduced by the relevant current.
基金supported by senior research fellowship of CSIR,India
文摘In this article, we extend the well known Wendel's theorem to the context of vector-valued L1-spaces on hypergroups. In this regard, various cases have been studied.
基金Supported by the Natural Science Foundation of Hunan Province(2019JJ50172)
文摘All continuous translation invariant complex-valued valuations on Lebesgue measurable functions are completely classified.And all continuous rotation invariant complex-valued valuations on spherical Lebesgue measurable functions are also completely classified.
文摘This paper discuss band-limited scaling function, especially on the interval band case and three interval bands case, its relationship to oversampling property and weakly translation invariance are also studied. At the end, we propose an open problem.