By using the two-mode Fresnel operator we derive a multiplication rule of two-dimensional （2D） Collins diffraction formula, the inverse of 2D Collins diffraction integration can also be conveniently derived in this ...By using the two-mode Fresnel operator we derive a multiplication rule of two-dimensional （2D） Collins diffraction formula, the inverse of 2D Collins diffraction integration can also be conveniently derived in this way in the context of quantum optics theory.展开更多
This paper studies the eigenfunction expansion method to solve the two dimensional （2D） elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problem...This paper studies the eigenfunction expansion method to solve the two dimensional （2D） elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problems is rewritten as an upper tri angular differential system based on the known results, and then the associated upper triangular operator matrix matrix is obtained. By further research, the two simpler com plete orthogonal systems of eigenfunctions in some space are obtained, which belong to the two block operators arising in the operator matrix. Then, a more simple and conve nient general solution to the 2D problem is given by the eigenfunction expansion method. Furthermore, the boundary conditions for the 2D problem, which can be solved by this method, are indicated. Finally, the validity of the obtained results is verified by a specific example.展开更多
Compared to surgery,interventional and hybrid-operating-room(OR) approaches diagnose or treat pathology with the most minimally invasive techniques possible.By minimizing the physical trauma to the patient,peripheral ...Compared to surgery,interventional and hybrid-operating-room(OR) approaches diagnose or treat pathology with the most minimally invasive techniques possible.By minimizing the physical trauma to the patient,peripheral or hybrid approaches can reduce infection rates and recovery time as well as shorten hospital stays.Minimally invasive approaches therefore are the trend and often the preferred choice,and may even be the only option for the patients associated with high surgery risks.Common interventional imaging modalities include 2-D X-ray fluoroscopy and ultrasound.However,fluoroscopic images do not display the anatomic structures without a contrast agent,which on the other hand,needs to be minimized for patients' safety.Ultrasound images suffer from relatively low image quality and tissue contrast problems.To augment the doctor's view of the patient's anatomy and help doctors navigate the devices to the targeted area with more confidence and a higher accuracy,high-resolution pre-operative volumetric data such as computed tomography and/or magnetic resonance can be fused with intra-operative 2-D images during interventions.A seamless workflow and accurate 2-D/3-D registrationas well as cardiac and/or respiratory motion compensation are the key components for a successful image guidance system using a patient-specific 3-D model.Dr.Liao's research has been focused on developing methods and systems of 3-D model guidance for various interventions and hybrid-OR applications.Dr.Liao' s work has led to several Siemens products with high clinical and/or market impact and a good number of scientific publications in leading journals/conferences on medical imaging.展开更多
The bilinear generating function for products of two Laguerre 2D polynomials with different arguments is calculated. It corresponds to the formula of Mehler for the generating function of products of two Hermite polyn...The bilinear generating function for products of two Laguerre 2D polynomials with different arguments is calculated. It corresponds to the formula of Mehler for the generating function of products of two Hermite polynomials. Furthermore, the generating function for mixed products of Laguerre 2D and Hermite 2D polynomials and for products of two Hermite 2D polynomials is calculated. A set of infinite sums over products of two Laguerre 2D polynomials as intermediate step to the generating function for products of Laguerre 2D polynomials is evaluated but these sums possess also proper importance for calculations with Laguerre polynomials. With the technique of operator disentanglement some operator identities are derived in an appendix. They allow calculating convolutions of Gaussian functions combined with polynomials in one- and two-dimensional case and are applied to evaluate the discussed generating functions.展开更多
2D J–INEPT NMR experiment is a combination of heteronuclear 2D J–Resolved and INEPT experiments. In this study, 2D J–INEPT experiment was analytically investigated by using product operator theory for weakly couple...2D J–INEPT NMR experiment is a combination of heteronuclear 2D J–Resolved and INEPT experiments. In this study, 2D J–INEPT experiment was analytically investigated by using product operator theory for weakly coupled ISn (I = ?, S=1;n = 1, 2, 3) spin systems. The obtained theoretical results represent the FID values of CD, CD2 and CD3groups. In order to make Fourier transform of the obtained FID values, a Maple program is used and then simulated spectra for of 2D J–INEPT experiment are obtained for CD, CD2 and CD3 groups. It is found that 2D J–INEPT is a useful experiment for both polarisation transfer and 2D J–resolved spectral assignment for CDn groups in complex molecules.展开更多
Forward modeling is the basis of inversion imaging and quantitative interpretation for DC resistivity exploration.Currently,a numerical model of the DC resistivity method must be finely divided to obtain a highly accu...Forward modeling is the basis of inversion imaging and quantitative interpretation for DC resistivity exploration.Currently,a numerical model of the DC resistivity method must be finely divided to obtain a highly accurate solution under complex conditions,resulting in a long calculation time and large storage.Therefore,we propose a 3D numerical simulation method in a mixed space-wavenumber domain to overcome this challenge.The partial differential equation about abnormal potential is transformed into many independent ordinary differential equations with different wavenumbers using a 2D Fourier transform along the x axis and y axis direction.In this way,a large-scale 3D numerical simulation problem is decomposed into several 1D numerical simulation problems,which significantly reduces the computational and storage requirements.In addition,these ordinary 1D differential equations with different wavenumbers are independent of each other and high parallelelism of the algorithm.They are solved using a finite-element algorithm combined with a chasing method,and the obtained solution is modified using a contraction operator.In this method,the vertical direction is reserved as the spatial domain,then grid size can be determined flexibly based on the underground current density distribution,which considers the solution accuracy and calculation efficiency.In addition,for the first time,we use the contraction operator in the integral equation method to iterate the algorithm.The algorithm takes advantage of the high efficiency of the standard Fourier transform and chasing method,as well as the fast convergence of the contraction operator.We verified the accuracy of the algorithm and the convergence of the contraction operator.Compared with a volume integral method and goal-oriented adaptive finite-element method,the proposed algorithm has lower memory requirements and high computational efficiency,making it suitable for calculating a model with large-scale nodes.Moreover,different examples are used to verify the high adaptability and parallelism of the proposed algorithm.The findings show that the 3D numerical simulation method of DC resistivity method in a mixed space-wavenumber domain is highly efficient,precise,and parallel.展开更多
After developing the mathematical means for the correspondence of classical phase-space function to quantum-mechanical operators with symmetrical ordering of the basic canonical operators in the sense of Weyl the appr...After developing the mathematical means for the correspondence of classical phase-space function to quantum-mechanical operators with symmetrical ordering of the basic canonical operators in the sense of Weyl the approach is applied to an infinite series of classical monomial functions of the canonical variables. These include as well as pure powers of the amplitude as also basic periodic functions of the phase φwith their quantum-mechanical correspondence. In the representation by number states, all the considered operators involve the Jacobi polynomials as the essential formative element. Whereas the quantity in normal ordering due to its indeterminacy leads to the introduction of the notions of sub- and super-Poissonian statistics the analogous quantity in (Weyl) symmetrical orderingis positive definite and satisfies an inequality. The notions of sub- and super-Poissonian statistics are problematic when they are used for the definition of nonclassicality of states since the mentioned measure in normal ordering does not determine the Poisson statistics in their middle in unique way but determines only a large set of statistics which may be very far in the sense of the Hilbert-Schmidt distance from a Poisson statistics that is discussed.展开更多
Emulation of advanced synaptic functions of the human brain with electronic devices contributes an important step toward constructing high‐efficiency neuromorphic systems.Ferroelectric materials are promising candida...Emulation of advanced synaptic functions of the human brain with electronic devices contributes an important step toward constructing high‐efficiency neuromorphic systems.Ferroelectric materials are promising candidates as synaptic weight elements in neural network hardware due to their controllable polarization states.However,the increased depolarization field at the na-noscale and the complex fabrication process of the traditional ferroelectric materials hamper the development of high‐density,low‐power,and highly sensitive synaptic devices.Here,we report the implementation of two‐dimensional(2D)ferroelectricα‐In_(2)Se_(3)as an active channel material to emulate typical synaptic functions.Theα‐In_(2)Se_(3)‐based synaptic device fea-tures multimode operations,enabled by the coupled ferroelectric polarization under various voltage pulses applied at both drain and gate terminals.Moreover,the energy consumption can be reduced to~1 pJ by using high‐κdielectric(Al2O3).The successful control of ferroelectric polarizations inα‐In_(2)Se_(3)and its application in artificial synapses are expected to inspire the implementation of 2D ferroelectric materials for future neuromorphic systems.展开更多
基金supported by the Doctoral Scientific Research Startup Fund of Anhui University, China (Grant No. 33190059)the National Natural Science Foundation of China (Grant No. 10874174)+1 种基金the Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20113401120004)the Open Funds from National Laboratory for Infrared Physics, Chinese Academy of Sciences (Grant No. 201117)
文摘By using the two-mode Fresnel operator we derive a multiplication rule of two-dimensional （2D） Collins diffraction formula, the inverse of 2D Collins diffraction integration can also be conveniently derived in this way in the context of quantum optics theory.
基金supported by the Specialized Research Fund for the Doctoral Program of Higher Education of China (No. 20070126002)the National Natural Science Foundation of China (No. 10962004)
文摘This paper studies the eigenfunction expansion method to solve the two dimensional （2D） elasticity problems based on the stress formulation. The fundamental system of partial differential equations of the 2D problems is rewritten as an upper tri angular differential system based on the known results, and then the associated upper triangular operator matrix matrix is obtained. By further research, the two simpler com plete orthogonal systems of eigenfunctions in some space are obtained, which belong to the two block operators arising in the operator matrix. Then, a more simple and conve nient general solution to the 2D problem is given by the eigenfunction expansion method. Furthermore, the boundary conditions for the 2D problem, which can be solved by this method, are indicated. Finally, the validity of the obtained results is verified by a specific example.
文摘Compared to surgery,interventional and hybrid-operating-room(OR) approaches diagnose or treat pathology with the most minimally invasive techniques possible.By minimizing the physical trauma to the patient,peripheral or hybrid approaches can reduce infection rates and recovery time as well as shorten hospital stays.Minimally invasive approaches therefore are the trend and often the preferred choice,and may even be the only option for the patients associated with high surgery risks.Common interventional imaging modalities include 2-D X-ray fluoroscopy and ultrasound.However,fluoroscopic images do not display the anatomic structures without a contrast agent,which on the other hand,needs to be minimized for patients' safety.Ultrasound images suffer from relatively low image quality and tissue contrast problems.To augment the doctor's view of the patient's anatomy and help doctors navigate the devices to the targeted area with more confidence and a higher accuracy,high-resolution pre-operative volumetric data such as computed tomography and/or magnetic resonance can be fused with intra-operative 2-D images during interventions.A seamless workflow and accurate 2-D/3-D registrationas well as cardiac and/or respiratory motion compensation are the key components for a successful image guidance system using a patient-specific 3-D model.Dr.Liao's research has been focused on developing methods and systems of 3-D model guidance for various interventions and hybrid-OR applications.Dr.Liao' s work has led to several Siemens products with high clinical and/or market impact and a good number of scientific publications in leading journals/conferences on medical imaging.
文摘The bilinear generating function for products of two Laguerre 2D polynomials with different arguments is calculated. It corresponds to the formula of Mehler for the generating function of products of two Hermite polynomials. Furthermore, the generating function for mixed products of Laguerre 2D and Hermite 2D polynomials and for products of two Hermite 2D polynomials is calculated. A set of infinite sums over products of two Laguerre 2D polynomials as intermediate step to the generating function for products of Laguerre 2D polynomials is evaluated but these sums possess also proper importance for calculations with Laguerre polynomials. With the technique of operator disentanglement some operator identities are derived in an appendix. They allow calculating convolutions of Gaussian functions combined with polynomials in one- and two-dimensional case and are applied to evaluate the discussed generating functions.
文摘2D J–INEPT NMR experiment is a combination of heteronuclear 2D J–Resolved and INEPT experiments. In this study, 2D J–INEPT experiment was analytically investigated by using product operator theory for weakly coupled ISn (I = ?, S=1;n = 1, 2, 3) spin systems. The obtained theoretical results represent the FID values of CD, CD2 and CD3groups. In order to make Fourier transform of the obtained FID values, a Maple program is used and then simulated spectra for of 2D J–INEPT experiment are obtained for CD, CD2 and CD3 groups. It is found that 2D J–INEPT is a useful experiment for both polarisation transfer and 2D J–resolved spectral assignment for CDn groups in complex molecules.
文摘Forward modeling is the basis of inversion imaging and quantitative interpretation for DC resistivity exploration.Currently,a numerical model of the DC resistivity method must be finely divided to obtain a highly accurate solution under complex conditions,resulting in a long calculation time and large storage.Therefore,we propose a 3D numerical simulation method in a mixed space-wavenumber domain to overcome this challenge.The partial differential equation about abnormal potential is transformed into many independent ordinary differential equations with different wavenumbers using a 2D Fourier transform along the x axis and y axis direction.In this way,a large-scale 3D numerical simulation problem is decomposed into several 1D numerical simulation problems,which significantly reduces the computational and storage requirements.In addition,these ordinary 1D differential equations with different wavenumbers are independent of each other and high parallelelism of the algorithm.They are solved using a finite-element algorithm combined with a chasing method,and the obtained solution is modified using a contraction operator.In this method,the vertical direction is reserved as the spatial domain,then grid size can be determined flexibly based on the underground current density distribution,which considers the solution accuracy and calculation efficiency.In addition,for the first time,we use the contraction operator in the integral equation method to iterate the algorithm.The algorithm takes advantage of the high efficiency of the standard Fourier transform and chasing method,as well as the fast convergence of the contraction operator.We verified the accuracy of the algorithm and the convergence of the contraction operator.Compared with a volume integral method and goal-oriented adaptive finite-element method,the proposed algorithm has lower memory requirements and high computational efficiency,making it suitable for calculating a model with large-scale nodes.Moreover,different examples are used to verify the high adaptability and parallelism of the proposed algorithm.The findings show that the 3D numerical simulation method of DC resistivity method in a mixed space-wavenumber domain is highly efficient,precise,and parallel.
文摘After developing the mathematical means for the correspondence of classical phase-space function to quantum-mechanical operators with symmetrical ordering of the basic canonical operators in the sense of Weyl the approach is applied to an infinite series of classical monomial functions of the canonical variables. These include as well as pure powers of the amplitude as also basic periodic functions of the phase φwith their quantum-mechanical correspondence. In the representation by number states, all the considered operators involve the Jacobi polynomials as the essential formative element. Whereas the quantity in normal ordering due to its indeterminacy leads to the introduction of the notions of sub- and super-Poissonian statistics the analogous quantity in (Weyl) symmetrical orderingis positive definite and satisfies an inequality. The notions of sub- and super-Poissonian statistics are problematic when they are used for the definition of nonclassicality of states since the mentioned measure in normal ordering does not determine the Poisson statistics in their middle in unique way but determines only a large set of statistics which may be very far in the sense of the Hilbert-Schmidt distance from a Poisson statistics that is discussed.
基金Ministry of Education—Singapore,Grant/Award Number:MOE‐2019‐T2‐1‐002National Natural Science Foundation of China,Grant/Award Numbers:21872100,U2032147Agency for Science,Technology and Research,Grant/Award Numbers:A1938c0035,A20G9b0135。
文摘Emulation of advanced synaptic functions of the human brain with electronic devices contributes an important step toward constructing high‐efficiency neuromorphic systems.Ferroelectric materials are promising candidates as synaptic weight elements in neural network hardware due to their controllable polarization states.However,the increased depolarization field at the na-noscale and the complex fabrication process of the traditional ferroelectric materials hamper the development of high‐density,low‐power,and highly sensitive synaptic devices.Here,we report the implementation of two‐dimensional(2D)ferroelectricα‐In_(2)Se_(3)as an active channel material to emulate typical synaptic functions.Theα‐In_(2)Se_(3)‐based synaptic device fea-tures multimode operations,enabled by the coupled ferroelectric polarization under various voltage pulses applied at both drain and gate terminals.Moreover,the energy consumption can be reduced to~1 pJ by using high‐κdielectric(Al2O3).The successful control of ferroelectric polarizations inα‐In_(2)Se_(3)and its application in artificial synapses are expected to inspire the implementation of 2D ferroelectric materials for future neuromorphic systems.
