A shift sampling theory established by author （1997a） is a generalization of Fourier transform computation theory. Based on this theory, I develop an Algorithm-Error （A-E） equation of potential field transformatio...A shift sampling theory established by author （1997a） is a generalization of Fourier transform computation theory. Based on this theory, I develop an Algorithm-Error （A-E） equation of potential field transformations in the wavenumber domain, which not only gives a more flexible algorithm of potential field transformations, but also reveals the law of error of potential field transformations in the wavenumber domain. The DFT0η η（0.5, 0.5） reduction-to-pole （RTP） technique derived from the A-E equation significantly improves the resolution and accuracy of RTP anomalies at low magnetic latitudes, including the magnetic equator. The law （origin, form mechanism, and essential properties） of the edge oscillation revealed by the A-E equation points out theoretically a way of improving the effect of existing padding methods in high-pass transformations in the wavenumber domain.展开更多
This paper introduces some concepts such as q- process in random environment, Laplace transformation, ergodic potential kernel, error function and some basic lemmas.We study the continuity and Laplace transformation o...This paper introduces some concepts such as q- process in random environment, Laplace transformation, ergodic potential kernel, error function and some basic lemmas.We study the continuity and Laplace transformation of random transition function. Finally, we give the sufficient condition for the existence of ergodic potential kernel for homogeneous q- processes in random environments.展开更多
We show that the technique of integration within an ordered product of operators can be extended to Hilbert transform. In so doing we derive normally ordered expansion of Coulomb potential-type operators directly by u...We show that the technique of integration within an ordered product of operators can be extended to Hilbert transform. In so doing we derive normally ordered expansion of Coulomb potential-type operators directly by using the mathematical Hilbert transform formula.展开更多
Despite substantial efforts in developing high-performance catalysts for the oxygen reduction reaction(ORR),the persistent challenge lies in the high onset overpotential of the ORR,and the effect of the elec-trolyte s...Despite substantial efforts in developing high-performance catalysts for the oxygen reduction reaction(ORR),the persistent challenge lies in the high onset overpotential of the ORR,and the effect of the elec-trolyte solution cannot be ignored.Consequently,we have systematically investigated the impact of adsorbate species and concentration,as well as solution pH,on the ORR activity on Pt(111)and Pt(poly)electrodes.The results all tend to establish a linear quantitative relationship between the onset potential for ORR and the adsorption equilibrium potential of the adsorbate.This finding indicates the decisive role of adsorbates in the onset potential for ORR,suggesting that the adsorption potential of adsorbates can serve as an intuitive criterion for ORR activity.Additional support for this conclusion is derived from experimental results obtained from the oxygen evolution reaction on Pt(poly)with different adsorbate species and from the hydrogen evolution reaction on Pt(111)with iodine adsorption.We further propose both an empirical equation for the onset potential for ORR and the concept of a potential-regulated adsor-bate shielding effect to elucidate the influence of adsorbates on ORR activity.This study provides new insights into the high onset overpotential of the ORR and offers potential strategies for predicting and enhancingORRactivity inthefuture.展开更多
In this paper, we made a new breakthrough, which proposes a new recursion–transform（RT） method with potential parameters to evaluate the nodal potential in arbitrary resistor networks. For the first time, we found ...In this paper, we made a new breakthrough, which proposes a new recursion–transform（RT） method with potential parameters to evaluate the nodal potential in arbitrary resistor networks. For the first time, we found the exact potential formulae of arbitrary m × n cobweb and fan networks by the RT method, and the potential formulae of infinite and semi-infinite networks are derived. As applications, a series of interesting corollaries of potential formulae are given by using the general formula, the equivalent resistance formula is deduced by using the potential formula, and we find a new trigonometric identity by comparing two equivalence results with different forms.展开更多
For the sustainable supply of mineral resources, blind deposits are becoming the emphasis of exploration after long-period exploitation of exposed deposits.The collection and analysis of gravity or magnetic data repre...For the sustainable supply of mineral resources, blind deposits are becoming the emphasis of exploration after long-period exploitation of exposed deposits.The collection and analysis of gravity or magnetic data represents one of the cheapest forms of large-scale geophysical exploration.With the identification of potential fields,we can get the map of worms or skeletonizations showing the three-dimension structure of shallow crust,and find the展开更多
For the sustainable supply of mineral resources, blind deposits are becoming the emphasis of exploration after long-period exploitation of exposed deposits.The collection and analysis of gravity or magnetic data repre...For the sustainable supply of mineral resources, blind deposits are becoming the emphasis of exploration after long-period exploitation of exposed deposits.The collection and analysis of gravity or magnetic data represents one of the cheapest ways of large-scale geophysical exploration.With the identification of potential mineral fields,we can get the map of worms or skeletonizations showing展开更多
A relativistic Mie-type potential for spin-1/2 particles is studied. The Dirac Hamiltonian contains a scalar S（r） and a vector V（r） Mie-type potential in the radial coordinates, as well as a tensor potential U（r...A relativistic Mie-type potential for spin-1/2 particles is studied. The Dirac Hamiltonian contains a scalar S（r） and a vector V（r） Mie-type potential in the radial coordinates, as well as a tensor potential U（r） in the form of Coulomb potential. In the pseudospin（p-spin） symmetry setting Σ = Cps and Δ = V（r）, an analytical solution for exact bound states of the corresponding Dirac equation is found. The eigenenergies and normalized wave functions are presented and particular cases are discussed with any arbitrary spin–orbit coupling number κ. Special attention is devoted to the caseΣ = 0 for which p-spin symmetry is exact. The Laplace transform approach（LTA） is used in our calculations. Some numerical results are obtained and compared with those of other methods.展开更多
To study the osteogenic potential of cultured bone marrow stromal cells transfected with transforming growth factor β 1 gene in vitro , cultured BMSCs were transfected with the complexes of pcDNA 3 TGF β ...To study the osteogenic potential of cultured bone marrow stromal cells transfected with transforming growth factor β 1 gene in vitro , cultured BMSCs were transfected with the complexes of pcDNA 3 TGF β 1 and Lipofectamine Reagent in vitro . The cell proliferation was detected by MTT method and the morphological features of transfected BMSCs was observed. ALP stains and PNP method were used to measure ALP activity. In addition, the collagen type Ⅰ propeptides and mineralized matrixes were examined by immunohistochemical staining and tetracycline fluorescence labeling respectively. The morphological and biological characters of the transfected BMSCs were similar to those of osteoblasts and the cell proliferation was promoted. The cell layer displayed strong positive reaction for ALP stains and immunohistochemical staining. ALP activity and collagen type Ⅰ expression increased remarkably after transfection. Mineralized matrixes formed earlier and more in transfected BMSCs as compared with control group. It is concluded that transfecting with TGF β 1 gene could promote the osteogenic potential of cultured BMSCs.展开更多
Based on pair potential, the Bragg Williams (B-W) model is modified to takeinto account the effect of the lattice parameter on theoretical order-disorder transformationanalysis. The main purpose of this work is to und...Based on pair potential, the Bragg Williams (B-W) model is modified to takeinto account the effect of the lattice parameter on theoretical order-disorder transformationanalysis. The main purpose of this work is to understand the basic aspects of this effect andrelated reasonable model on order-disorder transformation. In the present approach, theconfiguration free energy is chosen as function of the lattice parameter and the long-range order.This energy is calculated through Taylor's expansion, starting from the disordered state. It wasfound that the configuration free energy has been strongly modified when the lattice parameter istaken into account. It was also found only one type of order-disorder transformation exists in ABalloy and three kinds of order-disorder transformations for non-equiatomic alloy system such as A_3Balloy. This result is in agreement with experiments.展开更多
A vector potential of a magnetic field in Lagrangian is defined as the necessary partial solution of a inhomogeneous differential equation. The ＂gradient transformation＂ is an addition of arbitrary general solution ...A vector potential of a magnetic field in Lagrangian is defined as the necessary partial solution of a inhomogeneous differential equation. The ＂gradient transformation＂ is an addition of arbitrary general solution of the corresponding homogeneous equation that does not change the Lagrange equations. When dynamics is described by momenta and coordinates, this transformation is not the vector potential modification, which does not change expressions for other physical quantities, but a canonical transformation of momentum, which changes expressions for all fimctions of momentum, not changing the Poisson brackets, and, hence, the integrals of motion. The generating function of this transformation must reverse sign under the time-charge reversal. In quantum mechanics the unitary transformation corresponds to this canonical transformation. It also does not change the commutation relations. The phase of this unitary operator also must reverse sign under the time-charge reversal. Examples of necessary vector potentials for some magnetic fields are presented.展开更多
Using the Landau and symmetric gauges for the vector potential of a constant magnetic field and the quantum problem of a charged particle moving on a flat surface, we show the classical electromagnetic gauge transform...Using the Landau and symmetric gauges for the vector potential of a constant magnetic field and the quantum problem of a charged particle moving on a flat surface, we show the classical electromagnetic gauge transformation does not correspond to a one-dimensional unitary group transformation U(1) of the wave function for the quantum case. In addition, with the re-examination of the relation between the magnetic field B and its vector potential A, we found that, in order to have a consistent formulation of the dynamics of the charged particle with both expressions, we must have that B=∇×A if and only if B≠0.展开更多
By the Backlund transformation method, an important （2＋1）-dimensional nonlinear barotropie and quasigeostrophic potential vorticity （BQGPV） equation is investigated. Some simple special Backlund transformation th...By the Backlund transformation method, an important （2＋1）-dimensional nonlinear barotropie and quasigeostrophic potential vorticity （BQGPV） equation is investigated. Some simple special Backlund transformation theorems are proposed and used to get explicit solutions of the BQGPV equation. Furthermore, all solutions of a second order linear ordinary differential equation including an arbitrary function can be used to construct explicit solutions of the （2＋1）-dimensional BQGPV equation. Some figures are also given out to describe these solutions.展开更多
文摘A shift sampling theory established by author （1997a） is a generalization of Fourier transform computation theory. Based on this theory, I develop an Algorithm-Error （A-E） equation of potential field transformations in the wavenumber domain, which not only gives a more flexible algorithm of potential field transformations, but also reveals the law of error of potential field transformations in the wavenumber domain. The DFT0η η（0.5, 0.5） reduction-to-pole （RTP） technique derived from the A-E equation significantly improves the resolution and accuracy of RTP anomalies at low magnetic latitudes, including the magnetic equator. The law （origin, form mechanism, and essential properties） of the edge oscillation revealed by the A-E equation points out theoretically a way of improving the effect of existing padding methods in high-pass transformations in the wavenumber domain.
基金Supported by the National Natural Science Foundation of China (10371092)
文摘This paper introduces some concepts such as q- process in random environment, Laplace transformation, ergodic potential kernel, error function and some basic lemmas.We study the continuity and Laplace transformation of random transition function. Finally, we give the sufficient condition for the existence of ergodic potential kernel for homogeneous q- processes in random environments.
基金The project supported by the President Foundation of the Chinese Academy of Sciences and National Natural Science Foundation of China under Grant No. 10475056.
文摘We show that the technique of integration within an ordered product of operators can be extended to Hilbert transform. In so doing we derive normally ordered expansion of Coulomb potential-type operators directly by using the mathematical Hilbert transform formula.
基金supported by the National Natural Science Foundation of China(no.22372154,21972131).
文摘Despite substantial efforts in developing high-performance catalysts for the oxygen reduction reaction(ORR),the persistent challenge lies in the high onset overpotential of the ORR,and the effect of the elec-trolyte solution cannot be ignored.Consequently,we have systematically investigated the impact of adsorbate species and concentration,as well as solution pH,on the ORR activity on Pt(111)and Pt(poly)electrodes.The results all tend to establish a linear quantitative relationship between the onset potential for ORR and the adsorption equilibrium potential of the adsorbate.This finding indicates the decisive role of adsorbates in the onset potential for ORR,suggesting that the adsorption potential of adsorbates can serve as an intuitive criterion for ORR activity.Additional support for this conclusion is derived from experimental results obtained from the oxygen evolution reaction on Pt(poly)with different adsorbate species and from the hydrogen evolution reaction on Pt(111)with iodine adsorption.We further propose both an empirical equation for the onset potential for ORR and the concept of a potential-regulated adsor-bate shielding effect to elucidate the influence of adsorbates on ORR activity.This study provides new insights into the high onset overpotential of the ORR and offers potential strategies for predicting and enhancingORRactivity inthefuture.
基金Project supported by the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20161278)
文摘In this paper, we made a new breakthrough, which proposes a new recursion–transform（RT） method with potential parameters to evaluate the nodal potential in arbitrary resistor networks. For the first time, we found the exact potential formulae of arbitrary m × n cobweb and fan networks by the RT method, and the potential formulae of infinite and semi-infinite networks are derived. As applications, a series of interesting corollaries of potential formulae are given by using the general formula, the equivalent resistance formula is deduced by using the potential formula, and we find a new trigonometric identity by comparing two equivalence results with different forms.
文摘For the sustainable supply of mineral resources, blind deposits are becoming the emphasis of exploration after long-period exploitation of exposed deposits.The collection and analysis of gravity or magnetic data represents one of the cheapest forms of large-scale geophysical exploration.With the identification of potential fields,we can get the map of worms or skeletonizations showing the three-dimension structure of shallow crust,and find the
文摘For the sustainable supply of mineral resources, blind deposits are becoming the emphasis of exploration after long-period exploitation of exposed deposits.The collection and analysis of gravity or magnetic data represents one of the cheapest ways of large-scale geophysical exploration.With the identification of potential mineral fields,we can get the map of worms or skeletonizations showing
文摘A relativistic Mie-type potential for spin-1/2 particles is studied. The Dirac Hamiltonian contains a scalar S（r） and a vector V（r） Mie-type potential in the radial coordinates, as well as a tensor potential U（r） in the form of Coulomb potential. In the pseudospin（p-spin） symmetry setting Σ = Cps and Δ = V（r）, an analytical solution for exact bound states of the corresponding Dirac equation is found. The eigenenergies and normalized wave functions are presented and particular cases are discussed with any arbitrary spin–orbit coupling number κ. Special attention is devoted to the caseΣ = 0 for which p-spin symmetry is exact. The Laplace transform approach（LTA） is used in our calculations. Some numerical results are obtained and compared with those of other methods.
文摘To study the osteogenic potential of cultured bone marrow stromal cells transfected with transforming growth factor β 1 gene in vitro , cultured BMSCs were transfected with the complexes of pcDNA 3 TGF β 1 and Lipofectamine Reagent in vitro . The cell proliferation was detected by MTT method and the morphological features of transfected BMSCs was observed. ALP stains and PNP method were used to measure ALP activity. In addition, the collagen type Ⅰ propeptides and mineralized matrixes were examined by immunohistochemical staining and tetracycline fluorescence labeling respectively. The morphological and biological characters of the transfected BMSCs were similar to those of osteoblasts and the cell proliferation was promoted. The cell layer displayed strong positive reaction for ALP stains and immunohistochemical staining. ALP activity and collagen type Ⅰ expression increased remarkably after transfection. Mineralized matrixes formed earlier and more in transfected BMSCs as compared with control group. It is concluded that transfecting with TGF β 1 gene could promote the osteogenic potential of cultured BMSCs.
基金This work was financially supported by the National Natural Science Foundation of China under contract No. 59895151-01.
文摘Based on pair potential, the Bragg Williams (B-W) model is modified to takeinto account the effect of the lattice parameter on theoretical order-disorder transformationanalysis. The main purpose of this work is to understand the basic aspects of this effect andrelated reasonable model on order-disorder transformation. In the present approach, theconfiguration free energy is chosen as function of the lattice parameter and the long-range order.This energy is calculated through Taylor's expansion, starting from the disordered state. It wasfound that the configuration free energy has been strongly modified when the lattice parameter istaken into account. It was also found only one type of order-disorder transformation exists in ABalloy and three kinds of order-disorder transformations for non-equiatomic alloy system such as A_3Balloy. This result is in agreement with experiments.
文摘A vector potential of a magnetic field in Lagrangian is defined as the necessary partial solution of a inhomogeneous differential equation. The ＂gradient transformation＂ is an addition of arbitrary general solution of the corresponding homogeneous equation that does not change the Lagrange equations. When dynamics is described by momenta and coordinates, this transformation is not the vector potential modification, which does not change expressions for other physical quantities, but a canonical transformation of momentum, which changes expressions for all fimctions of momentum, not changing the Poisson brackets, and, hence, the integrals of motion. The generating function of this transformation must reverse sign under the time-charge reversal. In quantum mechanics the unitary transformation corresponds to this canonical transformation. It also does not change the commutation relations. The phase of this unitary operator also must reverse sign under the time-charge reversal. Examples of necessary vector potentials for some magnetic fields are presented.
文摘Using the Landau and symmetric gauges for the vector potential of a constant magnetic field and the quantum problem of a charged particle moving on a flat surface, we show the classical electromagnetic gauge transformation does not correspond to a one-dimensional unitary group transformation U(1) of the wave function for the quantum case. In addition, with the re-examination of the relation between the magnetic field B and its vector potential A, we found that, in order to have a consistent formulation of the dynamics of the charged particle with both expressions, we must have that B=∇×A if and only if B≠0.
基金Supported by the National Natural Science Foundation of China under Grant Nos. 10735030, 90718041, and 40975038Shanghai Leading Academic Discipline Project under Grant No. B412Program for Changjiang Scholars and Innovative Research Team in University (IRT0734)
文摘By the Backlund transformation method, an important （2＋1）-dimensional nonlinear barotropie and quasigeostrophic potential vorticity （BQGPV） equation is investigated. Some simple special Backlund transformation theorems are proposed and used to get explicit solutions of the BQGPV equation. Furthermore, all solutions of a second order linear ordinary differential equation including an arbitrary function can be used to construct explicit solutions of the （2＋1）-dimensional BQGPV equation. Some figures are also given out to describe these solutions.
