By means of the reductive perturbation method, three types of generalized （2＋l）-dimensional Kadomtsev- Petviashvili （KP） equations are derived from the baroclinic potential vorticity （BPV） equation, including t...By means of the reductive perturbation method, three types of generalized （2＋l）-dimensional Kadomtsev- Petviashvili （KP） equations are derived from the baroclinic potential vorticity （BPV） equation, including the modified KP （mKP） equation, standard KP equation and cylindrical KP （cKP） equation. Then some solutions of generalized cKP and KP equations with certain conditions are given directly and a relationship between the generalized mKP equation and the mKP equation is established by the symmetry group direct method proposed by Lou et al. From the relationship and the solutions of the mKP equation, some solutions of the generalized mKP equation can be obtained. Furthermore, some approximate solutions of the baroclinic potential vorticity equation are derived from three types of generalized KP equations.展开更多
The aim of this paper is to investigate the superstability problem for the pexiderized trigonometric functional equation∑ v∈Φ∫Kf（xkv（y）k^-1）dwK（k）= Φ g（x）h（y）, x, y ∈ G,where G is any topological group...The aim of this paper is to investigate the superstability problem for the pexiderized trigonometric functional equation∑ v∈Φ∫Kf（xkv（y）k^-1）dwK（k）= Φ g（x）h（y）, x, y ∈ G,where G is any topological group, K is a compact subgroup of G, ωK is the normalized Haar measure of K, Φ is a finite group of K-invariant morphisms of G and f, g, h are continuous complex-valued functions.Consequently, we have generalized the results of stability for d＇Alembert＇s and Wilson＇s equations by R. Badora, J. Baker, B. Bouikhalene, P. Gavruta, S. Kabbaj, Pl. Kannappan, G. H.Kim, J.M. Rassias, A. Roukbi, L. Sz′ekelyhidi, D. Zeglami, etc.展开更多
A new viewpoint of computer program poubaix diagram was proposed on traditional φ pH diagrams. All equilibrium principle and activity term method were used to plot φ pH diagrams for M H 2O systems based on the therm...A new viewpoint of computer program poubaix diagram was proposed on traditional φ pH diagrams. All equilibrium principle and activity term method were used to plot φ pH diagrams for M H 2O systems based on the thermochemical database developed. And a new method——arithmetic geometric method is used to solve nonlinear equations group. The calculation procedure is proved to be efficient and convergent. The method seldom depends on artificial intervention and can extend to multi component all equilibrium φ pH diagrams such as M ligand H 2O system. [展开更多
Most of previous work on applying the conformal group to quantum fields has emphasized its invariant aspects, whereas in this paper we find that the conformal group can give us running quantum fields, with some consta...Most of previous work on applying the conformal group to quantum fields has emphasized its invariant aspects, whereas in this paper we find that the conformal group can give us running quantum fields, with some constants, vertex and Green functions running, compatible with the scaling properties of renormalization group method （RGM）. We start with the renormalization group equation （RGE）, in which the differential operator happens to be a generator of the conformal group, named dilatation operator. In addition we link the operator/spatial representation and unitary/spinor representation of the conformal group by inquiring a conformal-invariant interaction vertex mimicking the similar process of Lorentz transformation applied to Dirac equation. By this kind of application, we find out that quite a few interaction vertices are separately invaxiant under certain transformations （generators） of the conformal group. The significance of these transformations and vertices is explained. Using a particular generator of the conformal group, we suggest a new equation analogous to RGE which may lead a system to evolve from asymptotic regime to nonperturbative regime, in contrast to the effect of the conventional RGE from nonperturbative regime to asymptotic regime.展开更多
Diffraction intensities of the 3D ptychographic iterative engine(3PIE)were written as a set of linear equations of the selfcorrelations of Fourier components of all sample slices,and an effective computing method was ...Diffraction intensities of the 3D ptychographic iterative engine(3PIE)were written as a set of linear equations of the selfcorrelations of Fourier components of all sample slices,and an effective computing method was developed to solve these linear equations for the transmission functions of all sample slices analytically.With both theoretical analysis and numerical simulations,this study revealed the underlying physics and mathematics of 3PIE and demonstrated for the first time,to our knowledge,that 3PIE can generate mathematically unique reconstruction even with noisy data.展开更多
In this study,we reanalyze the top-quark pair production at next-to-next-to-leading order(NNLO)in quantum chromodynamics(QCD)at future e^(+)e^(−)colliders using the Principle of Maximum Conformality(PMC)method.The PMC...In this study,we reanalyze the top-quark pair production at next-to-next-to-leading order(NNLO)in quantum chromodynamics(QCD)at future e^(+)e^(−)colliders using the Principle of Maximum Conformality(PMC)method.The PMC renormalization scales inαs are determined by absorbing the non-conformalβterms by recursively using the Renormalization Group Equation(RGE).Unlike the conventional scale-setting method of fixing the scale at the center-of-mass energyμ_(r)=√s,the determined PMC scale Q_(⋆)is far smaller than the √sand increases with the √s,yielding the correct physical behavior for the top-quark pair production process.Moreover,the convergence of the pQCD series for the top-quark pair production is greatly improved owing to the elimination of the renormalon divergence.For a typical collision energy of √s=500 GeV,the PMC scale is Q_(⋆)=107 GeV;the QCD correction factor K for conventional results is K∼1+0.1244+0.0102+0.0012−0.0087−0.0011+0.0184−0.0086+0.0002+0.0061−0.0003,where the first error is caused by varying the scaleμr∈[√s/2,2√s]and the second error is from the top-quark massΔm_(t)=±0.7 GeV.After applying the PMC,the renormalization scale uncertainty is eliminated,and the QCD correction factor K is improved to K∼1+0.1507_(−0.0015)^(+0.0015)−0.0057_(−0.0000)^(+0.0001),where the error is from the top-quark massΔm_(t)=±0.7 GeV.The PMC improved predictions for the top-quark pair production are helpful for detailed studies of the properties of the top-quark at future e^(+)e^(−)colliders.展开更多
The polarized distribution functions of mesons, including pion, kaon and eta, using the proton structure function, are calculated. We are looking for a relationship between the polarized distribution of mesons and the...The polarized distribution functions of mesons, including pion, kaon and eta, using the proton structure function, are calculated. We are looking for a relationship between the polarized distribution of mesons and the polarized structure of nucleons. We show that the meson polarized parton distributions leads to zero total spin for the concerned mesons, considering the orbital angular momentum of quarks and gluons inside the meson. Two separate Monte Carlo algorithms are applied to compute the polarized parton distributions of the kaon. Via the mass dependence of quark distributions, the distribution function of the eta meson is obtained. A new method by which the polarized sea quark distributions of protons are evolved separately which cannot be performed easily using the standard solution of DGLAP equations - is introduced. The mass dependence of these distributions is obtained, using the renormalization group equation which makes their evolutions more precise. Comparison between the evolved distributions and the available experimental data validates the suggested solutions for separated evolutions.展开更多
The recent global analysis of three-flavor neutrino oscillation data indicates that the normal neutrino mass ordering is favored over the inverted one at the 3σ level, and the best-fit values of the largest neutrino ...The recent global analysis of three-flavor neutrino oscillation data indicates that the normal neutrino mass ordering is favored over the inverted one at the 3σ level, and the best-fit values of the largest neutrino mixing angle 023 and the Dirac CP-violating phase δ are located in the higher octant and third quadrant, respectively. We show that all these important issues can be naturally explained by the μ-τ reflection symmetry breaking of massive neutrinos from a superhigh energy scale down to the electroweak scale owing to the one-loop renormalization-group equations （RGEs） in the minimal supersymmetric standard model （MSSM）. The complete parameter space is explored for the first time in both the Majorana and Dirac cases, by allowing the smallest neutrino mass m1 and the MSSM parameter tanβ to vary within their reasonable regions.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos.10735030 and 40775042)Ningbo Natural Science Foundation (Grant No. 2008A610017)+1 种基金National Basic Research Program of China (973 Program) (Grant Nos. 2005CB422301 and 2007CB814800)K.C. Wong Magna Fund in Ningbo University
文摘By means of the reductive perturbation method, three types of generalized （2＋l）-dimensional Kadomtsev- Petviashvili （KP） equations are derived from the baroclinic potential vorticity （BPV） equation, including the modified KP （mKP） equation, standard KP equation and cylindrical KP （cKP） equation. Then some solutions of generalized cKP and KP equations with certain conditions are given directly and a relationship between the generalized mKP equation and the mKP equation is established by the symmetry group direct method proposed by Lou et al. From the relationship and the solutions of the mKP equation, some solutions of the generalized mKP equation can be obtained. Furthermore, some approximate solutions of the baroclinic potential vorticity equation are derived from three types of generalized KP equations.
文摘The aim of this paper is to investigate the superstability problem for the pexiderized trigonometric functional equation∑ v∈Φ∫Kf（xkv（y）k^-1）dwK（k）= Φ g（x）h（y）, x, y ∈ G,where G is any topological group, K is a compact subgroup of G, ωK is the normalized Haar measure of K, Φ is a finite group of K-invariant morphisms of G and f, g, h are continuous complex-valued functions.Consequently, we have generalized the results of stability for d＇Alembert＇s and Wilson＇s equations by R. Badora, J. Baker, B. Bouikhalene, P. Gavruta, S. Kabbaj, Pl. Kannappan, G. H.Kim, J.M. Rassias, A. Roukbi, L. Sz′ekelyhidi, D. Zeglami, etc.
文摘A new viewpoint of computer program poubaix diagram was proposed on traditional φ pH diagrams. All equilibrium principle and activity term method were used to plot φ pH diagrams for M H 2O systems based on the thermochemical database developed. And a new method——arithmetic geometric method is used to solve nonlinear equations group. The calculation procedure is proved to be efficient and convergent. The method seldom depends on artificial intervention and can extend to multi component all equilibrium φ pH diagrams such as M ligand H 2O system. [
文摘Most of previous work on applying the conformal group to quantum fields has emphasized its invariant aspects, whereas in this paper we find that the conformal group can give us running quantum fields, with some constants, vertex and Green functions running, compatible with the scaling properties of renormalization group method （RGM）. We start with the renormalization group equation （RGE）, in which the differential operator happens to be a generator of the conformal group, named dilatation operator. In addition we link the operator/spatial representation and unitary/spinor representation of the conformal group by inquiring a conformal-invariant interaction vertex mimicking the similar process of Lorentz transformation applied to Dirac equation. By this kind of application, we find out that quite a few interaction vertices are separately invaxiant under certain transformations （generators） of the conformal group. The significance of these transformations and vertices is explained. Using a particular generator of the conformal group, we suggest a new equation analogous to RGE which may lead a system to evolve from asymptotic regime to nonperturbative regime, in contrast to the effect of the conventional RGE from nonperturbative regime to asymptotic regime.
基金This work was supported by the National Natural Science Foundation of China(No.61827816).
文摘Diffraction intensities of the 3D ptychographic iterative engine(3PIE)were written as a set of linear equations of the selfcorrelations of Fourier components of all sample slices,and an effective computing method was developed to solve these linear equations for the transmission functions of all sample slices analytically.With both theoretical analysis and numerical simulations,this study revealed the underlying physics and mathematics of 3PIE and demonstrated for the first time,to our knowledge,that 3PIE can generate mathematically unique reconstruction even with noisy data.
基金the Natural Science Foundation of China(12175025,12147102,12265011)by the Projects of Guizhou Provincial Department(YQK[2023]016,ZK[2023]141,[2020]1Y027,GZMUZK[2022]PT01)。
文摘In this study,we reanalyze the top-quark pair production at next-to-next-to-leading order(NNLO)in quantum chromodynamics(QCD)at future e^(+)e^(−)colliders using the Principle of Maximum Conformality(PMC)method.The PMC renormalization scales inαs are determined by absorbing the non-conformalβterms by recursively using the Renormalization Group Equation(RGE).Unlike the conventional scale-setting method of fixing the scale at the center-of-mass energyμ_(r)=√s,the determined PMC scale Q_(⋆)is far smaller than the √sand increases with the √s,yielding the correct physical behavior for the top-quark pair production process.Moreover,the convergence of the pQCD series for the top-quark pair production is greatly improved owing to the elimination of the renormalon divergence.For a typical collision energy of √s=500 GeV,the PMC scale is Q_(⋆)=107 GeV;the QCD correction factor K for conventional results is K∼1+0.1244+0.0102+0.0012−0.0087−0.0011+0.0184−0.0086+0.0002+0.0061−0.0003,where the first error is caused by varying the scaleμr∈[√s/2,2√s]and the second error is from the top-quark massΔm_(t)=±0.7 GeV.After applying the PMC,the renormalization scale uncertainty is eliminated,and the QCD correction factor K is improved to K∼1+0.1507_(−0.0015)^(+0.0015)−0.0057_(−0.0000)^(+0.0001),where the error is from the top-quark massΔm_(t)=±0.7 GeV.The PMC improved predictions for the top-quark pair production are helpful for detailed studies of the properties of the top-quark at future e^(+)e^(−)colliders.
文摘The polarized distribution functions of mesons, including pion, kaon and eta, using the proton structure function, are calculated. We are looking for a relationship between the polarized distribution of mesons and the polarized structure of nucleons. We show that the meson polarized parton distributions leads to zero total spin for the concerned mesons, considering the orbital angular momentum of quarks and gluons inside the meson. Two separate Monte Carlo algorithms are applied to compute the polarized parton distributions of the kaon. Via the mass dependence of quark distributions, the distribution function of the eta meson is obtained. A new method by which the polarized sea quark distributions of protons are evolved separately which cannot be performed easily using the standard solution of DGLAP equations - is introduced. The mass dependence of these distributions is obtained, using the renormalization group equation which makes their evolutions more precise. Comparison between the evolved distributions and the available experimental data validates the suggested solutions for separated evolutions.
基金Supported by the National Natural Science Foundation of China(11775231,11775232)
文摘The recent global analysis of three-flavor neutrino oscillation data indicates that the normal neutrino mass ordering is favored over the inverted one at the 3σ level, and the best-fit values of the largest neutrino mixing angle 023 and the Dirac CP-violating phase δ are located in the higher octant and third quadrant, respectively. We show that all these important issues can be naturally explained by the μ-τ reflection symmetry breaking of massive neutrinos from a superhigh energy scale down to the electroweak scale owing to the one-loop renormalization-group equations （RGEs） in the minimal supersymmetric standard model （MSSM）. The complete parameter space is explored for the first time in both the Majorana and Dirac cases, by allowing the smallest neutrino mass m1 and the MSSM parameter tanβ to vary within their reasonable regions.
