In this article, we study the nonlinear stochastic heat equation in the spatial domain R^d subject to a Gaussian noise which is white in time and colored in space. The spatial correlation can be any symmetric, nonnega...In this article, we study the nonlinear stochastic heat equation in the spatial domain R^d subject to a Gaussian noise which is white in time and colored in space. The spatial correlation can be any symmetric, nonnegative and nonnegative-definite function that satisfies Dalang's condition. We establish the existence and uniqueness of a random field solution starting from measure-valued initial data. We find the upper and lower bounds for the second moment. With these moment bounds, we first establish some necessary and sufficient conditions for the phase transition of the moment Lyapunov exponents, which extends the classical results from the stochastic heat equation on Z^d to that on R^d.Then, we prove a localization result for the intermittency fronts, which extends results by Conus and Khoshnevisan [9] from one space dimension to higher space dimension. The linear case has been recently proved by Huang et al [17] using different techniques.展开更多
Carbon sulfide cation (CS^+) plays a dominant role in some astrophysical atmosphere environments.In this work,the rovibrational transition lines are computed for the lowest three electronic states,in which the interna...Carbon sulfide cation (CS^+) plays a dominant role in some astrophysical atmosphere environments.In this work,the rovibrational transition lines are computed for the lowest three electronic states,in which the internally contracted multireference configuration interaction approach (MRCI) with Davison size-extensivity correction (+Q) is employed to calculate the potential curves and dipole moments,and then the vibrational energies and spectroscopic constants are extracted.The Frank–Condon factors are calculated for the bands of X^2∑^+,A^2П and X^2∑^+–B^2∑^+ systems,and the band of X^2∑^+–A^2П is in good agreement with the available experimental results.Transition dipole moments and the radiative lifetimes of the low-lying three states are evaluated.The opacities of the CS+ molecule are computed at different temperatures under the pressure of 100 atms.It is found that as temperature increases,the band systems associated with different transitions for the three states become dim because of the increased population on the vibrational states and excited electronic states at high temperature.展开更多
A novel method for estimation of an aerodynamic force and moment acting on an irregularly shaped body (such as HE projectile fragments) during its flight through the atmosphere is presented. The model assumes that fra...A novel method for estimation of an aerodynamic force and moment acting on an irregularly shaped body (such as HE projectile fragments) during its flight through the atmosphere is presented. The model assumes that fragments can be approximated with a tri-axial ellipsoid that has continuous surface given as a mathematical function. The model was validated with CFD data for a tri-axial ellipsoid and verified using CFD data on aerodynamic forces and moments acting on an irregularly shaped fragment. The contribution of this method is that it represents a significant step toward a modeling that does not require a cumbersome CFD simulation results for estimation of fragment dynamic and kinematic parameters. Due to this advantage, the model can predict the fragment motion consuming a negligible time when compared to the corresponding time consumed by CFD simulations. Parametric representation (generalization) of the fragment geometrical data and the conditions provides the way to analyze various correlations and how parameters influence the dynamics of the fragment flight.展开更多
In this paper, an empirical model based on self-evolving neural network is proposed for predicting the flexural behavior of ferrocement elements. The model is meant to serve as a simple but reliable tool for estimatin...In this paper, an empirical model based on self-evolving neural network is proposed for predicting the flexural behavior of ferrocement elements. The model is meant to serve as a simple but reliable tool for estimating the moment capacity of ferrocement members. The proposed model is trained and validated using experimental data obtained from the literature. The data consists of information regarding flexural tests on ferrocement specimens which include moment capacity and cross-sectional dimensions of specimens, concrete cube compressive strength, tensile strength and volume fraction of wire mesh. Comparisons of predictions of the proposed models with experimental data indicated that the models are capable of accurately estimating the moment capacity of ferrocement members. The proposed models also make better predictions compared to methods such as the plastic analysis method and the mechanism approach. Further comparisons with other data mining techniques including the back-propagation network, the adaptive spline, and the Kriging regression models indicated that the proposed models are superior in terms prediction accuracy despite being much simpler models. The performance of the proposed models was also found to be comparable to the GEP-based surrogate model.展开更多
In this paper,we first derive two types of transformed Franklin polynomial:substituted and weighted radial Franklin polynomials.Two radial orthogonal moments are proposed based on these two types of polynomials,namely...In this paper,we first derive two types of transformed Franklin polynomial:substituted and weighted radial Franklin polynomials.Two radial orthogonal moments are proposed based on these two types of polynomials,namely substituted Franklin-Fourier moments and weighted Franklin-Fourier moments(SFFMs and WFFMs),which are orthogonal in polar coordinates.The radial kernel functions of SFFMs and WFFMs are transformed Franklin functions and Franklin functions are composed of a class of complete orthogonal splines function system of degree one.Therefore,it provides the possibility of avoiding calculating high order polynomials,and thus the accurate values of SFFMs and WFFMs can be obtained directly with little computational cost.Theoretical and experimental results show that Franklin functions are not well suited for constructing higher-order moments of SFFMs and WFFMs,but compared with traditional orthogonal moments(e.g.,BFMs,OFMs and ZMs)in polar coordinates,the proposed two types of Franklin-Fourier Moments have better performance respectively in lower-order moments.展开更多
This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations (for example, stochastic heat equations) driven by Gaussian noise of various covarianc...This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations (for example, stochastic heat equations) driven by Gaussian noise of various covariance structures. The focus is on the existence and uniqueness of the classical (square integrable) solution (mild solution, weak solution). It is also concerned with the Feynman-Kac formula for the solution;Feynman-Kac formula for the moments of the solution;and their applications to the asymptotic moment bounds of the solution. It also briefly touches the exact asymptotics of the moments of the solution.展开更多
The newly observed isomer and ground-state band in the odd-Z neutron-rich rare-earth nucleus 163 Eu are investigated by using the cranked shell model(CSM), with pairing treated by the particle-number conserving(PNC)me...The newly observed isomer and ground-state band in the odd-Z neutron-rich rare-earth nucleus 163 Eu are investigated by using the cranked shell model(CSM), with pairing treated by the particle-number conserving(PNC)method. This is the first time detailed theoretical investigations are performed of the observed 964(1) keV isomer and ground-state rotational band in 163 Eu. The experimental data are reproduced very well by the theoretical results. The configuration of the 964(1) keV isomer is assigned as the three-particle state 13^-/2(v7^+/2 [633]■v1^-/2[521]■π5^+/2[413]).More low-lying multi-particle states are predicted in 163 Eu. Due to its significant effect on the nuclear mean field, the high-order ε6 deformation plays an important role in the energy and configuration assignment of the multi-particle states. Compared to its neighboring even-even nuclei 162 Sm and 164 Gd,there is a 10%15% increase of J(1) of the oneparticle ground-state band in 163 Eu. This is explained by the pairing reduction due to the blocking of the nucleon on the proton π5+/2 [413] orbital in 163 Eu.展开更多
Photoionization time delays have been studied in many streaking experiments in which an attosecond pulse is used to ionize the atomic or solid state target in the presence of a dressing infrared laser field. Among the...Photoionization time delays have been studied in many streaking experiments in which an attosecond pulse is used to ionize the atomic or solid state target in the presence of a dressing infrared laser field. Among the methods of extracting the time delay from the streaking spectrogram, the simplest one is to calculate the first moment of the spectrogram and to measure its offset relative to the vector potential of the infrared field. The first moment method has been used in many theoretical simulations and analysis of experimental data, but the meaning of this offset needs to be investigated. We simulate the spectrograms and compare the extracted time delay from the first moment with the input Wigner delay. In this study, we show that the first moment method is valid only when the group delay dispersions corresponding to both the spectral phase of the attosecond pulse and the phase of the single-photon transition dipole matrix element of the target are small. Under such circumstance, the electron wave packet behaves like a classical particle and the extracted time delay can be related to a group delay in the photoionization process. To avoid ambiguity and confusion, we also suggest that the photoionization time delay be replaced by photoionization group delay and the Wigner time delay be replaced by Wigner group delay.展开更多
We theoretically investigate the excited state intramolecular proton transfer(ESIPT) behavior of the novel fluorophore bis-imine derivative molecule HNP which was designed based on the intersection of 1-(hydrazonometh...We theoretically investigate the excited state intramolecular proton transfer(ESIPT) behavior of the novel fluorophore bis-imine derivative molecule HNP which was designed based on the intersection of 1-(hydrazonomethyl)-naphthalene-2-ol and 1-pyrenecarboxaldehyde. Especially, the density functional theory(DFT) and time-dependent density functional theory(TDDFT) methods for HNP monomer are introduced. Moreover, the 'our own n-layered integrated molecular orbital and molecular mechanics'(ONIOM) method(TDDFT:universal force field(UFF)) is used to reveal the aggregation-induced emission(AIE) effect on the ESIPT process for HNP in crystal. Our results confirm that the ESIPT process happens upon the photoexcitation for the HNP monomer and HNP in crystal, which is distinctly monitored by the optimized geometric structures and the potential energy curves. In addition, the results of potential energy curves reveal that the ESIPT process in HNP will be promoted by the AIE effect. Furthermore, the highest occupied molecular orbital(HOMO) and lowest unoccupied molecular orbital(LUMO) for the HNP monomer and HNP in crystal have been calculated. The calculation demonstrates that the electron density decrease of proton donor caused by excitation promotes the ESIPT process. In addition, we find that the variation of atomic dipole moment corrected Hirshfeld population(ADCH) charge for proton acceptor induced by the AIE effect facilitates the ESIPT process. The results will be expected to deepen the understanding of ESIPT dynamics for luminophore under the AIE effect and provide insight into future design of high-efficient AIE compounds.展开更多
This paper addresses the narrative construction of the moment of death as depicted in Tolstoy’s Anna Karenina and in Barnes’s The Sense of an Ending. Following Orr’s definition of positive influence, described as a...This paper addresses the narrative construction of the moment of death as depicted in Tolstoy’s Anna Karenina and in Barnes’s The Sense of an Ending. Following Orr’s definition of positive influence, described as a “site for cultural renewal”, it pursues the analysis of complexity and confluence of literary traditions in these texts. Though both Anna Karenina and The Sense of an Ending seem to insist on portraying a chronicle of struggle between a moment and a process of dying, it is nevertheless a physical moment of life ending which becomes an intensely condensed, and almost photographic, representation of the intimate, psychologically depicted, dying process. It is argued that the moment of death reveals, for instance, Anna’s unresolved internal conflict between psychological and physiological phenomena shaping human behaviour. Similarly, Barnes’s The Sense of an Ending builds upon a subtle dialogic tension between a process of psychological dying and a moment of physically conceived death. Specifically, this paper brings to light the repetitive occurence of the intense epiphanic moments which shape the thematic and the structural development of both Anna Karenina and The Sense of an Ending.展开更多
Last night,I went to see a movie with my friends.I was immersed in the story.It was my first time going out at night.Because my parents never let me do that before.Now they think I have grown up and I can protect myse...Last night,I went to see a movie with my friends.I was immersed in the story.It was my first time going out at night.Because my parents never let me do that before.Now they think I have grown up and I can protect myself,so they allowed me to go out at night.It was such a happy moment for me.展开更多
This note is concerned with a new direct(non-iterative)method for the solution of an elliptic inverse problem.This method is based on the application of the Green's second identity which leads to a moment problem ...This note is concerned with a new direct(non-iterative)method for the solution of an elliptic inverse problem.This method is based on the application of the Green's second identity which leads to a moment problem for the unknown boundary condition.Tikhonov regularization is used to obtain a stable and close approximation of the missing boundary condition without any need for iterations.Four examples are used to study the applicability of the method with the presence of noise.展开更多
The melt-spun SmFe12Bx(x = 0, 0.50, 0.75,1.00, 1.25 and 1.50) ribbons were prepared at 40 m·s-1,and their structure and magnetic properties were studied by powder X-ray diffraction(XRD), vibrating sample magnetom...The melt-spun SmFe12Bx(x = 0, 0.50, 0.75,1.00, 1.25 and 1.50) ribbons were prepared at 40 m·s-1,and their structure and magnetic properties were studied by powder X-ray diffraction(XRD), vibrating sample magnetometer(VSM) and transmission electron microscopy(TEM). XRD results indicate that SmFe12Bx alloys with 0.50 ≤ x ≤ 1.00 are composed of single-phase TbCu7-type structure. Moreover, it is found that the boron addition can inhibit the emergence of soft magnetic phase a-Fe and result in the increase in the axial ratio c/a. After annealing at 650 ℃ for 0.5 h, the metastable phase TbCu7 initially decomposes into the stable phase Sm2Fe14B(Nd2Fe14B-type) and a-Fe. The value of magnetic moment per Fe atom increases slightly from 1.75 uB for boron-free sample to 1.80 uB for the x = 0.75 sample and then decreases again.In addition, the best magnetic properties of maximum energy product [(BH)max] of 14.56 kJ·m^-3, coercivity(Hcj)of 172.6 kA·m^-1 and remanence(Br) of 0.45 T are obtained for the SmFe12B1.00 alloy. Based on transmission electron microscopy(TEM) results, the average size of grains is around 197 nm for B-free sample and decreases to 95 nm for x = 1.00 sample, indicating that the addition of boron can refine grains.展开更多
The p-th moment and almos t sure st ability with general decay rate of the exact solutions of neutral stochastic differential delayed equations with Markov switching are investigated under given conditions. Two exampl...The p-th moment and almos t sure st ability with general decay rate of the exact solutions of neutral stochastic differential delayed equations with Markov switching are investigated under given conditions. Two examples are provided to support the conclusions.展开更多
基金the National Research Foundation of Korea (NRF-2017R1 C1B1005436)the TJ Park Science Fellowship of POSCO TJ Park Foundation.
文摘In this article, we study the nonlinear stochastic heat equation in the spatial domain R^d subject to a Gaussian noise which is white in time and colored in space. The spatial correlation can be any symmetric, nonnegative and nonnegative-definite function that satisfies Dalang's condition. We establish the existence and uniqueness of a random field solution starting from measure-valued initial data. We find the upper and lower bounds for the second moment. With these moment bounds, we first establish some necessary and sufficient conditions for the phase transition of the moment Lyapunov exponents, which extends the classical results from the stochastic heat equation on Z^d to that on R^d.Then, we prove a localization result for the intermittency fronts, which extends results by Conus and Khoshnevisan [9] from one space dimension to higher space dimension. The linear case has been recently proved by Huang et al [17] using different techniques.
基金the National Key Research and Development Program of China (Grant Nos.2017YFA0402300 and 2017YFA0403200)the National Natural Science Foundation of China (Grant Nos.11474032,11534011,U15302611,and 1404180)China Postdoctoral Science Foundation (Grant No.2018M631404).
文摘Carbon sulfide cation (CS^+) plays a dominant role in some astrophysical atmosphere environments.In this work,the rovibrational transition lines are computed for the lowest three electronic states,in which the internally contracted multireference configuration interaction approach (MRCI) with Davison size-extensivity correction (+Q) is employed to calculate the potential curves and dipole moments,and then the vibrational energies and spectroscopic constants are extracted.The Frank–Condon factors are calculated for the bands of X^2∑^+,A^2П and X^2∑^+–B^2∑^+ systems,and the band of X^2∑^+–A^2П is in good agreement with the available experimental results.Transition dipole moments and the radiative lifetimes of the low-lying three states are evaluated.The opacities of the CS+ molecule are computed at different temperatures under the pressure of 100 atms.It is found that as temperature increases,the band systems associated with different transitions for the three states become dim because of the increased population on the vibrational states and excited electronic states at high temperature.
文摘A novel method for estimation of an aerodynamic force and moment acting on an irregularly shaped body (such as HE projectile fragments) during its flight through the atmosphere is presented. The model assumes that fragments can be approximated with a tri-axial ellipsoid that has continuous surface given as a mathematical function. The model was validated with CFD data for a tri-axial ellipsoid and verified using CFD data on aerodynamic forces and moments acting on an irregularly shaped fragment. The contribution of this method is that it represents a significant step toward a modeling that does not require a cumbersome CFD simulation results for estimation of fragment dynamic and kinematic parameters. Due to this advantage, the model can predict the fragment motion consuming a negligible time when compared to the corresponding time consumed by CFD simulations. Parametric representation (generalization) of the fragment geometrical data and the conditions provides the way to analyze various correlations and how parameters influence the dynamics of the fragment flight.
文摘In this paper, an empirical model based on self-evolving neural network is proposed for predicting the flexural behavior of ferrocement elements. The model is meant to serve as a simple but reliable tool for estimating the moment capacity of ferrocement members. The proposed model is trained and validated using experimental data obtained from the literature. The data consists of information regarding flexural tests on ferrocement specimens which include moment capacity and cross-sectional dimensions of specimens, concrete cube compressive strength, tensile strength and volume fraction of wire mesh. Comparisons of predictions of the proposed models with experimental data indicated that the models are capable of accurately estimating the moment capacity of ferrocement members. The proposed models also make better predictions compared to methods such as the plastic analysis method and the mechanism approach. Further comparisons with other data mining techniques including the back-propagation network, the adaptive spline, and the Kriging regression models indicated that the proposed models are superior in terms prediction accuracy despite being much simpler models. The performance of the proposed models was also found to be comparable to the GEP-based surrogate model.
基金the National Natural Science Foundation of China(61572092,61702403)the Fundamental Research Funds for the Central Universities(JB170308,JBF180301)+2 种基金the Project Funded by China Postdoctoral Science Foundation(2018M633473)the Basic Research Project of Weinan Science and Technology Bureau(ZDYF-JCYJ-17)the Project of Shaanxi Provincial Supports Discipline(Mathematics).
文摘In this paper,we first derive two types of transformed Franklin polynomial:substituted and weighted radial Franklin polynomials.Two radial orthogonal moments are proposed based on these two types of polynomials,namely substituted Franklin-Fourier moments and weighted Franklin-Fourier moments(SFFMs and WFFMs),which are orthogonal in polar coordinates.The radial kernel functions of SFFMs and WFFMs are transformed Franklin functions and Franklin functions are composed of a class of complete orthogonal splines function system of degree one.Therefore,it provides the possibility of avoiding calculating high order polynomials,and thus the accurate values of SFFMs and WFFMs can be obtained directly with little computational cost.Theoretical and experimental results show that Franklin functions are not well suited for constructing higher-order moments of SFFMs and WFFMs,but compared with traditional orthogonal moments(e.g.,BFMs,OFMs and ZMs)in polar coordinates,the proposed two types of Franklin-Fourier Moments have better performance respectively in lower-order moments.
基金an NSERC grant and a startup fund of University of Alberta.
文摘This article attempts to give a short survey of recent progress on a class of elementary stochastic partial differential equations (for example, stochastic heat equations) driven by Gaussian noise of various covariance structures. The focus is on the existence and uniqueness of the classical (square integrable) solution (mild solution, weak solution). It is also concerned with the Feynman-Kac formula for the solution;Feynman-Kac formula for the moments of the solution;and their applications to the asymptotic moment bounds of the solution. It also briefly touches the exact asymptotics of the moments of the solution.
基金National Natural Science Foundation of China (11775112)the Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘The newly observed isomer and ground-state band in the odd-Z neutron-rich rare-earth nucleus 163 Eu are investigated by using the cranked shell model(CSM), with pairing treated by the particle-number conserving(PNC)method. This is the first time detailed theoretical investigations are performed of the observed 964(1) keV isomer and ground-state rotational band in 163 Eu. The experimental data are reproduced very well by the theoretical results. The configuration of the 964(1) keV isomer is assigned as the three-particle state 13^-/2(v7^+/2 [633]■v1^-/2[521]■π5^+/2[413]).More low-lying multi-particle states are predicted in 163 Eu. Due to its significant effect on the nuclear mean field, the high-order ε6 deformation plays an important role in the energy and configuration assignment of the multi-particle states. Compared to its neighboring even-even nuclei 162 Sm and 164 Gd,there is a 10%15% increase of J(1) of the oneparticle ground-state band in 163 Eu. This is explained by the pairing reduction due to the blocking of the nucleon on the proton π5+/2 [413] orbital in 163 Eu.
基金the Talent Introduction Foundation of Qiannan Normal University of Nationalities,China(Grant No.qnsyrc201619)Natural Science Foundation of Guizhou Provincial Education Department for Young Talents,China(Grant No.Qian Education Contract KY[2017]339)Chemical Sciences,Geosciences and Biosciences Division,Office of Basic Energy Sciences,Office of Science,U.S.Department of Energy(Grant No.DE-FG02-86ER13491).
文摘Photoionization time delays have been studied in many streaking experiments in which an attosecond pulse is used to ionize the atomic or solid state target in the presence of a dressing infrared laser field. Among the methods of extracting the time delay from the streaking spectrogram, the simplest one is to calculate the first moment of the spectrogram and to measure its offset relative to the vector potential of the infrared field. The first moment method has been used in many theoretical simulations and analysis of experimental data, but the meaning of this offset needs to be investigated. We simulate the spectrograms and compare the extracted time delay from the first moment with the input Wigner delay. In this study, we show that the first moment method is valid only when the group delay dispersions corresponding to both the spectral phase of the attosecond pulse and the phase of the single-photon transition dipole matrix element of the target are small. Under such circumstance, the electron wave packet behaves like a classical particle and the extracted time delay can be related to a group delay in the photoionization process. To avoid ambiguity and confusion, we also suggest that the photoionization time delay be replaced by photoionization group delay and the Wigner time delay be replaced by Wigner group delay.
基金the National Natural Science Foundation of China(Grant Nos.11574115 and 11704146).
文摘We theoretically investigate the excited state intramolecular proton transfer(ESIPT) behavior of the novel fluorophore bis-imine derivative molecule HNP which was designed based on the intersection of 1-(hydrazonomethyl)-naphthalene-2-ol and 1-pyrenecarboxaldehyde. Especially, the density functional theory(DFT) and time-dependent density functional theory(TDDFT) methods for HNP monomer are introduced. Moreover, the 'our own n-layered integrated molecular orbital and molecular mechanics'(ONIOM) method(TDDFT:universal force field(UFF)) is used to reveal the aggregation-induced emission(AIE) effect on the ESIPT process for HNP in crystal. Our results confirm that the ESIPT process happens upon the photoexcitation for the HNP monomer and HNP in crystal, which is distinctly monitored by the optimized geometric structures and the potential energy curves. In addition, the results of potential energy curves reveal that the ESIPT process in HNP will be promoted by the AIE effect. Furthermore, the highest occupied molecular orbital(HOMO) and lowest unoccupied molecular orbital(LUMO) for the HNP monomer and HNP in crystal have been calculated. The calculation demonstrates that the electron density decrease of proton donor caused by excitation promotes the ESIPT process. In addition, we find that the variation of atomic dipole moment corrected Hirshfeld population(ADCH) charge for proton acceptor induced by the AIE effect facilitates the ESIPT process. The results will be expected to deepen the understanding of ESIPT dynamics for luminophore under the AIE effect and provide insight into future design of high-efficient AIE compounds.
文摘This paper addresses the narrative construction of the moment of death as depicted in Tolstoy’s Anna Karenina and in Barnes’s The Sense of an Ending. Following Orr’s definition of positive influence, described as a “site for cultural renewal”, it pursues the analysis of complexity and confluence of literary traditions in these texts. Though both Anna Karenina and The Sense of an Ending seem to insist on portraying a chronicle of struggle between a moment and a process of dying, it is nevertheless a physical moment of life ending which becomes an intensely condensed, and almost photographic, representation of the intimate, psychologically depicted, dying process. It is argued that the moment of death reveals, for instance, Anna’s unresolved internal conflict between psychological and physiological phenomena shaping human behaviour. Similarly, Barnes’s The Sense of an Ending builds upon a subtle dialogic tension between a process of psychological dying and a moment of physically conceived death. Specifically, this paper brings to light the repetitive occurence of the intense epiphanic moments which shape the thematic and the structural development of both Anna Karenina and The Sense of an Ending.
文摘Last night,I went to see a movie with my friends.I was immersed in the story.It was my first time going out at night.Because my parents never let me do that before.Now they think I have grown up and I can protect myself,so they allowed me to go out at night.It was such a happy moment for me.
文摘This note is concerned with a new direct(non-iterative)method for the solution of an elliptic inverse problem.This method is based on the application of the Green's second identity which leads to a moment problem for the unknown boundary condition.Tikhonov regularization is used to obtain a stable and close approximation of the missing boundary condition without any need for iterations.Four examples are used to study the applicability of the method with the presence of noise.
基金the National Natural Science Foundation of China (No. 51401028).
文摘The melt-spun SmFe12Bx(x = 0, 0.50, 0.75,1.00, 1.25 and 1.50) ribbons were prepared at 40 m·s-1,and their structure and magnetic properties were studied by powder X-ray diffraction(XRD), vibrating sample magnetometer(VSM) and transmission electron microscopy(TEM). XRD results indicate that SmFe12Bx alloys with 0.50 ≤ x ≤ 1.00 are composed of single-phase TbCu7-type structure. Moreover, it is found that the boron addition can inhibit the emergence of soft magnetic phase a-Fe and result in the increase in the axial ratio c/a. After annealing at 650 ℃ for 0.5 h, the metastable phase TbCu7 initially decomposes into the stable phase Sm2Fe14B(Nd2Fe14B-type) and a-Fe. The value of magnetic moment per Fe atom increases slightly from 1.75 uB for boron-free sample to 1.80 uB for the x = 0.75 sample and then decreases again.In addition, the best magnetic properties of maximum energy product [(BH)max] of 14.56 kJ·m^-3, coercivity(Hcj)of 172.6 kA·m^-1 and remanence(Br) of 0.45 T are obtained for the SmFe12B1.00 alloy. Based on transmission electron microscopy(TEM) results, the average size of grains is around 197 nm for B-free sample and decreases to 95 nm for x = 1.00 sample, indicating that the addition of boron can refine grains.
基金The authors would like to thank Professor Chenggui Yuan (Swansea University, UK) for useful suggestions. This work was supported in part by the National Natural Science Foundation of China (Grant No. 11601025)the Beijing Municipal Natural Science Foundation (1192013).
文摘The p-th moment and almos t sure st ability with general decay rate of the exact solutions of neutral stochastic differential delayed equations with Markov switching are investigated under given conditions. Two examples are provided to support the conclusions.