In the present paper,we consider the nonlocal Kirchhoff problem-(ε^2a+εb∫|■u|^2)Δu+u=Q(x)u^p,u>0 in R^3,,where a,b>0,1<p<5 andε>0 is a parameter.Under some assumptions on Q(x),we show the existenc...In the present paper,we consider the nonlocal Kirchhoff problem-(ε^2a+εb∫|■u|^2)Δu+u=Q(x)u^p,u>0 in R^3,,where a,b>0,1<p<5 andε>0 is a parameter.Under some assumptions on Q(x),we show the existence and local uniqueness of positive multi-peak solutions by LyapunovSchmidt reduction method and the local Pohozaev identity method,respectly.展开更多
A new method for quantitative phase analysis is proposed by using X-ray diffraction multi-peak match intensity ratio. This method can obtain the multi-peak match intensity ratio among each phase in the mixture sample ...A new method for quantitative phase analysis is proposed by using X-ray diffraction multi-peak match intensity ratio. This method can obtain the multi-peak match intensity ratio among each phase in the mixture sample by using all diffraction peak data in the mixture sample X-ray diffraction spectrum and combining the relative intensity distribution data of each phase standard peak in JCPDS card to carry on the least square method regression analysis. It is benefit to improve the precision of quantitative phase analysis that the given single line ratio which is usually adopted is taken the place of the multi-peak match intensity ratio and is used in X-ray diffraction quantitative phase analysis of the mixture sample. By analyzing four-group mixture sample, adopting multi-peak match intensity ratio and X-ray diffraction quantitative phase analysis principle of combining the adiabatic and matrix flushing method, it is tested that the experimental results are identical with theory.展开更多
Absorption and refraction of the inner transition F2 ←→F3 of the closed four level N-type atom have been investigated under a weak field. The outer transitions F1←→F3 and F2←→F4 are resonantly interacted with dr...Absorption and refraction of the inner transition F2 ←→F3 of the closed four level N-type atom have been investigated under a weak field. The outer transitions F1←→F3 and F2←→F4 are resonantly interacted with drive field with frequency ωc and Rabi frequency Ωc, and saturation field with ωs and Ωs, respectively. For the suitable Rabi frequencies Ωc and Ωs, we obtain the Mellow absorption spectrum of probe field. The reason is that the drive field excites the atom to the upper level F3 and simultaneously the saturation field takes the atom out of the lower level F2, leading to the stimulated emission. Meanwhile, due to the dynamic energy splitting induced by the drive and saturation fields, the two- and four-peaked absorption spectra are observed. At the zero off-resonance detuning of probe field, we also find the transfer of dispersion from negative to positive with an increment of Ωs. Finally, the refractive index enhancement is predicted for a wide spectral region.展开更多
In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate cri...In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate critical points of the potential function V(x),where a,b>0,1<p<5 are constants,andε>0 is a parameter.Applying the Lyapunov-Schmidt reduction method and a local Pohozaev type identity,we establish the existence and local uniqueness results of multi-peak solutions,which concentrate at{a_(i)}1≤i≤k,where{a_(i)}1≤i≤k are non-degenerate critical points of V(x)asε→0.展开更多
The optical frequency comb has been widely used in precision measurement. In this study, a multi-peak fitting approach is first proposed to fit the two-photon transition spectrum which overlaps with the neighboring tr...The optical frequency comb has been widely used in precision measurement. In this study, a multi-peak fitting approach is first proposed to fit the two-photon transition spectrum which overlaps with the neighboring transition in Rb-87. The multi-peak fitting approach is used to eliminate the frequency shift affected by the neighboring transition. With locking the carrier envelope offset frequency at 1/4 repetition frequency, the transition frequency is measured to be 770569132739.9 +/- 5.8 kHz, which agrees well with the previous result recommended by Comite International des Poids et Mesures.展开更多
Multi-peak structures in photoluminescence spectra of InAs/GaAs quantum dots are investigated. Excitation power-dependent photoluminescence spectra are used to identify the nature of different peaks. By combining expe...Multi-peak structures in photoluminescence spectra of InAs/GaAs quantum dots are investigated. Excitation power-dependent photoluminescence spectra are used to identify the nature of different peaks. By combining experimental results and an energy-level structure analysis,origins of the multi-peaks are identified. Furthermore,inter-subband spacing of electrons and holes are deduced.展开更多
In this study, a hybrid algorithm combining genetic algorithm （GA） with back propagation （BP） neural network （GA-BP） was proposed for extracting the characteristics of multi-peak Brillouin scattering spectrum. S...In this study, a hybrid algorithm combining genetic algorithm （GA） with back propagation （BP） neural network （GA-BP） was proposed for extracting the characteristics of multi-peak Brillouin scattering spectrum. Simulations and experimental results show that the GA-BP hybrid algorithm can accurately identify the position and amount of peaks in multi-peak Brillouin scattering spectrum. Moreover, the proposed algorithm obtains a fitting degree of 0.9923 and a mean square error of 0.0094. Therefore, the GA-BP hybrid algorithm possesses a good fitting precision and is suitable for extracting the characteristics of multi-peak Brillouin scattering spectrum.展开更多
Until now, a high-efficiency demodulation method for fiber Bragg grating(FBG) sensors has been a challenge.In this Letter, by employing multi-peak FBGs, an FBG sensor with a partial wavelength scan is proposed and ini...Until now, a high-efficiency demodulation method for fiber Bragg grating(FBG) sensors has been a challenge.In this Letter, by employing multi-peak FBGs, an FBG sensor with a partial wavelength scan is proposed and initially demonstrated. By demodulating a near-symmetrical multi-peak FBG and an asymmetrical multi-peak FBG in the strain experiment, sensor sensitivities of 1.02 pm/με and 1.01 pm/με are measured for the interrogation system, respectively. The average demodulation deviations for the two sensors are 1.81% and 0.4%,respectively. The proposed method is expected to realize high-efficiency and low-cost FBG interrogators.展开更多
Gray cross correlation matching technique is adopted to extract candidate matches with gray cross correlation coefficients less than some certain range of maximal correlation coefficient called multi-peak candidate ma...Gray cross correlation matching technique is adopted to extract candidate matches with gray cross correlation coefficients less than some certain range of maximal correlation coefficient called multi-peak candidate matches. Multi-peak candidates are extracted corresponding to three closest feature points at first. The corresponding multi-peak candidate matches are used to construct the model polygon. Correspondence is determined based on the local geometric relations between the three feature points and the multi-peak candidates. The disparity test and the global consistency checkout are applied to eliminate the remaining ambiguous matches that are not removed by the local geometric relational test. Experimental results show that the proposed algorithm is feasible and accurate.展开更多
This paper presents a theoretical analysis of the existence and stability of multi-peak solitons in parity-time-symmetric Bessel optical lattices with defects in nonlinear media. The results demonstrate that there alw...This paper presents a theoretical analysis of the existence and stability of multi-peak solitons in parity-time-symmetric Bessel optical lattices with defects in nonlinear media. The results demonstrate that there always exists a critical propagation constant μc for the existence of multi-peak solitons regardless of whether the nonlinearity is self-focusing or self-defocusing. In self-focusing media, multi-peak solitons exist when the propagation constant μ 〉 μc. In the self-defocusing case, solitons exist only when μ 〈 μc. Only low-power solitons can propagate stably when random noise perturbations are present. Positive defects help stabilize the propagation of multi-peak solitons when the nonlinearity is self-focusing. When the nonlinearity is self-defocusing, however, multi-peak solitons in negative defects have wider stable regions than those in positive defects.展开更多
The multi-peak spectrum of Ti: sapphire pulses observed experimentally under ultra-broad bandwidth conditions ( 【 15 fs pulse length) has been explained theoretically. It is shown that the self-phase-modulation effec...The multi-peak spectrum of Ti: sapphire pulses observed experimentally under ultra-broad bandwidth conditions ( 【 15 fs pulse length) has been explained theoretically. It is shown that the self-phase-modulation effect is equivalent to the process of degenerate four-wave frequency-mixing. Based on this theoretical underpinning, the presence or absence of a multipeak spectrum provides a practical measure of whether the intracavity group-velocity-dispersion is ideally compensated for or not.展开更多
We consider the boundary value problem△u＋︳x︳^2α︳u︳p-1u=0,-1〈α≠0.in the unit ballB with the homogeneous Dirichlet boundary condition, when p is a large exponent. By a constructive way, weprove that for any po...We consider the boundary value problem△u＋︳x︳^2α︳u︳p-1u=0,-1〈α≠0.in the unit ballB with the homogeneous Dirichlet boundary condition, when p is a large exponent. By a constructive way, weprove that for any positive integer m, there exists a multi-peak nodal solution vp whose maxima and minima arelocated alternately near the origin and the other m points q1=（λcos^2Л（1-1）/m,λsin 2Л（1-1）/m,1=2,…,m＋1such that as p goes to ＋∞ ,p︳x︳2α︳up︳p-1 up→8Лe（1＋α）（1＋α）δ0＋∑^m＋1δ_1=28Лe（-1）l-1δql,whereλ∈（0, 1）, m is an odd number with（1＋α）（m＋2） -- 1 〉 0, or m is an even number. The same techniqueslead also to a more general result on general domains.展开更多
In this paper, we are concerned with the the Schrödinger-Newton system with L^(2)-constraint. Precisely, we prove that there cannot exist multi-peak normalized solutions concentrating at k different critical poin...In this paper, we are concerned with the the Schrödinger-Newton system with L^(2)-constraint. Precisely, we prove that there cannot exist multi-peak normalized solutions concentrating at k different critical points of V(x) under certain assumptions on asymptotic behavior of V(x) and its first derivatives near these points. Especially, the critical points of V(x) in this paper must be degenerate.The main tools are a local Pohozaev type of identity and the blow-up analysis. Our results also show that the asymptotic behavior of concentrated points to Schrödinger-Newton problem is quite different from the classical Schrödinger equations, which is mainly caused by the nonlocal term.展开更多
基金supported by Natural Science Foundation of China(11771166)Hubei Key Laboratory of Mathematical Sciences and Program for Changjiang Scholars and Innovative Research Team in University#IRT 17R46financially supported by funding for basic research business in Central Universities(innovative funding projects)(2018CXZZ090)。
文摘In the present paper,we consider the nonlocal Kirchhoff problem-(ε^2a+εb∫|■u|^2)Δu+u=Q(x)u^p,u>0 in R^3,,where a,b>0,1<p<5 andε>0 is a parameter.Under some assumptions on Q(x),we show the existence and local uniqueness of positive multi-peak solutions by LyapunovSchmidt reduction method and the local Pohozaev identity method,respectly.
文摘A new method for quantitative phase analysis is proposed by using X-ray diffraction multi-peak match intensity ratio. This method can obtain the multi-peak match intensity ratio among each phase in the mixture sample by using all diffraction peak data in the mixture sample X-ray diffraction spectrum and combining the relative intensity distribution data of each phase standard peak in JCPDS card to carry on the least square method regression analysis. It is benefit to improve the precision of quantitative phase analysis that the given single line ratio which is usually adopted is taken the place of the multi-peak match intensity ratio and is used in X-ray diffraction quantitative phase analysis of the mixture sample. By analyzing four-group mixture sample, adopting multi-peak match intensity ratio and X-ray diffraction quantitative phase analysis principle of combining the adiabatic and matrix flushing method, it is tested that the experimental results are identical with theory.
基金Project supported by the National Natural Science Foundation of China （Grant Nos 10334010 10304001, 10521002, 10434020, 10328407 and 90501007）. We are grateful to Professor Zhang J X for her helpful discussions.
文摘Absorption and refraction of the inner transition F2 ←→F3 of the closed four level N-type atom have been investigated under a weak field. The outer transitions F1←→F3 and F2←→F4 are resonantly interacted with drive field with frequency ωc and Rabi frequency Ωc, and saturation field with ωs and Ωs, respectively. For the suitable Rabi frequencies Ωc and Ωs, we obtain the Mellow absorption spectrum of probe field. The reason is that the drive field excites the atom to the upper level F3 and simultaneously the saturation field takes the atom out of the lower level F2, leading to the stimulated emission. Meanwhile, due to the dynamic energy splitting induced by the drive and saturation fields, the two- and four-peaked absorption spectra are observed. At the zero off-resonance detuning of probe field, we also find the transfer of dispersion from negative to positive with an increment of Ωs. Finally, the refractive index enhancement is predicted for a wide spectral region.
基金supported by the Natural Science Foundation of China(11771166,12071169)the Hubei Key Laboratory of Mathematical Sciences and Program for Changjiang Scholars and Innovative Research Team in University#IRT17R46。
文摘In this paper,we study the existence and local uniqueness of multi-peak solutions to the Kirchhoff type equations-(ε^(2)a+εb∫_(R^(3))|■u|^(2))△u+V(x)u=u^(p),u>0 in R^(3),which concentrate at non-degenerate critical points of the potential function V(x),where a,b>0,1<p<5 are constants,andε>0 is a parameter.Applying the Lyapunov-Schmidt reduction method and a local Pohozaev type identity,we establish the existence and local uniqueness results of multi-peak solutions,which concentrate at{a_(i)}1≤i≤k,where{a_(i)}1≤i≤k are non-degenerate critical points of V(x)asε→0.
基金Supported by the National Natural Science Foundation of China under Grant Nos 91336103,10934010 and 61078026
文摘The optical frequency comb has been widely used in precision measurement. In this study, a multi-peak fitting approach is first proposed to fit the two-photon transition spectrum which overlaps with the neighboring transition in Rb-87. The multi-peak fitting approach is used to eliminate the frequency shift affected by the neighboring transition. With locking the carrier envelope offset frequency at 1/4 repetition frequency, the transition frequency is measured to be 770569132739.9 +/- 5.8 kHz, which agrees well with the previous result recommended by Comite International des Poids et Mesures.
基金the State Key Development Program for Basic Research of China(No.2006CB604904)the National Natural Science Foundation of China(Nos.60776037,60676029)~~
文摘Multi-peak structures in photoluminescence spectra of InAs/GaAs quantum dots are investigated. Excitation power-dependent photoluminescence spectra are used to identify the nature of different peaks. By combining experimental results and an energy-level structure analysis,origins of the multi-peaks are identified. Furthermore,inter-subband spacing of electrons and holes are deduced.
文摘In this study, a hybrid algorithm combining genetic algorithm （GA） with back propagation （BP） neural network （GA-BP） was proposed for extracting the characteristics of multi-peak Brillouin scattering spectrum. Simulations and experimental results show that the GA-BP hybrid algorithm can accurately identify the position and amount of peaks in multi-peak Brillouin scattering spectrum. Moreover, the proposed algorithm obtains a fitting degree of 0.9923 and a mean square error of 0.0094. Therefore, the GA-BP hybrid algorithm possesses a good fitting precision and is suitable for extracting the characteristics of multi-peak Brillouin scattering spectrum.
基金supported by the National Key R&D Program of China(Nos.2017YFA0206401 and 2018YFB2201801)the National Natural Science Foundation of China(No.61435014)+1 种基金the Key R&D Program of Jiangsu Province(No.BE2017003)the Natural Science Foundation of Jiangsu Province(No.BK20160907)
文摘Until now, a high-efficiency demodulation method for fiber Bragg grating(FBG) sensors has been a challenge.In this Letter, by employing multi-peak FBGs, an FBG sensor with a partial wavelength scan is proposed and initially demonstrated. By demodulating a near-symmetrical multi-peak FBG and an asymmetrical multi-peak FBG in the strain experiment, sensor sensitivities of 1.02 pm/με and 1.01 pm/με are measured for the interrogation system, respectively. The average demodulation deviations for the two sensors are 1.81% and 0.4%,respectively. The proposed method is expected to realize high-efficiency and low-cost FBG interrogators.
基金the Leading Academic Discipline Project of Shanghai Educational Committee of China(J50104)the Shanghai Leading Academic Disciplines of China(T0102)
文摘Gray cross correlation matching technique is adopted to extract candidate matches with gray cross correlation coefficients less than some certain range of maximal correlation coefficient called multi-peak candidate matches. Multi-peak candidates are extracted corresponding to three closest feature points at first. The corresponding multi-peak candidate matches are used to construct the model polygon. Correspondence is determined based on the local geometric relations between the three feature points and the multi-peak candidates. The disparity test and the global consistency checkout are applied to eliminate the remaining ambiguous matches that are not removed by the local geometric relational test. Experimental results show that the proposed algorithm is feasible and accurate.
基金Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant No. 61308019） and the Foundation for Distinguished Young Talents in Higher Education of Guangdong （Grant No. Yq2013157）. H. Wang also acknowledges the financial support from China Scholarship Council.
文摘This paper presents a theoretical analysis of the existence and stability of multi-peak solitons in parity-time-symmetric Bessel optical lattices with defects in nonlinear media. The results demonstrate that there always exists a critical propagation constant μc for the existence of multi-peak solitons regardless of whether the nonlinearity is self-focusing or self-defocusing. In self-focusing media, multi-peak solitons exist when the propagation constant μ 〉 μc. In the self-defocusing case, solitons exist only when μ 〈 μc. Only low-power solitons can propagate stably when random noise perturbations are present. Positive defects help stabilize the propagation of multi-peak solitons when the nonlinearity is self-focusing. When the nonlinearity is self-defocusing, however, multi-peak solitons in negative defects have wider stable regions than those in positive defects.
文摘The multi-peak spectrum of Ti: sapphire pulses observed experimentally under ultra-broad bandwidth conditions ( 【 15 fs pulse length) has been explained theoretically. It is shown that the self-phase-modulation effect is equivalent to the process of degenerate four-wave frequency-mixing. Based on this theoretical underpinning, the presence or absence of a multipeak spectrum provides a practical measure of whether the intracavity group-velocity-dispersion is ideally compensated for or not.
基金Supported by the National Natural Science Foundation of China(No.11171214)
文摘We consider the boundary value problem△u＋︳x︳^2α︳u︳p-1u=0,-1〈α≠0.in the unit ballB with the homogeneous Dirichlet boundary condition, when p is a large exponent. By a constructive way, weprove that for any positive integer m, there exists a multi-peak nodal solution vp whose maxima and minima arelocated alternately near the origin and the other m points q1=（λcos^2Л（1-1）/m,λsin 2Л（1-1）/m,1=2,…,m＋1such that as p goes to ＋∞ ,p︳x︳2α︳up︳p-1 up→8Лe（1＋α）（1＋α）δ0＋∑^m＋1δ_1=28Лe（-1）l-1δql,whereλ∈（0, 1）, m is an odd number with（1＋α）（m＋2） -- 1 〉 0, or m is an even number. The same techniqueslead also to a more general result on general domains.
基金supported by the National Natural Science Foundation of China(No.11771469)Qing Guo is supported by National Natural Science Foundation of China(No.11771469)。
文摘In this paper, we are concerned with the the Schrödinger-Newton system with L^(2)-constraint. Precisely, we prove that there cannot exist multi-peak normalized solutions concentrating at k different critical points of V(x) under certain assumptions on asymptotic behavior of V(x) and its first derivatives near these points. Especially, the critical points of V(x) in this paper must be degenerate.The main tools are a local Pohozaev type of identity and the blow-up analysis. Our results also show that the asymptotic behavior of concentrated points to Schrödinger-Newton problem is quite different from the classical Schrödinger equations, which is mainly caused by the nonlocal term.
