THE EXISTENCE AND LOCAL UNIQUENESS OF MULTI-PEAK POSITIVE SOLUTIONS TO A CLASS OF KIRCHHOFF EQUATION

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.

MULTI-PEAK MATCH INTENSITY RATIO METHOD OF QUANTI-TATIVE X-RAY DIFFRACTION PHASE ANALYSIS

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.

Stimulated emission and multi-peaked absorption in a four level N-type atom

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.

THE EXISTENCE AND LOCAL UNIQUENESS OF MULTI-PEAK SOLUTIONS TO A CLASS OF KIRCHHOFF TYPE EQUATIONS

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.

Absolutely Direct Frequency Measurement of Two-Photon Transition Using Multi-Peak Fitting Approach

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.

GRADIENT OF REFERENCE DIFFERENCE BASED MATCHING ALGORITHM FOR IMAGE FEATURE POINT

During matching on feature point, gray correlation matching technology is utilized to extract multi-peaks as a coarse matching set. A pair of given corresponding reference points within the left and right images is used to calculate gradients of reference difference between the reference points and each feature point within the multi-peaks set. The unique correspondence is determined by criterion of minimal gradients of reference difference. The obtained correspondence is taken as a new pair of reference points to update the reference points continuously until all feature points in the left (or right) image being matched with the right (or left) image. The gradients of reference difference can be calculated easily by means of pre-setting a pair of obvious feature points in the left and right images as a pair of corresponding reference points. Besides, the efficiency of matching can be improved greatly by taking the obtained matching point as a new pair of reference points, and by updating the reference point continuously. It is proved that the proposed algorithm is valid and reliable by 3D reconstruction on two pairs of actual natural images with abundant and weak texture, respectively.

GBO algorithm for seismic source parameters inversion

The use of geodetic observation data for seismic fault parameters inversion is the research hotspot of geodetic inversion, and it is also the focus of studying the mechanism of earthquake occurrence. Seismic fault parameters inversion has nonlinear characteristics, and the gradient-based optimizer(GBO) has the characteristics of fast convergence speed and falling into local optimum hardly. This paper applies GBO algorithm to simulated earthquakes and real LuShan earthquakes in the nonlinear inversion of the Okada model to obtain the source parameters. The simulated earthquake experiment results show that the algorithm is stable, and the seismic source parameters obtained by GBO are slightly closer to the true value than the multi peak particle swarm optimization(MPSO). In the 2013 LuShan earthquake experiment, the root mean square error between the deformation after forwarding of fault parameters obtained by the introduced GBO algorithm and the surface observation deformation was 3.703 mm, slightly better than 3.708 mm calculated by the MPSO. Moreover, the inversion result of GBO algorithm is better than MPSO algorithm in stability. The above results show that the introduced GBO algorithm has a certain practical application value in seismic fault source parameters inversion.

A matching algorithm based on hybrid matrices consisting of reference differences and disparities

Unique correct correspondence cannot be obtained only by use of gray correlation technique, which describes gray similar degree of feature points between the left and right images too unilaterally. The gray correlation technique is adopted to extract gray correlation peaks as a coarse matching set called multi-peak set. The disparity gradient limited constraint is utilized to optimize the multi-peak set. Unique match will be obtained by calculating the correlation of hybrid matrices consisting of reference differences and disparities from the multi-peak set. Two of the known corresponding points in the left and right images, respectively, are set as a pair of reference points to determine search direction and search scope at first. After the unique correspondence is obtained by calculating the correlation of the hybrid matrices from the multi-peak set, the obtained match is regarded as a new reference point till all feature points in the left (or right) image have been processed. Experimental results proved that the proposed algorithm was feasible and accurate.

Evaluation method of coal rank based on X-ray diffraction analysis an example from SE Qinshui Basin

Based on analysis on X-ray diffraction, the metamorphic grade of coal in southeast Qinshui Basin was discussed, and a precise evaluation of coal rank through XRD analysis was made, in addition, the correlation of coal rank and vitrinite reflectance （Ro） was compared. XRD spectra of coal shows （002）-band and γ-band, and based on fitting calculation and multi-peak separation methods, the values of 2θ002 and 2θγ can be obtained, as well as corresponding intensities I002 and Iγ, consequently the coal rank can be quantized as the ratio of I002 and Iγ, that is coal rank=I002/Iγ. The research shows that the values of θ002 and θγ increase with the metamorphic grade, and a very good linear positive correlation exists between calculated Coal Rank and Ro.

The Origin of Multi-Peak Structures Observed in Photoluminescence Spectra of InAs/GaAs Quantum Dots

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.

Hybrid algorithm combining genetic algorithm with back propagation neural network for extracting the characteristics of multi-peak Brillouin scattering spectrum

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.

Demodulation of the multi-peak fiber Bragg grating sensor based on partial wavelength scan

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.

A stereo matching algorithm using multi-peak candidate matches and geometric constraints

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.

Multi-peak solitons in PT-symmetric Bessel optical lattices with defects

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.

Multi-peak spectrum of KML Ti:sapphire pulse

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.

Non-existence of Multi-peak Solutions to the Schrödinger-Newton System with L2-constraint

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.

Multi-peak Nodal Solutions for a Two-dimensional Elliptic Problem with Large Exponent in Weighted Nonlinearity

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.

Research on BeiDou anti-spoofing technology based on comprehensive radio determination satellite service

The BeiDou system(BDS)plays a significant role in people’s lives,but its security is easily affected by spoofing attacks.The radio determination satellite service(RDSS)is a special service of BDS that provides two-way communication,positioning,and timing services independently of the traditional radio navigation satellite service(RNSS).It can additionally be combined with RNSS to provide a comprehensive RDSS(CRDSS)service.In RDSS,after receiving a signal from the master station,the user needs to send a response signal back to the master station through a satellite.Therefore,the RDSS signal is difficult to spoof.In this study,based on the security feature of RDSS signals,an anti-spoofing method based on CRDSS is proposed to detect and mitigate spoofing attacks,verifying the advantages of the BeiDou system over other satellite navigation systems.