MULTIPLICITY OF NORMALIZED SOLUTIONS FOR THE FRACTIONAL SCHR?DINGER-POISSON SYSTEM WITH DOUBLY CRITICAL GROWTH

In this paper,we are concerned with solutions to the fractional Schrodinger-Poisson system■ with prescribed mass ∫_(R^(3))|u|^(2)dx=a^(2),where a> 0 is a prescribed number,μ> 0 is a paremeter,s ∈(0,1),2 <q <2_(s)^(*),and 2_(s)^(*)=6/(3-2s) is the fractional critical Sobolev exponent.In the L2-subcritical case,we show the existence of multiple normalized solutions by using the genus theory and the truncation technique;in the L^(2)-supercritical case,we obtain a couple of normalized solutions by developing a fiber map.Under both cases,to recover the loss of compactness of the energy functional caused by the doubly critical growth,we need to adopt the concentration-compactness principle.Our results complement and improve upon some existing studies on the fractional Schrodinger-Poisson system with a nonlocal critical term.

Normalized Ground State Solutions of Nonlinear Choquard Equations with Nonconstant Potential

In this paper,we mainly focus on the following Choquard equation-{△u-V(x)(I_(a*)|u|^(p))|u|^(p-2)u=λu,x∈R^(N),u∈H^(1)(R^(N))where N≥1,λ∈R will arise as a Lagrange multiplier,0<a<N and N+a/N<p<N+a+2/N Under appropriate hypotheses on V(x),we prove that the above Choquard equation has a normalized ground state solution by utilizing variational methods.

Three-dimensional color particle image velocimetry based on a cross-correlation and optical flow method

Rainbow particle image velocimetry(PIV)can restore the three-dimensional velocity field of particles with a single camera;however,it requires a relatively long time to complete the reconstruction.This paper proposes a hybrid algorithm that combines the fast Fourier transform(FFT)based co-correlation algorithm and the Horn–Schunck(HS)optical flow pyramid iterative algorithm to increase the reconstruction speed.The Rankine vortex simulation experiment was performed,in which the particle velocity field was reconstructed using the proposed algorithm and the rainbow PIV method.The average endpoint error and average angular error of the proposed algorithm were roughly the same as those of the rainbow PIV algorithm;nevertheless,the reconstruction time was 20%shorter.Furthermore,the effect of velocity magnitude and particle density on the reconstruction results was analyzed.In the end,the performance of the proposed algorithm was verified using real experimental single-vortex and double-vortex datasets,from which a similar particle velocity field was obtained compared with the rainbow PIV algorithm.The results show that the reconstruction speed of the proposed hybrid algorithm is approximately 25%faster than that of the rainbow PIV algorithm.

New normalized nonlocal hybrid level set method for image segmentation

This article introduces a new normalized nonlocal hybrid level set method for image segmentation.Due to intensity overlapping,blurred edges with complex backgrounds,simple intensity and texture information,such kind of image segmentation is still a challenging task.The proposed method uses both the region and boundary information to achieve accurate segmentation results.The region information can help to identify rough region of interest and prevent the boundary leakage problem.It makes use of normalized nonlocal comparisons between pairs of patches in each region,and a heuristic intensity model is proposed to suppress irrelevant strong edges and constrain the segmentation.The boundary information can help to detect the precise location of the target object,it makes use of the geodesic active contour model to obtain the target boundary.The corresponding variational segmentation problem is implemented by a level set formulation.We use an internal energy term for geometric active contours to penalize the deviation of the level set function from a signed distance function.At last,experimental results on synthetic images and real images are shown in the paper with promising results.

Aggregation operators and CRITIC-VIKOR method for confidence complex q-rung orthopair normal fuzzy information and their applications

Supply chain management is an essential part of an organisation's sustainable programme.Understanding the concentration of natural environment,public,and economic influence and feasibility of your suppliers and purchasers is becoming progressively familiar as all industries are moving towards a massive sustainable potential.To handle such sort of developments in supply chain management the involvement of fuzzy settings and their generalisations is playing an important role.Keeping in mind this role,the aim of this study is to analyse the role and involvement of complex q-rung orthopair normal fuzzy(CQRONF)information in supply chain management.The major impact of this theory is to analyse the notion of confidence CQRONF weighted averaging,confidence CQRONF ordered weighted averaging,confidence CQRONF hybrid averaging,confidence CQRONF weighted geometric,confidence CQRONF ordered weighted geometric,confidence CQRONF hybrid geometric operators and try to diagnose various properties and results.Furthermore,with the help of the CRITIC and VIKOR models,we diagnosed the novel theory of the CQRONF-CRITIC-VIKOR model to check the sensitivity analysis of the initiated method.Moreover,in the availability of diagnosed operators,we constructed a multi-attribute decision-making tool for finding a beneficial sustainable supplier to handle complex dilemmas.Finally,the initiated operator's efficiency is proved by comparative analysis.

First-Arrival Picking Method for Active Source Data with Ocean Bottom Seismometers Based on Spatial Waveform Variation Characteristics

The precision and reliability of first-arrival picking are crucial for determining the accuracy of geological structure inversion using active source ocean bottom seismometer(OBS)refraction data.Traditional methods for first-arrival picking based on sample points are characterized by theoretical errors,especially in low-sampling-frequency OBS data because the travel time of seismic waves is not an integer multiple of the sampling interval.In this paper,a first-arrival picking method that utilizes the spatial waveform variation characteristics of active source OBS data is presented.First,the distribution law of theoretical error is examined;adjacent traces exhibit variation characteristics in their waveforms.Second,a label cross-correlation superposition method for extracting highfrequency signals is presented to enhance the first-arrival picking precision.Results from synthetic and field data verify that the proposed approach is robust,successfully overcomes the limitations of low sampling frequency,and achieves precise outcomes that are comparable with those of high-sampling-frequency data.

结合小波系数的normalized cut分割算法

为了提高normalized cut分割算法的准确率,结合小波系数调整图像的亲和矩阵。首先采用小波系数计算图像的边缘信息,然后使用边缘信息对原始图像构造一个图,求取图的拉普拉斯矩阵的前K个特征值,并对第二个特征值对应的特征向量进行分类,得到最终的分割结果。使用一些自然图像进行了验证,结果证明新方法能提取目标更为细致的细节,保留更多有用的信息。

基于图论的Normalized Cut图像分割方法研究

基于图论的图像分割是近年来国际上研究图像分割算法领域中一个新的热点研究方向,Normalized Cut(规一化分割)是基于图论的分割方法中比较典型的一种。本文介绍Normalized Cut方法的相关内容,分析它的优缺点并提出几种有效的改进方法。最后,实验显示Normalized Cut在特定图片的分割上取得了不错的效果。

Grey Clustering Evaluation on Regional Eco-environmental Quality Based on Normalized Index Value

[Objective] The aim was to assess regional eco-environmental quality by means of grey clustering method based on normalized index value. [Method] Eco-environmental quality in Chaohu basin was assessed by using grey clustering method based on normalized index value, and the evaluation results were compared with those of unascertained measure method to verify the feasibility of grey clustering method used to evaluate regional eco-environmental quality. [Result] In the grey clustering assessment method based on normalized index value, indices whose standard normalized values in the same grade were close to each other were classified into one class and had the same whitening function, which reduced the number of whitening functions. Grey clustering method based on normalized index value was used to assess eco-environmental quality in Chaohu basin, and the evaluation results were basically in accordance with those of unascertained measure method, namely eco-environmental quality in Hefei, Chaohu and Lu’an belonged to the third (pass), fourth (worse) and fifth grade (bad), except for one grade difference in overall basin, and the results showed that the method had practicality and could be applied to assess regional eco-environmental quality. [Conclusion] The study could provide theoretical foundation for the establishment of comprehensive management countermeasures of regional ecological environment.

A NEW MOMENT METHOD FOR THE FAST AND ACCURATE ANALYSIS OF NORMAL MODE HELICAL ANTENNAS

In this letter, a new moment method using helical segments is presented to model Normal Mode Helical Antenna (NMHA). Using this method, the NMHA can be modeled by a few segments. The current distributions and radiation patterns of some NMHAs are calculated.A comparison is made between results obtained using this helical segment algorithm and a linear segment algorithm, and the results of the two algorithms agree fairly well. When calculating the impedance matrix [Z], all the elements of the matrix can be obtained by only calculating a few elements with the application of the symmetric and periodic characteristics of the NMHA.Therefore, the CPU time and the memory storage are significantly reduced, with the accuracy and speed enhanced.

Applying invariant eigen-operator method to deriving normal coordinates of general classical Hamiltonian

For classical Hamiltonian with general form H = 1/2∑ijMijpipj＋1/2∑ijLijqiqj we find a new convenient way to obtain its normal coordinates, namely, let H be quantised and then employ the invariant eigen-operator （IEO） method （Fan et al. 2004 Phys. Lett. A 321 75） to derive them. The general matrix equation, which relies on M and L, for obtaining the normal coordinates of H is derived.

Dombi-Normalized Weighted Bonferroni Mean Operators with Novel Multiple-Valued Complex Neutrosophic Uncertain Linguistic Sets and Their Application in Decision Making

Although fuzzy set concepts have evolved,neutrosophic sets are attractingmore attention due to the greater power of the structure of neutrosophic sets.The ability to account for components that are true,false or neither true nor false is useful in the resolution of real-life problems.However,simultaneous variations render neutrosophic sets unsuitable in specific circumstances.To enable the management of these sorts of issues,we combine the principle of multi-valued neutrosophic uncertain linguistic sets and complex fuzzy sets to develop the principle of multivalued complex neutrosophic uncertain linguistic sets.Multi-valued complex neutrosophic uncertain linguistic sets can contain grades of truth,abstinence,and falsity,and uncertain linguistic terms,which are expressed as complex numbers whose real and imaginary parts are limited to the unit interval.Some important Dombi laws are elaborated along with Bonferroni mean operators,which offer a flexible general structure with modifiable factors.Bonferroni means aggregation operators perform a significant role in conveying the magnitude level of options and characteristics.To determine relationships among any number of attributes,we develop multi-valued complex neutrosophic uncertain linguistic Dombi-normalized weighted Bonferroni mean operators and discuss their important properties with some special cases.By using these laws,we can deploy themulti-attribute decisionmaking(MADM)technique using the novel principle of multi-valued complex neutrosophic uncertain linguistic sets.To determine the power and flexibility of the elaborated approach,we resolve some numerical examples based on the proposed operator.Finally,the work is validated with the help of comparative analysis,a discussion of its advantages,and geometric expressions of the elaborated theories.

COMPLEX INNER PRODUCT AVERAGING METHOD FOR CALCULATING NORMAL FORM OF ODE

This paper puts forward a complex inner product averaging method for calculating normal form of ODE. Compared with conventional averaging method, the theoretic analytical process has such simple forms as to realize computer program easily. Results can be applied in both autonomous and non-autonomous systems. At last, an example is resolved to verify the method.

ADJOINT OPERATOR METHOD AND NORMAL FORMS OF HIGHER ORDER FOR NONLINEAR DYNAMICAL SYSTEM

Normal form theory is a very effective method when we study degenerate bifurcations of nonlinear dynamical systems. In this paper by using adjoint operator method, normal forms of order 3 and 4 for nonlinear dynamical system with nilpotent linear part and Z(2)-asymmetry are computed. According to normal forms obtained, universal unfoldings for some degenerate bifurcation cases of codimension 3 and simple global characterizations, are studied.

Stochastic resonance in a gain-noise model of a single-mode laser driven by pump noise and quantum noise with cross-correlation between real and imaginary parts under direct signal modulation

Stochastic resonance （SR） is studied in a gain-noise model of a single-mode laser driven by a coloured pump noise and a quantum noise with cross-correlation between real and imaginary parts under a direct signal modulation. By using a linear approximation method, we find that the SR appears during the variation of signal-to-noise ratio （SNR） separately with the pump noise self-correlation time τ, the noise correlation coefficient between the real part and the imaginary part of the quantum noise λq, the attenuation coefficient γ＇ and the deterministic steady-state intensity I0. In addition, it is found that the SR can be characterized not only by the dependence of SNR on the noise variables of and λq, but also by the dependence of SNR on the laser system variables of γ and I0. Thus our investigation extends the characteristic quantity of SR proposed before.

Secrecy sum-rate analysis of massive MIMO systems under dual-threat attacks using normalization methods

Massive Multiple Input Multiple Output(MIMO)has been considered as an emerging technology to enhance the spectral and energy efficiency for the upcoming wireless communication systems.This paper derives a closedform approximation for the Ergodic Achievable Secrecy Sum-Rate(EASSR)by considering the joint impact of eavesdroppers and jammers.Two widely used linear precoding techniques,Zero-Forcing(ZF)and Maximum Ratio Transmission(MRT),were used in conjunction with matrix and vector normalization to analyze the secrecy performance.Closed-form expressions are used to explain how the secrecy performance is affected when using the ZF and MRT precoding in the eavesdropping and jamming attack models.We also analyze and compare the performances of different combinations of normalization method and precoding technique in various scenarios.From the analytical expressions and simulation results,we observe that the vector and matrix normalization perform better for the ZF precoding than for the MRT precoding in high Signal-to-Noise Ratio(SNR)scenarios.However,in low SNR,the MRT with matrix normalization outperforms the ZF with vector normalization regardless of the number of users in the system.Further,we observe that the MRT fails to serve more than two users in high SNR scenario.Numerical results obtained from Monte Carlo simulation are used to corroborate the accuracy of the asymptotic secrecy analysis.

Finite element analysis on stresses field of normalized layer thickness within ceramic coating on aluminized steel

Multilayer ceramic coatings were fabricated on steel substrate using a combined technique of hot dipping aluminum(HDA) and plasma electrolytic oxidation(PEO). A triangle of normalized layer thickness was created for describing thickness ratios of HDA/PEO coatings. Then, the effect of thickness ratio on stresses field of HDA/PEO coatings subjected to uniform normal contact load was investigated by finite element method. Results show that the surface tensile stress is mainly affected by the thickness ratio of Al layer when the total thickness of coating is unchanged. With the increase of Al layer thickness, the surface tensile stress rises quickly. When Al2O3 layer thickness increases, surface tensile stress is diminished. Meanwhile, the maximum shear stress moves rapidly towards internal part of HDA/PEO coatings. Shear stress at the Al2O3 /Al interface is minimal when Al2O3 layer and Al layer have the same thickness.

师范院校高等数学教学存在的问题与对策

高等数学是诸多师范专业必修的公共基础课,对于培养学生的专业学科素养和思维能力发挥着不可替代的作用。师范院校高等数学教学存在教学大纲一刀切,教学方法因循守旧,评价方式单一的问题,应对教学大纲进行优化调整,细化到每个学院的每个专业;改进教学方法,以线上线下的混合式教学模式代替单一的线下教学模式,同时将翻转课堂引进高数课堂;建立以专业为导向的多元、科学、有效的课程评价方式,以更大程度上促进高等数学课程目标的实现。

基于组合赋权与灰云模型的综合能源系统需求响应效益评价

考虑到当前综合能源系统研究缺乏完善的需求响应量化评估方案,难以在优化运行层面综合评估需求响应效益这一问题,提出了一种基于改进AHP群决策—CRITIC组合赋权与灰云模型的综合能源系统需求响应效益评价方法。首先,从综合能效性、社会经济性和需求侧互动性三个维度构建了需求响应效益评价指标体系。其次,采用一致性和权重拟合性更优的指数标度法构造判断矩阵,降低赋值误差,并通过AHP群决策法确定主观权重,从而削弱主观极值偏差对权重的影响;在由CRITIC法确定客观权重后,基于最小欧氏距离建立组合权重模型,并通过非线性规划求取最优组合权重;针对评价等级信息的模糊性与隶属等级的随机性,采用正态灰云白化权模型确定指标分类等级与场景评分。最后,以北方某综合能源系统为例,根据用户参与需求响应方式设置了4种运行场景,分析了不同需求响应对系统运行的影响与作用,算例结果表明所提指标体系与评价方法科学有效。

基于勒让德-扫描法的机械结合部法向接触刚度区间分析

由于机械结合部实际接触时存在诸多不确定因素,利用传统接触刚度模型对机械结合部进行分析时,难以确定其法向接触刚度的合理区间。为此,将微凸体曲率半径、分布密度和微凸体高度方差视为不确定性参数,基于KE弹塑性接触刚度模型和勒让德-扫描法,建立结合部法向接触刚度区间模型并进行求解。通过与接触刚度试验数据及传统模型求解结果的对比,验证了该模型的有效性和准确性。基于该模型对结合部法向接触刚度进行分析,结果表明:勒让德-扫描法具有较高的求解精度,粗糙表面形貌参数不确定性对于结合部法向接触刚度有着明显影响,且随着无量纲接触距离的减小,影响程度逐渐增加,其中微凸体高度方差的不确定性对粗糙表面法向接触刚度影响程度最大。机械结合部法向接触刚度区间模型的建立与分析,可为结合部的研究提供参考。