Normalized Solutions of Nonlinear Choquard Equations with Nonconstant Potential

In this paper,we mainly focus on a type of nonlinear Choquard equations with nonconstant potential.Under appropriate hypotheses on potential function and nonlinear terms,we prove that the above Choquard equation with prescribed 2-norm has some normalized solutions by introducing variational methods.

The Supply-Side Structural Reforms——Adapting to and Leading China's New Normal

The Central Economic Working Conference proposed supplyside structural reforms which can be regarded as major innovations and necessary measures that adapt to and lead the new normal of economic development. The 13^(th) Five Year Plan is a critical period for the transformation of economic development patterns and economic restructuring, so clarifying the theoretical values and practical significances of the supply-side structural reforms, making a clear explanation of the scientific connotations and policy implications of these reforms from a scientific standpoint, and discussing concrete measures to promote the reforms against the background of the economic new normal not only has academic values but also has important practical implications. Viewed from the practical standpoint of China' s new normal and through analyzing the basic national conditions, this article proposes a roadmap for implementing the proposed reforms and points out that only by doing well in the hybrid operation of "addition, subtraction, multiplication and division", based on the framework of the "five policy pillars", an innovative path of the supply-side structural reforms with Chinese characteristics can be paved.

NORMALIZED SOLUTIONS FOR THE GENERAL KIRCHHOFF TYPE EQUATIONS

In the present paper,we prove the existence,non-existence and multiplicity of positive normalized solutions(λ_(c),u_(c))∈R×H^(1)(R^(N))to the general Kirchhoff problem-M■,satisfying the normalization constraint f_(R)^N u^2dx=c,where M∈C([0,∞))is a given function satisfying some suitable assumptions.Our argument is not by the classical variational method,but by a global branch approach developed by Jeanjean et al.[J Math Pures Appl,2024,183:44–75]and a direct correspondence,so we can handle in a unified way the nonlinearities g(s),which are either mass subcritical,mass critical or mass supercritical.

Normalized glandular dose coefficients for digital breast tomosynthesis using detailed Chinese breast models

The rise in breast cancer diagnoses among Chinese women has necessitated the use of X-ray breast screening,which carries a radiation risk.This study aimed to provide a dosimetry protocol for the Chinese female population to replace the traditional standard that utilizes simplified breast models,for the accurate estimation of the mean glandular dose of a patient undergoing digital breast tomosynthesis(DBT).The first set of detailed Chinese female breast models and representative breast parameters was constructed.Considering backscatter radiation and computational efficiency,we improved the combination of these models and the Chinese reference adult female whole-body voxel phantom.Image acquisition for four commercial DBT systems that are widely employed in China was simulated using the Monte Carlo method to obtain the normalized glandular dose coefficients of DBT(D_(gN)^(DBT))and the glandular depth dose(D_(g)^(dep)(z))for different breast characteristics and X-ray spectra.We calculated a series of D_(gN)^(DBT) values for breasts with different percentage mass glandularities(5%,25%,50%,75%,and 100%)and compressed breast thicknesses(2,3,4,5,6,and 7 cm)at various tube potentials(25,28,30,32,35,and 49 kV)and target/filter combinations(W/Rh,W/Al,Mo/Mo,Rh/Rh,and Rh/Ag).The parameter dependence of the breast characteristics and beam conditions on D_(gN)^(DBT) in detailed breast models was investigated.The D_(gN)^(DBT) results were 14.6-51.0%lower than those of the traditional dosimetry standard in China.The difference in D_(gN)^(DBT) was mainly due to a decrease in the depth of the main energy deposition area caused by the glandular distribution along the depth direction.The results obtained in this study may be used to improve breast dosimetry in China and provide more detailed information on risk assessment during DBT.

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.

Assessment of vegetation cover changes and the contributing factors in the Al-Ahsa Oasis using Normalized Difference Vegetation Index(NDVI)

The abandonment of date palm grove of the former Al-Ahsa Oasis in the eastern region of Saudi Arabia has resulted in the conversion of delicate agricultural area into urban area.The current state of the oasis is influenced by both expansion and degradation factors.Therefore,it is important to study the spatiotemporal variation of vegetation cover for the sustainable management of oasis resources.This study used Landsat satellite images in 1987,2002,and 2021 to monitor the spatiotemporal variation of vegetation cover in the Al-Ahsa Oasis,applied multi-temporal Normalized Difference Vegetation Index(NDVI)data spanning from 1987 to 2021 to assess environmental and spatiotemporal variations that have occurred in the Al-Ahsa Oasis,and investigated the factors influencing these variation.This study reveals that there is a significant improvement in the ecological environment of the oasis during 1987–2021,with increase of NDVI values being higher than 0.10.In 2021,the highest NDVI value is generally above 0.70,while the lowest value remains largely unchanged.However,there is a remarkable increase in NDVI values between 0.20 and 0.30.The area of low NDVI values(0.00–0.20)has remained almost stable,but the region with high NDVI values(above 0.70)expands during 1987–2021.Furthermore,this study finds that in 1987–2002,the increase of vegetation cover is most notable in the northern region of the study area,whereas from 2002 to 2021,the increase of vegetation cover is mainly concentrated in the northern and southern regions of the study area.From 1987 to 2021,NDVI values exhibit the most pronounced variation,with a significant increase in the“green”zone(characterized by NDVI values exceeding 0.40),indicating a substantial enhancement in the ecological environment of the oasis.The NDVI classification is validated through 50 ground validation points in the study area,demonstrating a mean accuracy of 92.00%in the detection of vegetation cover.In general,both the user’s and producer’s accuracies of NDVI classification are extremely high in 1987,2002,and 2021.Finally,this study suggests that environmental authorities should strengthen their overall forestry project arrangements to combat sand encroachment and enhance the ecological environment of the Al-Ahsa Oasis.

Relationship between drought and soil erosion based on the normalized differential water index(NDWI)and revised universal soil loss equation(RUSLE)model

The Langat River Basin in Malaysia is vulnerable to soil erosion risks because of its exposure to intensive land use activities and its topography,which primarily consists of steep slopes and mountainous areas.Furthermore,climate change frequently exposes this basin to drought,which negatively affects soil and water conservation.However,recent studies have rarely shown how soil reacts to drought,such as soil erosion.Therefore,the purpose of this study is to evaluate the relationship between drought and soil erosion in the Langat River Basin.We analyzed drought indices using Landsat 8 satellite images in November 2021,and created the normalized differential water index(NDWI)via Landsat 8 data to produce a drought map.We used the revised universal soil loss equation(RUSLE)model to predict soil erosion.We verified an association between the NDWI and soil erosion data using a correlation analysis.The results revealed that the southern and northern regions of the study area experienced drought events.We predicted an average annual soil erosion of approximately 58.11 t/(hm^(2)·a).Analysis of the association between the NDWI and soil erosion revealed a strong positive correlation,with a Pearson correlation coefficient of 0.86.We assumed that the slope length and steepness factor was the primary contributor to soil erosion in the study area.As a result,these findings can help authorities plan effective measures to reduce the impacts of drought and soil erosion in the future.

Advances in Normalized cDNA Library and Its Applications

The cDNA library normalized by reassociation is a newly-developed and effective platform for EST acquisition and gene discovery.It decreases the prevalence of clones representing abundant transcripts and dramatically increases the efficiency of random sequencing and rare gene discovery.The principle,procedure and applications of normalized cDNA library were reviewed in this paper,which provides theoretical basis for the development of normalized cDNA library and discover more novel genes.

用Normalized Cut法自动提取乳腺超声图像中的肿瘤边缘

提出一种带权重邻域灰度信息的normalized cut(Ncut)方法,该方法能够全自动提取乳腺超声图像的肿瘤边缘.通过Ncut分块乳腺超声图像中的各块灰度及空间分布特征来识别待检测肿瘤的轮廓.对于少数分割不精确的结果,可用结合局部能量项的动态轮廓模型对所提取的初始边缘进行修正,使其更接近真实目标轮廓.对包含112幅乳腺肿瘤超声图像的数据库进行边缘提取,结果表明:该方法无需人工干预,能够准确有效地实现肿瘤分割,且计算量小,有望提高计算机辅助诊断的自动化程度.

A normalized wavefield separation cross-correlation imaging condition for reverse time migration based on Poynting vector

Prestack reverse time migration（PSTM） is a common imaging method; however low-frequency noises reduce the structural imaging precision. Thus, the suppression of migration noises must be considered. The generation mechanism of low-frequency noises is analyzed and the up-, down-, left-, and right-going waves are separated using the Poynting vector of the acoustic wave equation. The computational complexity and memory capacitance of the proposed method are far smaller than that required when using the conventional separation algorithm of 2D Fourier transform. The normalized wavefield separation crosscorrelation imaging condition is used to suppress low-frequency noises in reverse time migration and improve the imaging precision. Numerical experiments using the Marmousi model are performed and the results show that the up-, down-, left-, and right-going waves are well separated in the continuation of the wavefield using the Poynting vector. We compared the imaging results with the conventional method, Laplacian filtering, and wavefield separation with the 2D Fourier transform. The comparison shows that the migration noises are well suppressed using the normalized wavefield separation cross-correlation imaging condition and higher precision imaging results are obtained.

Normalized edge detection, and the horizontal extent and depth of geophysical anomalies

Edge detection is an image processing technique for finding the boundaries of objects within images. It is typically used to interpret gravity and magnetic data, and find the horizontal boundaries of geological bodies. Large deviations between model and true edges are common because of the interference of depth and errors in computing the derivatives; thus, edge detection methods cannot provide information about the depth of the source. To simultaneously obtain the horizontal extent and depth of geophysical anomalies, we use normalized edge detection filters, which normalize the edge detection function at different depths, and the maxima that correspond to the location of the source. The errors between model and actual edges are minimized as the depth of the source decreases and the normalized edge detection method recognizes the extent of the source based on the maxima, allowing for reliable model results. We demonstrate the applicability of the normalized edge detection filters in defining the horizontal extent and depth using synthetic and actual aeromagnetic data.

Supply-Side Structural Reforms and China's Potential Economic Growth Rate

This paper examines the effect of supply-side structural reforms on China＇s potential economic growth rate in the coming decade according to the data the authors have gathered. Under the rapid growth scenario with the implementation of supply-side structural reforms, China＇s potential economic growth rate will reach an average of 6.5% and 5.8% respectively in the 13th Five-year Plan （2016-2020） and 14th Five-year Plan （2021-2025） periods. These rates are 0.2 and 0.3 percentage points higher, respectively, than that under the baseline scenario with the inertia of historic trends. In implementing supply-side structural reforms, China must transform governmental functions, break monopolies, create a comprehensive competitive market environment, foster the creation of pro-innovation mechanisms, refocus on quality and efficiency, and raise capital utilization and labor productivity.

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。

Bi-normalized response spectra and scalar periods for developing uniform seismic design spectra

Aiming at the uniform features of acceleration response spectra, two scalar periods-the response spectral predominant period Tp and the smoothed spectral predominant period To are employed to normalize the abscissa of the normalized response spectra （NRS） of ground motions, respectively. Engineering characteristics of 5% -damped NRS, and the bi-normalized response spectra （BNRS） are investigated accounting for the effects of soil condition and fault distance. Nearly 600 horizontal ground motion components during the Chi-Chi earthquake are included in the analysis. It shows that the NRS strongly depends on soil condition and fault distance. However, soil condition and distance have only a slight influence on two kinds of BNRS. Dispersion analysis indicates that such normalization can reduce scatter in the derivation of response spectral shapes. Finally, a parametric analysis of the scalar periods （Tp, To） is performed and then compared with those of previous studies. These special and particular aspects of earthquake response spectra and scalar periods need to be considered in developing earthquake-resistant design criteria.

China's Infrastructure Development and Supply-Side Structural Reforms

Despite significant improvements in transport, energy and information communication technology （ICT） infrastructures, inadequacies still exist in China＇s infrastructure development in light of emerging demand and industrial transition and upgrade. China lags far behind advanced economies such as the United States, Germany and Japan in terms of the quality of transport infrastructures except railroad,＂ electricity infrastructure is insufficient and service efficiency needs improvement; ICT infrastructure requires all-round upgrade and gaps in Internet bandwidth are striking. This paper suggests that, based on the needs of supply-side structural reform, China must reform its investment and financing systems to enhance the efficiency of infrastructure investment. Efforts must be made to enhance air transport and port infrastructure to support industrial upgrade; to develop the energy Internet to address emerging demands; and to forge a new generation of ICT infrastructure with industrial Internet as the priority to prepare China for the new round of industrial competition.

基于Normalized Cut的图像分割改进算法

用Normalized Cu(tN-Cut)准则分割图片时,会出现诸如过分割或者欠分割的不理想情况。在N-Cut结果的基础上提出了一种改进算法:利用合并-分裂方法,将颜色和纹理相似的区域合并,并对某些区域做进一步N-Cut分割。实验证明,改进后的算法不仅保留了N-Cut方法的优点,而且从一定程度上解决了过分割和欠分割的缺点,能够处理一些自然界的彩色图片,得到了比较理想的分割结果。

Methods and Countermeasures for Urban Agricultural Supply-Side Structural Reform in the New Era

Based on the theoretical basis of structural reform of agricultural supply side, the status quo and existing problems of urban agricultural supply side in Tian- jin under the new normal were analyzed. On this basis, the paper analyzed the paths of urban agricultural supply-side structural reform separately from the perspec- tives of factors, investment structure and system innovation, and proposed specific policies and opinions on the structural reform of urban agricultural supply side, pro- viding the theoretical basis and realistic basis for the sustainable development of ur- ban agriculture.

International Normalized Ratio:青年脑梗死危险因素

目的评估入院时国际标准化比值水平对青年脑梗死患者出院时短期预后的影响。方法分析585例患脑梗死的青年患者,这些患者从来未服用华法令。所有患者都在发病48h后入院,脑影像学检查(CT或者MRI)在入院后24～48h后进行。结果通过logistic回归模型,笔者发现较高的INR和纤维蛋白原水平预示着患者在出院时有较差的预后。结论应用该回归分析模型,笔者确定INR是青年脑梗死患者临床预后的独立危险因素,因此入院时INR的水平不仅仅是凝血功能检测的指标,而且将为青年脑梗死患者提供一个实用的临床预后信息。

基于鱼群算法优化normalized cut的彩色图像分割方法

为了克服传统的谱聚类算法求解normalized cut彩色图像分割时,分割效果差、算法复杂度高的缺点,提出了一种基于鱼群算法优化normalized cut的彩色图像分割方法。先对图像进行模糊C-均值聚类预处理,然后用鱼群优化算法替代谱聚类算法求解Ncut的最小值,最后通过最优个体鱼得到分割结果。实验表明,该方法耗时少,且分割效果好。