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\left(\int_{\mathbb{R}^N}\vert\nabla u\vert^2{\rm d}x\right)\Delta u+\lambda u=g(u)~\hbox{in}~\mathbb{R}^N,u\in H^1(\mathbb{R}^N),N\geq 1,satisfying the normalization constraint\int_{\mathbb{R}^N}u^2{\rm d}x=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.

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.

THE EXISTENCE AND STABILITY OF NORMALIZED SOLUTIONS FOR A BI-HARMONIC NONLINEAR SCHR?DINGER EQUATION WITH MIXED DISPERSION

In this paper,we study the ground state standing wave solutions for the focusing bi-harmonic nonlinear Schrodinger equation with aμ-Laplacian term(BNLS).Such BNLS models the propagation of intense laser beams in a bulk medium with a second-order dispersion term.Denoting by Qpthe ground state for the BNLS withμ=0,we prove that in the mass-subcritical regime p∈(1,1+8/d),there exist orbit ally stable ground state solutions for the BNLS when p∈(-λ0,∞)for someλ0=λ0(p,d,‖Qp‖L2)>0.Moreover,in the mass-critical case p=1+8/d,we prove the orbital stability on a certain mass level below‖Q*‖L2,provided thatμ∈(-λ1,0),where■and Q*=Q1+8/d.The proofs are mainly based on the profile decomposition and a sharp Gagliardo-Nirenberg type inequality.Our treatment allows us to fill the gap concerning the existence of the ground states for the BNLS when p is negative and p∈(1,1+8/d].

THE EXISTENCE OF GROUND STATE NORMALIZED SOLUTIONS FOR CHERN-SIMONS-SCHRODINGER SYSTEMS

In this paper,we study normalized solutions of the Chern-Simons-Schrödinger system with general nonlinearity and a potential in H^(1)(ℝ^(2)).When the nonlinearity satisfies some general 3-superlinear conditions,we obtain the existence of ground state normalized solutions by using the minimax procedure proposed by Jeanjean in[L.Jeanjean,Existence of solutions with prescribed norm for semilinear elliptic equations,Nonlinear Anal.(1997)].

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.

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.

Normalized fatigue properties of asphalt mixture at various temperatures

This study normalized the mixture's fatigue behavior at various temperatures,and the strength and fatigue tests of the mixture were conducted.The stress state of the asphalt mixture includes direct tensile,uniaxial compression,and indirect tensile.The Desai yield surface and fatigue path were proposed.And a normalized fatigue characteristics model of the mixture was established.The following conclusions were obtained.With the increases in the loading rate,the strength of the asphalt mixture increased.As the temperature increases,the strength of the mixture is reduced.At various temperatures and rates,the strength forms a closed curved surface.The Desai strength yield surface was established,which forms a closed curved surface.When the loading rate and temperature are below a certain critical line,the asphalt mixture will not undergo strength damage.At a fixed stress state,the fatigue damage path of the mixture was determined.The stress ratio was determined considering the influence of the loading rate.In this way,a normalized model can be described to express the asphalt mixture fatigue properties at various temperatures and stress levels.For the asphalt mixture in an indirect tensile state,the normalized fatigue equation parameter is 4.09.This model is more suitable for reflecting the viscous-elastic behavior of the mixtures than the fatigue equation determined by the notional stress ratio.

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.

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.

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 spectral characteristics of the 1999 Chi-Chi earthquake

To develop uniform and seismic environment-dependent design spectrum,common acceleration response spectral characteristics need to be identified.In this paper,a bi-normalized response spectrum (BNRS) is proposed,which is defined as a spectrum of peak response acceleration normalized with respect to peak acceleration of the excitation plotted vs.the natural period of the system normalized with respect to the spectrum predominant period,Tp.Based on a statistical analysis of records from the 1999 Chi-Chi earthquake,the conventionally normalized response spectrum(NRS) and the BNRS are examined to account for the effects of soil conditions,epicentral distance,hanging wall and damping.It is found that compared to the NRS the BNRS is much less dependent on these factors.Finally,some simple relationships between the BNRS for a specified damping ratio and that for a damping ratio of 5%,and between the spectra predominant period and epicentral distance for different soil types are provided.

Drought trend analysis in a semi-arid area of Iraq based on Normalized Difference Vegetation Index, Normalized Difference Water Index and Standardized Precipitation Index

Drought was a severe recurring phenomenon in Iraq over the past two decades due to climate change despite the fact that Iraq has been one of the most water-rich countries in the Middle East in the past.The Iraqi Kurdistan Region(IKR)is located in the north of Iraq,which has also suffered from extreme drought.In this study,the drought severity status in Sulaimaniyah Province,one of four provinces of the IKR,was investigated for the years from 1998 to 2017.Thus,Landsat time series dataset,including 40 images,were downloaded and used in this study.The Normalized Difference Vegetation Index(NDVI)and the Normalized Difference Water Index(NDWI)were utilized as spectral-based drought indices and the Standardized Precipitation Index(SPI)was employed as a meteorological-based drought index,to assess the drought severity and analyse the changes of vegetative cover and water bodies.The study area experienced precipitation deficiency and severe drought in 1999,2000,2008,2009,and 2012.Study findings also revealed a drop in the vegetative cover by 33.3%in the year 2000.Furthermore,the most significant shrinkage in water bodies was observed in the Lake Darbandikhan(LDK),which lost 40.5%of its total surface area in 2009.The statistical analyses revealed that precipitation was significantly positively correlated with the SPI and the surface area of the LDK(correlation coefficients of 0.92 and 0.72,respectively).The relationship between SPI and NDVI-based vegetation cover was positive but not significant.Low precipitation did not always correspond to vegetative drought;the delay of the effect of precipitation on NDVI was one year.

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Normalized Cut的基因表达数据聚类

利用基因表达数据进行聚类分析可提高肿瘤诊断的正确率,对生物医学研究具有重要意义.该文将Normalized Cut应用于基因表达数据的聚类中,将样本映射为高维空间的点,利用亲近矩阵和度矩阵构造正规Laplacian矩阵,经SVD分解得到反映原始样本类别信息的指示向量,利用指示向量各分量的符号差异实现基因表达数据的聚类.通过对白血病和结肠癌数据集的实验,证明了该文方法的有效性.

一种与图论Normalized Cut方法相结合的双阈值图像分割

提出了一种与图论方法相结合的双阈值分割方法,先采用双阈值划分图像区域,然后建立无向图,采用 Normalized Cut 方法划分图,完成图像分割。本文的方法综合考虑了像素间的灰度值和空间距离的相似性,并且运算量比传统的图论方法要小很多。实验结果表明,算法可以取得很好的分割效果。

多分辨率下基于Normalized Cut的图像分割

提出了一种图像分割的新方法。该方法首先对低分辨率下的小图像使用Normalized Cut,快速地提取这幅小图像中高层视觉信息,然后将这一高层信息有效地还原回高分辨率下并进行平滑处理。实验中得到了很好的全局分割效果。该方法既充分利用了Normalized Cut的全局分割特性,又有效地克服了Normalized Cut的大运算量问题,提高了图像分割的速度。

基于形态学分水岭的Normalized Cut图像分割方法

针对传统分水岭分割后所产生的过分割问题,提出了一种基于形态学分水岭算法和Normalized Cut算法相结合的图像分割方法。在传统分水岭分割的基础上,融合形态学算法进行初步分割,并将分割后各个子区域的形心和平均灰度值作为Normalized Cut算法的输入参数,完成图像分割。结果表明,组合算法既避免了过分割现象,也达到了Normalized Cut算法的分割精度,是一种有效的图像分割算法。

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.