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Risk factors for thoracic-osteoporotic thoracic vertebral compression fractures during the normalized prevention and control period of COVID-19 认领 引用
1
作者 Yi-Fan Li Chen-Qiong Wu +5 位作者 Yang Long Qi-Feng Yu Wei Xu Jian-Jie Zhao Xiang-Yang Zhang Zhi-Kun Li 《World Journal of Orthopedics》 2026年第2期56-67,共12页
BACKGROUND Some scholars believe that there is a certain correlation between coronavirus disease 2019(COVID-19)infection and the occurrence of osteoporotic vertebral compression fractures(OVCF),but no relevant domesti... BACKGROUND Some scholars believe that there is a certain correlation between coronavirus disease 2019(COVID-19)infection and the occurrence of osteoporotic vertebral compression fractures(OVCF),but no relevant domestic research reports have been published yet.This study retrospectively analyzed the clinical data of patients admitted for OVCF and treated with percutaneous vertebroplasty during the normalized prevention and control period of COVID-19 in Shanghai(after June 1,2022),aiming to explore the individual differences of OVCF patients during this special period and analyze the risk factors for OVCF.AIM To explore risk factors for senile OVCF during COVID-19 normalization.METHODS Retrospective analysis of 230 OVCF patients(June 2022 to June 2023,percutaneous vertebroplasty,observation group)and 236 controls(June 2020 to June 2021,OVCF surgery).Observation group was split into nucleic acidpositive(n=85)and negative(n=145)subgroups.Fracture location/cause,visual analogue scale,activity scores were compared;risk factors identified.RESULTS Observation group had 42.2%thoracic fractures and 38.2%cough-induced fractures(both higher than controls,P0.05).Nucleic acid results,fracture cause/location correlated(P<0.05;cause-location r=0.827).Logistic regression showed fracture cause,nucleic acid result,body mass index,bone mineral density as high-risk factors.CONCLUSION During COVID-19 normalization,cough is the top OVCF cause;thoracic fractures rise.The four factors above are independent risks.For elderly COVID-positive patients with recurrent cough,lung disease treatment,antiosteoporosis therapy,and thoracic braces prevent thoracic OVCF. 展开更多
关键词 COVID-19 Normalized prevention and control Osteoporotic vertebral compression fracture Risk factor Cough
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MULTIPLICITY OF NORMALIZED SOLUTIONS FOR NONLINEAR KIRCHHOFF-TYPE PROBLEMS 认领 引用
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作者 Liping XU Haibo CHEN 《Acta Mathematica Scientia》 SCIE CSCD 2026年第3期1248-1268,共21页
This paper addresses the existence of multiple nonradial and radial normalized solutions for the following Kirchhoff-type equations{-(a+b∫Rn|▽u|2dx)△u=f(x)-pu in RN,||u||2L^(2RN)=m,u∈H1(RN)... This paper addresses the existence of multiple nonradial and radial normalized solutions for the following Kirchhoff-type equations{-(a+b∫Rn|▽u|2dx)△u=f(x)-pu in RN,||u||2L^(2RN)=m,u∈H1(RN),where f∈C(R,R),a,b>0 are constants,μ∈R is not fixed and instead appears as a Lagrange multiplier and m>0 is a given constant.In a mass subcritical case,using a version of the minimax theorem([32,Theorem 2.1])for a class of constrained even functionals,we demonstrate the existence of one nonradial normalized solution when N≥4.Additionally,if N≥4 and N≠5,we obtain multiple nonradial normalized solutions.Moreover,the existence of infinitely many radial normalized solutions is explored for N≥2.Furthermore,all solutions discussed above are sign-changing.As a supplementary result,we also prove the nonexistence of nontrivial solutions.Lastly,we analyze the asymptotic behavior of all solutions obtained above as b→0. 展开更多
关键词 Kirchhoff-type equations multiple nonradial and radial normalized solutions sign-changing solutions asymptotic behavior
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EXISTENCE OF NORMALIZED SOLUTIONS TO LAPLACIAN-LIKE EQUATIONS AT SUBCRITICAL GROWTH 认领 引用
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作者 Zhouxin LI Yuan XIANG 《Acta Mathematica Scientia》 SCIE CSCD 2026年第4期1841-1861,共21页
In this paper,we study a class of Laplacian-like equation.We first deduce the Pohozaev identity of the equation and consider the minimum of the functional on the Pohozaev manifold and then study the properties of the ... In this paper,we study a class of Laplacian-like equation.We first deduce the Pohozaev identity of the equation and consider the minimum of the functional on the Pohozaev manifold and then study the properties of the minimum energy of the functional.Based on the properties obtained,we prove the existence of normalized solution to the equation. 展开更多
关键词 normalized solutions Laplacian-like equations Pohozaev identity
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EXISTENCE AND MULTIPLICITY OF NORMALIZED SOLUTIONS FOR THE PLANAR SCHRODINGER-POISSON SYSTEM WITH EXPONENTIAL CRITICAL GROWTH 认领 引用
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作者 Xueqin PENG 《Acta Mathematica Scientia》 SCIE CSCD 2026年第2期529-548,共20页
The paper deals with the following planar Schrödinger-Poisson system{-Δu+λu+φu=f(u), in ℝ2,-Δuφ=u2,in ℝ2,fR2u2dx=a2,u∈H1(ℝ2),where a∈(0,1),λ∈ℝis an undetermined parameter which... The paper deals with the following planar Schrödinger-Poisson system{-Δu+λu+φu=f(u), in ℝ2,-Δuφ=u2,in ℝ2,fR2u2dx=a2,u∈H1(ℝ2),where a∈(0,1),λ∈ℝis an undetermined parameter which appears as a Lagrange multiplier and f satisfies the exponential critical growth.Under suitable conditions on f,we manage to establish such critical points which emerge as a local minimizer or correspond to a mountain pass.Furthermore,by using genus theory,we obtain infinitely many solutions.The proofs are based upon the reduction method by working on a natural constraint,which is introduced by Bartsch and Soave[J Funct Anal,2017,272:4998–5037].Our results complement the results made by Cingolani and Jeanjean[SIAM J Math Anal,2019,51:3533–3568]where handle the Sobolev subcritical case. 展开更多
关键词 Schrödinger-Poisson system normalized solution exponential critical growth variational methods
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Intermediate crack initiation during liquid core reduction of regular slabs:ERLS-based 3D simulation with calibrated normalized Cockcroft–Latham criterion 认领 引用
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作者 Junlong Ju Zhida Zhang +1 位作者 Cheng Ji Miaoyong Zhu 《International Journal of Minerals,Metallurgy and Materials》 SCIE EI CAS CSCD 2026年第3期861-873,共13页
Liquid core reduction(LCR)technology,originally developed for continuous thin-slab casting,allows space for a submerged entry nozzle in a mold while improving production efficiency.Recent experimental attempts explore... Liquid core reduction(LCR)technology,originally developed for continuous thin-slab casting,allows space for a submerged entry nozzle in a mold while improving production efficiency.Recent experimental attempts explore the implementation of LCR in regular slab casting processes.However,regular slabs(2–3 times thicker than thin slabs)face critical challenges in terms of excessive deformation and stress concentration under external forces,which induce intermediate cracks and thus hinder successful LCR adoption in regular slab production.This study evaluates the feasibility of LCR for producing regular slabs and identifies optimal reduction parameters to prevent crack initiation.A three-dimensional thermal–mechanical coupled model is proposed using the finite element method(FEM),integrated with the equivalent replacement liquid steel(ERLS)method and the normalized Cockcroft–Latham damage model,to achieve quantitative prediction of intermediate crack risk during the LCR process.The ERLS model simulates the extrusion flow and expulsion behavior of the liquid core,and its accuracy is validated against actual production measurements.To identify the critical damage value leading to intermediate crack initiation,this study conducts a consistency analysis between high-temperature tensile tests and FEM-based simulations using damage models.Based on this value,crack prediction is performed for Q355 slabs with cross-sectional dimensions of 170 mm×1450 mm.Using the prediction results,an optimal reduction scheme is determined,wherein the second segment accounts for 50%of the total reduction,the third segment for 32.5%,and the fourth segment for 17.5%,with the theoretical value of maximum reduction being 34 mm.These results provide actionable guidelines for the potential implementation of LCR in regular slab-casting systems. 展开更多
关键词 continuous slab casting liquid core reduction intermediate cracking thermo-mechanical behavior finite element method normalized Cockcroft-Latham damage criterion
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Normalized Solutions for Nonhomogeneous Chern–Simons–Schrödinger Equations with Critical Exponential Growth 认领 引用
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作者 Chenlu Wei Sitong Chen Xin’ao Zhou 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2026年第7期1821-1847,共27页
This paper investigates the existence of normalized solutions for the following Chern–Simons–Schrödinger equation$$\begin{cases}-\Delta u+\lambda u+\left(\dfrac{h^2(|x|)}{|x|^2}+\int_{|x|}^{\infty}\dfrac{h(s)}{... This paper investigates the existence of normalized solutions for the following Chern–Simons–Schrödinger equation$$\begin{cases}-\Delta u+\lambda u+\left(\dfrac{h^2(|x|)}{|x|^2}+\int_{|x|}^{\infty}\dfrac{h(s)}{s}u^2(s)\,dsight)u=(e^{u^2}-1)u+g(x),&x\in\mathbb{R}^2,\\u\in H_r^1(\mathbb{R}^2),\quad\int_{\mathbb{R}^2}u^2\,dx=c,\end{cases}$$where c>0,λ∈ℝacts as a Lagrange multiplier and g∈C(∝2,[0,+∞))satisfies suitable assumptions.In addition to the loss of compactness caused by the nonlinearity with critical exponential growth,the intricate interactions among it,the nonlocal term,and the nonhomogeneous term significantly affect the geometric structure of the constrained functional,thereby making this research particularly challenging.By specifying explicit conditions on c,we subtly establish a structure of local minima of the constrained functional.Based on the structure,we employ new analytical techniques to prove the existence of two solutions:one being a local minimizer and one of mountain-pass type.Our results are entirely new,even for the Schrödinger equation that is when nonlocal terms are absent.We believe our methods may be adapted and modified to deal with more constrained problems with nonhomogeneous perturbation. 展开更多
关键词 Nonhomogeneous Chern-Simons-Schrödinger equation normalized solution critical exponential growth Trudinger-Moser inequality
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Multiple Normalized Solutions for Nonlinear Biharmonic Schrödinger Equations in RNwith L2-Subcritical Growth 认领 引用
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作者 Jun WANG Li WANG Ji-xiu WANG 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2026年第3期810-828,共19页
In this article,we consider the existence of normalized solutions for the following nonlinear biharmonic Schrödinger equations:∆2u=λu+h(εx)f(u),x∈R N,∫RN|u|2 dx=c 2,x∈R N,where c,ε>0,N≥5,λ∈R is a Lagr... In this article,we consider the existence of normalized solutions for the following nonlinear biharmonic Schrödinger equations:∆2u=λu+h(εx)f(u),x∈R N,∫RN|u|2 dx=c 2,x∈R N,where c,ε>0,N≥5,λ∈R is a Lagrange multiplier and is unknown,h∈C(RN,[0,∞)),f:R→R is continuous function satisfying L2-subcritical growth.Whenεis small enough,we get multiple normalized solutions.Moreover,we also obtain orbital stability of the solutions. 展开更多
关键词 biharmonic Schrödinger equations multiplicity normalized solutions variational methods
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Ground State Normalized Solution for Nonhomogeneous Schrödinger-Poisson-Slater Equations with Potential 认领 引用
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作者 QIU Shuang-shuang XU Li-ping 《Chinese Quarterly Journal of Mathematics》 2026年第2期147-161,共15页
In this paper,we primarily investigate the existence of ground state normalized solutions to the following nonhomogeneous Schrödinger-Poisson-Slater equation:−Δu+λu+V(∣x∣)u+(∣x∣−1∗∣u∣2)u=g(u)+h(∣x... In this paper,we primarily investigate the existence of ground state normalized solutions to the following nonhomogeneous Schrödinger-Poisson-Slater equation:−Δu+λu+V(∣x∣)u+(∣x∣−1∗∣u∣2)u=g(u)+h(∣x∣)in R3,∫R3∣u∣2dx=m,00 is prescribed.Under suitable assumptions on V(|x|)and h(|x|),and assuming that the nonlinear term g is mass subcritical,we establish the existence of a ground state normalized solution through variational methods,thereby extending previous results in the literature. 展开更多
关键词 Nonlinear Schrödinger-Poisson-Slater equations Ground state normalized solutions Variational methods Potential Perturbation
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A Spatial-Temporal Normalized Contrastive Embedding for Robust Motion Similarity Retrieval 认领 引用
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作者 Seung-su Lee Young-Been Noh +1 位作者 Hwa Young Jeong Kwang-il Hwang 《Computers, Materials & Continua》 SCIE EI 2026年第9期127-158,共32页
Robust motion similarity retrieval from monocular 2D pose sequences is challenged by body-scale variation,viewpoint inconsistency,translation drift,and temporal misalignment.Existing contrastive skeleton learning meth... Robust motion similarity retrieval from monocular 2D pose sequences is challenged by body-scale variation,viewpoint inconsistency,translation drift,and temporal misalignment.Existing contrastive skeleton learning methods primarily address action recognition and rarely integrate explicit geometric canonicalization for retrievaloriented metric learning.This paper proposes a spatial-temporal normalized contrastive embedding framework that unifies structured nuisance suppression with scalable similarity representation learning.A four-stage normalization pipeline—torso-scale normalization,pelvis-centered alignment,posture-axis alignment,and phase-synchronized temporal resampling—removes geometric and temporal distortions prior to embedding.The normalized sequences are encoded using an acausal dilated temporal convolutional network trained with a hybrid contrastive objective combining NT-Xent and semi-hard triplet loss,enabling both global separation and fine-grained stylistic discrimination.A prototype-based representation further supports interpretable amateur-to-professional style mapping.Experiments on a golf swing benchmark achieve a Top-1 accuracy of 91.3%,outperforming BiLSTM and Dynamic Time Warping baselines.The framework establishes an invariant and interpretable paradigmfor motion similarity retrieval applicable to broader human movement analysis tasks. 展开更多
关键词 Motion similarity retrieval spatial-temporal normalization contrastive representation learning temporal convolutional networks(TCN) prototype-based embedding
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The influence of International Normalized Ratio on the prognosis of acute coronary syndrome patients in intensive care units:A retrospective analysis based on MIMIC-Ⅳdatabase 认领 引用
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作者 Yaxin Xiong Jiuyue Sun +6 位作者 Yu Song Jia Xu Yingfei Zhi Yuan Gao Huaming Li Mingyan Zhao Xianglin Meng 《Journal of Acute Disease》 2025年第9期1-9,共9页
Objective:To investigate the infulence of the International Normalized Ratio(INR)on the prognosis of patients with acute coronary syndrome(ACS)admitted to intensive care units(ICUs).Methods:A retrospective analysis wa... Objective:To investigate the infulence of the International Normalized Ratio(INR)on the prognosis of patients with acute coronary syndrome(ACS)admitted to intensive care units(ICUs).Methods:A retrospective analysis was conducted on ACS patients from the MIMIC-Ⅳ2.0 database,who were admitted to ICUs for the first time between 2008 and 2019 and met the study criteria.The association between the initial INR upon admission and the prognosis of ACS patients was assessed using a restricted cubic spline model at a continuous level.Based on the restricted cubic spline(RCS)curve,patients were stratified into three groups,and a multivariate Cox regression model was applied to analyze the effect of INR on the prognosis of ACS patients.Results:When INR was≤1.0,the mortality risk gradually decreased with increasing INR levels;when INR ranged between 1.0 and 1.5,the mortality risk rose significantly with further elevation of INR;when INR exceeded 1.5,the mortality risk stabilized at a persistently high level,with minimal fluctuations observed despite substantial changes in INR values.Multivariate Cox regression analysis also demonstrated that patients in the medium(1.0-1.5)and high(>1.5)INR groups exhibited significantly higher mortality risks compared to those in the low(≤1.0)INR group.Conclusions:Fluctuations in the INR among patients with ACS admitted to the ICU are associated with an increased risk of mortality and adversely affect patient prognosis. 展开更多
关键词 International Normalized Ratio Acute coronary syndrome Prognosis
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MULTIPLE NORMALIZED SOLUTIONS FOR FRACTIONAL SCHRÖDINGER EQUATIONS WITH COMPETING POWER NONLINEARITY 认领 引用
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作者 Huifang JIA Chunjiang ZHENG 《Acta Mathematica Scientia》 SCIE CSCD 2025年第5期1961-1980,共20页
In this paper,we investigate the existence and multiplicity of normalized solutions for the following fractional Schrödinger equations{(-△)su+λu=|u|p-2u-|u|q-2u,x∈RN,∫RN|u|2dx=c>0,wher... In this paper,we investigate the existence and multiplicity of normalized solutions for the following fractional Schrödinger equations{(-△)su+λu=|u|p-2u-|u|q-2u,x∈RN,∫RN|u|2dx=c>0,where N≥2,s∈(0,1),2+4s/N0 such that if c>c,then the problem(P)has at least two normalized solutions,including a normalized ground state solution and a mountain pass type solution.We mainly extend the results in[Commun Pure Appl Anal,2022,21:4113–4145],which dealt with the problem(P)for the case 2<p<q<2+4s/N. 展开更多
关键词 fractional Schrodinger equation normalized solutions variational methods com-peting power
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Source apportionment of PM2.5 using dispersion normalized positive matrix factorization(DN-PMF)in Beijing and Baoding,China 认领 引用 被引量：1
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作者 Ilhan Ryoo Taeyeon Kim +6 位作者 Jiwon Ryu Yeonseung Cheong Kwang-joo Moon Kwon-ho Jeon Philip K.Hopke Seung-Muk Yi Jieun Park 《Journal of Environmental Sciences》 SCIE EI CAS CSCD 2025年第9期395-408,共14页
Fine particulatematter(PM2.5)samples were collected in two neighboring cities,Beijing and Baoding,China.High-concentration events of PM2.5 in which the average mass concentration exceeded 75μg/m3 were freque... Fine particulatematter(PM2.5)samples were collected in two neighboring cities,Beijing and Baoding,China.High-concentration events of PM2.5 in which the average mass concentration exceeded 75μg/m3 were frequently observed during the heating season.Dispersion Normalized Positive Matrix Factorization was applied for the source apportionment of PM2.5 as minimize the dilution effects of meteorology and better reflect the source strengths in these two cities.Secondary nitrate had the highest contribution for Beijing(37.3%),and residential heating/biomass burning was the largest for Baoding(27.1%).Secondary nitrate,mobile,biomass burning,district heating,oil combustion,aged sea salt sources showed significant differences between the heating and non-heating seasons in Beijing for same period(2019.01.10–2019.08.22)(Mann-Whitney Rank Sum Test P<0.05).In case of Baoding,soil,residential heating/biomass burning,incinerator,coal combustion,oil combustion sources showed significant differences.The results of Pearson correlation analysis for the common sources between the two cities showed that long-range transported sources and some sources with seasonal patterns such as oil combustion and soil had high correlation coefficients.Conditional Bivariate Probability Function(CBPF)was used to identify the inflow directions for the sources,and joint-PSCF(Potential Source Contribution Function)was performed to determine the common potential source areas for sources affecting both cities.These models facilitated a more precise verification of city-specific influences on PM2.5 sources.The results of this study will aid in prioritizing air pollution mitigation strategies during the heating season and strengthening air quality management to reduce the impact of downwind neighboring cities. 展开更多
关键词 Source apportionment Dispersion normalized positive matrix factorization Adjacent cities Inter-city impact Source location Heating season Air quality management
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Computing the ground state solution of Bose-Einstein condensates by an energy-minimizing normalized residual network 认领 引用
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作者 Ren-Tao Wu Ji-Dong Gao +3 位作者 Yu-Han Wang Zhen-Wei Deng Ming-Jun Li Rong-Pei Zhang 《Chinese Physics B》 SCIE EI CAS CSCD 2025年第10期321-329,共9页
This paper introduces a novel numerical method based on an energy-minimizing normalized residual network(EMNorm Res Net)to compute the ground-state solution of Bose-Einstein condensates at zero or low temperatures.Sta... This paper introduces a novel numerical method based on an energy-minimizing normalized residual network(EMNorm Res Net)to compute the ground-state solution of Bose-Einstein condensates at zero or low temperatures.Starting from the three-dimensional Gross-Pitaevskii equation(GPE),we reduce it to the 1D and 2D GPEs because of the radial symmetry and cylindrical symmetry.The ground-state solution is formulated by minimizing the energy functional under constraints,which is directly solved using the EM-Norm Res Net approach.The paper provides detailed solutions for the ground states in 1D,2D(with radial symmetry),and 3D(with cylindrical symmetry).We use the Thomas-Fermi approximation as the target function to pre-train the neural network.Then,the formal network is trained using the energy minimization method.In contrast to traditional numerical methods,our neural network approach introduces two key innovations:(i)a novel normalization technique designed for high-dimensional systems within an energy-based loss function;(ii)improved training efficiency and model robustness by incorporating gradient stabilization techniques into residual networks.Extensive numerical experiments validate the method's accuracy across different spatial dimensions. 展开更多
关键词 Bose-Einstein condensate Gross-Pitaevskii equation energy minimization normalized residual network
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Design of China’s ice-class fleet scale and economic viability assessment under normalized operation of the Northeast Passage 认领 引用
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作者 HOU Jiaojiao HU Maixiu 《Advances in Polar Science》 CSCD 2025年第3期213-228,共16页
Global warming has led to a gradual extension of the navigable window for the Arctic Route,providing a realistic possibility for the normalized commercial operation of the Northeast Passage(NEP).Based on the changes i... Global warming has led to a gradual extension of the navigable window for the Arctic Route,providing a realistic possibility for the normalized commercial operation of the Northeast Passage(NEP).Based on the changes in the navigable window of the NEP,Russia’s proposed nuclear-powered icebreaker construction scheme,and China’s potential development of a moderately sized ice-class fleet,this study establishes three scenarios for the commercial operation of the NEP.These scenarios include:(a)normalized summer operational scenario(from July to October each year),(b)normalized summer-autumn operational scenario(from June to January of the following year),and(c)normalized year-round operational scenario(12 months per year).The cargo transportation potential of the NEP under three normalized operational scenarios was predicted based on the grey prediction model.On this basis,construction scale plans for China’s ice-class fleet to meet cargo transportation demands under the three normalized operational scenarios were designed.The economic benefits of different plans were evaluated using a profit-maximization linear programming model.The research results show the following:(1)The cargo transportation potential of the NEP demonstrates a rapid growth trend in the future,with annual throughput under year-round normalized operations expected to exceed 100 million tonnes and reach 297 million tonnes.(2)Under different normalized operational scenarios,the fleet scale and vessel type composition vary.Under the normalized summer operational scenario,the optimal scale for China’s ice-class fleet is 20 vessels,consisting solely of ships classed as PC7 by the International Association of Classification Societies(IACS).Under the normalized summer-autumn operational scenario,the optimal fleet scale is 31 vessels,including 30 IACS PC7 ships and 1 IACS PC3 ship.Under the normalized year-round operational scenario,the optimal fleet scale is 45 vessels,composed of 30 IACS PC7 ships,8 IACS PC3 ships,and 7 IACS PC2 ships.(3)Among the three normalized operational scenarios,the normalized year-round operational scenario yields the best economic benefits for the fleet scale,while the normalized summer operational scenario yields the lowest economic benefits. 展开更多
关键词 ice-class fleet linear programming the Northeast Passage(NEP) normalized operation
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Normalized Solutions of Nonlinear Choquard Equations with Nonconstant Potential 认领 引用
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作者 LI Nan XU Liping 《应用数学》 北大核心 2025年第1期14-29,共16页
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 ... 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. 展开更多
关键词 Nonlinear Choquard equation Potential function Variational method Normalized solution
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Normalized Positive Ground State Solutions for Nonhomogeneous Kirchhoff Equations 认领 引用
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作者 ZHANG Xiaocang XU Liping 《应用数学》 北大核心 2025年第3期711-720,共10页
This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of norm... This article studies a class of nonlinear Kirchhoff equations with exponential critical growth,trapping potential,and perturbation.Under appropriate assumptions about f and h,the article obtained the existence of normalized positive solutions for this equation via the Trudinger-Moser inequality and variational methods.Moreover,these solutions are also ground state solutions.Additionally,the article also characterized the asymptotic behavior of solutions.The results of this article expand the research of relevant literature. 展开更多
关键词 Normalized positive ground state solution Nonhomogeneous Kirchhoff equation Variational method Exponential critical growth Trapping potential
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High Energy Normalized Solutions for the Schrodinger Equations with Exponential Critical Growth 认领 引用
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作者 ZHANG Xiao-cang XULi-ping 《Chinese Quarterly Journal of Mathematics》 2025年第1期1-19,共19页
In this paper,we study high energy normalized solutions for the following Schr?dinger equation{-Δu+V(x)u+λu=f(u),in R2,∫R2|u|2dx=c,where c>0,λ∈R will appear as a Lagrange multiplier,V(x)=ω|x|2 rep... In this paper,we study high energy normalized solutions for the following Schr?dinger equation{-Δu+V(x)u+λu=f(u),in R2,∫R2|u|2dx=c,where c>0,λ∈R will appear as a Lagrange multiplier,V(x)=ω|x|2 represents a trapping potential,and f has an exponential critical growth.Under the appropriate assumptions of f,we have obtained the existence of normalized solutions to the above Schr?dinger equation by introducing a variational method.And these solutions are also high energy solutions with positive energy. 展开更多
关键词 High energy normalized solutions Schrodinger equation Trapping potential Exponential critical growth Variational method
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Normalized edge detection, and the horizontal extent and depth of geophysical anomalies 认领 引用 被引量：4
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作者 李丽丽 韩立国 黄大年 《Applied Geophysics》 SCIE CSCD 2014年第2期149-157,252,253,共9页
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... 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. 展开更多
关键词 geophysical anomalies normalized edge detection normalized total horizontal derivative regularization tilt angle theta map
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Bi-normalized response spectral characteristics of the 1999 Chi-Chi earthquake 认领 引用 被引量：16
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作者 徐龙军 谢礼立 《Earthquake Engineering and Engineering Vibration》 EI 2004年第2期147-155,共9页
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... 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. 展开更多
关键词 earthquake design spectra normalized response spectrum bi-normalized response spectrum spectral predominant period Chi-Chi earthquake
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Drought trend analysis in a semi-arid area of Iraq based on Normalized Difference Vegetation Index, Normalized Difference Water Index and Standardized Precipitation Index 认领 引用 被引量：3
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作者 Ayad M F AL-QURAISHI Heman A GAZNAYEE Mattia CRESPI 《Journal of Arid Land》 SCIE CSCD 2021年第4期413-430,共18页
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 Kurdi... 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. 展开更多
关键词 climate change drought Normalized Difference Vegetation Index(NDVI) Normalized Difference Water Index(NDWI) Standardized Precipitation Index(SPI) delay effect
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