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
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
This paper presents new generalizations of the Hermite-Hadamard inequality for convex functions via(p,q)-quantum integrals.First,based on the definitions of(p,q)-derivatives and integrals over finite intervals,we esta...This paper presents new generalizations of the Hermite-Hadamard inequality for convex functions via(p,q)-quantum integrals.First,based on the definitions of(p,q)-derivatives and integrals over finite intervals,we establish a unified(p,q)-Hermite-Hadamard inequality framework,combining midpoint-type and trapezoidal-type inequalities into a single form.Furthermore,by introducing a parameterλ,we propose a generalized(p,q)-integral inequality,whose special cases reduce to classical quantum Hermite-Hadamard inequalities and existing results in the literature.Furthermore,using hybrid integral techniques,we construct refined inequalities that incorporate(p,q)-integral terms,and by adjustingλ,we demonstrate their improvements and extensions to known inequalities.Specific examples are provided to validate the applicability of the results.The findings indicate that the proposed(p,q)-integral approach offers more flexible mathematical tools for the estimation of numerical integration error,convex optimization problems,and analysis of system performance in control theory,thus enriching the research results of quantum calculus in the field of inequalities.展开更多
Consider the Kirchhoff equation with Hartree type nonlinearity■where a,b>0,λ,μ∈R,2<q<6,0<α<3,and Iαis the Riesz potential integral operator of orderα.Solutions with prescribed mass■,also known a...Consider the Kirchhoff equation with Hartree type nonlinearity■where a,b>0,λ,μ∈R,2<q<6,0<α<3,and Iαis the Riesz potential integral operator of orderα.Solutions with prescribed mass■,also known as normalized solutions,are of particular interest in the current paper.Under various assumptions onμ,c and q,we establish the existence,nonexistence and asymptotic behavior of normalized solutions for the above elliptic equation.展开更多
In this paper,we investigate the existence and multiplicity of normalized solutions for the following fractional Schrödinger equations{(-△)^(s)u+λu=|u|^(p-2)u-|u|^(q-2)u,x∈R^(N),∫_(R^(N))|u|^(2)dx=c>0,wher...In this paper,we investigate the existence and multiplicity of normalized solutions for the following fractional Schrödinger equations{(-△)^(s)u+λu=|u|^(p-2)u-|u|^(q-2)u,x∈R^(N),∫_(R^(N))|u|^(2)dx=c>0,where N≥2,s∈(0,1),2+4s/N<p<q≤2_(s)^(*)=2N/N-2s,(-△)^(s)represents the fractional Laplacian operator of order s,and the frequencyλ∈R is unknown and appears as a Lagrange multiplier.Specifically,we show that there exists a c>0 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
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
Anomaly detection in wind turbines involves emphasizing its ability to improve operational efficiency,reduce maintenance costs,extend their lifespan,and enhance reliability in the wind energy sector.This is particular...Anomaly detection in wind turbines involves emphasizing its ability to improve operational efficiency,reduce maintenance costs,extend their lifespan,and enhance reliability in the wind energy sector.This is particularly necessary in offshore wind,currently one of the most critical assets for achieving sustainable energy generation goals,due to the harsh marine environment and the difficulty of maintenance tasks.To address this problem,this work proposes a data-driven methodology for detecting power generation anomalies in offshore wind turbines,using normalized and linearized operational data.The proposed framework transforms heterogeneous wind speed and power measurements into a unified scale,enabling the development of a new wind power index(WPi)that quantifies deviations from expected performance.Additionally,spatial and temporal coherence analyses of turbines within a wind farm ensure the validity of these normalized measurements across different wind turbine models and operating conditions.Furthermore,a Support Vector Machine(SVM)refines the classification process,effectively distinguishing measurement errors from actual power generation failures.Validation of this strategy using real-world data from the Alpha Ventus wind farm demonstrates that the proposed approach not only improves predictive maintenance but also optimizes energy production,highlighting its potential for broad application in offshore wind installations.展开更多
In this paper,we consider the p-Laplacian Schrödinger-Poisson equation with L^(2)-norm constraint-Δ_(p)u+|u|^(p-2)u+λu+(1/4π|x|*|u|^(2))u=|u|^(q-2)u,x∈R^(3),where 2≤p<3,5p/3<q<p*=3p/3-p,λ>0 is a...In this paper,we consider the p-Laplacian Schrödinger-Poisson equation with L^(2)-norm constraint-Δ_(p)u+|u|^(p-2)u+λu+(1/4π|x|*|u|^(2))u=|u|^(q-2)u,x∈R^(3),where 2≤p<3,5p/3<q<p*=3p/3-p,λ>0 is a Lagrange multiplier.We obtain the critical point of the corresponding functional of the problem on mass constraint by the variational method and the Mountain pass lemma,and then find a normalized solution to this equation.展开更多
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
In this paper,we consider the following logarithmic Schrödinger equation:−Δu+ωu=u log|u|^(2),u∈H^(1)(R^(N)),where N≥3,and ω>0 is a constant.With an auxiliary equation,we obtain the existence of normalized...In this paper,we consider the following logarithmic Schrödinger equation:−Δu+ωu=u log|u|^(2),u∈H^(1)(R^(N)),where N≥3,and ω>0 is a constant.With an auxiliary equation,we obtain the existence of normalized solutions by using the constrained variational method.展开更多
In this paper,we study high energy normalized solutions for the following Schr?dinger equation{-Δu+V(x)u+λu=f(u),in R^(2),∫_(R^(2))|u|^(2)dx=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 R^(2),∫_(R^(2))|u|^(2)dx=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
Fine particulatematter(PM_(2.5))samples were collected in two neighboring cities,Beijing and Baoding,China.High-concentration events of PM_(2.5) in which the average mass concentration exceeded 75μg/m^(3) were freque...Fine particulatematter(PM_(2.5))samples were collected in two neighboring cities,Beijing and Baoding,China.High-concentration events of PM_(2.5) in which the average mass concentration exceeded 75μg/m^(3) were frequently observed during the heating season.Dispersion Normalized Positive Matrix Factorization was applied for the source apportionment of PM_(2.5) 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 PM_(2.5) 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
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 ...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.展开更多
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 me...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.展开更多
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
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...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.展开更多
In this paper, we proposed a novel resolution criterion（improved calibrated normalized resolution product, r＊＇） to evaluate separation quality of fingerprints. By comparing with the calibrated normalized resolutio...In this paper, we proposed a novel resolution criterion（improved calibrated normalized resolution product, r＊＇） to evaluate separation quality of fingerprints. By comparing with the calibrated normalized resolution product（r＊） and the hierarchical chromatographic response function（HCRF）, the validity of this criterion was demonstrated by experimental chromatograms. The soy isoflavone extract was selected as the analytical object. The initial and end percentages of methanol and elution time affecting gradient elution were tested by orthogonal design. The final optimized conditions were as follows. It was detected by UV absorbance at 254 nm, column temperature was maintained at 36 oC, solvent A was 0.1%（v/v） acetic acid, solvent B was methanol, gradient elution was from 34% to 65% B in a linear gradient in 25 min, and the flow-rate was set at 1.0 m L/min. In addition, the main ingredients of the soy isoflavone extract were confirmed by LC-ESI/MS.展开更多
基金Supported by the National Natural Science Foundation of China(11671403,11671236,12101192)Henan Provincial General Natural Science Foundation Project(232300420113)。
文摘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.
基金Supported by National Natural Science Foundation of China(11671403,11671236)Henan Provincial General Natural Science Foundation Project(232300420113)。
文摘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.
文摘This paper presents new generalizations of the Hermite-Hadamard inequality for convex functions via(p,q)-quantum integrals.First,based on the definitions of(p,q)-derivatives and integrals over finite intervals,we establish a unified(p,q)-Hermite-Hadamard inequality framework,combining midpoint-type and trapezoidal-type inequalities into a single form.Furthermore,by introducing a parameterλ,we propose a generalized(p,q)-integral inequality,whose special cases reduce to classical quantum Hermite-Hadamard inequalities and existing results in the literature.Furthermore,using hybrid integral techniques,we construct refined inequalities that incorporate(p,q)-integral terms,and by adjustingλ,we demonstrate their improvements and extensions to known inequalities.Specific examples are provided to validate the applicability of the results.The findings indicate that the proposed(p,q)-integral approach offers more flexible mathematical tools for the estimation of numerical integration error,convex optimization problems,and analysis of system performance in control theory,thus enriching the research results of quantum calculus in the field of inequalities.
基金supported by National Natural Science Foundation of China(Grant Nos.12271313,12071266,12101376)supported by National Natural Science Foundation of China(Grant Nos.12171204,12371107)+3 种基金National Natural Science Foundation of China(Grant No.12031015)Fundamental Research Program of Shanxi Province(Grant Nos.202203021211300,202203021211309,20210302124528)Shanxi Scholarship Council of China(Grant No.2020-005)supported by National Key R&D Program of China(Grant No.2022YFA1005601)。
文摘Consider the Kirchhoff equation with Hartree type nonlinearity■where a,b>0,λ,μ∈R,2<q<6,0<α<3,and Iαis the Riesz potential integral operator of orderα.Solutions with prescribed mass■,also known as normalized solutions,are of particular interest in the current paper.Under various assumptions onμ,c and q,we establish the existence,nonexistence and asymptotic behavior of normalized solutions for the above elliptic equation.
基金supported by the NNSF of China(12471103)the Natural Science Foundation of Guangdong Province(2024A1515012370)the Guangzhou Basic and Applied Basic Research(2023A04J1316)。
文摘In this paper,we investigate the existence and multiplicity of normalized solutions for the following fractional Schrödinger equations{(-△)^(s)u+λu=|u|^(p-2)u-|u|^(q-2)u,x∈R^(N),∫_(R^(N))|u|^(2)dx=c>0,where N≥2,s∈(0,1),2+4s/N<p<q≤2_(s)^(*)=2N/N-2s,(-△)^(s)represents the fractional Laplacian operator of order s,and the frequencyλ∈R is unknown and appears as a Lagrange multiplier.Specifically,we show that there exists a c>0 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.
基金supported by the National Natural Science Foundation of China(Grant No.11971411)。
文摘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.
基金supported by the Spanish Ministry of Science and Innovation under the MCI/AEI/FEDER project number PID2021-123543OBC21.
文摘Anomaly detection in wind turbines involves emphasizing its ability to improve operational efficiency,reduce maintenance costs,extend their lifespan,and enhance reliability in the wind energy sector.This is particularly necessary in offshore wind,currently one of the most critical assets for achieving sustainable energy generation goals,due to the harsh marine environment and the difficulty of maintenance tasks.To address this problem,this work proposes a data-driven methodology for detecting power generation anomalies in offshore wind turbines,using normalized and linearized operational data.The proposed framework transforms heterogeneous wind speed and power measurements into a unified scale,enabling the development of a new wind power index(WPi)that quantifies deviations from expected performance.Additionally,spatial and temporal coherence analyses of turbines within a wind farm ensure the validity of these normalized measurements across different wind turbine models and operating conditions.Furthermore,a Support Vector Machine(SVM)refines the classification process,effectively distinguishing measurement errors from actual power generation failures.Validation of this strategy using real-world data from the Alpha Ventus wind farm demonstrates that the proposed approach not only improves predictive maintenance but also optimizes energy production,highlighting its potential for broad application in offshore wind installations.
基金supported by the National Natural Science Foundation of China(No.12461024)the Natural Science Research Project of Department of Education of Guizhou Province(Nos.QJJ2023012,QJJ2023061,QJJ2023062)the Natural Science Research Project of Guizhou Minzu University(No.GZMUZK[2022]YB06)。
文摘In this paper,we consider the p-Laplacian Schrödinger-Poisson equation with L^(2)-norm constraint-Δ_(p)u+|u|^(p-2)u+λu+(1/4π|x|*|u|^(2))u=|u|^(q-2)u,x∈R^(3),where 2≤p<3,5p/3<q<p*=3p/3-p,λ>0 is a Lagrange multiplier.We obtain the critical point of the corresponding functional of the problem on mass constraint by the variational method and the Mountain pass lemma,and then find a normalized solution to this equation.
基金Funding by Social Science Research of Ministry of Education of the People’s Republic of China“Study on issues related on the development and utilization of the Arctic Passage”(Grant no.20JHQ016)is acknowledged.
文摘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.
基金supported by the Natural Science Research Project of Department of Education of Guizhou Province(No.QJJ2023062)the National Natural Science Foundation of China(No.52174184)。
文摘In this paper,we consider the following logarithmic Schrödinger equation:−Δu+ωu=u log|u|^(2),u∈H^(1)(R^(N)),where N≥3,and ω>0 is a constant.With an auxiliary equation,we obtain the existence of normalized solutions by using the constrained variational method.
基金Supported by National Natural Science Foundation of China(Grant Nos.11671403 and 11671236)Henan Provincial General Natural Science Foundation Project(Grant No.232300420113)。
文摘In this paper,we study high energy normalized solutions for the following Schr?dinger equation{-Δu+V(x)u+λu=f(u),in R^(2),∫_(R^(2))|u|^(2)dx=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.
基金supported by the National Institute of Environmental Research(NIER)funded by the Ministry of Environment(No.NIER-2019-04-02-039)supported by Particulate Matter Management Specialized Graduate Program through the Korea Environmental Industry&Technology Institute(KEITI)funded by the Ministry of Environment(MOE).
文摘Fine particulatematter(PM_(2.5))samples were collected in two neighboring cities,Beijing and Baoding,China.High-concentration events of PM_(2.5) in which the average mass concentration exceeded 75μg/m^(3) were frequently observed during the heating season.Dispersion Normalized Positive Matrix Factorization was applied for the source apportionment of PM_(2.5) 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 PM_(2.5) 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.
基金Supported by the 973 Program of China (No. 2006CB101600)~~
文摘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.
基金supported by the National Natural Science Foundation of China(No.41174087,41204089)the National Oil and Gas Major Project(No.2011ZX05005-005)
文摘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.
基金supported by the China Postdoctoral Science Foundation (No.2014M551188)the Deep Exploration in China Sinoprobe-09-01 (No.201011078)
文摘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.
基金China Postdoctoral Science Foundation ( No20060400826)
文摘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.
基金National Higher-Education Institution General Research and Development Funding(Grant No.JKP2011010)
文摘In this paper, we proposed a novel resolution criterion（improved calibrated normalized resolution product, r＊＇） to evaluate separation quality of fingerprints. By comparing with the calibrated normalized resolution product（r＊） and the hierarchical chromatographic response function（HCRF）, the validity of this criterion was demonstrated by experimental chromatograms. The soy isoflavone extract was selected as the analytical object. The initial and end percentages of methanol and elution time affecting gradient elution were tested by orthogonal design. The final optimized conditions were as follows. It was detected by UV absorbance at 254 nm, column temperature was maintained at 36 oC, solvent A was 0.1%（v/v） acetic acid, solvent B was methanol, gradient elution was from 34% to 65% B in a linear gradient in 25 min, and the flow-rate was set at 1.0 m L/min. In addition, the main ingredients of the soy isoflavone extract were confirmed by LC-ESI/MS.
