In this paper,we study the self-similar solutions of the degenerate diffusion equation ut-div(|▽u^(m)|^(p-2)▽u^(m))=0 of polytropic filtration diffusion in R^(N)×(0,±∞)or(R^(N)/{0})×(0,±∞)with ...In this paper,we study the self-similar solutions of the degenerate diffusion equation ut-div(|▽u^(m)|^(p-2)▽u^(m))=0 of polytropic filtration diffusion in R^(N)×(0,±∞)or(R^(N)/{0})×(0,±∞)with N≥1,m>0,p>1,such that m(p-1)>1.We give a clear classification of the self-similar solutions of the form u(x,t)=(βt)^(-α/β)((βt)^(-1/β)|x|)withα∈R andβ=α[m(p-1)-1]+p,regular or singular at the origin point.The existence and uniqueness of some solutions are established by the phase plane analysis method,and the asymptotic properties of the solutions near the origin and the infinity are also described.This paper extends the classical results of self-similar solutions for degeneratep-Laplace heat equation by Bidaut-Véron[Proc Royal Soc Edinburgh,2009,139:1-43]to the doubly nonlinear degenerate diffusion equations.展开更多
In this study,a straightforward one-step hydrothermal method was successfully utilized to synthesize the solid solution Na_(0.9)Mg_(0.45)Ti_(3.55)O_(8)-Na_(2)Ni_(2)Ti_(6)O_(16)(NNMTO-x),where x denotes the molar perce...In this study,a straightforward one-step hydrothermal method was successfully utilized to synthesize the solid solution Na_(0.9)Mg_(0.45)Ti_(3.55)O_(8)-Na_(2)Ni_(2)Ti_(6)O_(16)(NNMTO-x),where x denotes the molar percentage of Na_(2)Ni_(2)Ti_(6)O_(16)(NNTO)within Na_(0.9)Mg_(0.45)Ti_(3.55)O_(8)(NMTO),with x values of 10,20,30,40,and 50.Both XPS(X-ray Photoelectron Spectroscopy)and EDX(Energy Dispersive X-ray Spectroscopy)analyses unequivocally validated the formation of the NNMTO-x solid solutions.It was observed that when x is below 40,the NNMTO-x solid solution retains the structural characteristics of the original NMTO.However,beyond this threshold,significant alterations in crystal morphology were noted,accompanied by a noticeable decline in photocatalytic activity.Notably,the absorption edge of NNMTO-x(x<40)exhibited a shift towards the visible-light spectrum,thereby substantially broadening the absorption range.The findings highlight that NNMTO-30 possesses the most pronounced photocatalytic activity for the reduction of CO_(2).Specifically,after a 6 h irradiation period,the production rates of CO and CH_(4)were recorded at 42.38 and 1.47μmol/g,respectively.This investigation provides pivotal insights that are instrumental in the advancement of highly efficient and stable photocatalysts tailored for CO_(2)reduction processes.展开更多
In recent decades,the proliferation of email communication has markedly escalated,resulting in a concomitant surge in spam emails that congest networks and presenting security risks.This study introduces an innovative...In recent decades,the proliferation of email communication has markedly escalated,resulting in a concomitant surge in spam emails that congest networks and presenting security risks.This study introduces an innovative spam detection method utilizing the Horse Herd Optimization Algorithm(HHOA),designed for binary classification within multi⁃objective framework.The method proficiently identifies essential features,minimizing redundancy and improving classification precision.The suggested HHOA attained an impressive accuracy of 97.21%on the Kaggle email dataset,with precision of 94.30%,recall of 90.50%,and F1⁃score of 92.80%.Compared to conventional techniques,such as Support Vector Machine(93.89%accuracy),Random Forest(96.14%accuracy),and K⁃Nearest Neighbours(92.08%accuracy),HHOA exhibited enhanced performance with reduced computing complexity.The suggested method demonstrated enhanced feature selection efficiency,decreasing the number of selected features while maintaining high classification accuracy.The results underscore the efficacy of HHOA in spam identification and indicate its potential for further applications in practical email filtering systems.展开更多
Near-Earth objects are important not only in studying the early formation of the Solar System,but also because they pose a serious hazard to humanity when they make close approaches to the Earth.Study of their physica...Near-Earth objects are important not only in studying the early formation of the Solar System,but also because they pose a serious hazard to humanity when they make close approaches to the Earth.Study of their physical properties can provide useful information on their origin,evolution,and hazard to human beings.However,it remains challenging to investigate small,newly discovered,near-Earth objects because of our limited observational window.This investigation seeks to determine the visible colors of near-Earth asteroids(NEAs),perform an initial taxonomic classification based on visible colors and analyze possible correlations between the distribution of taxonomic classification and asteroid size or orbital parameters.Observations were performed in the broadband BVRI Johnson−Cousins photometric system,applied to images from the Yaoan High Precision Telescope and the 1.88 m telescope at the Kottamia Astronomical Observatory.We present new photometric observations of 84 near-Earth asteroids,and classify 80 of them taxonomically,based on their photometric colors.We find that nearly half(46.3%)of the objects in our sample can be classified as S-complex,26.3%as C-complex,6%as D-complex,and 15.0%as X-complex;the remaining belong to the A-or V-types.Additionally,we identify three P-type NEAs in our sample,according to the Tholen scheme.The fractional abundances of the C/X-complex members with absolute magnitude H≥17.0 were more than twice as large as those with H<17.0.However,the fractions of C-and S-complex members with diameters≤1 km and>1 km are nearly equal,while X-complex members tend to have sub-kilometer diameters.In our sample,the C/D-complex objects are predominant among those with a Jovian Tisserand parameter of T_(J)<3.1.These bodies could have a cometary origin.C-and S-complex members account for a considerable proportion of the asteroids that are potentially hazardous.展开更多
Graph Neural Networks(GNNs)have proven highly effective for graph classification across diverse fields such as social networks,bioinformatics,and finance,due to their capability to learn complex graph structures.Howev...Graph Neural Networks(GNNs)have proven highly effective for graph classification across diverse fields such as social networks,bioinformatics,and finance,due to their capability to learn complex graph structures.However,despite their success,GNNs remain vulnerable to adversarial attacks that can significantly degrade their classification accuracy.Existing adversarial attack strategies primarily rely on label information to guide the attacks,which limits their applicability in scenarios where such information is scarce or unavailable.This paper introduces an innovative unsupervised attack method for graph classification,which operates without relying on label information,thereby enhancing its applicability in a broad range of scenarios.Specifically,our method first leverages a graph contrastive learning loss to learn high-quality graph embeddings by comparing different stochastic augmented views of the graphs.To effectively perturb the graphs,we then introduce an implicit estimator that measures the impact of various modifications on graph structures.The proposed strategy identifies and flips edges with the top-K highest scores,determined by the estimator,to maximize the degradation of the model’s performance.In addition,to defend against such attack,we propose a lightweight regularization-based defense mechanism that is specifically tailored to mitigate the structural perturbations introduced by our attack strategy.It enhances model robustness by enforcing embedding consistency and edge-level smoothness during training.We conduct experiments on six public TU graph classification datasets:NCI1,NCI109,Mutagenicity,ENZYMES,COLLAB,and DBLP_v1,to evaluate the effectiveness of our attack and defense strategies.Under an attack budget of 3,the maximum reduction in model accuracy reaches 6.67%on the Graph Convolutional Network(GCN)and 11.67%on the Graph Attention Network(GAT)across different datasets,indicating that our unsupervised method induces degradation comparable to state-of-the-art supervised attacks.Meanwhile,our defense achieves the highest accuracy recovery of 3.89%(GCN)and 5.00%(GAT),demonstrating improved robustness against structural perturbations.展开更多
Skin diseases affect millions worldwide.Early detection is key to preventing disfigurement,lifelong disability,or death.Dermoscopic images acquired in primary-care settings show high intra-class visual similarity and ...Skin diseases affect millions worldwide.Early detection is key to preventing disfigurement,lifelong disability,or death.Dermoscopic images acquired in primary-care settings show high intra-class visual similarity and severe class imbalance,and occasional imaging artifacts can create ambiguity for state-of-the-art convolutional neural networks(CNNs).We frame skin lesion recognition as graph-based reasoning and,to ensure fair evaluation and avoid data leakage,adopt a strict lesion-level partitioning strategy.Each image is first over-segmented using SLIC(Simple Linear Iterative Clustering)to produce perceptually homogeneous superpixels.These superpixels form the nodes of a region-adjacency graph whose edges encode spatial continuity.Node attributes are 1280-dimensional embeddings extracted with a lightweight yet expressive EfficientNet-B0 backbone,providing strong representational power at modest computational cost.The resulting graphs are processed by a five-layer Graph Attention Network(GAT)that learns to weight inter-node relationships dynamically and aggregates multi-hop context before classifying lesions into seven classes with a log-softmax output.Extensive experiments on the DermaMNIST benchmark show the proposed pipeline achieves 88.35%accuracy and 98.04%AUC,outperforming contemporary CNNs,AutoML approaches,and alternative graph neural networks.An ablation study indicates EfficientNet-B0 produces superior node descriptors compared with ResNet-18 and DenseNet,and that roughly five GAT layers strike a good balance between being too shallow and over-deep while avoiding oversmoothing.The method requires no data augmentation or external metadata,making it a drop-in upgrade for clinical computer-aided diagnosis systems.展开更多
This paper is concerned with an initial boundary value problem for the planar magnetohydrodynamic compressible flow with temperature dependent heat conductivity in a half-line.In particular,the transverse magnetic fie...This paper is concerned with an initial boundary value problem for the planar magnetohydrodynamic compressible flow with temperature dependent heat conductivity in a half-line.In particular,the transverse magnetic field is assumed to satisfy the Neumann boundary condition,which was first investigated by Kazhikhov in 1987.We establish the global existence of the unique strong solutions to the MHD equations without any smallness conditions on the initial data.More precisely,our result can be regarded as a natural generalization of Kazhikov’s result for applying the constant heat-conductivity in bounded domains to the degenerate case in unbounded domains.展开更多
This systematic review aims to comprehensively examine and compare deep learning methods for brain tumor segmentation and classification using MRI and other imaging modalities,focusing on recent trends from 2022 to 20...This systematic review aims to comprehensively examine and compare deep learning methods for brain tumor segmentation and classification using MRI and other imaging modalities,focusing on recent trends from 2022 to 2025.The primary objective is to evaluate methodological advancements,model performance,dataset usage,and existing challenges in developing clinically robust AI systems.We included peer-reviewed journal articles and highimpact conference papers published between 2022 and 2025,written in English,that proposed or evaluated deep learning methods for brain tumor segmentation and/or classification.Excluded were non-open-access publications,books,and non-English articles.A structured search was conducted across Scopus,Google Scholar,Wiley,and Taylor&Francis,with the last search performed in August 2025.Risk of bias was not formally quantified but considered during full-text screening based on dataset diversity,validation methods,and availability of performance metrics.We used narrative synthesis and tabular benchmarking to compare performance metrics(e.g.,accuracy,Dice score)across model types(CNN,Transformer,Hybrid),imaging modalities,and datasets.A total of 49 studies were included(43 journal articles and 6 conference papers).These studies spanned over 9 public datasets(e.g.,BraTS,Figshare,REMBRANDT,MOLAB)and utilized a range of imaging modalities,predominantly MRI.Hybrid models,especially ResViT and UNetFormer,consistently achieved high performance,with classification accuracy exceeding 98%and segmentation Dice scores above 0.90 across multiple studies.Transformers and hybrid architectures showed increasing adoption post2023.Many studies lacked external validation and were evaluated only on a few benchmark datasets,raising concerns about generalizability and dataset bias.Few studies addressed clinical interpretability or uncertainty quantification.Despite promising results,particularly for hybrid deep learning models,widespread clinical adoption remains limited due to lack of validation,interpretability concerns,and real-world deployment barriers.展开更多
In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→...In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→∞)x′(t)e^(t)=0,where t_(0) and ψ_(0) are real constants,φ(s)=s/√1−s^(2),s∈R with s∈(−1,1),f:[t_(0),∞)×R→R satisfies the Lipschitz or Osgood-type conditions.展开更多
Honeycombing Lung(HCL)is a chronic lung condition marked by advanced fibrosis,resulting in enlarged air spaces with thick fibrotic walls,which are visible on Computed Tomography(CT)scans.Differentiating between normal...Honeycombing Lung(HCL)is a chronic lung condition marked by advanced fibrosis,resulting in enlarged air spaces with thick fibrotic walls,which are visible on Computed Tomography(CT)scans.Differentiating between normal lung tissue,honeycombing lungs,and Ground Glass Opacity(GGO)in CT images is often challenging for radiologists and may lead to misinterpretations.Although earlier studies have proposed models to detect and classify HCL,many faced limitations such as high computational demands,lower accuracy,and difficulty distinguishing between HCL and GGO.CT images are highly effective for lung classification due to their high resolution,3D visualization,and sensitivity to tissue density variations.This study introduces Honeycombing Lungs Network(HCL Net),a novel classification algorithm inspired by ResNet50V2 and enhanced to overcome the shortcomings of previous approaches.HCL Net incorporates additional residual blocks,refined preprocessing techniques,and selective parameter tuning to improve classification performance.The dataset,sourced from the University Malaya Medical Centre(UMMC)and verified by expert radiologists,consists of CT images of normal,honeycombing,and GGO lungs.Experimental evaluations across five assessments demonstrated that HCL Net achieved an outstanding classification accuracy of approximately 99.97%.It also recorded strong performance in other metrics,achieving 93%precision,100%sensitivity,89%specificity,and an AUC-ROC score of 97%.Comparative analysis with baseline feature engineering methods confirmed the superior efficacy of HCL Net.The model significantly reduces misclassification,particularly between honeycombing and GGO lungs,enhancing diagnostic precision and reliability in lung image analysis.展开更多
Sudden wildfires cause significant global ecological damage.While satellite imagery has advanced early fire detection and mitigation,image-based systems face limitations including high false alarm rates,visual obstruc...Sudden wildfires cause significant global ecological damage.While satellite imagery has advanced early fire detection and mitigation,image-based systems face limitations including high false alarm rates,visual obstructions,and substantial computational demands,especially in complex forest terrains.To address these challenges,this study proposes a novel forest fire detection model utilizing audio classification and machine learning.We developed an audio-based pipeline using real-world environmental sound recordings.Sounds were converted into Mel-spectrograms and classified via a Convolutional Neural Network(CNN),enabling the capture of distinctive fire acoustic signatures(e.g.,crackling,roaring)that are minimally impacted by visual or weather conditions.Internet of Things(IoT)sound sensors were crucial for generating complex environmental parameters to optimize feature extraction.The CNN model achieved high performance in stratified 5-fold cross-validation(92.4%±1.6 accuracy,91.2%±1.8 F1-score)and on test data(94.93%accuracy,93.04%F1-score),with 98.44%precision and 88.32%recall,demonstrating reliability across environmental conditions.These results indicate that the audio-based approach not only improves detection reliability but also markedly reduces computational overhead compared to traditional image-based methods.The findings suggest that acoustic sensing integrated with machine learning offers a powerful,low-cost,and efficient solution for real-time forest fire monitoring in complex,dynamic environments.展开更多
The performance of Mg alloys is significantly influenced by the concentrations and solid solution behavior of the alloying elements.In this work,the solid solution behavior of 20 alloying elements in 190 ternary Mg al...The performance of Mg alloys is significantly influenced by the concentrations and solid solution behavior of the alloying elements.In this work,the solid solution behavior of 20 alloying elements in 190 ternary Mg alloy systems at 500℃are systematically investigated.The solid solution behavior of a set of two different alloying elements in Mg alloy systems are suggested to be classified into three categories:inclusivity,exclusivity and proportionality.Inclusivity classification indicates that the two alloying elements are inclusive inα-Mg,increasing the joint solubility of both elements.Exclusivity classification suggests that the two alloying elements have a low joint solid solubility inα-Mg,since they prefer to form stable second phases.For the proportionality classification,the solubility curve of the ternary Mg alloy systems is a straight line connecting the solubility points of the two sub-binary systems.The proposed classification theory was validated by key experiments and the calculation of formation energies.The interaction effects between alloying elements and the preference of formation of second phases are the main factors determining the solid solution behavior classifications.Based on the observed solid solution features of multi-component Mg alloys,principles for alloy design of different types of high-performance Mg alloys were proposed in this work.展开更多
Accurate extraction of surface water extent is a fundamental prerequisite for monitoring its dynamic changes.Although machine learning algorithms have been widely applied to surface water mapping,most studies focus pr...Accurate extraction of surface water extent is a fundamental prerequisite for monitoring its dynamic changes.Although machine learning algorithms have been widely applied to surface water mapping,most studies focus primarily on algorithmic outputs,with limited systematic evaluation of their applicability and constrained classification accuracy.In this study,we focused on the Songnen Plain in Northeast China and employed Sentinel-2 imagery acquired during 2020-2021 via the Google Earth Engine(GEE)platform to evaluate the performance of Classification and Regression Trees(CART),Random Forest(RF),and Support Vector Machine(SVM)for surface water classification.The classification process was optimized by incorporating automated training sample selection and integration of time series features.Validation with independent samples demonstrated the feasibility of automatic sample selection,yielding mean overall accuracies of 91.16%,90.99%,and 90.76%for RF,SVM,and CART,respectively.After integrating time series features,the mean overall accuracies of the three algorithms improved by 4.51%,5.45%,and 6.36%,respectively.In addition,spectral features such as MNDWI(Modified Normalized Difference Water Index),SWIR(Short Wave Infrared),and NDVI(Normalized Difference Vegetation Index)were identified as more important for surface water classification.This study establishes a more consistent framework for surface water mapping,offering new perspectives for improving and automating classification processes in the era of big and open data.展开更多
Under the travelling wave transformation, the Camassa-Holm equation with dispersion is reduced to an integrable ordinary differential equation （ODE）, whose general solution can be obtained using the trick of one-par...Under the travelling wave transformation, the Camassa-Holm equation with dispersion is reduced to an integrable ordinary differential equation （ODE）, whose general solution can be obtained using the trick of one-parameter group. Furthermore, by using a complete discrimination system for polynomial, the classification of all single travelling wave solutions to the Camassa-Holm equation with dispersion is obtained. In particular, an affine subspace structure in the set of the solutions of the reduced ODE is obtained. More generally, an implicit linear structure in the Camassa-Holm equation with dispersion is found. According to the linear structure, we obtain the superposition of multi-solutions to Camassa-Holm equation with dispersion.展开更多
Alzheimer’s Disease(AD)is a progressive neurodegenerative disorder that significantly affects cognitive function,making early and accurate diagnosis essential.Traditional Deep Learning(DL)-based approaches often stru...Alzheimer’s Disease(AD)is a progressive neurodegenerative disorder that significantly affects cognitive function,making early and accurate diagnosis essential.Traditional Deep Learning(DL)-based approaches often struggle with low-contrast MRI images,class imbalance,and suboptimal feature extraction.This paper develops a Hybrid DL system that unites MobileNetV2 with adaptive classification methods to boost Alzheimer’s diagnosis by processing MRI scans.Image enhancement is done using Contrast-Limited Adaptive Histogram Equalization(CLAHE)and Enhanced Super-Resolution Generative Adversarial Networks(ESRGAN).A classification robustness enhancement system integrates class weighting techniques and a Matthews Correlation Coefficient(MCC)-based evaluation method into the design.The trained and validated model gives a 98.88%accuracy rate and 0.9614 MCC score.We also performed a 10-fold cross-validation experiment with an average accuracy of 96.52%(±1.51),a loss of 0.1671,and an MCC score of 0.9429 across folds.The proposed framework outperforms the state-of-the-art models with a 98%weighted F1-score while decreasing misdiagnosis results for every AD stage.The model demonstrates apparent separation abilities between AD progression stages according to the results of the confusion matrix analysis.These results validate the effectiveness of hybrid DL models with adaptive preprocessing for early and reliable Alzheimer’s diagnosis,contributing to improved computer-aided diagnosis(CAD)systems in clinical practice.展开更多
Benthic habitat mapping is an emerging discipline in the international marine field in recent years,providing an effective tool for marine spatial planning,marine ecological management,and decision-making applications...Benthic habitat mapping is an emerging discipline in the international marine field in recent years,providing an effective tool for marine spatial planning,marine ecological management,and decision-making applications.Seabed sediment classification is one of the main contents of seabed habitat mapping.In response to the impact of remote sensing imaging quality and the limitations of acoustic measurement range,where a single data source does not fully reflect the substrate type,we proposed a high-precision seabed habitat sediment classification method that integrates data from multiple sources.Based on WorldView-2 multi-spectral remote sensing image data and multibeam bathymetry data,constructed a random forests(RF)classifier with optimal feature selection.A seabed sediment classification experiment integrating optical remote sensing and acoustic remote sensing data was carried out in the shallow water area of Wuzhizhou Island,Hainan,South China.Different seabed sediment types,such as sand,seagrass,and coral reefs were effectively identified,with an overall classification accuracy of 92%.Experimental results show that RF matrix optimized by fusing multi-source remote sensing data for feature selection were better than the classification results of simple combinations of data sources,which improved the accuracy of seabed sediment classification.Therefore,the method proposed in this paper can be effectively applied to high-precision seabed sediment classification and habitat mapping around islands and reefs.展开更多
Under the travelling wave transformation, Calogero-Degasperis-Focas equation is reduced to an ordinary differential equation. Using a symmetry group of one parameter, this ODE is reduced to a second-order linear inhom...Under the travelling wave transformation, Calogero-Degasperis-Focas equation is reduced to an ordinary differential equation. Using a symmetry group of one parameter, this ODE is reduced to a second-order linear inhomogeneous ODE. Furthermore, we apply the change of the variable and complete discrimination system for polynomial to solve the corresponding integrals and obtained the classification of all single travelling wave solutions to Calogero- Degasperis-Focas equation.展开更多
The clinical course of infections with the hepatitis B virus (HBV) substantially varies between individuals, as a consequence of a complex interplay between viral, host, environmental and other factors. Due to the hig...The clinical course of infections with the hepatitis B virus (HBV) substantially varies between individuals, as a consequence of a complex interplay between viral, host, environmental and other factors. Due to the high genetic variability of HBV, the virus can be categorized into different HBV genotypes and subgenotypes, which considerably differ with respect to geographical distribution, transmission routes, disease progression, responses to antiviral therapy or vaccination, and clinical outcome measures such as cirrhosis or hepatocellular carcinoma. However, HBV (sub)genotyping has caused some controversies in the past due to misclassifications and incorrect interpretations of different genotyping methods. Thus, an accurate, holistic and dynamic classification system is essential. In this review article, we aimed at highlighting potential pitfalls in genetic and phylogenetic analyses of HBV and suggest novel terms for HBV classification. Analyzing full-length genome sequences when classifying genotypes and subgenotypes is the foremost prerequisite of this classification system. Careful attention must be paid to all aspects of phylogenetic analysis, such as bootstrapping values and meeting the necessary thresholds for (sub)genotyping. Quasi-subgenotype refers to subgenotypes that were incorrectly suggested to be novel. As many of these strains were misclassified due to genetic differences resulting from recombination, we propose the term “recombino-subgenotype”. Moreover, immigration is an important confounding facet of global HBV distribution and substantially changes the geographic pattern of HBV (sub)genotypes. We therefore suggest the term “immigro-subgenotype” to distinguish exotic (sub)genotypes from native ones. We are strongly convinced that applying these two proposed terms in HBV classification will help harmonize this rapidly progressing field and allow for improved prophylaxis, diagnosis and treatment.展开更多
Generalised reduced masses with a set of equations governing the three relative motions between two of 3-bodies in their gravitational field are established,of which the dynamic characteristics of 3-body dynamics,fund...Generalised reduced masses with a set of equations governing the three relative motions between two of 3-bodies in their gravitational field are established,of which the dynamic characteristics of 3-body dynamics,fundamental bases of this paper,are revealed.Based on these findings,an equivalent system is developed,which is a 2-body system with its total mass,constant angular momentum,kinetic and potential energies same as the total ones of three relative motions,so that it can be solved using the well-known theory of the 2-body system.From the solution of an equivalent system with the revealed characteristics of three relative motions,the general theoretical solutions of the 3-body system are obtained in the curve-integration forms along the orbits in the imaged radial motion space.The possible periodical orbits with generalised Kepler’s law are presented.Following the description and mathematical demonstrations of the proposed methods,the examples including Euler’s/Lagrange’s problems,and a reported numerical one are solved to validate the proposed methods.The methods derived from the 3-body system are extended to N-body problems.展开更多
Under the travelling wave transformation, some nonlinear partial differential equations such as Camassa-Holm equation, High-order KdV equation, etc., are reduced to an integrable ODE expressed by u＂ ＋p（u）（u＇）^2...Under the travelling wave transformation, some nonlinear partial differential equations such as Camassa-Holm equation, High-order KdV equation, etc., are reduced to an integrable ODE expressed by u＂ ＋p（u）（u＇）^2 ＋ q（u） = 0 whose generai solution can be given. Furthermore, combining complete discrimination system for polynomiai, the classifications of all single travelling wave solutions to these equations are obtained. The equation u＂＋p（u）（u＇）^2＋q（u） = 0 includes the equation （u＇）^2 = f（u） as a special case, so the proposed method can be also applied to a large number of nonlinear equations. These complete results cannot be obtained by any indirect method.展开更多
基金supported by the NSFC(12271178,12171166)the Guangzhou Basic and Applied Basic Research Foundation(2024A04J2022)the TCL Young Scholar(2024-2027).
文摘In this paper,we study the self-similar solutions of the degenerate diffusion equation ut-div(|▽u^(m)|^(p-2)▽u^(m))=0 of polytropic filtration diffusion in R^(N)×(0,±∞)or(R^(N)/{0})×(0,±∞)with N≥1,m>0,p>1,such that m(p-1)>1.We give a clear classification of the self-similar solutions of the form u(x,t)=(βt)^(-α/β)((βt)^(-1/β)|x|)withα∈R andβ=α[m(p-1)-1]+p,regular or singular at the origin point.The existence and uniqueness of some solutions are established by the phase plane analysis method,and the asymptotic properties of the solutions near the origin and the infinity are also described.This paper extends the classical results of self-similar solutions for degeneratep-Laplace heat equation by Bidaut-Véron[Proc Royal Soc Edinburgh,2009,139:1-43]to the doubly nonlinear degenerate diffusion equations.
基金Supported by the Doctoral Research Start-up Project of Yuncheng University(YQ-2023067)Project of Shanxi Natural Science Foundation(202303021211189)+1 种基金Fund Program for the Scientific Activities of Selected Returned Overseas Professionals in Shanxi Provinces(20220036)Shanxi ProvinceIntelligent Optoelectronic Sensing Application Technology Innovation Center and Shanxi Province Optoelectronic Information Science and TechnologyLaboratory,Yuncheng University.
文摘In this study,a straightforward one-step hydrothermal method was successfully utilized to synthesize the solid solution Na_(0.9)Mg_(0.45)Ti_(3.55)O_(8)-Na_(2)Ni_(2)Ti_(6)O_(16)(NNMTO-x),where x denotes the molar percentage of Na_(2)Ni_(2)Ti_(6)O_(16)(NNTO)within Na_(0.9)Mg_(0.45)Ti_(3.55)O_(8)(NMTO),with x values of 10,20,30,40,and 50.Both XPS(X-ray Photoelectron Spectroscopy)and EDX(Energy Dispersive X-ray Spectroscopy)analyses unequivocally validated the formation of the NNMTO-x solid solutions.It was observed that when x is below 40,the NNMTO-x solid solution retains the structural characteristics of the original NMTO.However,beyond this threshold,significant alterations in crystal morphology were noted,accompanied by a noticeable decline in photocatalytic activity.Notably,the absorption edge of NNMTO-x(x<40)exhibited a shift towards the visible-light spectrum,thereby substantially broadening the absorption range.The findings highlight that NNMTO-30 possesses the most pronounced photocatalytic activity for the reduction of CO_(2).Specifically,after a 6 h irradiation period,the production rates of CO and CH_(4)were recorded at 42.38 and 1.47μmol/g,respectively.This investigation provides pivotal insights that are instrumental in the advancement of highly efficient and stable photocatalysts tailored for CO_(2)reduction processes.
文摘In recent decades,the proliferation of email communication has markedly escalated,resulting in a concomitant surge in spam emails that congest networks and presenting security risks.This study introduces an innovative spam detection method utilizing the Horse Herd Optimization Algorithm(HHOA),designed for binary classification within multi⁃objective framework.The method proficiently identifies essential features,minimizing redundancy and improving classification precision.The suggested HHOA attained an impressive accuracy of 97.21%on the Kaggle email dataset,with precision of 94.30%,recall of 90.50%,and F1⁃score of 92.80%.Compared to conventional techniques,such as Support Vector Machine(93.89%accuracy),Random Forest(96.14%accuracy),and K⁃Nearest Neighbours(92.08%accuracy),HHOA exhibited enhanced performance with reduced computing complexity.The suggested method demonstrated enhanced feature selection efficiency,decreasing the number of selected features while maintaining high classification accuracy.The results underscore the efficacy of HHOA in spam identification and indicate its potential for further applications in practical email filtering systems.
基金funded by the China National Space Administration(KJSP2023020105)supported by the National Key R&D Program of China(Grant No.2023YFA1608100)+2 种基金the NSFC(Grant No.62227901)the Minor Planet Foundationsupported by the Egyptian Science,Technology&Innovation Funding Authority(STDF)under Grant No.48102.
文摘Near-Earth objects are important not only in studying the early formation of the Solar System,but also because they pose a serious hazard to humanity when they make close approaches to the Earth.Study of their physical properties can provide useful information on their origin,evolution,and hazard to human beings.However,it remains challenging to investigate small,newly discovered,near-Earth objects because of our limited observational window.This investigation seeks to determine the visible colors of near-Earth asteroids(NEAs),perform an initial taxonomic classification based on visible colors and analyze possible correlations between the distribution of taxonomic classification and asteroid size or orbital parameters.Observations were performed in the broadband BVRI Johnson−Cousins photometric system,applied to images from the Yaoan High Precision Telescope and the 1.88 m telescope at the Kottamia Astronomical Observatory.We present new photometric observations of 84 near-Earth asteroids,and classify 80 of them taxonomically,based on their photometric colors.We find that nearly half(46.3%)of the objects in our sample can be classified as S-complex,26.3%as C-complex,6%as D-complex,and 15.0%as X-complex;the remaining belong to the A-or V-types.Additionally,we identify three P-type NEAs in our sample,according to the Tholen scheme.The fractional abundances of the C/X-complex members with absolute magnitude H≥17.0 were more than twice as large as those with H<17.0.However,the fractions of C-and S-complex members with diameters≤1 km and>1 km are nearly equal,while X-complex members tend to have sub-kilometer diameters.In our sample,the C/D-complex objects are predominant among those with a Jovian Tisserand parameter of T_(J)<3.1.These bodies could have a cometary origin.C-and S-complex members account for a considerable proportion of the asteroids that are potentially hazardous.
基金funded by the National Key Research and Development Program of China(Grant No.2024YFE0209000)the NSFC(Grant No.U23B2019).
文摘Graph Neural Networks(GNNs)have proven highly effective for graph classification across diverse fields such as social networks,bioinformatics,and finance,due to their capability to learn complex graph structures.However,despite their success,GNNs remain vulnerable to adversarial attacks that can significantly degrade their classification accuracy.Existing adversarial attack strategies primarily rely on label information to guide the attacks,which limits their applicability in scenarios where such information is scarce or unavailable.This paper introduces an innovative unsupervised attack method for graph classification,which operates without relying on label information,thereby enhancing its applicability in a broad range of scenarios.Specifically,our method first leverages a graph contrastive learning loss to learn high-quality graph embeddings by comparing different stochastic augmented views of the graphs.To effectively perturb the graphs,we then introduce an implicit estimator that measures the impact of various modifications on graph structures.The proposed strategy identifies and flips edges with the top-K highest scores,determined by the estimator,to maximize the degradation of the model’s performance.In addition,to defend against such attack,we propose a lightweight regularization-based defense mechanism that is specifically tailored to mitigate the structural perturbations introduced by our attack strategy.It enhances model robustness by enforcing embedding consistency and edge-level smoothness during training.We conduct experiments on six public TU graph classification datasets:NCI1,NCI109,Mutagenicity,ENZYMES,COLLAB,and DBLP_v1,to evaluate the effectiveness of our attack and defense strategies.Under an attack budget of 3,the maximum reduction in model accuracy reaches 6.67%on the Graph Convolutional Network(GCN)and 11.67%on the Graph Attention Network(GAT)across different datasets,indicating that our unsupervised method induces degradation comparable to state-of-the-art supervised attacks.Meanwhile,our defense achieves the highest accuracy recovery of 3.89%(GCN)and 5.00%(GAT),demonstrating improved robustness against structural perturbations.
基金funded by the Deanship of Graduate Studies and Scientific Research at Jouf University under grant No.(DGSSR-2025-02-01296).
文摘Skin diseases affect millions worldwide.Early detection is key to preventing disfigurement,lifelong disability,or death.Dermoscopic images acquired in primary-care settings show high intra-class visual similarity and severe class imbalance,and occasional imaging artifacts can create ambiguity for state-of-the-art convolutional neural networks(CNNs).We frame skin lesion recognition as graph-based reasoning and,to ensure fair evaluation and avoid data leakage,adopt a strict lesion-level partitioning strategy.Each image is first over-segmented using SLIC(Simple Linear Iterative Clustering)to produce perceptually homogeneous superpixels.These superpixels form the nodes of a region-adjacency graph whose edges encode spatial continuity.Node attributes are 1280-dimensional embeddings extracted with a lightweight yet expressive EfficientNet-B0 backbone,providing strong representational power at modest computational cost.The resulting graphs are processed by a five-layer Graph Attention Network(GAT)that learns to weight inter-node relationships dynamically and aggregates multi-hop context before classifying lesions into seven classes with a log-softmax output.Extensive experiments on the DermaMNIST benchmark show the proposed pipeline achieves 88.35%accuracy and 98.04%AUC,outperforming contemporary CNNs,AutoML approaches,and alternative graph neural networks.An ablation study indicates EfficientNet-B0 produces superior node descriptors compared with ResNet-18 and DenseNet,and that roughly five GAT layers strike a good balance between being too shallow and over-deep while avoiding oversmoothing.The method requires no data augmentation or external metadata,making it a drop-in upgrade for clinical computer-aided diagnosis systems.
基金supported by the National Natural Science Foundation of China(12401279,12371219)the Double-Thousand Plan of Jiangxi Province(jxsq2023201115)the Academic and Technical Leaders Training Plan of Jiangxi Province(20212BCJ23027).
文摘This paper is concerned with an initial boundary value problem for the planar magnetohydrodynamic compressible flow with temperature dependent heat conductivity in a half-line.In particular,the transverse magnetic field is assumed to satisfy the Neumann boundary condition,which was first investigated by Kazhikhov in 1987.We establish the global existence of the unique strong solutions to the MHD equations without any smallness conditions on the initial data.More precisely,our result can be regarded as a natural generalization of Kazhikov’s result for applying the constant heat-conductivity in bounded domains to the degenerate case in unbounded domains.
文摘This systematic review aims to comprehensively examine and compare deep learning methods for brain tumor segmentation and classification using MRI and other imaging modalities,focusing on recent trends from 2022 to 2025.The primary objective is to evaluate methodological advancements,model performance,dataset usage,and existing challenges in developing clinically robust AI systems.We included peer-reviewed journal articles and highimpact conference papers published between 2022 and 2025,written in English,that proposed or evaluated deep learning methods for brain tumor segmentation and/or classification.Excluded were non-open-access publications,books,and non-English articles.A structured search was conducted across Scopus,Google Scholar,Wiley,and Taylor&Francis,with the last search performed in August 2025.Risk of bias was not formally quantified but considered during full-text screening based on dataset diversity,validation methods,and availability of performance metrics.We used narrative synthesis and tabular benchmarking to compare performance metrics(e.g.,accuracy,Dice score)across model types(CNN,Transformer,Hybrid),imaging modalities,and datasets.A total of 49 studies were included(43 journal articles and 6 conference papers).These studies spanned over 9 public datasets(e.g.,BraTS,Figshare,REMBRANDT,MOLAB)and utilized a range of imaging modalities,predominantly MRI.Hybrid models,especially ResViT and UNetFormer,consistently achieved high performance,with classification accuracy exceeding 98%and segmentation Dice scores above 0.90 across multiple studies.Transformers and hybrid architectures showed increasing adoption post2023.Many studies lacked external validation and were evaluated only on a few benchmark datasets,raising concerns about generalizability and dataset bias.Few studies addressed clinical interpretability or uncertainty quantification.Despite promising results,particularly for hybrid deep learning models,widespread clinical adoption remains limited due to lack of validation,interpretability concerns,and real-world deployment barriers.
基金Supported by the National Natural Science Foundation of China(Grant Nos.12361040,12061064)the National Science Foundation of Gansu Province(Grant No.22JR5RA264)State Scholarship Fund(Grant No.20230862021).
文摘In this article,we show the existence,uniqueness and stability of bounded solutions to the following quasilinear problems with mean curvature operator(φ'(x′(t)))′=f(t,x),t≥t_(0),lim_(t→∞)x(t)=ψ_(0),lim_(t→∞)x′(t)e^(t)=0,where t_(0) and ψ_(0) are real constants,φ(s)=s/√1−s^(2),s∈R with s∈(−1,1),f:[t_(0),∞)×R→R satisfies the Lipschitz or Osgood-type conditions.
文摘Honeycombing Lung(HCL)is a chronic lung condition marked by advanced fibrosis,resulting in enlarged air spaces with thick fibrotic walls,which are visible on Computed Tomography(CT)scans.Differentiating between normal lung tissue,honeycombing lungs,and Ground Glass Opacity(GGO)in CT images is often challenging for radiologists and may lead to misinterpretations.Although earlier studies have proposed models to detect and classify HCL,many faced limitations such as high computational demands,lower accuracy,and difficulty distinguishing between HCL and GGO.CT images are highly effective for lung classification due to their high resolution,3D visualization,and sensitivity to tissue density variations.This study introduces Honeycombing Lungs Network(HCL Net),a novel classification algorithm inspired by ResNet50V2 and enhanced to overcome the shortcomings of previous approaches.HCL Net incorporates additional residual blocks,refined preprocessing techniques,and selective parameter tuning to improve classification performance.The dataset,sourced from the University Malaya Medical Centre(UMMC)and verified by expert radiologists,consists of CT images of normal,honeycombing,and GGO lungs.Experimental evaluations across five assessments demonstrated that HCL Net achieved an outstanding classification accuracy of approximately 99.97%.It also recorded strong performance in other metrics,achieving 93%precision,100%sensitivity,89%specificity,and an AUC-ROC score of 97%.Comparative analysis with baseline feature engineering methods confirmed the superior efficacy of HCL Net.The model significantly reduces misclassification,particularly between honeycombing and GGO lungs,enhancing diagnostic precision and reliability in lung image analysis.
基金funded by the Directorate of Research and Community Service,Directorate General of Research and Development,Ministry of Higher Education,Science and Technologyin accordance with the Implementation Contract for the Operational Assistance Program for State Universities,Research Program Number:109/C3/DT.05.00/PL/2025.
文摘Sudden wildfires cause significant global ecological damage.While satellite imagery has advanced early fire detection and mitigation,image-based systems face limitations including high false alarm rates,visual obstructions,and substantial computational demands,especially in complex forest terrains.To address these challenges,this study proposes a novel forest fire detection model utilizing audio classification and machine learning.We developed an audio-based pipeline using real-world environmental sound recordings.Sounds were converted into Mel-spectrograms and classified via a Convolutional Neural Network(CNN),enabling the capture of distinctive fire acoustic signatures(e.g.,crackling,roaring)that are minimally impacted by visual or weather conditions.Internet of Things(IoT)sound sensors were crucial for generating complex environmental parameters to optimize feature extraction.The CNN model achieved high performance in stratified 5-fold cross-validation(92.4%±1.6 accuracy,91.2%±1.8 F1-score)and on test data(94.93%accuracy,93.04%F1-score),with 98.44%precision and 88.32%recall,demonstrating reliability across environmental conditions.These results indicate that the audio-based approach not only improves detection reliability but also markedly reduces computational overhead compared to traditional image-based methods.The findings suggest that acoustic sensing integrated with machine learning offers a powerful,low-cost,and efficient solution for real-time forest fire monitoring in complex,dynamic environments.
基金financially supported by National Natural Science Foundation of China(grant numbers:52171100,U20A20234)National Key R&D Program of China(grant number:2021YFB3701100)。
文摘The performance of Mg alloys is significantly influenced by the concentrations and solid solution behavior of the alloying elements.In this work,the solid solution behavior of 20 alloying elements in 190 ternary Mg alloy systems at 500℃are systematically investigated.The solid solution behavior of a set of two different alloying elements in Mg alloy systems are suggested to be classified into three categories:inclusivity,exclusivity and proportionality.Inclusivity classification indicates that the two alloying elements are inclusive inα-Mg,increasing the joint solubility of both elements.Exclusivity classification suggests that the two alloying elements have a low joint solid solubility inα-Mg,since they prefer to form stable second phases.For the proportionality classification,the solubility curve of the ternary Mg alloy systems is a straight line connecting the solubility points of the two sub-binary systems.The proposed classification theory was validated by key experiments and the calculation of formation energies.The interaction effects between alloying elements and the preference of formation of second phases are the main factors determining the solid solution behavior classifications.Based on the observed solid solution features of multi-component Mg alloys,principles for alloy design of different types of high-performance Mg alloys were proposed in this work.
基金Under the auspices of National Key R&D Program of China(No.2024YFF1306405)。
文摘Accurate extraction of surface water extent is a fundamental prerequisite for monitoring its dynamic changes.Although machine learning algorithms have been widely applied to surface water mapping,most studies focus primarily on algorithmic outputs,with limited systematic evaluation of their applicability and constrained classification accuracy.In this study,we focused on the Songnen Plain in Northeast China and employed Sentinel-2 imagery acquired during 2020-2021 via the Google Earth Engine(GEE)platform to evaluate the performance of Classification and Regression Trees(CART),Random Forest(RF),and Support Vector Machine(SVM)for surface water classification.The classification process was optimized by incorporating automated training sample selection and integration of time series features.Validation with independent samples demonstrated the feasibility of automatic sample selection,yielding mean overall accuracies of 91.16%,90.99%,and 90.76%for RF,SVM,and CART,respectively.After integrating time series features,the mean overall accuracies of the three algorithms improved by 4.51%,5.45%,and 6.36%,respectively.In addition,spectral features such as MNDWI(Modified Normalized Difference Water Index),SWIR(Short Wave Infrared),and NDVI(Normalized Difference Vegetation Index)were identified as more important for surface water classification.This study establishes a more consistent framework for surface water mapping,offering new perspectives for improving and automating classification processes in the era of big and open data.
文摘Under the travelling wave transformation, the Camassa-Holm equation with dispersion is reduced to an integrable ordinary differential equation （ODE）, whose general solution can be obtained using the trick of one-parameter group. Furthermore, by using a complete discrimination system for polynomial, the classification of all single travelling wave solutions to the Camassa-Holm equation with dispersion is obtained. In particular, an affine subspace structure in the set of the solutions of the reduced ODE is obtained. More generally, an implicit linear structure in the Camassa-Holm equation with dispersion is found. According to the linear structure, we obtain the superposition of multi-solutions to Camassa-Holm equation with dispersion.
基金funded by the Deanship of Graduate Studies and Scientific Research at Jouf University under grant No.(DGSSR-2025-02-01295).
文摘Alzheimer’s Disease(AD)is a progressive neurodegenerative disorder that significantly affects cognitive function,making early and accurate diagnosis essential.Traditional Deep Learning(DL)-based approaches often struggle with low-contrast MRI images,class imbalance,and suboptimal feature extraction.This paper develops a Hybrid DL system that unites MobileNetV2 with adaptive classification methods to boost Alzheimer’s diagnosis by processing MRI scans.Image enhancement is done using Contrast-Limited Adaptive Histogram Equalization(CLAHE)and Enhanced Super-Resolution Generative Adversarial Networks(ESRGAN).A classification robustness enhancement system integrates class weighting techniques and a Matthews Correlation Coefficient(MCC)-based evaluation method into the design.The trained and validated model gives a 98.88%accuracy rate and 0.9614 MCC score.We also performed a 10-fold cross-validation experiment with an average accuracy of 96.52%(±1.51),a loss of 0.1671,and an MCC score of 0.9429 across folds.The proposed framework outperforms the state-of-the-art models with a 98%weighted F1-score while decreasing misdiagnosis results for every AD stage.The model demonstrates apparent separation abilities between AD progression stages according to the results of the confusion matrix analysis.These results validate the effectiveness of hybrid DL models with adaptive preprocessing for early and reliable Alzheimer’s diagnosis,contributing to improved computer-aided diagnosis(CAD)systems in clinical practice.
基金Supported by the National Natural Science Foundation of China(Nos.42376185,41876111)the Shandong Provincial Natural Science Foundation(No.ZR2023MD073)。
文摘Benthic habitat mapping is an emerging discipline in the international marine field in recent years,providing an effective tool for marine spatial planning,marine ecological management,and decision-making applications.Seabed sediment classification is one of the main contents of seabed habitat mapping.In response to the impact of remote sensing imaging quality and the limitations of acoustic measurement range,where a single data source does not fully reflect the substrate type,we proposed a high-precision seabed habitat sediment classification method that integrates data from multiple sources.Based on WorldView-2 multi-spectral remote sensing image data and multibeam bathymetry data,constructed a random forests(RF)classifier with optimal feature selection.A seabed sediment classification experiment integrating optical remote sensing and acoustic remote sensing data was carried out in the shallow water area of Wuzhizhou Island,Hainan,South China.Different seabed sediment types,such as sand,seagrass,and coral reefs were effectively identified,with an overall classification accuracy of 92%.Experimental results show that RF matrix optimized by fusing multi-source remote sensing data for feature selection were better than the classification results of simple combinations of data sources,which improved the accuracy of seabed sediment classification.Therefore,the method proposed in this paper can be effectively applied to high-precision seabed sediment classification and habitat mapping around islands and reefs.
基金The project supported by Scientific Research and of Education Department of Heilongjiang Province of China under Grant No. 11511008
文摘Under the travelling wave transformation, Calogero-Degasperis-Focas equation is reduced to an ordinary differential equation. Using a symmetry group of one parameter, this ODE is reduced to a second-order linear inhomogeneous ODE. Furthermore, we apply the change of the variable and complete discrimination system for polynomial to solve the corresponding integrals and obtained the classification of all single travelling wave solutions to Calogero- Degasperis-Focas equation.
基金Supported by Mahmoud Reza Pourkarim is supported by a postdoctoral grant from the''Fonds voor Wetenschappelijk Onderzoek Vlaanderen''
文摘The clinical course of infections with the hepatitis B virus (HBV) substantially varies between individuals, as a consequence of a complex interplay between viral, host, environmental and other factors. Due to the high genetic variability of HBV, the virus can be categorized into different HBV genotypes and subgenotypes, which considerably differ with respect to geographical distribution, transmission routes, disease progression, responses to antiviral therapy or vaccination, and clinical outcome measures such as cirrhosis or hepatocellular carcinoma. However, HBV (sub)genotyping has caused some controversies in the past due to misclassifications and incorrect interpretations of different genotyping methods. Thus, an accurate, holistic and dynamic classification system is essential. In this review article, we aimed at highlighting potential pitfalls in genetic and phylogenetic analyses of HBV and suggest novel terms for HBV classification. Analyzing full-length genome sequences when classifying genotypes and subgenotypes is the foremost prerequisite of this classification system. Careful attention must be paid to all aspects of phylogenetic analysis, such as bootstrapping values and meeting the necessary thresholds for (sub)genotyping. Quasi-subgenotype refers to subgenotypes that were incorrectly suggested to be novel. As many of these strains were misclassified due to genetic differences resulting from recombination, we propose the term “recombino-subgenotype”. Moreover, immigration is an important confounding facet of global HBV distribution and substantially changes the geographic pattern of HBV (sub)genotypes. We therefore suggest the term “immigro-subgenotype” to distinguish exotic (sub)genotypes from native ones. We are strongly convinced that applying these two proposed terms in HBV classification will help harmonize this rapidly progressing field and allow for improved prophylaxis, diagnosis and treatment.
文摘Generalised reduced masses with a set of equations governing the three relative motions between two of 3-bodies in their gravitational field are established,of which the dynamic characteristics of 3-body dynamics,fundamental bases of this paper,are revealed.Based on these findings,an equivalent system is developed,which is a 2-body system with its total mass,constant angular momentum,kinetic and potential energies same as the total ones of three relative motions,so that it can be solved using the well-known theory of the 2-body system.From the solution of an equivalent system with the revealed characteristics of three relative motions,the general theoretical solutions of the 3-body system are obtained in the curve-integration forms along the orbits in the imaged radial motion space.The possible periodical orbits with generalised Kepler’s law are presented.Following the description and mathematical demonstrations of the proposed methods,the examples including Euler’s/Lagrange’s problems,and a reported numerical one are solved to validate the proposed methods.The methods derived from the 3-body system are extended to N-body problems.
文摘Under the travelling wave transformation, some nonlinear partial differential equations such as Camassa-Holm equation, High-order KdV equation, etc., are reduced to an integrable ODE expressed by u＂ ＋p（u）（u＇）^2 ＋ q（u） = 0 whose generai solution can be given. Furthermore, combining complete discrimination system for polynomiai, the classifications of all single travelling wave solutions to these equations are obtained. The equation u＂＋p（u）（u＇）^2＋q（u） = 0 includes the equation （u＇）^2 = f（u） as a special case, so the proposed method can be also applied to a large number of nonlinear equations. These complete results cannot be obtained by any indirect method.
