Gauss radial basis functions(GRBF)are frequently employed in data fitting and machine learning.Their linear independence property can theoretically guarantee the avoidance of data redundancy.In this paper,one of the m...Gauss radial basis functions(GRBF)are frequently employed in data fitting and machine learning.Their linear independence property can theoretically guarantee the avoidance of data redundancy.In this paper,one of the main contributions is proving this property using linear algebra instead of profound knowledge.This makes it easy to read and understand this fundamental fact.The proof of linear independence of a set of Gauss functions relies on the constructing method for one-dimensional space and on the deducing method for higher dimensions.Additionally,under the condition of preserving the same moments between the original function and interpolating function,both the interpolating existence and uniqueness are proven for GRBF in one-dimensional space.The final work demonstrates the application of the GRBF method to locate lunar olivine.By combining preprocessed data using GRBF with the removing envelope curve method,a program is created to find the position of lunar olivine based on spectrum data,and the numerical experiment shows that it is an effective scheme.展开更多
Unlike mammals,zebrafish possess a remarkable ability to regenerate their spinal cord after injury,making them an ideal vertebrate model for studying regeneration.While previous research has identified key cell types ...Unlike mammals,zebrafish possess a remarkable ability to regenerate their spinal cord after injury,making them an ideal vertebrate model for studying regeneration.While previous research has identified key cell types involved in this process,the underlying molecular and cellular mechanisms remain largely unexplored.In this study,we used single-cell RNA sequencing to profile distinct cell populations at different stages of spinal cord injury in zebrafish.Our analysis revealed that multiple subpopulations of neurons showed persistent activation of genes associated with axonal regeneration post injury,while molecular signals promoting growth cone collapse were inhibited.Radial glial cells exhibited significant proliferation and differentiation potential post injury,indicating their intrinsic roles in promoting neurogenesis and axonal regeneration,respectively.Additionally,we found that inflammatory factors rapidly decreased in the early stages following spinal cord injury,creating a microenvironment permissive for tissue repair and regeneration.Furthermore,oligodendrocytes lost maturity markers while exhibiting increased proliferation following injury.These findings demonstrated that the rapid and orderly regulation of inflammation,as well as the efficient proliferation and redifferentiation of new neurons and glial cells,enabled zebrafish to reconstruct the spinal cord.This research provides new insights into the cellular transitions and molecular programs that drive spinal cord regeneration,offering promising avenues for future research and therapeutic strategies.展开更多
AIM:To describe the technique and the outcomes of manual Bowman layer and stroma transplant-onlay(BLST-o)for 2 cases of radial keratotomy(RK).METHODS:Two patients with visual fluctuations and corneal irregularity due ...AIM:To describe the technique and the outcomes of manual Bowman layer and stroma transplant-onlay(BLST-o)for 2 cases of radial keratotomy(RK).METHODS:Two patients with visual fluctuations and corneal irregularity due to RK were offered manual BLST-o as an alternative to penetrating keratoplasty(PKP).Visual acuity,refraction,corneal topography,corneal aberrometry,and corneal optical coherence tomography(OCT)pre-and postoperative were analyzed.Histology was obtained for 1 case.RESULTS:Both patients had corneal anatomical and morphological improvement,with elimination of the visual fluctuations.In one case,a subsequent excimer laser treatment improved corneal shape further,thus improving vision.The other case,whereas initially improved,developed epithelial ingrowth following suture removal.The latter was explanted and had a xenogeneic implant.The explanted sample was sent for histology,showing a viable graft of Bowman layer and anterior stroma.CONCLUSION:Manual BLST-o is a potential option for the management of symptoms post RK.These grafts may facilitate subsequent treatments such as laser corrections,and may not preclude from other interventions after explantation.展开更多
Mobile service robots(MSRs)in hospital environments require precise and robust trajectory tracking to ensure reliable operation under dynamic conditions,including model uncertainties and external disturbances.This stu...Mobile service robots(MSRs)in hospital environments require precise and robust trajectory tracking to ensure reliable operation under dynamic conditions,including model uncertainties and external disturbances.This study presents a cognitive control strategy that integrates a Numerical Feedforward Inverse Dynamic Controller(NFIDC)with a Feedback Radial Basis Function Neural Network(FRBFNN).The robot’s mechanical structure was designed in SolidWorks 2022 SP2.0 and validated under operational loads using finite element analysis in ANSYS 2022 R1.The NFIDC-FRBFNN framework merges proactive inverse dynamic compensation with adaptive neural learning to achieve smooth torque responses and accurate motion control.A two-stage simulation evaluation was conducted.In the first stage,the controller was tested in a simulated hospital environment under both ideal and non-ideal conditions.In the second,it was benchmarked against four established controllers-Neural Network Model Reference Adaptive(NNMRA),Z-number Fuzzy Logic(Z-FL),Adaptive Dynamic Controller(ADC),and Fuzzy Logic-PID(FL-PID)—using circular and lemniscate trajectories.Across ten runs,the proposed controller achieved the lowest tracking errors under all conditions.Under ideal conditions,it achieved average improvements of 55.24%,75.75%,and 55.20%in integral absolute error(IAE),integral squared error(ISE),and mean absolute error(MAE),respectively,with coefficient of variation(CV)reductions above 55%.Under non-ideal conditions,average improvements exceeded 64%in IAE,77%in ISE,and 66%in MAE,while maintaining CV reductions above 57%.These results confirm that the NFIDC-FRBFNN controller offers superior accuracy,robustness,and consistency for real-time path tracking in healthcare robotics.展开更多
The selection of an appropriate basic detonation wave flow field is crucial for improving the performance and geometric design of standing detonation vehicles.This paper employs a detailed chemical reaction model and ...The selection of an appropriate basic detonation wave flow field is crucial for improving the performance and geometric design of standing detonation vehicles.This paper employs a detailed chemical reaction model and solves the unsteady axisymmetric Euler equation to study the characteristics of the Axisymmetric Inward Turning Curved Detonation Wave(AIT-CDW)flow field and the parameters affecting the stability of the wave system structure of AIT-CDW flow field.The numerical results demonstrate a radial compression effect in the AIT-CDW flow field.This effect causes the detonation wave to have a shorter initiation length than oblique detonation wave flow field and the detonation wave angle to gradually increase with the flow direction postdetonation.The AIT-CDW flow field is confined space,making it prone to normal detonation waves when the detonation wave reflects from the wall.This phenomenon is detrimental to the stability of the wave system structure in the flow field.It has been observed that increasing the center body radius and decreasing the fuel equivalent ratio can effectively reduce the height of the normal detonation wave or even eliminate it.Additionally,a well-designed generatrix shape of the center body can enhance airflow,reduce choked flow,and promote the stability of the wave structure in the flow field.展开更多
Medium-high maturity continental shale oil is one of the hydrocarbon resources with the most potential for successful development in China.Nevertheless,the unique geological conditions of a multi-lithologic superposit...Medium-high maturity continental shale oil is one of the hydrocarbon resources with the most potential for successful development in China.Nevertheless,the unique geological conditions of a multi-lithologic superposition shield the vertical propagation of hydraulic fractures and limit the longitudinal reconstruction in reservoirs,posing a great challenge for large-scale volumetric fracturing.Radial wellbore crosslayer fracturing,which transforms the interaction between the hydraulic fractures and lithologic interface into longitudinal multilayer competitive initiation,could provide a potential solution for this engineering challenge.To determine the longitudinal propagation behaviors of fractures guided by radial wellbores,true triaxial fracturing experiments were performed on multilayer shale-sandstone samples,with a focus on the injection pressure response,fracture morphology,and cross-layer pattern.The effects of the radial borehole length L,vertical stress difference K_(v),injection rate Q,and viscosity m of the fracturing fluid were analyzed.The results indicate that radial wellbores can greatly facilitate fracture initiation and cross-layer propagation.Unlike conventional hydraulic fracturing,there are two distinct fracture propagation patterns in radial wellbore fracturing:cross-layering and skip-layering.The fracture height guided by a radial wellbore is positively correlated with K_(v),Q,and m.Increasing these parameters causes a shift in the fracture initiation from a single root to an asynchronous root/toe end and can improve the cross-layer propagation capacity.Critical parameter thresholds exist for fracture propagation through and across interlayers under the guidance of radial boreholes.A parameter combination of critical cross-layering/skip-layering or alternating displacement/viscosity is recommended to simultaneously improve the fracture height and degree of lateral activation.The degree of correlation of different parameters with the vertical fracture height can be written as L>Q/m>K_(v).Increasing the radial wellbore length can effectively facilitate fracture cross-/skip-layer propagation and reduce the critical threshold of injection parameters,which is conducive to maximizing the stimulated reservoir volume.展开更多
Two sharp Chernoff type inequalities are derived for star bodies in R2,one is an extension of the dual Chernoff-Ou-Pan inequality,and the other is the reverse Chernoff type inequality.Furthermore,we establish a genera...Two sharp Chernoff type inequalities are derived for star bodies in R2,one is an extension of the dual Chernoff-Ou-Pan inequality,and the other is the reverse Chernoff type inequality.Furthermore,we establish a generalized dual symmetric mixed Chernoff inequality for two planar star bodies.As a direct consequence,a new proof of the dual symmetric mixed isoperimetric inequality is presented.展开更多
Radial head(RH)arthroplasty(RHA)has emerged as a critical intervention in the management of complex elbow fractures,particularly Mason type III and IV injuries where the native RH is irreparable.Beyond its role in pai...Radial head(RH)arthroplasty(RHA)has emerged as a critical intervention in the management of complex elbow fractures,particularly Mason type III and IV injuries where the native RH is irreparable.Beyond its role in pain relief and joint congruity,RHA serves as a biomechanical cornerstone for restoring the lateral column and ensuring elbow stability,especially in the presence of associated ligamentous injuries or fracture-dislocations.This editorial synthesizes current evidence on RHA in Mason type III and IV RH fractures,with attention to biomechanical rationale,implant design,and complication trends.Aiming to reaffirm RHA’s position as a vital tool in contemporary elbow trauma care,a simplified treatment algorithm is presented to support individualized surgical decisionmaking.展开更多
Transradial access (TRA) has emerged as the preferred vascular access route forcoronary angiography and percutaneous coronary interventions due to itssuperior safety profile compared to transfemoral access. However, i...Transradial access (TRA) has emerged as the preferred vascular access route forcoronary angiography and percutaneous coronary interventions due to itssuperior safety profile compared to transfemoral access. However, its widespreadadoption raises concerns regarding structural alterations in the radial artery,which may impact long-term vascular health and future procedural feasibility.TRA is associated with histopathologic changes in the arterial wall, such asintimal injury and hyperplasia, medial remodeling and adventitial inflammation,collectively contributing to radial artery remodeling. Moreover, TRA can inducechanges in radial artery lumen diameter driven by an inflammatory response dueto arterial puncture and mechanical friction during the procedure. Nonetheless, amore clinically significant consequence is radial artery occlusion, which is influencedby various procedural and patient-related factors. Strategies to minimizeremodeling include meticulous pre-procedural ultrasound assessment to ensureappropriate sheath-to-artery size matching, periprocedural pharmacologicalinterventions and implementation of patent hemostasis techniques. This reviewsynthesizes current knowledge regarding the mechanisms, clinical implications,and preventive strategies related to radial artery remodeling following TRA. Further research is needed toelucidate the long-term consequences of radial artery remodeling and to refine preventive strategies for preservingradial artery patency and its suitability for future interventions.展开更多
Radial growth of trees is highly sensitive to environmental changes,but the effect of climate on tree rings in Qinghai spruce(Picea crassifolia),a widely distributed endemic conifer in western China,is more complex th...Radial growth of trees is highly sensitive to environmental changes,but the effect of climate on tree rings in Qinghai spruce(Picea crassifolia),a widely distributed endemic conifer in western China,is more complex than in many other conifers.A comprehensive understanding of the spatiotemporal climatic responses of its rings is needed to develop theoretical basis for designing strategies for its conservation and management.Here,our synthesis of the literature on responses of radial growth of Qinghai spruce to monthly climate variables in different environmental conditions by meta-analysis showed that precipitation and drought severity are the main limiting factors for Qinghai spruce radial growth in the semiarid region of northwestern China.In warmer and drier areas,radial growth of Qinghai spruce is mainly limited by drought.In the areas north of the 600-mm annual precipitation isoline,the tree-ring width(TRW)was significantly positively correlated with precipitation and significantly negatively correlated with temperature during the growing season(June-August).The limiting effect of drought on Qinghai spruce is also gradually increasing from southeast to northwest,to the west of 103°E and within 37°N-39°N.展开更多
BACKGROUND Radial head fractures constitute approximately one-third of all elbow fractures,significantly impacting the young and active population.While open reduction and internal fixation is the preferred treatment ...BACKGROUND Radial head fractures constitute approximately one-third of all elbow fractures,significantly impacting the young and active population.While open reduction and internal fixation is the preferred treatment for displaced fractures,its high complication rate in comminuted fractures has led to the increasing use of radial head arthroplasty(RHA).RHA provides improved functional outcomes with fewer complications,yet its long-term efficacy remains a topic of debate.AIM To evaluate the functional outcomes of patients undergoing RHA with a modular metallic prosthesis for comminuted Mason type III and IV radial head fractures.METHODS A prospective and retrospective hospital-based study was conducted at Dayanand Medical College and Hospital,Ludhiana over 32 months(January 2021-August 2023).A total of 26 patients with Mason type III and IV fractures were included,with six retrospective and 20 prospective cases.Functional outcomes were assessed using the Mayo Elbow Performance Score(MEPS),elbow range of motion,pain via Visual Analog Scale,and activities of daily living at immediate postoperative,three-month,and six-month follow-ups.RESULTS MEPS at 6 months follow up for 4 cases(15.38%)had good scores,and 22 cases(84.62%)had excellent scores,with a mean±SD of 97.31±6.67.Comparisons showed significant improvement from immediate post-operative to 3 months(P<0.0001),from immediate post-operative to 6 months(P<0.0001),and between 3 months and 6 months(P<0.0001).None of the patients had elbow instability after radial head replacement and 22 cases(84.62%)had no complications,while 3 cases(11.54%)had a stiff elbow,and 1 case(3.85%)had heterotopic ossification.CONCLUSION RHA is an effective treatment for comminuted radial head fractures,providing stable elbow function with minimal complications.展开更多
An experimental study of the diffusive mass transfer between a droplet and an oscillating immiscible liquid in a horizontal axisymmetricHele-Shaw cell is carried out.Theliquid oscillates radially in the cell.Thetransv...An experimental study of the diffusive mass transfer between a droplet and an oscillating immiscible liquid in a horizontal axisymmetricHele-Shaw cell is carried out.Theliquid oscillates radially in the cell.Thetransverse size of the droplet exceeds the cell thickness.The viscosities of the droplet and the surrounding liquid are comparable.Relevant effort is provided to design and test an experimental setup and validate a protocol for determining the mass transfer rate of a solute in a two-liquid system.In particular,fluorescent dye Rhodamine B is considered as the solute.A critical comparison of the situations with and without oscillation is implemented.A procedure is introduced and validated to determine the molecular and effective diffusion coefficients through evaluation of the growth of the diffusion zone width over time.It is shown that,in the presence of the liquid oscillations,there is a significant increase in the width of the zone in which Rhodamine B is present compared to the reference case with no oscillations.The oscillatory flow leads to an intensification of the solute diffusion due to intense time-averaged flows inside the droplet and the surrounding liquid and oscillations of the drop itself.Thestudy is of significant practical interest with particular relevance to typical processes for liquid-liquid extraction.展开更多
Climate warming causes mountainous species to shift their distributions towards higher elevations.How elevation influences growth-climate relationship in mountain regions has been intensively investigated.However,how ...Climate warming causes mountainous species to shift their distributions towards higher elevations.How elevation influences growth-climate relationship in mountain regions has been intensively investigated.However,how microtopography shapes tree growth and its drought resistance along the elevation gradient remains poorly understood.We used a network of Larix principis-rupprechtii tree-ring data comprising 1,918 trees from different age classes and mountain slopes,along an elevation gradient ranging from 970 to 1,869 m,to investigate how slope gradients mediate the growth and drought resilience of larch trees along an elevation gradient in North China.Growing season drought and temperature were the major limiting climatic factors for larch trees across the study region.Larch trees younger than 40 years exhibited a stronger positive correlation between basal area increment(BAI)and elevation on steep slopes(10°-35°)than on flat(0°-5°)or gentle(5°-10°)slopes.At low-elevation steep slopes,the growth of larch trees younger than 40 years showed a stronger correlation with the Palmer drought severity index(PDSI).Both resistance and resilience were found to increase along the elevation gradient on steep slopes for young larch trees but not for old larch trees.No significant differences were observed in the drought recovery ability of larch trees across all age groups at increasing elevation.Our results highlight that drought events may particularly affect the growth of young larch trees on low-elevation steep slopes,with potential repercussions on mortality rates.展开更多
Clarifying the climate change effects on the radial growth of trees has implications for sustainable forest management,especially under global warming.To investigate tree growth responses to regional climate change of...Clarifying the climate change effects on the radial growth of trees has implications for sustainable forest management,especially under global warming.To investigate tree growth responses to regional climate change of Xiaowutai Mountain,four Chinese pine(Pinus tabulaeformis)ring-width index chronologies were established at different elevations(1290–1600 m).Species growth trends were estimated using climate change projections derived from global climate models.The results show:(1)the four ring-width chronologies exhibited strong statistical characteristics,making them suitable for dendroclimatology studies.Radial growth-climate relationships were highly consistent,showing a negative correlation with previous September temperatures and current May–June temperatures,as well as a positively correlated with precipitation and Palmer Drought Severity Index during the corresponding period;and(2)climate change scenarios revealed that temperature will gradually increase on the Xiaowutai Mountain,and only a slight variation in precipitation is expected.Chinese pine radial growth may show a decline under future climate change.展开更多
This study examines the influence of magnetic field and temperature on the transient voltage of a polycrystalline silicon radial junction solar cell in a dynamic regime under multispectral illumination. Radial junctio...This study examines the influence of magnetic field and temperature on the transient voltage of a polycrystalline silicon radial junction solar cell in a dynamic regime under multispectral illumination. Radial junction solar cells represent a major advancement in photovoltaic technologies, as they optimize light absorption and charge collection efficiency. The focus is on the impact of the magnetic field and temperature on the decay of transient voltage, which provides crucial information on recombination processes and the lifetime of minority carriers. The results reveal that the magnetic field tends to increase the transient voltage by directly affecting the transient electron density. Indeed, for B > 7 × 10−5 T, the magnetic field prolongs the relaxation time by increasing the transient voltage amplitude. Additionally, rising temperatures accelerate (ranging from 290 K to 450 K) recombination processes, thereby reducing the transient voltage, although this effect is moderated by the presence of a magnetic field. The study highlights the complex interaction between magnetic field and temperature, with significant impacts on the transient behaviour.展开更多
Droughts have caused tree growth decline and high tree mortality across temperate forests,however,how to manage planted forests to alleviate drought stress is still challenging.We used tree-ring and forest inventory d...Droughts have caused tree growth decline and high tree mortality across temperate forests,however,how to manage planted forests to alleviate drought stress is still challenging.We used tree-ring and forest inventory data from different density stands to investigate how competition,tree diameter at breast height(DBH),tree age,and their interactions influence drought sensitivity and resistance for three widely-distributed and planted conifer species(Larix principis-rupprechtii,Picea meyeri,and Pinus sylvestris var.mongolica).Our results showed that the drought sensitivity of the three species was influenced by competition,tree size,and their interactions.Large L.principis-rupprechtii trees were particularly sensitive to drought during the growing season in medium to high-density stands,while the growth of large P.sylvestris var.mongolica was most affected by precipitation at low to medium density stands.Drought resistance of L.principis-rupprechtii trees decreased as tree size increased.Large L.principis-rupprechtii trees had lower drought resistance than small trees in all stands.Drought resistance of large P.meyeri trees exhibited high resistance to drought only in high-density stands.However,drought resistance of P.sylvestris var.mongolica trees was affected by tree size,competition,and their interactions.These results indicated that targeted silvicultural interventions,such as thinning,can be implemented to enhance drought resistance specifically for large L.principis-rupprechtii trees and small P.sylvestris var.mongolica trees in medium and high competition stands,and small P.meyeri trees in high competition stands.Our results highlight that properly conducted thinning can in some cases enhance growth resistance to droughts,depending on stand density,tree size,and tree species.展开更多
China's lacustrine shale oil reserves are abundant,making it a key area for future exploration and development.Most lacustrine shales feature a mix of mineral compositions and interlayer sedimentary structures.Hig...China's lacustrine shale oil reserves are abundant,making it a key area for future exploration and development.Most lacustrine shales feature a mix of mineral compositions and interlayer sedimentary structures.High-quality reservoirs exhibit significant heterogeneity,which influences the stress distribution during fracturing,leading to complex fracture network patterns.This complexity presents challenges for the comprehensive well logging evaluation of the geological-engineering"double sweet spots"in shale oil,severely restricting efficient development.This study focuses on the impact of shale sedimentary layering on the radial slowness of dipole shear waves.It employs rock physics experiments combined with advanced well logging techniques to explore the relationship between reservoir anisotropy caused by sedimentary layering and reservoir quality,thereby establishing a logging evaluation method for vertical identification of"sweet spots"in lacustrine shale oil.The shales in the Fengcheng Formation of the Mahu Sag into three types according to sedimentary structure scale:laminated,interlayer,and massive.Each type has different mineral compositions,affecting reservoir quality and fracturing potential.Laminated shales develop more fractures under stress along the beddings,showing moderate anisotropy,with reservoir capacity dependent on intercrystalline porosity within carbonate layers.Interlayer shales easily form complex fracture networks,exhibiting significant anisotropy,and their reservoir capacity depends on the porosity within sandy bands.Massive mudstones have the fewest fractures under stress,appearing isotropic with reservoir capacity dependent on matrix pore size.The intensity of reservoir anisotropy correlates positively with storage capacity and the propensity to form irregular and complex fracture networks during hydraulic fracturing.In sections without natural fractures,a larger difference between fast and slow shear waves corresponds to a radial profile shift towards warm tones,indicating stronger anisotropy and better reservoir quality,thus forming complex fracture networks during fracturing.Conversely,a smaller difference leads to a profile energy shift towards cooler tones,indicating stronger isotropy and poorer reservoir quality,hindering the formation of complex fracture networks during hydraulic fracturing.In sections with natural fractures,the difference between fast and slow shear waves exhibits erratic behavior,showing a cross-pattern in radial profiles,indicating strong anisotropy.The presence of natural fractures can synergize with induced fracture networks to form more complex systems,significantly enhancing reservoir productivity.展开更多
The tolerance of tree growth to drought in diverse mixed forests subjected to seasonal water shortage is understudied despite their ecological and economic relevance.By combining intra-and inter-annual analyses of rad...The tolerance of tree growth to drought in diverse mixed forests subjected to seasonal water shortage is understudied despite their ecological and economic relevance.By combining intra-and inter-annual analyses of radial growth responses to climate and drought at daily and monthly scales,different strategies to acclimate to hydroclimate variability of coexisting conifers and broadleaves were unveiled.We analyzed the growth patterns and responses to hydroclimate variability in two conifers(Pinus engelmannii,Juniperus deppeana)and two broadleaves(Quercus grisea,Arbutus arizonica)co-occurring in a Madrean pine-oak forest located in NW Mexico.The strongest positive response to daily precipitation was found in the two conifers,but this response peaked earlier in J.deppeana than in P.engelmannii,which presented a more delayed formation of radially-enlarging tracheids.The latest negative response to temperature was found in Q.grisea,which agrees with its more delayed xylogenesis than A.arizonica.P.engelmannii presented the highest responsiveness to water shortage,driven by lower precipitation and high maximum temperatures,responding to longer droughts ending in autumn(r=0.72),whilst A.arizonica showed the lowest responsiveness to short spring droughts(r=0.39).Growth of P.engelmannii was linked to climate-atmospheric circulation patterns over the near Pacific Ocean.Overall,P.engelmannii and A.arizonica showed high growth rates and earlier growth onset,whilst J.deppeana and Q.grisea showed slower growth rates and later growth onset.The Vaganov-Shashkin growth model evidenced that winterspring soil moisture was the key driver of growth.Under more arid conditions and more frequent and hotter droughts,pine stands could rapidly shift towards mixed pine-oak forests.展开更多
In this paper,we study an integral system involving m equations■where ui>0 in R^(n),0<α<n,and pi>1(i=1,2,…,m).Based on the optimal integrability intervals,we estimate the decay rates of the positive sol...In this paper,we study an integral system involving m equations■where ui>0 in R^(n),0<α<n,and pi>1(i=1,2,…,m).Based on the optimal integrability intervals,we estimate the decay rates of the positive solutions of the system at infinity.But estimating these rates is difficult because the relation between pi(i=1,2,…,m)is uncertain.To overcome this difficulty,we obtain the asymptotic behavior of all cases by discussing them separately.In addition,we also get the radial symmetry of positive solutions under some integrability condition.展开更多
基金Supported by the National Basic Research Program of China(2012CB025904)Zhengzhou Shengda University of Economics,Business and Management(SD-YB2025085)。
文摘Gauss radial basis functions(GRBF)are frequently employed in data fitting and machine learning.Their linear independence property can theoretically guarantee the avoidance of data redundancy.In this paper,one of the main contributions is proving this property using linear algebra instead of profound knowledge.This makes it easy to read and understand this fundamental fact.The proof of linear independence of a set of Gauss functions relies on the constructing method for one-dimensional space and on the deducing method for higher dimensions.Additionally,under the condition of preserving the same moments between the original function and interpolating function,both the interpolating existence and uniqueness are proven for GRBF in one-dimensional space.The final work demonstrates the application of the GRBF method to locate lunar olivine.By combining preprocessed data using GRBF with the removing envelope curve method,a program is created to find the position of lunar olivine based on spectrum data,and the numerical experiment shows that it is an effective scheme.
基金supported by the Jiangsu Province Traditional Chinese Medicine Technology Development Plan Project,Nos.MS2023113(to JC),MS2022090Young and Middle-aged Academic Leaders of Jiangsu Qing-Lan Project(to GL).
文摘Unlike mammals,zebrafish possess a remarkable ability to regenerate their spinal cord after injury,making them an ideal vertebrate model for studying regeneration.While previous research has identified key cell types involved in this process,the underlying molecular and cellular mechanisms remain largely unexplored.In this study,we used single-cell RNA sequencing to profile distinct cell populations at different stages of spinal cord injury in zebrafish.Our analysis revealed that multiple subpopulations of neurons showed persistent activation of genes associated with axonal regeneration post injury,while molecular signals promoting growth cone collapse were inhibited.Radial glial cells exhibited significant proliferation and differentiation potential post injury,indicating their intrinsic roles in promoting neurogenesis and axonal regeneration,respectively.Additionally,we found that inflammatory factors rapidly decreased in the early stages following spinal cord injury,creating a microenvironment permissive for tissue repair and regeneration.Furthermore,oligodendrocytes lost maturity markers while exhibiting increased proliferation following injury.These findings demonstrated that the rapid and orderly regulation of inflammation,as well as the efficient proliferation and redifferentiation of new neurons and glial cells,enabled zebrafish to reconstruct the spinal cord.This research provides new insights into the cellular transitions and molecular programs that drive spinal cord regeneration,offering promising avenues for future research and therapeutic strategies.
文摘AIM:To describe the technique and the outcomes of manual Bowman layer and stroma transplant-onlay(BLST-o)for 2 cases of radial keratotomy(RK).METHODS:Two patients with visual fluctuations and corneal irregularity due to RK were offered manual BLST-o as an alternative to penetrating keratoplasty(PKP).Visual acuity,refraction,corneal topography,corneal aberrometry,and corneal optical coherence tomography(OCT)pre-and postoperative were analyzed.Histology was obtained for 1 case.RESULTS:Both patients had corneal anatomical and morphological improvement,with elimination of the visual fluctuations.In one case,a subsequent excimer laser treatment improved corneal shape further,thus improving vision.The other case,whereas initially improved,developed epithelial ingrowth following suture removal.The latter was explanted and had a xenogeneic implant.The explanted sample was sent for histology,showing a viable graft of Bowman layer and anterior stroma.CONCLUSION:Manual BLST-o is a potential option for the management of symptoms post RK.These grafts may facilitate subsequent treatments such as laser corrections,and may not preclude from other interventions after explantation.
基金supported by the Malaysia Ministry of Higher Education under Fundamental Research Grant Scheme with Project Code:FRGS/1/2024/TK07/USM/02/3.
文摘Mobile service robots(MSRs)in hospital environments require precise and robust trajectory tracking to ensure reliable operation under dynamic conditions,including model uncertainties and external disturbances.This study presents a cognitive control strategy that integrates a Numerical Feedforward Inverse Dynamic Controller(NFIDC)with a Feedback Radial Basis Function Neural Network(FRBFNN).The robot’s mechanical structure was designed in SolidWorks 2022 SP2.0 and validated under operational loads using finite element analysis in ANSYS 2022 R1.The NFIDC-FRBFNN framework merges proactive inverse dynamic compensation with adaptive neural learning to achieve smooth torque responses and accurate motion control.A two-stage simulation evaluation was conducted.In the first stage,the controller was tested in a simulated hospital environment under both ideal and non-ideal conditions.In the second,it was benchmarked against four established controllers-Neural Network Model Reference Adaptive(NNMRA),Z-number Fuzzy Logic(Z-FL),Adaptive Dynamic Controller(ADC),and Fuzzy Logic-PID(FL-PID)—using circular and lemniscate trajectories.Across ten runs,the proposed controller achieved the lowest tracking errors under all conditions.Under ideal conditions,it achieved average improvements of 55.24%,75.75%,and 55.20%in integral absolute error(IAE),integral squared error(ISE),and mean absolute error(MAE),respectively,with coefficient of variation(CV)reductions above 55%.Under non-ideal conditions,average improvements exceeded 64%in IAE,77%in ISE,and 66%in MAE,while maintaining CV reductions above 57%.These results confirm that the NFIDC-FRBFNN controller offers superior accuracy,robustness,and consistency for real-time path tracking in healthcare robotics.
基金supported by the National Natural Science Foundation of China(Nos.U20A2069,62376234 and 123B2037)the Advanced Aero-Power Innovation Workstation,China(No.HKCX2024-01-017)。
文摘The selection of an appropriate basic detonation wave flow field is crucial for improving the performance and geometric design of standing detonation vehicles.This paper employs a detailed chemical reaction model and solves the unsteady axisymmetric Euler equation to study the characteristics of the Axisymmetric Inward Turning Curved Detonation Wave(AIT-CDW)flow field and the parameters affecting the stability of the wave system structure of AIT-CDW flow field.The numerical results demonstrate a radial compression effect in the AIT-CDW flow field.This effect causes the detonation wave to have a shorter initiation length than oblique detonation wave flow field and the detonation wave angle to gradually increase with the flow direction postdetonation.The AIT-CDW flow field is confined space,making it prone to normal detonation waves when the detonation wave reflects from the wall.This phenomenon is detrimental to the stability of the wave system structure in the flow field.It has been observed that increasing the center body radius and decreasing the fuel equivalent ratio can effectively reduce the height of the normal detonation wave or even eliminate it.Additionally,a well-designed generatrix shape of the center body can enhance airflow,reduce choked flow,and promote the stability of the wave structure in the flow field.
基金supported by the National Natural Science Foun-dation of China(52421002,U24B6001,52204019,and 52192624)the Open Foundation of the Shanxi Key Laboratory of Carbon Dioxide Sequestration and Enhanced Oil Recovery。
文摘Medium-high maturity continental shale oil is one of the hydrocarbon resources with the most potential for successful development in China.Nevertheless,the unique geological conditions of a multi-lithologic superposition shield the vertical propagation of hydraulic fractures and limit the longitudinal reconstruction in reservoirs,posing a great challenge for large-scale volumetric fracturing.Radial wellbore crosslayer fracturing,which transforms the interaction between the hydraulic fractures and lithologic interface into longitudinal multilayer competitive initiation,could provide a potential solution for this engineering challenge.To determine the longitudinal propagation behaviors of fractures guided by radial wellbores,true triaxial fracturing experiments were performed on multilayer shale-sandstone samples,with a focus on the injection pressure response,fracture morphology,and cross-layer pattern.The effects of the radial borehole length L,vertical stress difference K_(v),injection rate Q,and viscosity m of the fracturing fluid were analyzed.The results indicate that radial wellbores can greatly facilitate fracture initiation and cross-layer propagation.Unlike conventional hydraulic fracturing,there are two distinct fracture propagation patterns in radial wellbore fracturing:cross-layering and skip-layering.The fracture height guided by a radial wellbore is positively correlated with K_(v),Q,and m.Increasing these parameters causes a shift in the fracture initiation from a single root to an asynchronous root/toe end and can improve the cross-layer propagation capacity.Critical parameter thresholds exist for fracture propagation through and across interlayers under the guidance of radial boreholes.A parameter combination of critical cross-layering/skip-layering or alternating displacement/viscosity is recommended to simultaneously improve the fracture height and degree of lateral activation.The degree of correlation of different parameters with the vertical fracture height can be written as L>Q/m>K_(v).Increasing the radial wellbore length can effectively facilitate fracture cross-/skip-layer propagation and reduce the critical threshold of injection parameters,which is conducive to maximizing the stimulated reservoir volume.
基金supported by the Postgraduate Scientic Research Innovation Project of Chongqing Normal University(YKC24010)Chunna Zeng's research was supported by the Major Special Project of the National Natural Science Foundation of China(12141101)+2 种基金the Young Top-Talent program of Chongqing(CQYC2021059145)the Technology Research Foundation of Chongqing Educational committee(KJZD-K202200509)the Natural Science Foundation Project of Chongqing(CSTB2024NSCQ-MSX0937)。
文摘Two sharp Chernoff type inequalities are derived for star bodies in R2,one is an extension of the dual Chernoff-Ou-Pan inequality,and the other is the reverse Chernoff type inequality.Furthermore,we establish a generalized dual symmetric mixed Chernoff inequality for two planar star bodies.As a direct consequence,a new proof of the dual symmetric mixed isoperimetric inequality is presented.
文摘Radial head(RH)arthroplasty(RHA)has emerged as a critical intervention in the management of complex elbow fractures,particularly Mason type III and IV injuries where the native RH is irreparable.Beyond its role in pain relief and joint congruity,RHA serves as a biomechanical cornerstone for restoring the lateral column and ensuring elbow stability,especially in the presence of associated ligamentous injuries or fracture-dislocations.This editorial synthesizes current evidence on RHA in Mason type III and IV RH fractures,with attention to biomechanical rationale,implant design,and complication trends.Aiming to reaffirm RHA’s position as a vital tool in contemporary elbow trauma care,a simplified treatment algorithm is presented to support individualized surgical decisionmaking.
文摘Transradial access (TRA) has emerged as the preferred vascular access route forcoronary angiography and percutaneous coronary interventions due to itssuperior safety profile compared to transfemoral access. However, its widespreadadoption raises concerns regarding structural alterations in the radial artery,which may impact long-term vascular health and future procedural feasibility.TRA is associated with histopathologic changes in the arterial wall, such asintimal injury and hyperplasia, medial remodeling and adventitial inflammation,collectively contributing to radial artery remodeling. Moreover, TRA can inducechanges in radial artery lumen diameter driven by an inflammatory response dueto arterial puncture and mechanical friction during the procedure. Nonetheless, amore clinically significant consequence is radial artery occlusion, which is influencedby various procedural and patient-related factors. Strategies to minimizeremodeling include meticulous pre-procedural ultrasound assessment to ensureappropriate sheath-to-artery size matching, periprocedural pharmacologicalinterventions and implementation of patent hemostasis techniques. This reviewsynthesizes current knowledge regarding the mechanisms, clinical implications,and preventive strategies related to radial artery remodeling following TRA. Further research is needed toelucidate the long-term consequences of radial artery remodeling and to refine preventive strategies for preservingradial artery patency and its suitability for future interventions.
基金supported by the National Natural Science Foundation of China(Grants Nos.42130511,42261134537 and 41602192)funded by the Russian Science Foundation(Grant No.23-44-00067)+2 种基金supported by the Swedish Research Council(Vetenskaps lijeradet,Grant No.2023-00605)the Marianne and Marcus Wallenberg Foundation(Grant No.MMW 2022-0114)the Centre for Advanced Study(CAS)at the Norwegian Academy of Science and Letters,which funded and hosted the research project“The Nordic Little Ice Age”during the 2024-2025 academic year。
文摘Radial growth of trees is highly sensitive to environmental changes,but the effect of climate on tree rings in Qinghai spruce(Picea crassifolia),a widely distributed endemic conifer in western China,is more complex than in many other conifers.A comprehensive understanding of the spatiotemporal climatic responses of its rings is needed to develop theoretical basis for designing strategies for its conservation and management.Here,our synthesis of the literature on responses of radial growth of Qinghai spruce to monthly climate variables in different environmental conditions by meta-analysis showed that precipitation and drought severity are the main limiting factors for Qinghai spruce radial growth in the semiarid region of northwestern China.In warmer and drier areas,radial growth of Qinghai spruce is mainly limited by drought.In the areas north of the 600-mm annual precipitation isoline,the tree-ring width(TRW)was significantly positively correlated with precipitation and significantly negatively correlated with temperature during the growing season(June-August).The limiting effect of drought on Qinghai spruce is also gradually increasing from southeast to northwest,to the west of 103°E and within 37°N-39°N.
文摘BACKGROUND Radial head fractures constitute approximately one-third of all elbow fractures,significantly impacting the young and active population.While open reduction and internal fixation is the preferred treatment for displaced fractures,its high complication rate in comminuted fractures has led to the increasing use of radial head arthroplasty(RHA).RHA provides improved functional outcomes with fewer complications,yet its long-term efficacy remains a topic of debate.AIM To evaluate the functional outcomes of patients undergoing RHA with a modular metallic prosthesis for comminuted Mason type III and IV radial head fractures.METHODS A prospective and retrospective hospital-based study was conducted at Dayanand Medical College and Hospital,Ludhiana over 32 months(January 2021-August 2023).A total of 26 patients with Mason type III and IV fractures were included,with six retrospective and 20 prospective cases.Functional outcomes were assessed using the Mayo Elbow Performance Score(MEPS),elbow range of motion,pain via Visual Analog Scale,and activities of daily living at immediate postoperative,three-month,and six-month follow-ups.RESULTS MEPS at 6 months follow up for 4 cases(15.38%)had good scores,and 22 cases(84.62%)had excellent scores,with a mean±SD of 97.31±6.67.Comparisons showed significant improvement from immediate post-operative to 3 months(P<0.0001),from immediate post-operative to 6 months(P<0.0001),and between 3 months and 6 months(P<0.0001).None of the patients had elbow instability after radial head replacement and 22 cases(84.62%)had no complications,while 3 cases(11.54%)had a stiff elbow,and 1 case(3.85%)had heterotopic ossification.CONCLUSION RHA is an effective treatment for comminuted radial head fractures,providing stable elbow function with minimal complications.
基金supported by the Russian Science Foundation(Grant No.23-11-00242).
文摘An experimental study of the diffusive mass transfer between a droplet and an oscillating immiscible liquid in a horizontal axisymmetricHele-Shaw cell is carried out.Theliquid oscillates radially in the cell.Thetransverse size of the droplet exceeds the cell thickness.The viscosities of the droplet and the surrounding liquid are comparable.Relevant effort is provided to design and test an experimental setup and validate a protocol for determining the mass transfer rate of a solute in a two-liquid system.In particular,fluorescent dye Rhodamine B is considered as the solute.A critical comparison of the situations with and without oscillation is implemented.A procedure is introduced and validated to determine the molecular and effective diffusion coefficients through evaluation of the growth of the diffusion zone width over time.It is shown that,in the presence of the liquid oscillations,there is a significant increase in the width of the zone in which Rhodamine B is present compared to the reference case with no oscillations.The oscillatory flow leads to an intensification of the solute diffusion due to intense time-averaged flows inside the droplet and the surrounding liquid and oscillations of the drop itself.Thestudy is of significant practical interest with particular relevance to typical processes for liquid-liquid extraction.
基金funded by the National Natural Science Foundation of China(No.U24A20353)the S&T Program of Hebei(Nos.226Z6801G,C2021204002,and 20210365)+1 种基金the Talent Introduction Program in Hebei Agricultural University(No.YJ201918)supported by the SERI-funded ERC Starting Grant,project MB23.00011.
文摘Climate warming causes mountainous species to shift their distributions towards higher elevations.How elevation influences growth-climate relationship in mountain regions has been intensively investigated.However,how microtopography shapes tree growth and its drought resistance along the elevation gradient remains poorly understood.We used a network of Larix principis-rupprechtii tree-ring data comprising 1,918 trees from different age classes and mountain slopes,along an elevation gradient ranging from 970 to 1,869 m,to investigate how slope gradients mediate the growth and drought resilience of larch trees along an elevation gradient in North China.Growing season drought and temperature were the major limiting climatic factors for larch trees across the study region.Larch trees younger than 40 years exhibited a stronger positive correlation between basal area increment(BAI)and elevation on steep slopes(10°-35°)than on flat(0°-5°)or gentle(5°-10°)slopes.At low-elevation steep slopes,the growth of larch trees younger than 40 years showed a stronger correlation with the Palmer drought severity index(PDSI).Both resistance and resilience were found to increase along the elevation gradient on steep slopes for young larch trees but not for old larch trees.No significant differences were observed in the drought recovery ability of larch trees across all age groups at increasing elevation.Our results highlight that drought events may particularly affect the growth of young larch trees on low-elevation steep slopes,with potential repercussions on mortality rates.
基金supported by the National Natural Science Foundation of China(Grant NO.41601198,41701209)the key fund project of Beijing Municipal Research Institute of Eco-Environmental Protection(No.Y2024-002).
文摘Clarifying the climate change effects on the radial growth of trees has implications for sustainable forest management,especially under global warming.To investigate tree growth responses to regional climate change of Xiaowutai Mountain,four Chinese pine(Pinus tabulaeformis)ring-width index chronologies were established at different elevations(1290–1600 m).Species growth trends were estimated using climate change projections derived from global climate models.The results show:(1)the four ring-width chronologies exhibited strong statistical characteristics,making them suitable for dendroclimatology studies.Radial growth-climate relationships were highly consistent,showing a negative correlation with previous September temperatures and current May–June temperatures,as well as a positively correlated with precipitation and Palmer Drought Severity Index during the corresponding period;and(2)climate change scenarios revealed that temperature will gradually increase on the Xiaowutai Mountain,and only a slight variation in precipitation is expected.Chinese pine radial growth may show a decline under future climate change.
文摘This study examines the influence of magnetic field and temperature on the transient voltage of a polycrystalline silicon radial junction solar cell in a dynamic regime under multispectral illumination. Radial junction solar cells represent a major advancement in photovoltaic technologies, as they optimize light absorption and charge collection efficiency. The focus is on the impact of the magnetic field and temperature on the decay of transient voltage, which provides crucial information on recombination processes and the lifetime of minority carriers. The results reveal that the magnetic field tends to increase the transient voltage by directly affecting the transient electron density. Indeed, for B > 7 × 10−5 T, the magnetic field prolongs the relaxation time by increasing the transient voltage amplitude. Additionally, rising temperatures accelerate (ranging from 290 K to 450 K) recombination processes, thereby reducing the transient voltage, although this effect is moderated by the presence of a magnetic field. The study highlights the complex interaction between magnetic field and temperature, with significant impacts on the transient behaviour.
基金funded by State Key Research and Development Program of China(No.2023YFD2200401)S&T Program of Hebei(Nos.226Z6801G,22326807D)Talent Introduction Program in Hebei Agricultural University(No.YJ201918).
文摘Droughts have caused tree growth decline and high tree mortality across temperate forests,however,how to manage planted forests to alleviate drought stress is still challenging.We used tree-ring and forest inventory data from different density stands to investigate how competition,tree diameter at breast height(DBH),tree age,and their interactions influence drought sensitivity and resistance for three widely-distributed and planted conifer species(Larix principis-rupprechtii,Picea meyeri,and Pinus sylvestris var.mongolica).Our results showed that the drought sensitivity of the three species was influenced by competition,tree size,and their interactions.Large L.principis-rupprechtii trees were particularly sensitive to drought during the growing season in medium to high-density stands,while the growth of large P.sylvestris var.mongolica was most affected by precipitation at low to medium density stands.Drought resistance of L.principis-rupprechtii trees decreased as tree size increased.Large L.principis-rupprechtii trees had lower drought resistance than small trees in all stands.Drought resistance of large P.meyeri trees exhibited high resistance to drought only in high-density stands.However,drought resistance of P.sylvestris var.mongolica trees was affected by tree size,competition,and their interactions.These results indicated that targeted silvicultural interventions,such as thinning,can be implemented to enhance drought resistance specifically for large L.principis-rupprechtii trees and small P.sylvestris var.mongolica trees in medium and high competition stands,and small P.meyeri trees in high competition stands.Our results highlight that properly conducted thinning can in some cases enhance growth resistance to droughts,depending on stand density,tree size,and tree species.
基金supported by supportedby the China Postdoctoral Science Foundation under Grant Nos.2024M753612 and GZC20233101Supported by the Strategic Cooperation Technology Projects of CNPC and CUPB(ZLZX2020-05)the Science Foundation of China University of Petroleum,Beijing(No.2462023XKBH012).
文摘China's lacustrine shale oil reserves are abundant,making it a key area for future exploration and development.Most lacustrine shales feature a mix of mineral compositions and interlayer sedimentary structures.High-quality reservoirs exhibit significant heterogeneity,which influences the stress distribution during fracturing,leading to complex fracture network patterns.This complexity presents challenges for the comprehensive well logging evaluation of the geological-engineering"double sweet spots"in shale oil,severely restricting efficient development.This study focuses on the impact of shale sedimentary layering on the radial slowness of dipole shear waves.It employs rock physics experiments combined with advanced well logging techniques to explore the relationship between reservoir anisotropy caused by sedimentary layering and reservoir quality,thereby establishing a logging evaluation method for vertical identification of"sweet spots"in lacustrine shale oil.The shales in the Fengcheng Formation of the Mahu Sag into three types according to sedimentary structure scale:laminated,interlayer,and massive.Each type has different mineral compositions,affecting reservoir quality and fracturing potential.Laminated shales develop more fractures under stress along the beddings,showing moderate anisotropy,with reservoir capacity dependent on intercrystalline porosity within carbonate layers.Interlayer shales easily form complex fracture networks,exhibiting significant anisotropy,and their reservoir capacity depends on the porosity within sandy bands.Massive mudstones have the fewest fractures under stress,appearing isotropic with reservoir capacity dependent on matrix pore size.The intensity of reservoir anisotropy correlates positively with storage capacity and the propensity to form irregular and complex fracture networks during hydraulic fracturing.In sections without natural fractures,a larger difference between fast and slow shear waves corresponds to a radial profile shift towards warm tones,indicating stronger anisotropy and better reservoir quality,thus forming complex fracture networks during fracturing.Conversely,a smaller difference leads to a profile energy shift towards cooler tones,indicating stronger isotropy and poorer reservoir quality,hindering the formation of complex fracture networks during hydraulic fracturing.In sections with natural fractures,the difference between fast and slow shear waves exhibits erratic behavior,showing a cross-pattern in radial profiles,indicating strong anisotropy.The presence of natural fractures can synergize with induced fracture networks to form more complex systems,significantly enhancing reservoir productivity.
基金funding by the Science and Innovation Ministry(projects PID2021-123675OB-C43 and TED2021-129770B-C21).
文摘The tolerance of tree growth to drought in diverse mixed forests subjected to seasonal water shortage is understudied despite their ecological and economic relevance.By combining intra-and inter-annual analyses of radial growth responses to climate and drought at daily and monthly scales,different strategies to acclimate to hydroclimate variability of coexisting conifers and broadleaves were unveiled.We analyzed the growth patterns and responses to hydroclimate variability in two conifers(Pinus engelmannii,Juniperus deppeana)and two broadleaves(Quercus grisea,Arbutus arizonica)co-occurring in a Madrean pine-oak forest located in NW Mexico.The strongest positive response to daily precipitation was found in the two conifers,but this response peaked earlier in J.deppeana than in P.engelmannii,which presented a more delayed formation of radially-enlarging tracheids.The latest negative response to temperature was found in Q.grisea,which agrees with its more delayed xylogenesis than A.arizonica.P.engelmannii presented the highest responsiveness to water shortage,driven by lower precipitation and high maximum temperatures,responding to longer droughts ending in autumn(r=0.72),whilst A.arizonica showed the lowest responsiveness to short spring droughts(r=0.39).Growth of P.engelmannii was linked to climate-atmospheric circulation patterns over the near Pacific Ocean.Overall,P.engelmannii and A.arizonica showed high growth rates and earlier growth onset,whilst J.deppeana and Q.grisea showed slower growth rates and later growth onset.The Vaganov-Shashkin growth model evidenced that winterspring soil moisture was the key driver of growth.Under more arid conditions and more frequent and hotter droughts,pine stands could rapidly shift towards mixed pine-oak forests.
基金supported by the NSFC(11871278)the Postgraduate Research&Practice Innovation Program of Jiangsu Province(KYCX23-1669).
文摘In this paper,we study an integral system involving m equations■where ui>0 in R^(n),0<α<n,and pi>1(i=1,2,…,m).Based on the optimal integrability intervals,we estimate the decay rates of the positive solutions of the system at infinity.But estimating these rates is difficult because the relation between pi(i=1,2,…,m)is uncertain.To overcome this difficulty,we obtain the asymptotic behavior of all cases by discussing them separately.In addition,we also get the radial symmetry of positive solutions under some integrability condition.
