Medical Data Mining published an article entitled Mapping the global research trends and hotspots on hypertensive nephropathy:A novel bibliometrics overview on 10 October 2025.The author confirmed this article’s proo...Medical Data Mining published an article entitled Mapping the global research trends and hotspots on hypertensive nephropathy:A novel bibliometrics overview on 10 October 2025.The author confirmed this article’s proof on 28 September 2025 without any questions.However,on 13 November 2025,the Editorial Office of Medical Data Mining noticed an inconsistency between the data presented in the main text and Figure 1.Specifically,erroneous Figure 1 states“a total of 56,691 literatures were obtained through database search”,while the main text in the Search results section states“According to the search term,a total of 59,220 publications were retrieved from the database.”The authors acknowledge that the original version of Figure 1 was incorrect and have provided the revised,correct version in this corrigendum.The authors would like to assert that there is no change in the body text of the article.展开更多
Objective This study aimed to determine the temporal trends in sleep duration among Chinese adults.Methods In this series of repeated nationally representative cross-sectional surveys(China Chronic Disease and Risk Fa...Objective This study aimed to determine the temporal trends in sleep duration among Chinese adults.Methods In this series of repeated nationally representative cross-sectional surveys(China Chronic Disease and Risk Factors Surveillance)conducted between 2010 and 2018,a total of 645,420 adult participants(97,741 in 2010;175,749 in 2013;187,777 in 2015;and 184,153 in 2018)were included in the trend analysis.Linear and logistic regression models were utilized to assess trends in sleep duration.Results In 2018,the estimated overall mean sleep duration among the Chinese adult population was7.58(SD,1.45)hours per day,with no significant trend from 2010.A significant increase in short sleep duration(≤6 hours)was observed in the total population,from 15.3%(95%CI:14.1%–16.5%)in 2010 to18.5%(95%CI:17.7%–19.3%)in 2018(P<0.001).Similarly,the trend in long sleep duration(>9 hours)was also significant,increasing in weighted prevalence from 7.2%(95%CI:6.3%–8.1%)in 2010 to 9.0%(95%CI:8.2%–9.9%)in 2018(P<0.001).Conclusion The prevalence of both short and long sleep durations significantly increased among Chinese adults from 2010 to 2018,highlighting the urgency of health initiatives to promote optimal sleep duration in China.展开更多
During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive...During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive distance)to a moving target as quickly as possible,resulting in the extended minimum-time intercept problem(EMTIP).Existing research has primarily focused on the zero-distance intercept problem,MTIP,establishing the necessary or sufficient conditions for MTIP optimality,and utilizing analytic algorithms,such as root-finding algorithms,to calculate the optimal solutions.However,these approaches depend heavily on the properties of the analytic algorithm,making them inapplicable when problem settings change,such as in the case of a positive effective range or complicated target motions outside uniform rectilinear motion.In this study,an approach employing a high-accuracy and quality-guaranteed mixed-integer piecewise-linear program(QG-PWL)is proposed for the EMTIP.This program can accommodate different effective interception ranges and complicated target motions(variable velocity or complicated trajectories).The high accuracy and quality guarantees of QG-PWL originate from elegant strategies such as piecewise linearization and other developed operation strategies.The approximate error in the intercept path length is proved to be bounded to h^(2)/(4√2),where h is the piecewise length.展开更多
Owing to their global search capabilities and gradient-free operation,metaheuristic algorithms are widely applied to a wide range of optimization problems.However,their computational demands become prohibitive when ta...Owing to their global search capabilities and gradient-free operation,metaheuristic algorithms are widely applied to a wide range of optimization problems.However,their computational demands become prohibitive when tackling high-dimensional optimization challenges.To effectively address these challenges,this study introduces cooperative metaheuristics integrating dynamic dimension reduction(DR).Building upon particle swarm optimization(PSO)and differential evolution(DE),the proposed cooperative methods C-PSO and C-DE are developed.In the proposed methods,the modified principal components analysis(PCA)is utilized to reduce the dimension of design variables,thereby decreasing computational costs.The dynamic DR strategy implements periodic execution of modified PCA after a fixed number of iterations,resulting in the important dimensions being dynamically identified.Compared with the static one,the dynamic DR strategy can achieve precise identification of important dimensions,thereby enabling accelerated convergence toward optimal solutions.Furthermore,the influence of cumulative contribution rate thresholds on optimization problems with different dimensions is investigated.Metaheuristic algorithms(PSO,DE)and cooperative metaheuristics(C-PSO,C-DE)are examined by 15 benchmark functions and two engineering design problems(speed reducer and composite pressure vessel).Comparative results demonstrate that the cooperative methods achieve significantly superior performance compared to standard methods in both solution accuracy and computational efficiency.Compared to standard metaheuristic algorithms,cooperative metaheuristics achieve a reduction in computational cost of at least 40%.The cooperative metaheuristics can be effectively used to tackle both high-dimensional unconstrained and constrained optimization problems.展开更多
Existing problems of sewage treatment plants in small towns were summarized firstly,and then the developing trend of construction of sewage treatment plants in small towns was discussed from the aspects of project dec...Existing problems of sewage treatment plants in small towns were summarized firstly,and then the developing trend of construction of sewage treatment plants in small towns was discussed from the aspects of project decision,site selection,design,processing technology and construction financing models. Finally,outlooks for its future development were proposed to provide reference for the construction of sewage treatment plants in small towns in future.展开更多
With the development of the economy,film and television education has gradually received more and more attention.With the rapid development of new media technologies,there are still some problems in film and televisio...With the development of the economy,film and television education has gradually received more and more attention.With the rapid development of new media technologies,there are still some problems in film and television education in the new media environment.This paper mainly analyzes the problems faced by film and television education in the new media environment,and the development direction of film and television education in the new media era,and explores the forms of film and television education and film industry integration.展开更多
Background Cervical cancer is the only cancer that can be eliminated worldwide.Tracking the latest burden of cervical cancer is critical toward the targets set by World Health Organization(WHO)to eliminate cervical ca...Background Cervical cancer is the only cancer that can be eliminated worldwide.Tracking the latest burden of cervical cancer is critical toward the targets set by World Health Organization(WHO)to eliminate cervical cancer as a major public health problem.Methods All data were extracted from the Global Cancer Observatory(GLOBOCAN)2022.Age-standardized incidence rate(ASIR)and mortality rates(ASMR)of cervical cancer were compared and linked to Human Development Index(HDI)between populations.The estimated annual percentage changes(EAPCs)were used to characterize the temporal trend in ASIR/ASMR,and demographic estimates were projected up to 2050.Results Globally,an estimated 662,044 cases(ASIR:14.12/100,000)and 348,709 deaths(ASMR:7.08/100,000)from cervical cancer occurred in 2022,corresponding to the fourth cause of cancer morbidity and mortality in women worldwide.Specifically,42%of cases and 39%of deaths occurred in China(23%and 16%)and India(19%and 23%).Both ASIR and ASMR of cervical cancer decreased with HDI,and similar decreasing links were observed for both early-onset(0–39 years)and late-onset(≥40 years)cervical cancer.Both ASIR and ASMR of overall cervical cancer showed decreasing trends during 2003–2012(EAPC:0.04%and-1.03%);however,upward trends were observed for early-onset cervical cancer(EAPC:1.16%and 0.57%).If national rates in 2022 remain stable,the estimated cases and deaths from cervical cancer are projected to increase by 56.8%and 80.7%up to 2050.Moreover,the projected increase of early-onset cervical cancer is mainly observed in transitioning countries,while decreased burden is expected in transitioned countries.Conclusions Cervical cancer remains a common cause of cancer death in many countries,especially in transitioning countries.Unless scaling-up preventive interventions,human papillomavirus(HPV)vaccination and cervical cancer screening,as well as systematic cooperation within government,civil societies,and private enterprises,the global burden of cervical cancer would be expected to increase in the future.展开更多
Background Given the relatively unfavorable prognosis and significant geographic differences in lung cancer burden,it is critical to update the global landscape of lung cancer to inform local strategies.Methods Based ...Background Given the relatively unfavorable prognosis and significant geographic differences in lung cancer burden,it is critical to update the global landscape of lung cancer to inform local strategies.Methods Based on the GLOBOCAN 2022,the age-standardized incidence rate(ASIR)and mortality rate(ASMR)were compared and linked to the Human Development Index(HDI)across different populations.The temporal trends in ASIR/ASMR were characterized as estimated annual percentage change(EAPC),and demographic projections were performed up to 2050.Results Globally,an estimated 2,480,675 cases and 1,817,469 deaths from lung cancer occurred in 2022.Both ASIR and ASMR of lung cancer varied widely by world region,with ASIR ranging from 2.06 to 39.38 per 100,000 and ASMR from 1.95 to 31.70 per 100,000.China alone accounted for>40%of cases and deaths worldwide.Both ASIR and ARMR of lung cancer increased with HDI(R2:0.54 and 0.47,all P values<0.001),regardless of gender.Based on available data,both ASIR during 2001–2010 and ASMR during 2001–2015 showed decreasing trends in males(EAPC:1.50%and−2.22%)but increasing trends in females(EAPC:1.08%and 0.07%).Similar trends in ASIR and ASMR were observed among the elder population(≥50 years);however,downward trends were observed in the younger population(<50 years).Alongside the aging and growth of the population,estimated cases and deaths from overall lung cancer would increase by 86.2%and 95.2%up to 2050 as compared with estimates in 2022,respectively.Notably,increased early-onset lung cancer was only observed in transitioning countries,while decreased early-onset lung cancer was observed in transitioned countries.Conclusion Lung cancer maintained as the leading cancer burden worldwide.Unless timely preventive interventions in tobacco mitigation,early screening,and precise treatment,the global lung cancer burden is expected to increase in the future,especially for transitioning countries.展开更多
With the continuous improvement of industrial automation in our country and the use of high technology, promoted the scientific content of traditional industry. The development of electric automation control system in...With the continuous improvement of industrial automation in our country and the use of high technology, promoted the scientific content of traditional industry. The development of electric automation control system inevitably turn towards a systematic, comprehensive development direction. This article first analyze the present problems in electrical automation monitoring system, analyzes its future development trends, so as to provide some reference for the effective application of electrical automation in the future monitoring system, fundamentally realize the resources sharing.展开更多
Objective The Asia-Pacific region has a high chronic obstructive pulmonary disease(COPD)burden,but studies on its trends are limited.Using the Global Burden of Disease(GBD)2019 data,we analyzed COPD trends in 36 count...Objective The Asia-Pacific region has a high chronic obstructive pulmonary disease(COPD)burden,but studies on its trends are limited.Using the Global Burden of Disease(GBD)2019 data,we analyzed COPD trends in 36 countries and territories from 1990 to 2019 and predicted future incidence trends through 2034.Methods COPD data by age and sex from the GBD 2019 database were analyzed for incidence,prevalence,mortality,and disability-adjusted life years(DALY)rates from 1990 to 2019.Joinpoint regression identified significant annual trends,and age-standardized incidence rates were predicted through 2034 using age-period-cohort models.Results The incidence,prevalence,mortality,and disease burden of COPD have been decreasing,and the incidence rates will continue to decrease or remain stable until 2034 in most selected countries and territories,except for a few Southeastern Asian countries.The Lao People’s Democratic Republic and Vietnam are projected to experience an increase in COPD incidence from 165.3 per 100,000 in 2019 to 177 per 100,000 in 2034 and from 179.9 per 100,000 in 2019 to 192.5 per 100,000 in 2034,respectively.Older males had a higher incidence than any other sex or age group.The sex gap in incidence rates continues to widen,though it is smaller and less significant in the younger age group than in those in the older one.Conclusion COPD rates are expected to decline until 2034 but remain a health risk,especially in countries with rising rates.Urgent action on tobacco control,air pollution,and public education is needed.展开更多
Background While China’s socioeconomic transformation has driven divergent trends in gastrointestinal cancers,comprehensive data on esophageal,gastric,and liver cancer burden remain limited.This study examines the gl...Background While China’s socioeconomic transformation has driven divergent trends in gastrointestinal cancers,comprehensive data on esophageal,gastric,and liver cancer burden remain limited.This study examines the global burden of esophageal,gastric,and liver cancers in 2022 and analyzes the trends of age-standardized incidence and mortality rate(ASRs)in China from 2000 to 2018,thereby providing evidence for the formulation of cancer control strategies.Methods The global burden of esophageal,gastric and liver cancers including the estimated number of cases and deaths and the ASRs for incidence and mortality were from GLOBALCAN 2022 dataset.Data from 22 cancer registries in China were employed for the trend analysis of the ASRs for incidence and mortality of these three cancers.The Joinpoint model was used to compute the average annual percentage change(AAPC)of the incidence and mortality of the three cancers from 2000 to 2018.Results Globally,esophageal,gastric and liver cancers accounted for 11.8%of incident cancer cases and 19.1%of cancer deaths.China bore a disproportionately high burden,representing 43.8%,37.0%,and 42.4%of global esophageal,gastric,and liver cancer cases respectively,and 42.1%,39.4%,and 41.7%of corresponding deaths.However,the ASRs for incidence and mortality for all three cancers declined significantly in China(2000–2018),with absolute case numbers decreasing for gastric and esophageal cancers during 2010–2022.Age-specific analysis revealed most pronounced declines in incidence and mortality in populations under 40 years old,with AAPCs of less than–6.0%for esophageal cancer,around–4.0%for gastric cancer,and approximately–2.0%for liver cancer.Conclusions China has achieved remarkable progress in controlling esophageal,gastric and liver cancers,yet these malignancies remain major public health challenges.Future efforts should intensify existing prevention measures while expanding screening programs,particularly for aging populations.These findings offer valuable insights for regions undergoing similar epidemiological transitions.展开更多
Background Cotton crop is infested by numerous arthropod pests from sowing to harvesting,causing substantial direct and indirect yield losses.Knowledge of seasonal population trends and the relative occurrence of pest...Background Cotton crop is infested by numerous arthropod pests from sowing to harvesting,causing substantial direct and indirect yield losses.Knowledge of seasonal population trends and the relative occurrence of pests and their natural enemies is required to minimize the pest population and yield losses.In the current study,analysis of the seasonal population trend of pests and natural enemies and their relative occurrence on cultivars of three cotton species in Central India has been carried out.Results A higher number and diversity of sucking pests were observed during the vegetative cotton growth stage(60 days after sowing),declining as the crop matured.With the exception of cotton jassid(Amrasca biguttula biguttula Ishida),which caused significant crop damage mainly from August to September;populations of other sucking insects seldom reached economic threshold levels(ETL)throughout the studied period.The bollworm complex populations were minimal,except for the pink bollworm(Pectinophora gossypiella Saunders),which re-emerged as a menace to cotton crops during the cotton cropping season 2017–2018 due to resistance development against Bt-cotton.A reasonably good number of predatory arthropods,including coccinellids,lacewings,and spiders,were found actively preying on the arthropod pest complex of the cotton crop during the early vegetative growth stage.Linear regression indicates a significant relationship between green boll infestations and pink bollworm moths in pheromone traps.Multiple linear regression analyse showed mean weekly weather at one-or two-week lag periods had a significant impact on sucking pest population(cotton aphid,cotton jassid,cotton whitefly,and onion thrips)fluctuation.Gossypium hirsutum cultivars RCH 2 and DCH 32,and G.barbadense cultivar Suvin were found susceptible to cotton jassid and onion thrips.Phule Dhanvantary,an G.arboreum cotton cultivar,demonstrated the highest tolerance among all evaluated cultivars against all sucking pests.Conclusion These findings have important implications for pest management in cotton crops.Susceptible cultivars warrant more attention for plant protection measures,making them more input-intensive.The choice of appropriate cultivars can help minimize input costs,thereby increasing net returns for cotton farmers.展开更多
Machine-learning is a robust technique for understanding pollution characteristics of surface ozone,which are at high levels in urban China.This study introduced an innovative approach combining trend decomposition wi...Machine-learning is a robust technique for understanding pollution characteristics of surface ozone,which are at high levels in urban China.This study introduced an innovative approach combining trend decomposition with Random Forest algorithm to investigate ozone dynamics and formation regimes in a coastal area of China.During the period of 2017–2022,significant inter-annual fluctuations emerged,with peaks in mid-2017 attributed to volatile organic compounds(VOCs),and in late-2019 influenced by air temperature.Multifaceted periodicities(daily,weekly,holiday,and yearly)in ozone were revealed,elucidating substantial influences of daily and yearly components on ozone periodicity.A VOC-sensitive ozone formation regime was identified,characterized by lower VOCs/NO_(x) ratios(average=0.88)and significant positive correlations between ozone and VOCs.This interplay manifested in elevated ozone duringweekends,holidays,and pandemic lockdowns.Key variables influencing ozone across diverse timescaleswere uncovered,with solar radiation and temperature driving daily and yearly ozone variations,respectively.Precursor substances,particularly VOCs,significantly shaped weekly/holiday patterns and long-term trends of ozone.Specifically,acetone,ethane,hexanal,and toluene had a notable impact on the multi-year ozone trend,emphasizing the urgency of VOC regulation.Furthermore,our observations indicated that NO_(x) primarily drived the stochastic variations in ozone,a distinguishing characteristic of regions with heavy traffic.This research provides novel insights into ozone dynamics in coastal urban areas and highlights the importance of integrating statistical and machinelearning methods in atmospheric pollution studies,with implications for targeted mitigation strategies beyond this specific region and pollutant.展开更多
Atrial fibrillation(AF)/atrial flutter(AFL)is the most common sustained cardiac arrhythmia.The known risk factors for developing AF/AFL include age,structural heart disease,hypertension,diabetes mellitus,or hyperthyro...Atrial fibrillation(AF)/atrial flutter(AFL)is the most common sustained cardiac arrhythmia.The known risk factors for developing AF/AFL include age,structural heart disease,hypertension,diabetes mellitus,or hyperthyroidism.This study aims to attribute the trends in AF/AFL-related mortalities over the past two decades 1999-2020 concerning race and sex and disparity among them.To the best of our knowledge,this is the first study that estimates the trends and mortality due to AF/AFL from 1999-2020 in older adults in the United States.In this 21-year analysis of mortality data,we found a constant increase in mortality rates due to AF/AFL in older adults.From 1999 to 2020,the overall mortality in older adults aged 65 and above,regardless of sex and race,is found to be almost doubled i.e.about a 50.2%increase in the number of deaths due to AF/AFL.Furthermore,other confounding risk factors such has obesity,prior myocardial infarction,inflammation,hypertension,birth weight,diabetes mellitus,hyperthyroidism,hormone replacement therapy in menopausal women increases the risk in the occurrence or recurrent occurrence of AF.展开更多
Background Breast cancer(BC)incidence and mortality vary significantly across countries,highlighting the need to update the global burden of female BC,including current trends and future projections.Methods Data were ...Background Breast cancer(BC)incidence and mortality vary significantly across countries,highlighting the need to update the global burden of female BC,including current trends and future projections.Methods Data were sourced from GLOBOCAN 2022,including estimated new cases and deaths from BC across 21 United Nation(UN)regions and 185 countries,the age-standardized incidence rate(ASIR)and mortality rate(ASMR),the estimated annual percentage changes(EAPC),and demographic projections through 2050.The region-specific and country-specific BC burden for women of all ages and for young women(<40 years old)was reorganized and re-plotted to highlight subgroup differences.Linear regression was used to explore the link between ASIR/ASMR and the human development index(HDI).Transitioning countries referred to those with low or medium HDI,while transitioned countries were those with high or very high HDI.Results In 2022,an estimated 2.3 million new BC cases and 666,000 BC-related deaths occurred globally,accounting for 23.8%and 15.4%of all cancer cases and deaths in women,respectively.Regionally,Eastern Asia reported the highest number of cases(480,019,ASIR:37.54/100,000),while South-Central Asia had the highest number of deaths(135,348,ASMR:13.41/100,000).At the country level,China had the highest number of cases due to its large population,whereas India reported the highest number of deaths.ASIR for both overall and early-onset BC increased with HDI,while ASMR for early-onset BC decreased with HDI(P<0.05).Overall BC showed an increasing trend in ASIR during 2003–2015(EAPC:0.92%)and a decreasing trend in ASMR during 2006–2016(EAPC:-1.06%).Early-onset BC showed a more significant rise in ASIR(EAPCs:1.4%)and a slight increase in ASMR(EAPCs:0.16%).If national rates remain stable,BC cases and deaths will increase by 54.7%and 70.9%,respectively,by 2050.Notably,increased early-onset BC cases are only observed in transitioning countries,while decreased cases are seen in transitioned countries.Conclusions Breast cancer remains the leading cancer burden in women,particularly in transitioning countries.Addressing this growing burden requires urgent integration of primary prevention,early detection and high-quality treatment through multi-sectoral collaboration.展开更多
Background:Parenting exerts a profound influence on children’s mental health and behavioral development.Despite the high prevalence of children’s emotional and behavioral problems(CEBP)in China,evidence-based parent...Background:Parenting exerts a profound influence on children’s mental health and behavioral development.Despite the high prevalence of children’s emotional and behavioral problems(CEBP)in China,evidence-based parenting interventions remain scarcely investigated as preventive public health strategies.This pilot study evaluated a school-based intervention for preventing CEBP.Methods:We employed a quasi-experimental design with propensity score matching(PSM)to select 28 families(intervention:n=13;control:n=15)from two matched urban primary schools.Quantitative data from seven validated scales were analyzed using t-tests and ANCOVA.Qualitative insights were derived from 10 semi-structured interviews via thematic analysis.Results:Compared to the control group,the intervention group demonstrated significantly greater improvements in CEBP(p=0.020,Cohen’s d=0.92),parental adjustment(p=0.031,Cohen’s d=0.80),parenting confidence(p=0.003,Cohen’s d=1.04),and parentchild relationships(p=0.001,Cohen’s d=1.46).Non-significant effects were observed for parenting style,parental relationship,and parenting conflict(p>0.05).Qualitative analysis corroborated these findings and further identified contributing factors for non-significant outcomes,including challengeswithmeasurement adaptability and inconsistent co-parenting practices.Conclusions:This pilot study suggests that an authoritative parenting style may be effective and culturally adaptable in China.Positive parenting interventions appear to mitigate CEBP by reducing risk factors and enhancing protective factors.However,improving parental relationships and parenting conflict may require targeted strategies.Given the pilot nature of this PSM-matched study(n=28),the findings should be interpreted as exploratory and used primarily for intervention refinement.展开更多
The exponential growth in the scale of power systems has led to a significant increase in the complexity of dispatch problem resolution,particularly within multi-area interconnected power grids.This complexity necessi...The exponential growth in the scale of power systems has led to a significant increase in the complexity of dispatch problem resolution,particularly within multi-area interconnected power grids.This complexity necessitates the employment of distributed solution methodologies,which are not only essential but also highly desirable.In the realm of computational modelling,the multi-area economic dispatch problem(MAED)can be formulated as a linearly constrained separable convex optimization problem.The proximal point algorithm(PPA)is particularly adept at addressing such mathematical constructs effectively.This study introduces parallel(PPPA)and serial(SPPA)variants of the PPA as distributed algorithms,specifically designed for the computational modelling of the MAED.The PPA introduces a quadratic term into the objective function,which,while potentially complicating the iterative updates of the algorithm,serves to dampen oscillations near the optimal solution,thereby enhancing the convergence characteristics.Furthermore,the convergence efficiency of the PPA is significantly influenced by the parameter c.To address this parameter sensitivity,this research draws on trend theory from stock market analysis to propose trend theory-driven distributed PPPA and SPPA,thereby enhancing the robustness of the computational models.The computational models proposed in this study are anticipated to exhibit superior performance in terms of convergence behaviour,stability,and robustness with respect to parameter selection,potentially outperforming existing methods such as the alternating direction method of multipliers(ADMM)and Auxiliary Problem Principle(APP)in the computational simulation of power system dispatch problems.The simulation results demonstrate that the trend theory-based PPPA,SPPA,ADMM and APP exhibit significant robustness to the initial value of parameter c,and show superior convergence characteristics compared to the residual balancing ADMM.展开更多
Let Pr denote an almost-prime with at most r prime factors,counted according to multiplicity.In this paper,it is proved that,for every sufficiently large even integer N,the equation N=x^(2)+p_(2)^(2)+p_(3)^(3)+p_(4)^(...Let Pr denote an almost-prime with at most r prime factors,counted according to multiplicity.In this paper,it is proved that,for every sufficiently large even integer N,the equation N=x^(2)+p_(2)^(2)+p_(3)^(3)+p_(4)^(3)+p_(5)^(5)+_6^(5)is solvable with being an almost-prime P_(6) and the other variables primes.This result constitutes an enhancement upon the previous result of Hooley[Recent Progress in Analytic Number Theory,Vol.1(Durham,1979),London:Academic Press,1981,127-191].展开更多
Let d(n;r_(1),q_(1),r_(2),q_(2))be the number of factorization n=n_(1)n_(2)satisfying n_i≡r_i(mod q_i)(i=1,2)andΔ(x;r_(1),q_(1),r_(2),q_(2))be the error term of the summatory function of d(n;r_(1),q_(1),r_(2),q_(2))...Let d(n;r_(1),q_(1),r_(2),q_(2))be the number of factorization n=n_(1)n_(2)satisfying n_i≡r_i(mod q_i)(i=1,2)andΔ(x;r_(1),q_(1),r_(2),q_(2))be the error term of the summatory function of d(n;r_(1),q_(1),r_(2),q_(2)).Suppose x≥(q_(1)q_(2))^(1+ε),1≤r_i≤q_i,and(r_i,q_i)=1(i=1,2).This paper studies the power moments and sign changes ofΔ(x;r_(1),q_(1),r_(2),q_(2)).We prove that for sufficiently large constant C,Δ(q_(1)q_(2)x:r_(1),q_(1),r_(2),q_(2))changes sign in the interval[T,T+C√T]for any large T.Meanwhile,we show that for small constants c and c,there exist infinitely many subintervals of length c√log^(-7)T in[T,2T]where±Δ(q_(1)q_(2)x:r_(1),q_(1),r_(2),q_(2))>cx^(1/4)always holds.展开更多
文摘Medical Data Mining published an article entitled Mapping the global research trends and hotspots on hypertensive nephropathy:A novel bibliometrics overview on 10 October 2025.The author confirmed this article’s proof on 28 September 2025 without any questions.However,on 13 November 2025,the Editorial Office of Medical Data Mining noticed an inconsistency between the data presented in the main text and Figure 1.Specifically,erroneous Figure 1 states“a total of 56,691 literatures were obtained through database search”,while the main text in the Search results section states“According to the search term,a total of 59,220 publications were retrieved from the database.”The authors acknowledge that the original version of Figure 1 was incorrect and have provided the revised,correct version in this corrigendum.The authors would like to assert that there is no change in the body text of the article.
基金supported by the National Natural Science Foundation of China(82341245,82371491)the Chinese Central Government(Key Project of Public Health Program)the National Key Research and Development Program of China(2018YFC1311706,2018YFC1311702)。
文摘Objective This study aimed to determine the temporal trends in sleep duration among Chinese adults.Methods In this series of repeated nationally representative cross-sectional surveys(China Chronic Disease and Risk Factors Surveillance)conducted between 2010 and 2018,a total of 645,420 adult participants(97,741 in 2010;175,749 in 2013;187,777 in 2015;and 184,153 in 2018)were included in the trend analysis.Linear and logistic regression models were utilized to assess trends in sleep duration.Results In 2018,the estimated overall mean sleep duration among the Chinese adult population was7.58(SD,1.45)hours per day,with no significant trend from 2010.A significant increase in short sleep duration(≤6 hours)was observed in the total population,from 15.3%(95%CI:14.1%–16.5%)in 2010 to18.5%(95%CI:17.7%–19.3%)in 2018(P<0.001).Similarly,the trend in long sleep duration(>9 hours)was also significant,increasing in weighted prevalence from 7.2%(95%CI:6.3%–8.1%)in 2010 to 9.0%(95%CI:8.2%–9.9%)in 2018(P<0.001).Conclusion The prevalence of both short and long sleep durations significantly increased among Chinese adults from 2010 to 2018,highlighting the urgency of health initiatives to promote optimal sleep duration in China.
基金supported by the National Natural Sci‐ence Foundation of China(Grant No.62306325)。
文摘During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive distance)to a moving target as quickly as possible,resulting in the extended minimum-time intercept problem(EMTIP).Existing research has primarily focused on the zero-distance intercept problem,MTIP,establishing the necessary or sufficient conditions for MTIP optimality,and utilizing analytic algorithms,such as root-finding algorithms,to calculate the optimal solutions.However,these approaches depend heavily on the properties of the analytic algorithm,making them inapplicable when problem settings change,such as in the case of a positive effective range or complicated target motions outside uniform rectilinear motion.In this study,an approach employing a high-accuracy and quality-guaranteed mixed-integer piecewise-linear program(QG-PWL)is proposed for the EMTIP.This program can accommodate different effective interception ranges and complicated target motions(variable velocity or complicated trajectories).The high accuracy and quality guarantees of QG-PWL originate from elegant strategies such as piecewise linearization and other developed operation strategies.The approximate error in the intercept path length is proved to be bounded to h^(2)/(4√2),where h is the piecewise length.
基金funded by National Natural Science Foundation of China(Nos.12402142,11832013 and 11572134)Natural Science Foundation of Hubei Province(No.2024AFB235)+1 种基金Hubei Provincial Department of Education Science and Technology Research Project(No.Q20221714)the Opening Foundation of Hubei Key Laboratory of Digital Textile Equipment(Nos.DTL2023019 and DTL2022012).
文摘Owing to their global search capabilities and gradient-free operation,metaheuristic algorithms are widely applied to a wide range of optimization problems.However,their computational demands become prohibitive when tackling high-dimensional optimization challenges.To effectively address these challenges,this study introduces cooperative metaheuristics integrating dynamic dimension reduction(DR).Building upon particle swarm optimization(PSO)and differential evolution(DE),the proposed cooperative methods C-PSO and C-DE are developed.In the proposed methods,the modified principal components analysis(PCA)is utilized to reduce the dimension of design variables,thereby decreasing computational costs.The dynamic DR strategy implements periodic execution of modified PCA after a fixed number of iterations,resulting in the important dimensions being dynamically identified.Compared with the static one,the dynamic DR strategy can achieve precise identification of important dimensions,thereby enabling accelerated convergence toward optimal solutions.Furthermore,the influence of cumulative contribution rate thresholds on optimization problems with different dimensions is investigated.Metaheuristic algorithms(PSO,DE)and cooperative metaheuristics(C-PSO,C-DE)are examined by 15 benchmark functions and two engineering design problems(speed reducer and composite pressure vessel).Comparative results demonstrate that the cooperative methods achieve significantly superior performance compared to standard methods in both solution accuracy and computational efficiency.Compared to standard metaheuristic algorithms,cooperative metaheuristics achieve a reduction in computational cost of at least 40%.The cooperative metaheuristics can be effectively used to tackle both high-dimensional unconstrained and constrained optimization problems.
文摘Existing problems of sewage treatment plants in small towns were summarized firstly,and then the developing trend of construction of sewage treatment plants in small towns was discussed from the aspects of project decision,site selection,design,processing technology and construction financing models. Finally,outlooks for its future development were proposed to provide reference for the construction of sewage treatment plants in small towns in future.
文摘With the development of the economy,film and television education has gradually received more and more attention.With the rapid development of new media technologies,there are still some problems in film and television education in the new media environment.This paper mainly analyzes the problems faced by film and television education in the new media environment,and the development direction of film and television education in the new media era,and explores the forms of film and television education and film industry integration.
基金supported by the National Key R&D Program of China(grant number:2021YFC2500400)National Natural Science Foundation of China(grant numbers:82172894,82073028,82204121)China Postdoctoral Science Foundation(grant number:2023M742617).
文摘Background Cervical cancer is the only cancer that can be eliminated worldwide.Tracking the latest burden of cervical cancer is critical toward the targets set by World Health Organization(WHO)to eliminate cervical cancer as a major public health problem.Methods All data were extracted from the Global Cancer Observatory(GLOBOCAN)2022.Age-standardized incidence rate(ASIR)and mortality rates(ASMR)of cervical cancer were compared and linked to Human Development Index(HDI)between populations.The estimated annual percentage changes(EAPCs)were used to characterize the temporal trend in ASIR/ASMR,and demographic estimates were projected up to 2050.Results Globally,an estimated 662,044 cases(ASIR:14.12/100,000)and 348,709 deaths(ASMR:7.08/100,000)from cervical cancer occurred in 2022,corresponding to the fourth cause of cancer morbidity and mortality in women worldwide.Specifically,42%of cases and 39%of deaths occurred in China(23%and 16%)and India(19%and 23%).Both ASIR and ASMR of cervical cancer decreased with HDI,and similar decreasing links were observed for both early-onset(0–39 years)and late-onset(≥40 years)cervical cancer.Both ASIR and ASMR of overall cervical cancer showed decreasing trends during 2003–2012(EAPC:0.04%and-1.03%);however,upward trends were observed for early-onset cervical cancer(EAPC:1.16%and 0.57%).If national rates in 2022 remain stable,the estimated cases and deaths from cervical cancer are projected to increase by 56.8%and 80.7%up to 2050.Moreover,the projected increase of early-onset cervical cancer is mainly observed in transitioning countries,while decreased burden is expected in transitioned countries.Conclusions Cervical cancer remains a common cause of cancer death in many countries,especially in transitioning countries.Unless scaling-up preventive interventions,human papillomavirus(HPV)vaccination and cervical cancer screening,as well as systematic cooperation within government,civil societies,and private enterprises,the global burden of cervical cancer would be expected to increase in the future.
基金supported by the National Key Research and Development Program of China(grant number:2021YFC2500400)Tianjin Health Committee Foundation(grant number:TJWJ2021MS008)+2 种基金Tianjin Key Medical Discipline(Specialty)Construction Project(grant number:TYXZDXK-009A)Science and Technology Program of the Joint Fund of Scientific Research for the Public Hospitals of Inner Mongolia Academy of Medical Sciences(grant number:2023GLLH0132)Scientific Research Fund for the Demonstration Project of Public Hospital Reform and Quality Development(Gastrointestinal Tumour)that is approved by Peking University Cancer Hospital(Inner Mongolia Campus)(grant number:2023SGGZ068)。
文摘Background Given the relatively unfavorable prognosis and significant geographic differences in lung cancer burden,it is critical to update the global landscape of lung cancer to inform local strategies.Methods Based on the GLOBOCAN 2022,the age-standardized incidence rate(ASIR)and mortality rate(ASMR)were compared and linked to the Human Development Index(HDI)across different populations.The temporal trends in ASIR/ASMR were characterized as estimated annual percentage change(EAPC),and demographic projections were performed up to 2050.Results Globally,an estimated 2,480,675 cases and 1,817,469 deaths from lung cancer occurred in 2022.Both ASIR and ASMR of lung cancer varied widely by world region,with ASIR ranging from 2.06 to 39.38 per 100,000 and ASMR from 1.95 to 31.70 per 100,000.China alone accounted for>40%of cases and deaths worldwide.Both ASIR and ARMR of lung cancer increased with HDI(R2:0.54 and 0.47,all P values<0.001),regardless of gender.Based on available data,both ASIR during 2001–2010 and ASMR during 2001–2015 showed decreasing trends in males(EAPC:1.50%and−2.22%)but increasing trends in females(EAPC:1.08%and 0.07%).Similar trends in ASIR and ASMR were observed among the elder population(≥50 years);however,downward trends were observed in the younger population(<50 years).Alongside the aging and growth of the population,estimated cases and deaths from overall lung cancer would increase by 86.2%and 95.2%up to 2050 as compared with estimates in 2022,respectively.Notably,increased early-onset lung cancer was only observed in transitioning countries,while decreased early-onset lung cancer was observed in transitioned countries.Conclusion Lung cancer maintained as the leading cancer burden worldwide.Unless timely preventive interventions in tobacco mitigation,early screening,and precise treatment,the global lung cancer burden is expected to increase in the future,especially for transitioning countries.
文摘With the continuous improvement of industrial automation in our country and the use of high technology, promoted the scientific content of traditional industry. The development of electric automation control system inevitably turn towards a systematic, comprehensive development direction. This article first analyze the present problems in electrical automation monitoring system, analyzes its future development trends, so as to provide some reference for the effective application of electrical automation in the future monitoring system, fundamentally realize the resources sharing.
基金supported by a major project of the Zhejiang Natural Science Foundation(LD21G030001).
文摘Objective The Asia-Pacific region has a high chronic obstructive pulmonary disease(COPD)burden,but studies on its trends are limited.Using the Global Burden of Disease(GBD)2019 data,we analyzed COPD trends in 36 countries and territories from 1990 to 2019 and predicted future incidence trends through 2034.Methods COPD data by age and sex from the GBD 2019 database were analyzed for incidence,prevalence,mortality,and disability-adjusted life years(DALY)rates from 1990 to 2019.Joinpoint regression identified significant annual trends,and age-standardized incidence rates were predicted through 2034 using age-period-cohort models.Results The incidence,prevalence,mortality,and disease burden of COPD have been decreasing,and the incidence rates will continue to decrease or remain stable until 2034 in most selected countries and territories,except for a few Southeastern Asian countries.The Lao People’s Democratic Republic and Vietnam are projected to experience an increase in COPD incidence from 165.3 per 100,000 in 2019 to 177 per 100,000 in 2034 and from 179.9 per 100,000 in 2019 to 192.5 per 100,000 in 2034,respectively.Older males had a higher incidence than any other sex or age group.The sex gap in incidence rates continues to widen,though it is smaller and less significant in the younger age group than in those in the older one.Conclusion COPD rates are expected to decline until 2034 but remain a health risk,especially in countries with rising rates.Urgent action on tobacco control,air pollution,and public education is needed.
基金supported by the National Natural Science Foundation of China(grant numbers:82273721,82304220)Cooperation Fund of CHCAMS and SZCH(grant number:CFA202201003).
文摘Background While China’s socioeconomic transformation has driven divergent trends in gastrointestinal cancers,comprehensive data on esophageal,gastric,and liver cancer burden remain limited.This study examines the global burden of esophageal,gastric,and liver cancers in 2022 and analyzes the trends of age-standardized incidence and mortality rate(ASRs)in China from 2000 to 2018,thereby providing evidence for the formulation of cancer control strategies.Methods The global burden of esophageal,gastric and liver cancers including the estimated number of cases and deaths and the ASRs for incidence and mortality were from GLOBALCAN 2022 dataset.Data from 22 cancer registries in China were employed for the trend analysis of the ASRs for incidence and mortality of these three cancers.The Joinpoint model was used to compute the average annual percentage change(AAPC)of the incidence and mortality of the three cancers from 2000 to 2018.Results Globally,esophageal,gastric and liver cancers accounted for 11.8%of incident cancer cases and 19.1%of cancer deaths.China bore a disproportionately high burden,representing 43.8%,37.0%,and 42.4%of global esophageal,gastric,and liver cancer cases respectively,and 42.1%,39.4%,and 41.7%of corresponding deaths.However,the ASRs for incidence and mortality for all three cancers declined significantly in China(2000–2018),with absolute case numbers decreasing for gastric and esophageal cancers during 2010–2022.Age-specific analysis revealed most pronounced declines in incidence and mortality in populations under 40 years old,with AAPCs of less than–6.0%for esophageal cancer,around–4.0%for gastric cancer,and approximately–2.0%for liver cancer.Conclusions China has achieved remarkable progress in controlling esophageal,gastric and liver cancers,yet these malignancies remain major public health challenges.Future efforts should intensify existing prevention measures while expanding screening programs,particularly for aging populations.These findings offer valuable insights for regions undergoing similar epidemiological transitions.
基金Funding support for the Crop Pest Surveillance and Advisory Project(CROPSAP)。
文摘Background Cotton crop is infested by numerous arthropod pests from sowing to harvesting,causing substantial direct and indirect yield losses.Knowledge of seasonal population trends and the relative occurrence of pests and their natural enemies is required to minimize the pest population and yield losses.In the current study,analysis of the seasonal population trend of pests and natural enemies and their relative occurrence on cultivars of three cotton species in Central India has been carried out.Results A higher number and diversity of sucking pests were observed during the vegetative cotton growth stage(60 days after sowing),declining as the crop matured.With the exception of cotton jassid(Amrasca biguttula biguttula Ishida),which caused significant crop damage mainly from August to September;populations of other sucking insects seldom reached economic threshold levels(ETL)throughout the studied period.The bollworm complex populations were minimal,except for the pink bollworm(Pectinophora gossypiella Saunders),which re-emerged as a menace to cotton crops during the cotton cropping season 2017–2018 due to resistance development against Bt-cotton.A reasonably good number of predatory arthropods,including coccinellids,lacewings,and spiders,were found actively preying on the arthropod pest complex of the cotton crop during the early vegetative growth stage.Linear regression indicates a significant relationship between green boll infestations and pink bollworm moths in pheromone traps.Multiple linear regression analyse showed mean weekly weather at one-or two-week lag periods had a significant impact on sucking pest population(cotton aphid,cotton jassid,cotton whitefly,and onion thrips)fluctuation.Gossypium hirsutum cultivars RCH 2 and DCH 32,and G.barbadense cultivar Suvin were found susceptible to cotton jassid and onion thrips.Phule Dhanvantary,an G.arboreum cotton cultivar,demonstrated the highest tolerance among all evaluated cultivars against all sucking pests.Conclusion These findings have important implications for pest management in cotton crops.Susceptible cultivars warrant more attention for plant protection measures,making them more input-intensive.The choice of appropriate cultivars can help minimize input costs,thereby increasing net returns for cotton farmers.
基金supported by Ningbo Natural Science Foundation(No.2023J059)Ningbo Commonweal Programme Key Project(No.2023S038)Guangxi Key Research and Development Programme(No.GuikeAB21220063).
文摘Machine-learning is a robust technique for understanding pollution characteristics of surface ozone,which are at high levels in urban China.This study introduced an innovative approach combining trend decomposition with Random Forest algorithm to investigate ozone dynamics and formation regimes in a coastal area of China.During the period of 2017–2022,significant inter-annual fluctuations emerged,with peaks in mid-2017 attributed to volatile organic compounds(VOCs),and in late-2019 influenced by air temperature.Multifaceted periodicities(daily,weekly,holiday,and yearly)in ozone were revealed,elucidating substantial influences of daily and yearly components on ozone periodicity.A VOC-sensitive ozone formation regime was identified,characterized by lower VOCs/NO_(x) ratios(average=0.88)and significant positive correlations between ozone and VOCs.This interplay manifested in elevated ozone duringweekends,holidays,and pandemic lockdowns.Key variables influencing ozone across diverse timescaleswere uncovered,with solar radiation and temperature driving daily and yearly ozone variations,respectively.Precursor substances,particularly VOCs,significantly shaped weekly/holiday patterns and long-term trends of ozone.Specifically,acetone,ethane,hexanal,and toluene had a notable impact on the multi-year ozone trend,emphasizing the urgency of VOC regulation.Furthermore,our observations indicated that NO_(x) primarily drived the stochastic variations in ozone,a distinguishing characteristic of regions with heavy traffic.This research provides novel insights into ozone dynamics in coastal urban areas and highlights the importance of integrating statistical and machinelearning methods in atmospheric pollution studies,with implications for targeted mitigation strategies beyond this specific region and pollutant.
文摘Atrial fibrillation(AF)/atrial flutter(AFL)is the most common sustained cardiac arrhythmia.The known risk factors for developing AF/AFL include age,structural heart disease,hypertension,diabetes mellitus,or hyperthyroidism.This study aims to attribute the trends in AF/AFL-related mortalities over the past two decades 1999-2020 concerning race and sex and disparity among them.To the best of our knowledge,this is the first study that estimates the trends and mortality due to AF/AFL from 1999-2020 in older adults in the United States.In this 21-year analysis of mortality data,we found a constant increase in mortality rates due to AF/AFL in older adults.From 1999 to 2020,the overall mortality in older adults aged 65 and above,regardless of sex and race,is found to be almost doubled i.e.about a 50.2%increase in the number of deaths due to AF/AFL.Furthermore,other confounding risk factors such has obesity,prior myocardial infarction,inflammation,hypertension,birth weight,diabetes mellitus,hyperthyroidism,hormone replacement therapy in menopausal women increases the risk in the occurrence or recurrent occurrence of AF.
基金supported by the National Key R&D Program of China(grant number:2021YFC2500400)Tianjin Health Committee Foundation(grant number:TJWJ2021MS008).
文摘Background Breast cancer(BC)incidence and mortality vary significantly across countries,highlighting the need to update the global burden of female BC,including current trends and future projections.Methods Data were sourced from GLOBOCAN 2022,including estimated new cases and deaths from BC across 21 United Nation(UN)regions and 185 countries,the age-standardized incidence rate(ASIR)and mortality rate(ASMR),the estimated annual percentage changes(EAPC),and demographic projections through 2050.The region-specific and country-specific BC burden for women of all ages and for young women(<40 years old)was reorganized and re-plotted to highlight subgroup differences.Linear regression was used to explore the link between ASIR/ASMR and the human development index(HDI).Transitioning countries referred to those with low or medium HDI,while transitioned countries were those with high or very high HDI.Results In 2022,an estimated 2.3 million new BC cases and 666,000 BC-related deaths occurred globally,accounting for 23.8%and 15.4%of all cancer cases and deaths in women,respectively.Regionally,Eastern Asia reported the highest number of cases(480,019,ASIR:37.54/100,000),while South-Central Asia had the highest number of deaths(135,348,ASMR:13.41/100,000).At the country level,China had the highest number of cases due to its large population,whereas India reported the highest number of deaths.ASIR for both overall and early-onset BC increased with HDI,while ASMR for early-onset BC decreased with HDI(P<0.05).Overall BC showed an increasing trend in ASIR during 2003–2015(EAPC:0.92%)and a decreasing trend in ASMR during 2006–2016(EAPC:-1.06%).Early-onset BC showed a more significant rise in ASIR(EAPCs:1.4%)and a slight increase in ASMR(EAPCs:0.16%).If national rates remain stable,BC cases and deaths will increase by 54.7%and 70.9%,respectively,by 2050.Notably,increased early-onset BC cases are only observed in transitioning countries,while decreased cases are seen in transitioned countries.Conclusions Breast cancer remains the leading cancer burden in women,particularly in transitioning countries.Addressing this growing burden requires urgent integration of primary prevention,early detection and high-quality treatment through multi-sectoral collaboration.
基金supported by the National Social Science Fund of China[18BSH146].
文摘Background:Parenting exerts a profound influence on children’s mental health and behavioral development.Despite the high prevalence of children’s emotional and behavioral problems(CEBP)in China,evidence-based parenting interventions remain scarcely investigated as preventive public health strategies.This pilot study evaluated a school-based intervention for preventing CEBP.Methods:We employed a quasi-experimental design with propensity score matching(PSM)to select 28 families(intervention:n=13;control:n=15)from two matched urban primary schools.Quantitative data from seven validated scales were analyzed using t-tests and ANCOVA.Qualitative insights were derived from 10 semi-structured interviews via thematic analysis.Results:Compared to the control group,the intervention group demonstrated significantly greater improvements in CEBP(p=0.020,Cohen’s d=0.92),parental adjustment(p=0.031,Cohen’s d=0.80),parenting confidence(p=0.003,Cohen’s d=1.04),and parentchild relationships(p=0.001,Cohen’s d=1.46).Non-significant effects were observed for parenting style,parental relationship,and parenting conflict(p>0.05).Qualitative analysis corroborated these findings and further identified contributing factors for non-significant outcomes,including challengeswithmeasurement adaptability and inconsistent co-parenting practices.Conclusions:This pilot study suggests that an authoritative parenting style may be effective and culturally adaptable in China.Positive parenting interventions appear to mitigate CEBP by reducing risk factors and enhancing protective factors.However,improving parental relationships and parenting conflict may require targeted strategies.Given the pilot nature of this PSM-matched study(n=28),the findings should be interpreted as exploratory and used primarily for intervention refinement.
基金funded by Guangxi Science and Technology Base and Talent Special Project,grant number GuiKeAD20159077Foundation of Guilin University of Technology,grant number GLUTQD2018001.
文摘The exponential growth in the scale of power systems has led to a significant increase in the complexity of dispatch problem resolution,particularly within multi-area interconnected power grids.This complexity necessitates the employment of distributed solution methodologies,which are not only essential but also highly desirable.In the realm of computational modelling,the multi-area economic dispatch problem(MAED)can be formulated as a linearly constrained separable convex optimization problem.The proximal point algorithm(PPA)is particularly adept at addressing such mathematical constructs effectively.This study introduces parallel(PPPA)and serial(SPPA)variants of the PPA as distributed algorithms,specifically designed for the computational modelling of the MAED.The PPA introduces a quadratic term into the objective function,which,while potentially complicating the iterative updates of the algorithm,serves to dampen oscillations near the optimal solution,thereby enhancing the convergence characteristics.Furthermore,the convergence efficiency of the PPA is significantly influenced by the parameter c.To address this parameter sensitivity,this research draws on trend theory from stock market analysis to propose trend theory-driven distributed PPPA and SPPA,thereby enhancing the robustness of the computational models.The computational models proposed in this study are anticipated to exhibit superior performance in terms of convergence behaviour,stability,and robustness with respect to parameter selection,potentially outperforming existing methods such as the alternating direction method of multipliers(ADMM)and Auxiliary Problem Principle(APP)in the computational simulation of power system dispatch problems.The simulation results demonstrate that the trend theory-based PPPA,SPPA,ADMM and APP exhibit significant robustness to the initial value of parameter c,and show superior convergence characteristics compared to the residual balancing ADMM.
基金Supported by NSFC (Nos.12471009,12301006,12001047,11901566)Beijing Natural Science Foundation (No.1242003)National Training Program of Innovation and Entrepreneurship for Undergraduates(No.202307011)。
文摘Let Pr denote an almost-prime with at most r prime factors,counted according to multiplicity.In this paper,it is proved that,for every sufficiently large even integer N,the equation N=x^(2)+p_(2)^(2)+p_(3)^(3)+p_(4)^(3)+p_(5)^(5)+_6^(5)is solvable with being an almost-prime P_(6) and the other variables primes.This result constitutes an enhancement upon the previous result of Hooley[Recent Progress in Analytic Number Theory,Vol.1(Durham,1979),London:Academic Press,1981,127-191].
基金supported by the Talent Fund of Beijing Jiaotong University(No.2020RC012)NSFC(No.11871295),supported by NSFC(No.11971476),supported by NSFC(No.12071421)。
文摘Let d(n;r_(1),q_(1),r_(2),q_(2))be the number of factorization n=n_(1)n_(2)satisfying n_i≡r_i(mod q_i)(i=1,2)andΔ(x;r_(1),q_(1),r_(2),q_(2))be the error term of the summatory function of d(n;r_(1),q_(1),r_(2),q_(2)).Suppose x≥(q_(1)q_(2))^(1+ε),1≤r_i≤q_i,and(r_i,q_i)=1(i=1,2).This paper studies the power moments and sign changes ofΔ(x;r_(1),q_(1),r_(2),q_(2)).We prove that for sufficiently large constant C,Δ(q_(1)q_(2)x:r_(1),q_(1),r_(2),q_(2))changes sign in the interval[T,T+C√T]for any large T.Meanwhile,we show that for small constants c and c,there exist infinitely many subintervals of length c√log^(-7)T in[T,2T]where±Δ(q_(1)q_(2)x:r_(1),q_(1),r_(2),q_(2))>cx^(1/4)always holds.
