To study a class of boundary value problems of parabolic differential equations with deviating arguments, averaging technique, Green’s formula and symbol function sign(·) are used. The multi dimensional problem...To study a class of boundary value problems of parabolic differential equations with deviating arguments, averaging technique, Green’s formula and symbol function sign(·) are used. The multi dimensional problem was reduced to a one dimensional oscillation problem for ordinary differential equations or inequalities. Two oscillatory criteria of solutions for systems of parabolic differential equations with deviating arguments are obtained.展开更多
Aim To study properties of solutions to a class of second order differential inequality with continuous distributed deviating arguments. Methods A direct analysis technique was used. Results and Conclusion Some suf...Aim To study properties of solutions to a class of second order differential inequality with continuous distributed deviating arguments. Methods A direct analysis technique was used. Results and Conclusion Some sufficient conditions that ensure a class of second order delay differential inequality having no eventually positive solutions were obtained, which generalized some given results. Using the results, some oscillatory criteria for solutions of the hyperbolic equation with distributed deviating arguments can be established.展开更多
Based on Mansevich-Mawhin continuation theorem and some analysis skill,some sufficient conditions for the existence of periodic solutions for mixed type p-Laplacian equation with deviating arguments are established,...Based on Mansevich-Mawhin continuation theorem and some analysis skill,some sufficient conditions for the existence of periodic solutions for mixed type p-Laplacian equation with deviating arguments are established,which are complement of previously known results.展开更多
By means of Mawhin's continuation theorem,we study a kind of lie'nard functional differential equations:x"(t)+f(x(t))x'(t)+g(t,x(t-τ(t))) = e(t).Some new results on the existence and uniqueness of pe...By means of Mawhin's continuation theorem,we study a kind of lie'nard functional differential equations:x"(t)+f(x(t))x'(t)+g(t,x(t-τ(t))) = e(t).Some new results on the existence and uniqueness of periodic solutions are obtained.展开更多
By using the theory of coincidence degree, we study a kind of periodic solutions to second order differential equation with a deviating argument such as x″（t） ＋ f（x′（t）） ＋ h（x（t））x′（t） ＋ g（x（t - τ...By using the theory of coincidence degree, we study a kind of periodic solutions to second order differential equation with a deviating argument such as x″（t） ＋ f（x′（t）） ＋ h（x（t））x′（t） ＋ g（x（t - τ（t））） ≈ p（t）, some sufficient conditions on the existence of periodic solutions are obtained.展开更多
In this paper, by using the continuation theorem of coincidence degree theory and some analysis methods, we study a kind of periodic solutions to p-Laplacian neutral functional differential equation with a deviating a...In this paper, by using the continuation theorem of coincidence degree theory and some analysis methods, we study a kind of periodic solutions to p-Laplacian neutral functional differential equation with a deviating argument,some new results on the existence of periodic solutions is obtained.展开更多
A class of hyperbolic equations with continuous distributed deviating arguments is considered and its oscillation theorems are discussed.These theorems are of higher degree of generality and deal with the cases which ...A class of hyperbolic equations with continuous distributed deviating arguments is considered and its oscillation theorems are discussed.These theorems are of higher degree of generality and deal with the cases which are not covered by the known criteria.Particularly,these criteria extend and unify a number of existing results.展开更多
In this paper, we point out some small mistakes in [6] and revise them, we obtain some new oscillation results for certain even order neutral differential equations with deviating arguments. Our results extend and imp...In this paper, we point out some small mistakes in [6] and revise them, we obtain some new oscillation results for certain even order neutral differential equations with deviating arguments. Our results extend and improve many known oscillation criteria because the article just generalizes Meng and Xu’s results.展开更多
In this paper we establish new oscillation criteria for all solution of the first order differential equation with deviating argument. Our result can be applied to the case when coefficients and deviating arguments ar...In this paper we establish new oscillation criteria for all solution of the first order differential equation with deviating argument. Our result can be applied to the case when coefficients and deviating arguments are oscillatory and essentially improve the known results in the literature.展开更多
By using the method of coincidence degree and Lyapunov functional, a set ofeasily applicable criteria are established for the global existence and global asymptotic stabilityof strictly positive (componentwise) period...By using the method of coincidence degree and Lyapunov functional, a set ofeasily applicable criteria are established for the global existence and global asymptotic stabilityof strictly positive (componentwise) periodic solution of a periodic n-species Lotka-Volterracompetition system with feedback controls and several deviating arguments. The problem considered inthis paper is in many aspects more general and incorporate as special cases various problems whichhave been studied extensively in the literature. Moreover, our new criteria, which improve andgeneralize some well known results, can be easily checked.展开更多
In this paper,we use the Leray-Schauder degree theory to establish some new results on the existence and uniqueness of anti-periodic solutions to an nth-order nonlinear differential equation with multiple deviating ar...In this paper,we use the Leray-Schauder degree theory to establish some new results on the existence and uniqueness of anti-periodic solutions to an nth-order nonlinear differential equation with multiple deviating arguments.展开更多
In this paper, we consider the oscillatory and asymptotic behavior of solu-tions of first order nonlinear neutral differential equation with piecewise constantdeviating arguments. Several criteria are obtained for osc...In this paper, we consider the oscillatory and asymptotic behavior of solu-tions of first order nonlinear neutral differential equation with piecewise constantdeviating arguments. Several criteria are obtained for oscillatory and asymptoticbehavior of solutions of the equation.展开更多
By using the theory of coincidence degree, we study a kind of periodic solution to p-Laplacian differential equation with a deviating argument such as （φp（x＇（t）））＇ ＋ f（x（t）） ＋ g（x（t - τ（t））） = e...By using the theory of coincidence degree, we study a kind of periodic solution to p-Laplacian differential equation with a deviating argument such as （φp（x＇（t）））＇ ＋ f（x（t）） ＋ g（x（t - τ（t））） = e（t）, a result on the existence of periodic solution is obtained.展开更多
By the methods of differential inequality and eigenvalue, we obtain several sufficient conditions for oscillation of solutions for higher-order impulsive hyperbolic system with distributed deviating arguments under Ro...By the methods of differential inequality and eigenvalue, we obtain several sufficient conditions for oscillation of solutions for higher-order impulsive hyperbolic system with distributed deviating arguments under Robin and Dirichlet boundary value conditions.展开更多
In this paper, we study a class of higher order nonlinear integro-diferential equations with deviating arguments. With the aid of the integral inequality, we obtain some sufcient conditions under which all solutions t...In this paper, we study a class of higher order nonlinear integro-diferential equations with deviating arguments. With the aid of the integral inequality, we obtain some sufcient conditions under which all solutions to the equation have some asymptotic behavior.展开更多
Flight behavior analysis provides the fundamental basis for the future development of air traffic management(ATM).The characteristics of aircraft behavior are inherently reflected in their flight trajectories,impactin...Flight behavior analysis provides the fundamental basis for the future development of air traffic management(ATM).The characteristics of aircraft behavior are inherently reflected in their flight trajectories,impacting flight efficiency and safety levels.However,existing research largely addresses inefficient or abnormal trajectories from a single perspective,with an absence of a unified evaluation standard.This paper introduces a method for analyzing flight deviation behavior based on automatic dependent surveillance-broadcast(ADS-B)data,defining novel metrics of trajectory redundancy and trajectory deviation.An adaptive detection algorithm is developed to capture diverse deviation patterns.Results reveal that higher trajectory redundancy is linked to lower operational efficiency,while trajectory deviation effectively identify stepped descents,holding patterns,detours,and other behaviors.The approach offers data-driven support for anomaly detection,performance evaluation and air traffic management,with substantial significance for civil aviation applications.展开更多
FY-3G is the first polar-orbiting satellite equipped with a precipitation measurement radar(PMR)operating at Ku-andKa-band frequencies in China.In this study,we compare the reflectivity data from the FY-3G PMR Ku prod...FY-3G is the first polar-orbiting satellite equipped with a precipitation measurement radar(PMR)operating at Ku-andKa-band frequencies in China.In this study,we compare the reflectivity data from the FY-3G PMR Ku product and groundbasedradars(GRs)during 2024.Also,the FY-3G PMR is used as a third-party reference to evaluate the reflectivityconsistency among different GRs.The FY-3G PMR and GRs share similarities in their general distribution,characteristics,and intensity of reflectivity in strong precipitation cloud systems,though the former presents less detailed system structure.Systematic deviations between the FY-3G PMR and GRs and between GRs are comparable,albeit the reflectivity of the FY-3G PMR is generally slightly stronger than that of GRs(especially X-band GRs),with a mean bias ranging from 0.7 to 1.7dB.S-band GRs exhibit the smallest systematic deviation(STD=3.09 dB)from the FY-3G PMR,whereas the X-band GRsshow the largest(STD=3.61 dB),indirectly indicating the highest internal consistency among S-band GRs and the lowestamong X-band GRs.Besides,both S-and C-band GRs display similar deviations when paired with the FY-3G PMR as wellas when paired with their adjacent S/C-band GRs,suggesting good consistency between these two bands.In contrast,XbandGRs exhibit relatively poor consistency with S-band GRs and the FY-3G PMR,showing a deviation ranging from 3.0to 4.6 dB.展开更多
Asymmetric deformation and failure of surrounding rock are frequently observed in mountain tunnels and deep mining roadways,yet the underlying mechanisms remain poorly understood.To investigate asymmetric failure in r...Asymmetric deformation and failure of surrounding rock are frequently observed in mountain tunnels and deep mining roadways,yet the underlying mechanisms remain poorly understood.To investigate asymmetric failure in roadways adjacent to fault structures and mining panels,this study adopts an integrated approach combining theoretical derivation,numerical simulation,and field application,with particular emphasis on the second invariant of the stress deviator(J_(2) )in the surrounding rock.Based on the stress solution for a circular opening,an analytical expression for J_(2)(distortion energy)is derived by considering the reorientation of principal stresses.The study demonstrates that both the increase and reorientation of principal stresses induced by fault–mining interaction jointly govern the spatial distribution of J_(2) and the resulting asymmetric failure behavior.Specifically,the principal stress rotation angle determines the location of J_(2) concentration,whereas the principal stress ratio controls its magnitude.To mitigate asymmetric failure,it is recommended to optimize the J_(2) state through adjustments in roadway size,geometry,and support systems,while simultaneously controlling the asymmetric concentration of stress deviator to enhance roadway stability.This study systematically elucidates the chain mechanism of asymmetric surrounding rock failure driven by principal stress,and further proposes a rational asymmetric joint control strategy,providing theoretical guidance for similar underground engineering conditions.展开更多
Transit managers can use Intelligent Transportation System technologies to access large amounts of data to monitor network status.However,the presentation of the data lacks structural information.Existing single-netwo...Transit managers can use Intelligent Transportation System technologies to access large amounts of data to monitor network status.However,the presentation of the data lacks structural information.Existing single-network description technologies are ineffective in representing the temporal and spatial characteristics simultaneously.Therefore,there is a need for complementary methods to address these deficiencies.To address these limitations,this paper proposes an approach that combines Network Snapshots and Temporal Paths for the scheduled system.A dual information network is constructed to assess the degree of operational deviation considering the planning tasks.To validate the effectiveness,discussions are conducted through a modified cosine similarity calculation on theoretical analysis,delay level description,and the ability to identify abnormal dates.Compared to some state-of-the-art methods,the proposed method achieves an average Spearman delay correlation of 0.847 and a relative distance of 3.477.Furthermore,case analyses are invested in regions of China's Mainland,Europe,and the United States,investigating both the overall and sub-regional network fluctuations.To represent the impact of network fluctuations in sub-regions,a response loss value was developed.The times that are prone to fluctuations are also discussed through the classification of time series data.The research can offer a novel approach to system monitoring,providing a research direction that utilizes individual data combined to represent macroscopic states.Our code will be released at https://github.com/daozhong/STPN.git.展开更多
In this paper,the growth characteristic of meromorphic solutions for the following difference equation An(z)f(z+n)+…+A1(z)f(z+1)+A0(z)f(z)=0 with no dominating coefficient is studied.By imposing certain restriction o...In this paper,the growth characteristic of meromorphic solutions for the following difference equation An(z)f(z+n)+…+A1(z)f(z+1)+A0(z)f(z)=0 with no dominating coefficient is studied.By imposing certain restriction on the entire coefficients associated with Petrenko's deviation of the above equation,we obtain some results and partially address a question posed byⅠ.Laine and C.C.Yang.Furthermore,for the entire solutions f(z)of the difference equation An(z)f(z+n)+…+A1(z)f(z+1)+A0(z)f(z)=F(z),where Aj(z)(j=0,…,n),F(z)are entire functions,we discover a close relationship between the measure of common transcendental directions associated with classical difference operators of f(z)and Petrenko's deviations of the coefficients.展开更多
文摘To study a class of boundary value problems of parabolic differential equations with deviating arguments, averaging technique, Green’s formula and symbol function sign(·) are used. The multi dimensional problem was reduced to a one dimensional oscillation problem for ordinary differential equations or inequalities. Two oscillatory criteria of solutions for systems of parabolic differential equations with deviating arguments are obtained.
文摘Aim To study properties of solutions to a class of second order differential inequality with continuous distributed deviating arguments. Methods A direct analysis technique was used. Results and Conclusion Some sufficient conditions that ensure a class of second order delay differential inequality having no eventually positive solutions were obtained, which generalized some given results. Using the results, some oscillatory criteria for solutions of the hyperbolic equation with distributed deviating arguments can be established.
基金Foundation item： Supported by the Foundation of Education Department of Jiangxi Province（G J J11234） Supported by the Natural Science Foundation of Jiangxi Province（2009GQS0023） Supported by the Natural Science Foundation of Shangrao Normal University（1001）
文摘Based on Mansevich-Mawhin continuation theorem and some analysis skill,some sufficient conditions for the existence of periodic solutions for mixed type p-Laplacian equation with deviating arguments are established,which are complement of previously known results.
基金Foundation item： Supported by the Anhui Natural Science Foundation（050460103） Supported by the NSF of Anhui Educational Bureau（KJ2008B247） Supported by the RSPYT of Anhui Educational Bu- reau（2008jq1111）
文摘By means of Mawhin's continuation theorem,we study a kind of lie'nard functional differential equations:x"(t)+f(x(t))x'(t)+g(t,x(t-τ(t))) = e(t).Some new results on the existence and uniqueness of periodic solutions are obtained.
基金the Natural Science Foundation of Anhui Province(050460103)the Natural Science Foundation by the Bureau of Education of Anhui Province(2005kj031ZD)
文摘By using the theory of coincidence degree, we study a kind of periodic solutions to second order differential equation with a deviating argument such as x″（t） ＋ f（x′（t）） ＋ h（x（t））x′（t） ＋ g（x（t - τ（t））） ≈ p（t）, some sufficient conditions on the existence of periodic solutions are obtained.
基金Supported by the Key NSF of the Education Ministry of China(2007047)Supported by the Scientific Research Foundation of NUIST(09022)
文摘In this paper, by using the continuation theorem of coincidence degree theory and some analysis methods, we study a kind of periodic solutions to p-Laplacian neutral functional differential equation with a deviating argument,some new results on the existence of periodic solutions is obtained.
基金Supported by the NNSF of China（A011403）Supported by the Young Teachers Science Foundation of Beijing University of Civil Engineering and Architecture（100804107）
文摘A class of hyperbolic equations with continuous distributed deviating arguments is considered and its oscillation theorems are discussed.These theorems are of higher degree of generality and deal with the cases which are not covered by the known criteria.Particularly,these criteria extend and unify a number of existing results.
文摘In this paper, we point out some small mistakes in [6] and revise them, we obtain some new oscillation results for certain even order neutral differential equations with deviating arguments. Our results extend and improve many known oscillation criteria because the article just generalizes Meng and Xu’s results.
文摘In this paper we establish new oscillation criteria for all solution of the first order differential equation with deviating argument. Our result can be applied to the case when coefficients and deviating arguments are oscillatory and essentially improve the known results in the literature.
文摘By using the method of coincidence degree and Lyapunov functional, a set ofeasily applicable criteria are established for the global existence and global asymptotic stabilityof strictly positive (componentwise) periodic solution of a periodic n-species Lotka-Volterracompetition system with feedback controls and several deviating arguments. The problem considered inthis paper is in many aspects more general and incorporate as special cases various problems whichhave been studied extensively in the literature. Moreover, our new criteria, which improve andgeneralize some well known results, can be easily checked.
基金supported by the National Natural Science Foundation of China(10771001)the NSF of Educational Bureau of Anhui Province(KJ2009A005Z+2 种基金KJ2010B124)the NSF of Anhui Province(090416237)the Characteristic Speciality of Mathematics Education in Anhui Province and the Young Talents Support of Anhui Province(2010SQRL159)
文摘In this paper,we use the Leray-Schauder degree theory to establish some new results on the existence and uniqueness of anti-periodic solutions to an nth-order nonlinear differential equation with multiple deviating arguments.
文摘In this paper, we consider the oscillatory and asymptotic behavior of solu-tions of first order nonlinear neutral differential equation with piecewise constantdeviating arguments. Several criteria are obtained for oscillatory and asymptoticbehavior of solutions of the equation.
基金This research was supported by Natural Science Foundation of Anhui Province (No.050460103)Natural Science Foundation by the Bureau of Education of Anhui Province (No.2005kj031ZD).
文摘By using the theory of coincidence degree, we study a kind of periodic solution to p-Laplacian differential equation with a deviating argument such as （φp（x＇（t）））＇ ＋ f（x（t）） ＋ g（x（t - τ（t））） = e（t）, a result on the existence of periodic solution is obtained.
基金This work is supported by the National Natural Sciences Foundation of China under Grant 10361006 and the Natural Sciences Foundation of Yunnan Province under Grant 2003A0001M.
文摘By the methods of differential inequality and eigenvalue, we obtain several sufficient conditions for oscillation of solutions for higher-order impulsive hyperbolic system with distributed deviating arguments under Robin and Dirichlet boundary value conditions.
文摘In this paper, we study a class of higher order nonlinear integro-diferential equations with deviating arguments. With the aid of the integral inequality, we obtain some sufcient conditions under which all solutions to the equation have some asymptotic behavior.
基金supported in part by the National Key Research and Development Program of China(No.2023YFB4302903)the Fundamental Research Funds for the Central Universities(No.210525001464)。
文摘Flight behavior analysis provides the fundamental basis for the future development of air traffic management(ATM).The characteristics of aircraft behavior are inherently reflected in their flight trajectories,impacting flight efficiency and safety levels.However,existing research largely addresses inefficient or abnormal trajectories from a single perspective,with an absence of a unified evaluation standard.This paper introduces a method for analyzing flight deviation behavior based on automatic dependent surveillance-broadcast(ADS-B)data,defining novel metrics of trajectory redundancy and trajectory deviation.An adaptive detection algorithm is developed to capture diverse deviation patterns.Results reveal that higher trajectory redundancy is linked to lower operational efficiency,while trajectory deviation effectively identify stepped descents,holding patterns,detours,and other behaviors.The approach offers data-driven support for anomaly detection,performance evaluation and air traffic management,with substantial significance for civil aviation applications.
基金supported by the Innovation and Development Special Project of the China Meteorological Administration(Grant No.CXFZ2024J058)the Guangdong Province Basic and Applied Basic Research Foundation Meteorological Joint Fund Project(Grant No.2024A1515510036)+1 种基金the National Key R&D Program of China(Grant No.2022YFC3004101)the Technical Innovation Team Project of Guangzhou Meteorological Satellite Ground Station(Grant No.CXTD202401).
文摘FY-3G is the first polar-orbiting satellite equipped with a precipitation measurement radar(PMR)operating at Ku-andKa-band frequencies in China.In this study,we compare the reflectivity data from the FY-3G PMR Ku product and groundbasedradars(GRs)during 2024.Also,the FY-3G PMR is used as a third-party reference to evaluate the reflectivityconsistency among different GRs.The FY-3G PMR and GRs share similarities in their general distribution,characteristics,and intensity of reflectivity in strong precipitation cloud systems,though the former presents less detailed system structure.Systematic deviations between the FY-3G PMR and GRs and between GRs are comparable,albeit the reflectivity of the FY-3G PMR is generally slightly stronger than that of GRs(especially X-band GRs),with a mean bias ranging from 0.7 to 1.7dB.S-band GRs exhibit the smallest systematic deviation(STD=3.09 dB)from the FY-3G PMR,whereas the X-band GRsshow the largest(STD=3.61 dB),indirectly indicating the highest internal consistency among S-band GRs and the lowestamong X-band GRs.Besides,both S-and C-band GRs display similar deviations when paired with the FY-3G PMR as wellas when paired with their adjacent S/C-band GRs,suggesting good consistency between these two bands.In contrast,XbandGRs exhibit relatively poor consistency with S-band GRs and the FY-3G PMR,showing a deviation ranging from 3.0to 4.6 dB.
基金supported by the National Natural Science Foundation of China(Grant No.52274148)the Natural Science Foundation of Hebei Province(Grant No.E2023402103)+1 种基金the Science Research Project of Hebei Education Department(Grant No.QN2025247)Handan Science and Technology R&D Project(Grant No.23422093047)。
文摘Asymmetric deformation and failure of surrounding rock are frequently observed in mountain tunnels and deep mining roadways,yet the underlying mechanisms remain poorly understood.To investigate asymmetric failure in roadways adjacent to fault structures and mining panels,this study adopts an integrated approach combining theoretical derivation,numerical simulation,and field application,with particular emphasis on the second invariant of the stress deviator(J_(2) )in the surrounding rock.Based on the stress solution for a circular opening,an analytical expression for J_(2)(distortion energy)is derived by considering the reorientation of principal stresses.The study demonstrates that both the increase and reorientation of principal stresses induced by fault–mining interaction jointly govern the spatial distribution of J_(2) and the resulting asymmetric failure behavior.Specifically,the principal stress rotation angle determines the location of J_(2) concentration,whereas the principal stress ratio controls its magnitude.To mitigate asymmetric failure,it is recommended to optimize the J_(2) state through adjustments in roadway size,geometry,and support systems,while simultaneously controlling the asymmetric concentration of stress deviator to enhance roadway stability.This study systematically elucidates the chain mechanism of asymmetric surrounding rock failure driven by principal stress,and further proposes a rational asymmetric joint control strategy,providing theoretical guidance for similar underground engineering conditions.
文摘Transit managers can use Intelligent Transportation System technologies to access large amounts of data to monitor network status.However,the presentation of the data lacks structural information.Existing single-network description technologies are ineffective in representing the temporal and spatial characteristics simultaneously.Therefore,there is a need for complementary methods to address these deficiencies.To address these limitations,this paper proposes an approach that combines Network Snapshots and Temporal Paths for the scheduled system.A dual information network is constructed to assess the degree of operational deviation considering the planning tasks.To validate the effectiveness,discussions are conducted through a modified cosine similarity calculation on theoretical analysis,delay level description,and the ability to identify abnormal dates.Compared to some state-of-the-art methods,the proposed method achieves an average Spearman delay correlation of 0.847 and a relative distance of 3.477.Furthermore,case analyses are invested in regions of China's Mainland,Europe,and the United States,investigating both the overall and sub-regional network fluctuations.To represent the impact of network fluctuations in sub-regions,a response loss value was developed.The times that are prone to fluctuations are also discussed through the classification of time series data.The research can offer a novel approach to system monitoring,providing a research direction that utilizes individual data combined to represent macroscopic states.Our code will be released at https://github.com/daozhong/STPN.git.
基金Supported by the National Natural Science Foundation of China(Grant No.11661043)and the ScienceTechnology Research Project of Jiangxi Provincial Department of Education(Grant No.GJJ2200320).
文摘In this paper,the growth characteristic of meromorphic solutions for the following difference equation An(z)f(z+n)+…+A1(z)f(z+1)+A0(z)f(z)=0 with no dominating coefficient is studied.By imposing certain restriction on the entire coefficients associated with Petrenko's deviation of the above equation,we obtain some results and partially address a question posed byⅠ.Laine and C.C.Yang.Furthermore,for the entire solutions f(z)of the difference equation An(z)f(z+n)+…+A1(z)f(z+1)+A0(z)f(z)=F(z),where Aj(z)(j=0,…,n),F(z)are entire functions,we discover a close relationship between the measure of common transcendental directions associated with classical difference operators of f(z)and Petrenko's deviations of the coefficients.
