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
Pitch deviation at rack joints(PDRJ) is a common error in rack railways. It directly affects the contact characteristics between the rack and gear and leads to accelerated surface wear. This threatens the stability an...Pitch deviation at rack joints(PDRJ) is a common error in rack railways. It directly affects the contact characteristics between the rack and gear and leads to accelerated surface wear. This threatens the stability and service life of the rack system, and the theoretical understanding of this issue remains limited. To address this gap, this study develops an improved tooth wear model that simultaneously accounts for the instantaneous variations in meshing stiffness and dynamic transmission error(DTE) induced by PDRJ, as well as the real-time correlation between gear-rack contact position and meshing excitation. Subsequently, the rack tooth load and wear characteristics are evaluated through the rack vehicle-track coupled dynamics and gear-rack contact model. The model's reliability is verified through field measurements. Moreover, the influence of varying PDRJ levels on load sharing factors, surface wear depth, and rack displacement is investigated. The results show that PDRJ disrupts the theoretical gear-rack meshing process, resulting in non-uniform load distribution and accelerated wear, particularly in the addendum and dedendum regions of the rack teeth. This study provides valuable insights into the rack surface wear mechanism under PDRJ.展开更多
The deformation characteristics and thermal response of anchor rods are crucial for ensuring the stability and safety of surrounding rock support structures.However,existing research has predominantly concentrated on ...The deformation characteristics and thermal response of anchor rods are crucial for ensuring the stability and safety of surrounding rock support structures.However,existing research has predominantly concentrated on the mechanical performance of anchor rods,with limited attention to the coupled evolution of strain and temperature fields during tensile deformation.This knowledge gap hinders a comprehensive understanding of the synergistic mechanical-thermal response mechanisms in anchor rods under loading conditions.To address this limitation,the present study systematically investigated the evolution of strain and temperature fields,along with their correlation,during the test of micro-negative Poisson's ratio(NPR)and ordinary Poisson's ratio(PR)anchor rods.Digital image correlation(DIC)and infrared thermography(IRT)techniques were employed for this exploration.The uniaxial tensile tests were conducted at two different rates,and the ordinary PR anchor rod(Q235 anchor rod)was established as a control group for comparative analysis.The findings reveal that the micro-NPR anchor rod exhibit strain localization at multiple locations during the tensile process,whereas Q235 anchors show local strain concentration in only one region.The standard deviation evolution curves for both the strain and temperature field exhibit two distinct phases in the two anchor rods.The evolution patterns between these two types of curves are basically consistent.The two standard deviation curves for the micro-NPR anchor rod display a wavy increase in the second phase,while for the Q235 anchor rod,they increase steadily until the specimen is damaged.The correlation analysis reveals that the standard deviations of strain and temperature differences for both types of anchor rods are significantly correlated.These findings demonstrate the synergistic evolution mechanism of deformation and thermal response,providing a potential foundation for utilizing thermal monitoring to assess the stability of rock support structures.展开更多
Although machine learning models have achieved high enough accuracy in predicting shield position deviations,their“black box”nature makes the prediction mechanisms and decision-making processes opaque,leading to wea...Although machine learning models have achieved high enough accuracy in predicting shield position deviations,their“black box”nature makes the prediction mechanisms and decision-making processes opaque,leading to weaker explanations and practicability.This study introduces a novel explainable deep learning framework comprising the Informer model with enhanced attention mechanisms(EAMInfor)and deep learning important features(DeepLIFT),aimed at improving the prediction accuracy of shield position deviations and providing interpretability for predictive results.The EAMInfor model attempts to integrate channel attention,spatial attention,and simple attention modules to improve the Informer model's performance.The framework is tested with the four different geological conditions datasets generated from the Xiamen metro line 3,China.Results show that the EAMInfor model outperforms the traditional Informer and comparison models.The analysis with the DeepLIFT method indicates that the push thrust of push cylinder and the earth chamber pressure are the most significant features,while the stroke length of the push cylinder demonstrated lower importance.Furthermore,the variation trends in the significance of data points within input sequences exhibit substantial differences between single and composite strata.This framework not only improves predictive accuracy but also strengthens the credibility and reliability of the results.展开更多
In this paper,we study the asymptotic behavior of solutions to a class of higher order nonlinear integro-differential equations with deviating arguments.And some properties of the oscillatory solutions are given.Our r...In this paper,we study the asymptotic behavior of solutions to a class of higher order nonlinear integro-differential equations with deviating arguments.And some properties of the oscillatory solutions are given.Our results generalize and improve the previous results.展开更多
In this paper,we study an even order neutral differential equation with deviating arguments,and obtain new oscillation results without the assumptions which were required for related results given before.Our results e...In this paper,we study an even order neutral differential equation with deviating arguments,and obtain new oscillation results without the assumptions which were required for related results given before.Our results extend and improve many known oscillation criteria,based on the standard integral averaging technique.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 by the National Natural Science Foundation of China (Grant No.52388102)the Sichuan Science and Technology Program (Grant No.2024NSFTD0011)the Fundamental Research Funds for the State Key Laboratory of Rail Transit Vehicle System of Southwest Jiaotong University (Grant No.2023TPL-T11)。
文摘Pitch deviation at rack joints(PDRJ) is a common error in rack railways. It directly affects the contact characteristics between the rack and gear and leads to accelerated surface wear. This threatens the stability and service life of the rack system, and the theoretical understanding of this issue remains limited. To address this gap, this study develops an improved tooth wear model that simultaneously accounts for the instantaneous variations in meshing stiffness and dynamic transmission error(DTE) induced by PDRJ, as well as the real-time correlation between gear-rack contact position and meshing excitation. Subsequently, the rack tooth load and wear characteristics are evaluated through the rack vehicle-track coupled dynamics and gear-rack contact model. The model's reliability is verified through field measurements. Moreover, the influence of varying PDRJ levels on load sharing factors, surface wear depth, and rack displacement is investigated. The results show that PDRJ disrupts the theoretical gear-rack meshing process, resulting in non-uniform load distribution and accelerated wear, particularly in the addendum and dedendum regions of the rack teeth. This study provides valuable insights into the rack surface wear mechanism under PDRJ.
基金supported by State Key Laboratory for Geomechanics and Deep Underground Engineering,China University of Mining&Technology,Beijing(Grant No.SKLGDUEK2120)。
文摘The deformation characteristics and thermal response of anchor rods are crucial for ensuring the stability and safety of surrounding rock support structures.However,existing research has predominantly concentrated on the mechanical performance of anchor rods,with limited attention to the coupled evolution of strain and temperature fields during tensile deformation.This knowledge gap hinders a comprehensive understanding of the synergistic mechanical-thermal response mechanisms in anchor rods under loading conditions.To address this limitation,the present study systematically investigated the evolution of strain and temperature fields,along with their correlation,during the test of micro-negative Poisson's ratio(NPR)and ordinary Poisson's ratio(PR)anchor rods.Digital image correlation(DIC)and infrared thermography(IRT)techniques were employed for this exploration.The uniaxial tensile tests were conducted at two different rates,and the ordinary PR anchor rod(Q235 anchor rod)was established as a control group for comparative analysis.The findings reveal that the micro-NPR anchor rod exhibit strain localization at multiple locations during the tensile process,whereas Q235 anchors show local strain concentration in only one region.The standard deviation evolution curves for both the strain and temperature field exhibit two distinct phases in the two anchor rods.The evolution patterns between these two types of curves are basically consistent.The two standard deviation curves for the micro-NPR anchor rod display a wavy increase in the second phase,while for the Q235 anchor rod,they increase steadily until the specimen is damaged.The correlation analysis reveals that the standard deviations of strain and temperature differences for both types of anchor rods are significantly correlated.These findings demonstrate the synergistic evolution mechanism of deformation and thermal response,providing a potential foundation for utilizing thermal monitoring to assess the stability of rock support structures.
基金supported by the National Natural Science Foundation of China(Grant Nos.52378392,52408356)the Foal Eagle Program Youth Top-notch Talent Project of Fujian Province,China(Grant No.00387088).
文摘Although machine learning models have achieved high enough accuracy in predicting shield position deviations,their“black box”nature makes the prediction mechanisms and decision-making processes opaque,leading to weaker explanations and practicability.This study introduces a novel explainable deep learning framework comprising the Informer model with enhanced attention mechanisms(EAMInfor)and deep learning important features(DeepLIFT),aimed at improving the prediction accuracy of shield position deviations and providing interpretability for predictive results.The EAMInfor model attempts to integrate channel attention,spatial attention,and simple attention modules to improve the Informer model's performance.The framework is tested with the four different geological conditions datasets generated from the Xiamen metro line 3,China.Results show that the EAMInfor model outperforms the traditional Informer and comparison models.The analysis with the DeepLIFT method indicates that the push thrust of push cylinder and the earth chamber pressure are the most significant features,while the stroke length of the push cylinder demonstrated lower importance.Furthermore,the variation trends in the significance of data points within input sequences exhibit substantial differences between single and composite strata.This framework not only improves predictive accuracy but also strengthens the credibility and reliability of the results.
文摘In this paper,we study the asymptotic behavior of solutions to a class of higher order nonlinear integro-differential equations with deviating arguments.And some properties of the oscillatory solutions are given.Our results generalize and improve the previous results.
基金supported by the National Natural Science Foundation of China under Grant 10771118 and 10801089
文摘In this paper,we study an even order neutral differential equation with deviating arguments,and obtain new oscillation results without the assumptions which were required for related results given before.Our results extend and improve many known oscillation criteria,based on the standard integral averaging technique.
