In this paper,a robust and consistent COVID-19 emergency decision-making approach is proposed based on q-rung linear diophantine fuzzy set(q-RLDFS),differential evolutionary(DE)optimization principles,and evidential r...In this paper,a robust and consistent COVID-19 emergency decision-making approach is proposed based on q-rung linear diophantine fuzzy set(q-RLDFS),differential evolutionary(DE)optimization principles,and evidential reasoning(ER)methodology.The proposed approach uses q-RLDFS in order to represent the evaluating values of the alternatives corresponding to the attributes.DE optimization is used to obtain the optimal weights of the attributes,and ER methodology is used to compute the aggregated q-rung linear diophantine fuzzy values(q-RLDFVs)of each alternative.Then the score values of alternatives are computed based on the aggregated q-RLDFVs.An alternative with the maximum score value is selected as a better one.The applicability of the proposed approach has been illustrated in COVID-19 emergency decision-making system and sustainable energy planning management.Moreover,we have validated the proposed approach with a numerical example.Finally,a comparative study is provided with the existing models,where the proposed approach is found to be robust to perform better and consistent in uncertain environments.展开更多
BACKGROUND The clinical management and prognosis differ between benign and malignant solid focal liver lesions(FLLs),as well as among different pathological types of malignant FLLs.Accurate diagnosis of the possible t...BACKGROUND The clinical management and prognosis differ between benign and malignant solid focal liver lesions(FLLs),as well as among different pathological types of malignant FLLs.Accurate diagnosis of the possible types of solid FLLs is important.Our previous study confirmed the value of shear wave elastography(SWE)using maximal elasticity(Emax)as the parameter in the differential diagnosis between benign and malignant FLLs.However,the value of SWE in the differential diagnosis among different pathological types of malignant FLLs has not been proved.AIM To explore the value of two-dimensional SWE(2D-SWE)using Emax in the differential diagnosis of FLLs,especially among different pathological types of malignant FLLs.METHODS All the patients enrolled in this study were diagnosed as benign,malignant or undetermined FLLs by conventional ultrasound.Emax of FLLs and the periphery of FLLs was measured using 2D-SWE and compared between benign and malignant FLLs or among different pathological types of malignant FLLs.RESULTS The study included 32 benign FLLs in 31 patients and 100 malignant FLLs in 96 patients,including 16 cholangiocellular carcinomas(CCCs),72 hepatocellular carcinomas(HCCs)and 12 liver metastases.Thirty-five FLLs were diagnosed as undetermined by conventional ultrasound.There were significant differences between Emax of malignant(2.21±0.57 m/s)and benign(1.59±0.37 m/s)FLLs(P=0.000),and between Emax of the periphery of malignant(1.52±0.39 m/s)and benign(1.36±0.44 m/s)FLLs(P=0.040).Emax of liver metastases(2.73±0.99 m/s)was significantly higher than that of CCCs(2.14±0.34 m/s)and HCCs(2.14±0.46 m/s)(P=0.002).The sensitivity,specificity and accuracy were 71.00%,84.38%and 74.24%respectively,using Emax>1.905 m/s(AUC 0.843)to diagnose as malignant and 23 of 35(65.74%)FLLs with undetermined diagnosis by conventional ultrasound were diagnosed correctly.CONCLUSION Malignant FLLs were stiffer than benign ones and liver metastases were stiffer than primary liver carcinomas.2D-SWE with Emax was a useful complement to conventional ultrasound for the differential diagnosis of FLLs.展开更多
Objective： To establish and optimize the two-demensional electrophoresis maps of uterine leiomyoma and to study the difference of global protein patterns between uterine leiomyoma and normal myometrium. Methods： Usi...Objective： To establish and optimize the two-demensional electrophoresis maps of uterine leiomyoma and to study the difference of global protein patterns between uterine leiomyoma and normal myometrium. Methods： Using Two-dimensional electrophoresis followed by computer-assisted image analysis, the differential proteins between uterine leiomyoma and normal myometrium were compared. Results： The well-resolved and reproducible two-dimensional gel electrophoresis patterns of uterine leiomyoma and normal myometrium were established. Totally 1085±108 and 1103±151 protein spots were obtained by using the pH 4-7 IPG strips in uterine leiomyoma and normal myometrium map, respectively, of which 7 spots increased and 15 spots decreased in quantity in uterine leiomyoma compared with normal myometrium. Conclusion： The differentially expressed proteins are useful for studying the mechanism of the cause of uterine leiomyoma.展开更多
Objective： To establish and optimize the two-dimensional gel electrophoresis （2-DE） maps of squamous carcinoma of the cervix and to study the protein difference between squamous carcinoma of the cervix （SCC） and ...Objective： To establish and optimize the two-dimensional gel electrophoresis （2-DE） maps of squamous carcinoma of the cervix and to study the protein difference between squamous carcinoma of the cervix （SCC） and normal cervical tissue. Methods： Using Two-dimensional gel electrophoresis followed by computer-assisted image analysis, the differential proteins between squamous carcinoma of the cervical tissue and normal cervical tissue were compared. Then using matrix-assisted laser desorption/ionization-time of flight mass spectrometry, the differential proteins were identified. Results： The well-resolved and reproducible two-dimensional gel electrophoresis patterns of squamous carcinoma of the cervix tissue and normal cervical tissue were obtained. After silver staining, the average matching ratio of squamous carcinoma of the cervix was 86.1%. There was a good reproducibility of spot position in 2-DE map, with average deviation in IEF direction of 0.95±0.13 mm, while in SDS-PAGE direction it was 1.20±0.18 mm. Ten protein spots were identified by mass spectrometry, some of which were involved in cell proliferation, cell apoptosis, intracellular enzymes, structural proteins, cycle regulation, and tumor occurrence. Conclusion： The differentially expressed proteins provide a fundamental basis for further study of human squamous carcinoma of the cervix and screening of its specific markers.展开更多
This paper is concerned with the oscillation behavior of solution of the second order linear differential system u'= p(t)v,v'=-q(t)u,some sufficient conditions are given to improve some results in [1] where{p}...This paper is concerned with the oscillation behavior of solution of the second order linear differential system u'= p(t)v,v'=-q(t)u,some sufficient conditions are given to improve some results in [1] where{p},{q} :[0,+∞) → [0+∞) are locally summable functions.展开更多
The static behavior of piezoelectric circular spherical shallow shells under both electrical and mechanical loads is studied by using the differential quadrature element method (DQEM). Geometrical nonlinearity effect ...The static behavior of piezoelectric circular spherical shallow shells under both electrical and mechanical loads is studied by using the differential quadrature element method (DQEM). Geometrical nonlinearity effect is considered. Detailed formulations and procedures are given for the first time. Several examples are analyzed and accurate results are obtained by the DQEM. Based on the results in this paper, one may conclude that the DQEM is a useful tool for obtaining solutions of structural elements. It can be seen that the shell shape may be theore tically controlled and snap through may occur when the applied voltage reaches a critical value even without mechanical load for certain geometric configurations.展开更多
This paper deals with the numerical solution of initial value problems for systems of differential equations with a delay argument. The numerical stability of a linear multistep method is investigated by analysing the...This paper deals with the numerical solution of initial value problems for systems of differential equations with a delay argument. The numerical stability of a linear multistep method is investigated by analysing the solution of the lest equation y’(t)=Ay(t) + By(1-t),where A,B denote constant complex N×N-matrices,and t】0.We investigate carefully the characterization of the stability region.展开更多
In this article, the authors study the growth of certain second order linear differential equation f″＋A（z）f′＋B（z）f=0 and give precise estimates for the hyperorder of solutions of infinite order. Under similar ...In this article, the authors study the growth of certain second order linear differential equation f″＋A（z）f′＋B（z）f=0 and give precise estimates for the hyperorder of solutions of infinite order. Under similar conditions, higher order differential equations will be considered.展开更多
Assume that the fundamental solution matrix U (t, s ) of x’(t)=L(t, x,) satisfies |U(t,s)|≤Ke-e(t-s) for t≥s.If|(t,φ)|≤δ|φ(0)|with δ【a/K, then the fundamental solution matrix of the perturbed equation x’(t)=...Assume that the fundamental solution matrix U (t, s ) of x’(t)=L(t, x,) satisfies |U(t,s)|≤Ke-e(t-s) for t≥s.If|(t,φ)|≤δ|φ(0)|with δ【a/K, then the fundamental solution matrix of the perturbed equation x’(t)=L(t,x,)+(t ,x,) also possesses similar exponential estimate. For α=0, a similar result is given.展开更多
This paper deals with the stability of linear multistep methods for multidimensional differential systems with distributed delays. The delay-dependent stability of linear multistep methods with compound quadrature rul...This paper deals with the stability of linear multistep methods for multidimensional differential systems with distributed delays. The delay-dependent stability of linear multistep methods with compound quadrature rules is studied. Several new sufficient criteria of delay-dependent stability are obtained by means of the argument principle. An algorithm is provided to check delay-dependent stability. An example that illustrates the effectiveness of the derived theoretical results is given.展开更多
This paper studies a bounded discriminating domain for hybrid linear differential game with two players and two targets using viability theory. First of all, we prove that the convex hull of a closed set is also a dis...This paper studies a bounded discriminating domain for hybrid linear differential game with two players and two targets using viability theory. First of all, we prove that the convex hull of a closed set is also a discriminating domain if the set is a discriminating domain. Secondly, in order to determine that a bounded polyhedron is a discriminating domain, we give a result that it only needs to verify that the extreme points of the polyhedron meet the viability conditions. The difference between our result and the existing ones is that our result just needs to verify the finite points （extreme points） and the existing ones need to verify all points in the bounded polyhedron.展开更多
The measurements and analysis of deformation of engineering structures such as dams, bridges and high-rise buildings are important tasks for civil engineers. It is evident that, all civil engineering structures are su...The measurements and analysis of deformation of engineering structures such as dams, bridges and high-rise buildings are important tasks for civil engineers. It is evident that, all civil engineering structures are susceptible for deterioration over a period of time. Bridges in particular, deteriorate due to loading conditions, environmental changes, earth movement, material used during construction, age and corrosion of steel. Continuous monitoring of such structure is the most important aspect as it provides quantitative information, assesses the state of the structure, detects unsafe positions and proposes early safety measures to be taken before it can threaten the safety of vehicles, goods and human life. Despite government’s efforts to construct roads and highways, bridge deformation monitoring has not been given priority in most of African countries and ultimately causes some bridges to collapse unexpectedly. The purpose of this research is to integrate Global Positioning System (GPS) and Linear Variable Differential Transducers (LVDT) to monitor deformation of a bridge. The horizontal positions of reference and monitoring points were determined using Global Positioning System (GPS) while the vertical deflections, accelerations and strain were determined using Linear Variable Differential Transducers (LVDT). The maximum displacements obtained between zero and first epochs in x, y and z components were 0.798 m, at point LT08, 0.865 m at point BR13, and 0.56 m at point LT02 respectively. The maximum deflections for LVDT 1, 2 and 3 are 28.563 mm, 31.883 mm and 40.926 mm respectively. Finally, the correlation coefficient for the observations was 0.679 with standard deviations of 0.0168 and 0.0254 in x and y respectively. Our results identified some slight displacements in horizontal components at the bridge.展开更多
The main purpose of this article is to study the existence theories of global meromorphic solutions for some second-order linear differential equations with meromorphic coefficients, which perfect the solution theory ...The main purpose of this article is to study the existence theories of global meromorphic solutions for some second-order linear differential equations with meromorphic coefficients, which perfect the solution theory of such equations.展开更多
In this paper, we investigate the growth of solutions of higher order linear differential equations with meromorphic coefficients. Under certain conditions, we obtain precise estimation of growth order and hyper-order...In this paper, we investigate the growth of solutions of higher order linear differential equations with meromorphic coefficients. Under certain conditions, we obtain precise estimation of growth order and hyper-order of solutions of the equation.展开更多
The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was a...The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was analysed for the solution of the generalized system of linear neutral test equations, After the establishment of a sufficient condition for asymptotic stability of the solutions of the generalized system, it is shown that a linear multistep method is NGP(G)-stable if and only if it is A-stable.展开更多
A discrete differential evolution algorithm combined with the branch and bound method is developed to solve the integer linear bilevel programming problems, in which both upper level and lower level variables are forc...A discrete differential evolution algorithm combined with the branch and bound method is developed to solve the integer linear bilevel programming problems, in which both upper level and lower level variables are forced to be integer. An integer coding for upper level variables is adopted, and then a discrete differential evolution algorithm with an improved feasibility-based comparison is developed to directly explore the integer solution at the upper level. For a given upper level integer variable, the lower level integer programming problem is solved by the existing branch and bound algorithm to obtain the optimal integer solution at the lower level. In the same framework of the algorithm, two other constraint handling methods, i.e. the penalty function method and the feasibility-based comparison method are also tested. The experimental results demonstrate that the discrete differential evolution algorithm with different constraint handling methods is effective in finding the global optimal integer solutions, but the improved constraint handling method performs better than two compared constraint handling methods.展开更多
In this paper, the principle techinique of the differentiator method, and some examples using the method to obtain the general solution and special solution of the differential equation are introduced. The essential d...In this paper, the principle techinique of the differentiator method, and some examples using the method to obtain the general solution and special solution of the differential equation are introduced. The essential difference between this method and the others is that by this method special and general solutions can be obtained directly with the operations of the differentor in the differential equation and without the enlightenment of other scientific knowledge.展开更多
This article discusses the problems on the existence of meromorphic solutions of some higher order linear differential equations with meromorphic coefficients. Some nice results are obtained. And these results perfect...This article discusses the problems on the existence of meromorphic solutions of some higher order linear differential equations with meromorphic coefficients. Some nice results are obtained. And these results perfect the complex oscillation theory of meromorphic solutions of linear differential equations.展开更多
In this paper, we give some sufficient conditions of the instability for the fourth order linear differential equation with varied coefficient, at least one of the characteristic roots of which has positive real part,...In this paper, we give some sufficient conditions of the instability for the fourth order linear differential equation with varied coefficient, at least one of the characteristic roots of which has positive real part, by means of Liapunov's second method.展开更多
This paper deals with the stability analysis of the linear multistep (LM) methods in the numerical solution of delay differential equations. Here we provide a qualitative stability estimates, pertiment to the classica...This paper deals with the stability analysis of the linear multistep (LM) methods in the numerical solution of delay differential equations. Here we provide a qualitative stability estimates, pertiment to the classical scalar test problem of the form y′(t)=λy(t)+μy(t-τ) with τ>0 and λ,μ are complex, by using (vartiant to) the resolvent condition of Kreiss. We prove that for A stable LM methods the upper bound for the norm of the n th power of square matrix grows linearly with the order of the matrix.展开更多
文摘In this paper,a robust and consistent COVID-19 emergency decision-making approach is proposed based on q-rung linear diophantine fuzzy set(q-RLDFS),differential evolutionary(DE)optimization principles,and evidential reasoning(ER)methodology.The proposed approach uses q-RLDFS in order to represent the evaluating values of the alternatives corresponding to the attributes.DE optimization is used to obtain the optimal weights of the attributes,and ER methodology is used to compute the aggregated q-rung linear diophantine fuzzy values(q-RLDFVs)of each alternative.Then the score values of alternatives are computed based on the aggregated q-RLDFVs.An alternative with the maximum score value is selected as a better one.The applicability of the proposed approach has been illustrated in COVID-19 emergency decision-making system and sustainable energy planning management.Moreover,we have validated the proposed approach with a numerical example.Finally,a comparative study is provided with the existing models,where the proposed approach is found to be robust to perform better and consistent in uncertain environments.
基金Supported by Natural Science Foundation of Shanghai of China,No.19ZR1441500,No.22ZR1458200Science Research Foundation of Shanghai Municipal Health Commission,No.202140378Key Program of Science and Technology Commission Foundation of Changning,Shanghai,China,No.CNKW2020Z04.
文摘BACKGROUND The clinical management and prognosis differ between benign and malignant solid focal liver lesions(FLLs),as well as among different pathological types of malignant FLLs.Accurate diagnosis of the possible types of solid FLLs is important.Our previous study confirmed the value of shear wave elastography(SWE)using maximal elasticity(Emax)as the parameter in the differential diagnosis between benign and malignant FLLs.However,the value of SWE in the differential diagnosis among different pathological types of malignant FLLs has not been proved.AIM To explore the value of two-dimensional SWE(2D-SWE)using Emax in the differential diagnosis of FLLs,especially among different pathological types of malignant FLLs.METHODS All the patients enrolled in this study were diagnosed as benign,malignant or undetermined FLLs by conventional ultrasound.Emax of FLLs and the periphery of FLLs was measured using 2D-SWE and compared between benign and malignant FLLs or among different pathological types of malignant FLLs.RESULTS The study included 32 benign FLLs in 31 patients and 100 malignant FLLs in 96 patients,including 16 cholangiocellular carcinomas(CCCs),72 hepatocellular carcinomas(HCCs)and 12 liver metastases.Thirty-five FLLs were diagnosed as undetermined by conventional ultrasound.There were significant differences between Emax of malignant(2.21±0.57 m/s)and benign(1.59±0.37 m/s)FLLs(P=0.000),and between Emax of the periphery of malignant(1.52±0.39 m/s)and benign(1.36±0.44 m/s)FLLs(P=0.040).Emax of liver metastases(2.73±0.99 m/s)was significantly higher than that of CCCs(2.14±0.34 m/s)and HCCs(2.14±0.46 m/s)(P=0.002).The sensitivity,specificity and accuracy were 71.00%,84.38%and 74.24%respectively,using Emax>1.905 m/s(AUC 0.843)to diagnose as malignant and 23 of 35(65.74%)FLLs with undetermined diagnosis by conventional ultrasound were diagnosed correctly.CONCLUSION Malignant FLLs were stiffer than benign ones and liver metastases were stiffer than primary liver carcinomas.2D-SWE with Emax was a useful complement to conventional ultrasound for the differential diagnosis of FLLs.
基金This work was supported byTechnological Developing Committee of Wenzhou(No.Y2004A044).
文摘Objective： To establish and optimize the two-demensional electrophoresis maps of uterine leiomyoma and to study the difference of global protein patterns between uterine leiomyoma and normal myometrium. Methods： Using Two-dimensional electrophoresis followed by computer-assisted image analysis, the differential proteins between uterine leiomyoma and normal myometrium were compared. Results： The well-resolved and reproducible two-dimensional gel electrophoresis patterns of uterine leiomyoma and normal myometrium were established. Totally 1085±108 and 1103±151 protein spots were obtained by using the pH 4-7 IPG strips in uterine leiomyoma and normal myometrium map, respectively, of which 7 spots increased and 15 spots decreased in quantity in uterine leiomyoma compared with normal myometrium. Conclusion： The differentially expressed proteins are useful for studying the mechanism of the cause of uterine leiomyoma.
基金the National Natural Science Foundation of China (No.30700195)grant from Science and Technology Project of Wenzhou (No.Y2005A038)
文摘Objective： To establish and optimize the two-dimensional gel electrophoresis （2-DE） maps of squamous carcinoma of the cervix and to study the protein difference between squamous carcinoma of the cervix （SCC） and normal cervical tissue. Methods： Using Two-dimensional gel electrophoresis followed by computer-assisted image analysis, the differential proteins between squamous carcinoma of the cervical tissue and normal cervical tissue were compared. Then using matrix-assisted laser desorption/ionization-time of flight mass spectrometry, the differential proteins were identified. Results： The well-resolved and reproducible two-dimensional gel electrophoresis patterns of squamous carcinoma of the cervix tissue and normal cervical tissue were obtained. After silver staining, the average matching ratio of squamous carcinoma of the cervix was 86.1%. There was a good reproducibility of spot position in 2-DE map, with average deviation in IEF direction of 0.95±0.13 mm, while in SDS-PAGE direction it was 1.20±0.18 mm. Ten protein spots were identified by mass spectrometry, some of which were involved in cell proliferation, cell apoptosis, intracellular enzymes, structural proteins, cycle regulation, and tumor occurrence. Conclusion： The differentially expressed proteins provide a fundamental basis for further study of human squamous carcinoma of the cervix and screening of its specific markers.
基金Project supported by Hunan provincial Natural Science Foundation of China(07JJ6006).
文摘This paper is concerned with the oscillation behavior of solution of the second order linear differential system u'= p(t)v,v'=-q(t)u,some sufficient conditions are given to improve some results in [1] where{p},{q} :[0,+∞) → [0+∞) are locally summable functions.
文摘The static behavior of piezoelectric circular spherical shallow shells under both electrical and mechanical loads is studied by using the differential quadrature element method (DQEM). Geometrical nonlinearity effect is considered. Detailed formulations and procedures are given for the first time. Several examples are analyzed and accurate results are obtained by the DQEM. Based on the results in this paper, one may conclude that the DQEM is a useful tool for obtaining solutions of structural elements. It can be seen that the shell shape may be theore tically controlled and snap through may occur when the applied voltage reaches a critical value even without mechanical load for certain geometric configurations.
文摘This paper deals with the numerical solution of initial value problems for systems of differential equations with a delay argument. The numerical stability of a linear multistep method is investigated by analysing the solution of the lest equation y’(t)=Ay(t) + By(1-t),where A,B denote constant complex N×N-matrices,and t】0.We investigate carefully the characterization of the stability region.
基金the National Natural Science Foundation of China(10161006,10571044)the Natural Science Foundation of Guangdong Prov(06025059)
文摘In this article, the authors study the growth of certain second order linear differential equation f″＋A（z）f′＋B（z）f=0 and give precise estimates for the hyperorder of solutions of infinite order. Under similar conditions, higher order differential equations will be considered.
基金Research supported by China National Science Foundation
文摘Assume that the fundamental solution matrix U (t, s ) of x’(t)=L(t, x,) satisfies |U(t,s)|≤Ke-e(t-s) for t≥s.If|(t,φ)|≤δ|φ(0)|with δ【a/K, then the fundamental solution matrix of the perturbed equation x’(t)=L(t,x,)+(t ,x,) also possesses similar exponential estimate. For α=0, a similar result is given.
基金Project supported by the National Natural Science Foundation of China(No.11471217)
文摘This paper deals with the stability of linear multistep methods for multidimensional differential systems with distributed delays. The delay-dependent stability of linear multistep methods with compound quadrature rules is studied. Several new sufficient criteria of delay-dependent stability are obtained by means of the argument principle. An algorithm is provided to check delay-dependent stability. An example that illustrates the effectiveness of the derived theoretical results is given.
基金supported by National Science Foundation of China(11171221)Doctoral Program Foundation of Institutions of Higher Education of China(20123120110004)+2 种基金Natural Science Foundation of Shanghai(14ZR1429200)Innovation Program of Shanghai Municipal Education Commission(15ZZ073)Key Research Project Plan of Institutions of Higher of Henan Province(17A120010)
文摘This paper studies a bounded discriminating domain for hybrid linear differential game with two players and two targets using viability theory. First of all, we prove that the convex hull of a closed set is also a discriminating domain if the set is a discriminating domain. Secondly, in order to determine that a bounded polyhedron is a discriminating domain, we give a result that it only needs to verify that the extreme points of the polyhedron meet the viability conditions. The difference between our result and the existing ones is that our result just needs to verify the finite points （extreme points） and the existing ones need to verify all points in the bounded polyhedron.
文摘The measurements and analysis of deformation of engineering structures such as dams, bridges and high-rise buildings are important tasks for civil engineers. It is evident that, all civil engineering structures are susceptible for deterioration over a period of time. Bridges in particular, deteriorate due to loading conditions, environmental changes, earth movement, material used during construction, age and corrosion of steel. Continuous monitoring of such structure is the most important aspect as it provides quantitative information, assesses the state of the structure, detects unsafe positions and proposes early safety measures to be taken before it can threaten the safety of vehicles, goods and human life. Despite government’s efforts to construct roads and highways, bridge deformation monitoring has not been given priority in most of African countries and ultimately causes some bridges to collapse unexpectedly. The purpose of this research is to integrate Global Positioning System (GPS) and Linear Variable Differential Transducers (LVDT) to monitor deformation of a bridge. The horizontal positions of reference and monitoring points were determined using Global Positioning System (GPS) while the vertical deflections, accelerations and strain were determined using Linear Variable Differential Transducers (LVDT). The maximum displacements obtained between zero and first epochs in x, y and z components were 0.798 m, at point LT08, 0.865 m at point BR13, and 0.56 m at point LT02 respectively. The maximum deflections for LVDT 1, 2 and 3 are 28.563 mm, 31.883 mm and 40.926 mm respectively. Finally, the correlation coefficient for the observations was 0.679 with standard deviations of 0.0168 and 0.0254 in x and y respectively. Our results identified some slight displacements in horizontal components at the bridge.
基金Supported by the National Natural Science Foundation of China(11101096 )Guangdong Natural Science Foundation (S2012010010376, S201204006711)
文摘The main purpose of this article is to study the existence theories of global meromorphic solutions for some second-order linear differential equations with meromorphic coefficients, which perfect the solution theory of such equations.
文摘In this paper, we investigate the growth of solutions of higher order linear differential equations with meromorphic coefficients. Under certain conditions, we obtain precise estimation of growth order and hyper-order of solutions of the equation.
文摘The stability analysis of linear multistep methods for the numerical solutions of the systems of generalized neutral delay differential equations is discussed. The stability behaviour of linear multistep methods was analysed for the solution of the generalized system of linear neutral test equations, After the establishment of a sufficient condition for asymptotic stability of the solutions of the generalized system, it is shown that a linear multistep method is NGP(G)-stable if and only if it is A-stable.
基金supported by the Natural Science Basic Research Plan in Shaanxi Province of China(2013JM1022)the Fundamental Research Funds for the Central Universities(K50511700004)
文摘A discrete differential evolution algorithm combined with the branch and bound method is developed to solve the integer linear bilevel programming problems, in which both upper level and lower level variables are forced to be integer. An integer coding for upper level variables is adopted, and then a discrete differential evolution algorithm with an improved feasibility-based comparison is developed to directly explore the integer solution at the upper level. For a given upper level integer variable, the lower level integer programming problem is solved by the existing branch and bound algorithm to obtain the optimal integer solution at the lower level. In the same framework of the algorithm, two other constraint handling methods, i.e. the penalty function method and the feasibility-based comparison method are also tested. The experimental results demonstrate that the discrete differential evolution algorithm with different constraint handling methods is effective in finding the global optimal integer solutions, but the improved constraint handling method performs better than two compared constraint handling methods.
文摘In this paper, the principle techinique of the differentiator method, and some examples using the method to obtain the general solution and special solution of the differential equation are introduced. The essential difference between this method and the others is that by this method special and general solutions can be obtained directly with the operations of the differentor in the differential equation and without the enlightenment of other scientific knowledge.
基金supported by the National Natural Science Foundation of China (11101096)
文摘This article discusses the problems on the existence of meromorphic solutions of some higher order linear differential equations with meromorphic coefficients. Some nice results are obtained. And these results perfect the complex oscillation theory of meromorphic solutions of linear differential equations.
基金Provincial Science and Technology Foundation of Guizhou
文摘In this paper, we give some sufficient conditions of the instability for the fourth order linear differential equation with varied coefficient, at least one of the characteristic roots of which has positive real part, by means of Liapunov's second method.
文摘This paper deals with the stability analysis of the linear multistep (LM) methods in the numerical solution of delay differential equations. Here we provide a qualitative stability estimates, pertiment to the classical scalar test problem of the form y′(t)=λy(t)+μy(t-τ) with τ>0 and λ,μ are complex, by using (vartiant to) the resolvent condition of Kreiss. We prove that for A stable LM methods the upper bound for the norm of the n th power of square matrix grows linearly with the order of the matrix.
