This paper investigates the properties of solutions to a quasilinear parabolic system with nonlocal boundary conditions and localized sources. Conditions for the existence of global or blow-up solutions are given. Glo...This paper investigates the properties of solutions to a quasilinear parabolic system with nonlocal boundary conditions and localized sources. Conditions for the existence of global or blow-up solutions are given. Global blow-up property and blow- up rate estimates are also derived.展开更多
We study boundary value problems for fractional integro-differential equations involving Caputo derivative of order α∈ （n-1, n） in Banach spaces. Existence and uniqueness results of solutions are established by vi...We study boundary value problems for fractional integro-differential equations involving Caputo derivative of order α∈ （n-1, n） in Banach spaces. Existence and uniqueness results of solutions are established by virtue of the Holder＇s inequality, a suitable singular Cronwall＇s inequality and fixed point theorem via a priori estimate method. At last, examples are given to illustrate the results.展开更多
Non-equilibrium molecular dynamics （MD） method was performed to simulate the thermal transporta- tion process in graphene nanoribbons （GNRs）. A convenient way was conceived to introduce tilt grain boundaries （GBs...Non-equilibrium molecular dynamics （MD） method was performed to simulate the thermal transporta- tion process in graphene nanoribbons （GNRs）. A convenient way was conceived to introduce tilt grain boundaries （GBs） into the graphene lattice by repetitive removing C atom rows along certain directions. Comprehensive MD simulations reveal that larger-angle GBs are effective thermal barriers and substantially reduce the average thermal conductivity of GNRs. The GB thermal conductivity is ~ 10 W-m-1 .K-l for a bicrystal GNR with a misorientation of 21.8%, which is -97 % less than that of a prefect GNR with the same size. The total thermal resistance has a monotonic dependence on the den- sity of the 5-7 defects along the GBs. A theoretical model is proposed to capture this relation and resolve the contribu- tions by both the reduction in the phonon mean free path and the defect-induced thermal resistance.展开更多
The bounds on the discrepancy of approximate solutions constructed by Gedunov's scheme to IVP of isentropic equations of gas dynamics are obtained, Three well-knowu results obtained by Lax for shock waves with sma...The bounds on the discrepancy of approximate solutions constructed by Gedunov's scheme to IVP of isentropic equations of gas dynamics are obtained, Three well-knowu results obtained by Lax for shock waves with small jumps for general quasilinear hyperbolic systems of conservation laws are extended to shock waves for isentropic equations of gas dynamics in a bounded invariant region with ρ=0 as one of boundries of the region. Two counterexamples are given to show that two iuequalities given by Godunov do not hold for all rational numbers γ∈(1, 3]. It seems that the approach by Godunov to obtain the forementioned bounds may not be possible.展开更多
Aiming at the flexible flowshop group scheduling problem,taking sequence dependent setup time and machine skipping into account, a mathematical model for minimizing makespan is established,and a hybrid differential ev...Aiming at the flexible flowshop group scheduling problem,taking sequence dependent setup time and machine skipping into account, a mathematical model for minimizing makespan is established,and a hybrid differential evolution( HDE) algorithm based on greedy constructive procedure( GCP) is proposed,which combines differential evolution( DE) with tabu search( TS). DE is applied to generating the elite individuals of population,while TS is used for finding the optimal value by making perturbation in selected elite individuals. A lower bounding technique is developed to evaluate the quality of proposed algorithm. Experimental results verify the effectiveness and feasibility of proposed algorithm.展开更多
This paper presents an interpolation-based method(IBM)for approximating some trigonometric functions or their integrals as well.It provides two-sided bounds for each function,which also achieves much better approximat...This paper presents an interpolation-based method(IBM)for approximating some trigonometric functions or their integrals as well.It provides two-sided bounds for each function,which also achieves much better approximation effects than those of prevailing methods.In principle,the IBM can be applied for bounding more bounded smooth functions and their integrals as well,and its applications include approximating the integral of sin(x)/x function and improving the famous square root inequalities.展开更多
The state estimation strategy using the smooth variable structure filter （SVSF） is based on the variable structure and sliding mode concepts. As presented in its standard form with a fixed boundary layer limit, the ...The state estimation strategy using the smooth variable structure filter （SVSF） is based on the variable structure and sliding mode concepts. As presented in its standard form with a fixed boundary layer limit, the value of the boundary layer width is not precisely known at each step and may be selected based on a priori knowledge. The boundary layer width reflects the level of uncertainty in the model parameters and disturbance characteristics, where large values of the boundary layer width lead to robustness without optimality and small values of the boundary layer width provide optimality with poor robustness. As a solution and to overcome these limitations, an adaptive smoothing boundary layer is required to achieve greater robustness and suitable accuracy. This adapted value of the boundary layer width is obtained by minimizing the trace of the a posteriori covariance matrix. In this paper, the proposed new approach will be considered as another alternative to the extended Kalman filters （EKF）, nonlinear H∞ and standard SVSF-based data fusion techniques for the autonomous airborne navigation and self-localization problem. This alternative is based on strapdown inertial navigation system （SINS） and GPS data using the nonlinear SVSF with a covariance derivation and adaptive boundary layer width. Furthermore, the full mathematical model of the SINS/GPS navigation system considering the unmanned aerial vehicle （UAV） position, velocity and Euler angle as well as gyro and accelerometer biases will be used in this paper to estimate the airborne position and velocity with better accuracy.展开更多
基金The NSF(10771085)of Chinathe Key Lab of Symbolic Computation and Knowledge Engineering of Ministry of Educationthe 985 program of Jilin University and the Graduate Innovation Fund(20111034)of Jilin University
文摘This paper investigates the properties of solutions to a quasilinear parabolic system with nonlocal boundary conditions and localized sources. Conditions for the existence of global or blow-up solutions are given. Global blow-up property and blow- up rate estimates are also derived.
基金supported by Grant In Aid research fund of Virginia Military Instittue, USA
文摘We study boundary value problems for fractional integro-differential equations involving Caputo derivative of order α∈ （n-1, n） in Banach spaces. Existence and uniqueness results of solutions are established by virtue of the Holder＇s inequality, a suitable singular Cronwall＇s inequality and fixed point theorem via a priori estimate method. At last, examples are given to illustrate the results.
基金supported by Science Foundation of Chinese University(2011QNA4038)Scientific Research Fund of Zhe-jiang Provincial Education Department(Z200906194)Science and Technology Innovative Research Team of Zhejiang Province(2009R50010)
文摘Non-equilibrium molecular dynamics （MD） method was performed to simulate the thermal transporta- tion process in graphene nanoribbons （GNRs）. A convenient way was conceived to introduce tilt grain boundaries （GBs） into the graphene lattice by repetitive removing C atom rows along certain directions. Comprehensive MD simulations reveal that larger-angle GBs are effective thermal barriers and substantially reduce the average thermal conductivity of GNRs. The GB thermal conductivity is ~ 10 W-m-1 .K-l for a bicrystal GNR with a misorientation of 21.8%, which is -97 % less than that of a prefect GNR with the same size. The total thermal resistance has a monotonic dependence on the den- sity of the 5-7 defects along the GBs. A theoretical model is proposed to capture this relation and resolve the contribu- tions by both the reduction in the phonon mean free path and the defect-induced thermal resistance.
基金Project supported by National Natural Science Foundation of China.
文摘The bounds on the discrepancy of approximate solutions constructed by Gedunov's scheme to IVP of isentropic equations of gas dynamics are obtained, Three well-knowu results obtained by Lax for shock waves with small jumps for general quasilinear hyperbolic systems of conservation laws are extended to shock waves for isentropic equations of gas dynamics in a bounded invariant region with ρ=0 as one of boundries of the region. Two counterexamples are given to show that two iuequalities given by Godunov do not hold for all rational numbers γ∈(1, 3]. It seems that the approach by Godunov to obtain the forementioned bounds may not be possible.
基金Shanghai Municipal Natural Science Foundation of China(No.10ZR1431700)
文摘Aiming at the flexible flowshop group scheduling problem,taking sequence dependent setup time and machine skipping into account, a mathematical model for minimizing makespan is established,and a hybrid differential evolution( HDE) algorithm based on greedy constructive procedure( GCP) is proposed,which combines differential evolution( DE) with tabu search( TS). DE is applied to generating the elite individuals of population,while TS is used for finding the optimal value by making perturbation in selected elite individuals. A lower bounding technique is developed to evaluate the quality of proposed algorithm. Experimental results verify the effectiveness and feasibility of proposed algorithm.
基金Supported by the National Natural Science Foundation of China(61672009,61502130).
文摘This paper presents an interpolation-based method(IBM)for approximating some trigonometric functions or their integrals as well.It provides two-sided bounds for each function,which also achieves much better approximation effects than those of prevailing methods.In principle,the IBM can be applied for bounding more bounded smooth functions and their integrals as well,and its applications include approximating the integral of sin(x)/x function and improving the famous square root inequalities.
基金supported by the National Natural Science Foundation of China(No.61375082)
文摘The state estimation strategy using the smooth variable structure filter （SVSF） is based on the variable structure and sliding mode concepts. As presented in its standard form with a fixed boundary layer limit, the value of the boundary layer width is not precisely known at each step and may be selected based on a priori knowledge. The boundary layer width reflects the level of uncertainty in the model parameters and disturbance characteristics, where large values of the boundary layer width lead to robustness without optimality and small values of the boundary layer width provide optimality with poor robustness. As a solution and to overcome these limitations, an adaptive smoothing boundary layer is required to achieve greater robustness and suitable accuracy. This adapted value of the boundary layer width is obtained by minimizing the trace of the a posteriori covariance matrix. In this paper, the proposed new approach will be considered as another alternative to the extended Kalman filters （EKF）, nonlinear H∞ and standard SVSF-based data fusion techniques for the autonomous airborne navigation and self-localization problem. This alternative is based on strapdown inertial navigation system （SINS） and GPS data using the nonlinear SVSF with a covariance derivation and adaptive boundary layer width. Furthermore, the full mathematical model of the SINS/GPS navigation system considering the unmanned aerial vehicle （UAV） position, velocity and Euler angle as well as gyro and accelerometer biases will be used in this paper to estimate the airborne position and velocity with better accuracy.
