In this paper we apply fractional calculus to solve the 3rd order ordinary differential equation of the following form: (z-a)(z-b)(z-c)φ 3+(βz 2+γz+D)φ 2+(α(2β-3α-3)z+αγ+α(α+1)(a+b+c))φ 1+α(α-...In this paper we apply fractional calculus to solve the 3rd order ordinary differential equation of the following form: (z-a)(z-b)(z-c)φ 3+(βz 2+γz+D)φ 2+(α(2β-3α-3)z+αγ+α(α+1)(a+b+c))φ 1+α(α-1)(β-2α-2)φ=f.展开更多
The global stability problem of Takagi-Sugeno（T-S） fuzzy Hopfield neural networks（FHNNs） with time delays is investigated.Novel LMI-based stability criteria are obtained by using Lyapunov functional theory to guar...The global stability problem of Takagi-Sugeno（T-S） fuzzy Hopfield neural networks（FHNNs） with time delays is investigated.Novel LMI-based stability criteria are obtained by using Lyapunov functional theory to guarantee the asymptotic stability of the FHNNs with less conservatism.Firstly,using both Finsler＇s lemma and an improved homogeneous matrix polynomial technique,and applying an affine parameter-dependent Lyapunov-Krasovskii functional,we obtain the convergent LMI-based stability criteria.Algebraic properties of the fuzzy membership functions in the unit simplex are considered in the process of stability analysis via the homogeneous matrix polynomials technique.Secondly,to further reduce the conservatism,a new right-hand-side slack variables introducing technique is also proposed in terms of LMIs,which is suitable to the homogeneous matrix polynomials setting.Finally,two illustrative examples are given to show the efficiency of the proposed approaches.展开更多
By use of Hopfield model and basis solution of homogeneous linear equations which are established in accordance with consistent state, a practical decision method for the existence of optimal Hopfield model of combina...By use of Hopfield model and basis solution of homogeneous linear equations which are established in accordance with consistent state, a practical decision method for the existence of optimal Hopfield model of combinational circuits is provided. Finally, an example is given.展开更多
In this paper, we improve the algorithm and rewrite the function make- Pairing for computing a Gorni-Zampieri pair of a homogeneous polynomial map. As an application, some counterexamples to PLDP （dependence problem ...In this paper, we improve the algorithm and rewrite the function make- Pairing for computing a Gorni-Zampieri pair of a homogeneous polynomial map. As an application, some counterexamples to PLDP （dependence problem for power lin- car maps） are obtained, including one in the lowest dimension （n = 48） in all suchcounterexamples one has found up to now.展开更多
In this parer, applications of the fractional calculus to the form (Az 2+Bz+C)ψ 2+(Dz+G)ψ 1+Eψ=f and the partial differential equation 2μz 2(Az 2+Bz+C)+(Dz+G)μz+δμ(z,t)=M 2μT 2+NμT, where ψ 1...In this parer, applications of the fractional calculus to the form (Az 2+Bz+C)ψ 2+(Dz+G)ψ 1+Eψ=f and the partial differential equation 2μz 2(Az 2+Bz+C)+(Dz+G)μz+δμ(z,t)=M 2μT 2+NμT, where ψ 1= d ψ d z and ψ 2= d 2ψ d z 2 are presented.展开更多
To develop a larger in-line plasma enhanced chemical vapor deposition(PECVD)device,the length of the linear microwave plasma source needs to be increased to 1550 mm.This paper proposes a solution to the problem of pla...To develop a larger in-line plasma enhanced chemical vapor deposition(PECVD)device,the length of the linear microwave plasma source needs to be increased to 1550 mm.This paper proposes a solution to the problem of plasma inhomogeneity caused by increasing device length.Based on the COMSOL Multiphysics,a multi-physics field coupling model for in-line PECVD device is developed and validated.The effects of microwave power,chamber pressure,and magnetic flux density on the plasma distribution are investigated,respectively,and their corresponding optimized values are obtained.This paper also presents a new strategy to optimize the wafer position to achieve the balance between deposition rate and film quality.Numerical results have indicated that increasing microwave power and magnetic flux density or decreasing chamber pressure all play positive roles in improving plasma homogeneity,and among them,the microwave power is the most decisive influencing factor.It is found that the plasma homogeneity is optimal under the condition of microwave power at 2000 W,chamber pressure at 15 Pa,and magnetic field strength at 45 mT.The relative deviation is within−3.7%to 3.9%,which fully satisfies the process requirements of the equipment.The best position for the wafer is 88 mm from the copper antenna.The results are very valuable for improving the quality of the in-line PECVD device.展开更多
The discrete complex cubic Ginzburg-Landau equation is an important model to describe a number of physical systems such as Taylor and frustrated vortices in hydrodynamics and semiconductor laser arrays in optics. In t...The discrete complex cubic Ginzburg-Landau equation is an important model to describe a number of physical systems such as Taylor and frustrated vortices in hydrodynamics and semiconductor laser arrays in optics. In this paper, the exact solutions of the discrete complex cubic Ginzburg-Landau equation are derived using homogeneous balance principle and the GI/G-expansion method, and the linear stability of exact solutions is discussed.展开更多
The mechanical behavior of geomaterials is studied using an XFEM （extended finite element method）. Usually, the modeling of such heterogeneous material is performed either through an analytical homogenization approa...The mechanical behavior of geomaterials is studied using an XFEM （extended finite element method）. Usually, the modeling of such heterogeneous material is performed either through an analytical homogenization approach, or numerically, especially for complex microstructures. For comparison, the effective properties are obtained using a classical finite element analysis （through the so-called unit cell method） and an analytical homogenization approach. The use of XFEM proposed here retains the accuracy oftbe classical finite element approach, allowing one to use meshes that do not necessarily match the physical boundaries of the material constituents. Thanks to such methods, it is then possible to study materials with complex microstructures that have non-simplified assumptions commonly used by other methods, as well as quantify the impact of such simplification. The versatility of XFEM in dealing with complex microstructures, including polycrystalline-like microstructures, is also shown through the role of shape inclusions on the overall effective properties o fan argillite rock. Voronoi representation is used to describe the complex microstructure of argillite.展开更多
文摘In this paper we apply fractional calculus to solve the 3rd order ordinary differential equation of the following form: (z-a)(z-b)(z-c)φ 3+(βz 2+γz+D)φ 2+(α(2β-3α-3)z+αγ+α(α+1)(a+b+c))φ 1+α(α-1)(β-2α-2)φ=f.
基金Project supported by the National Natural Science Foundation of China (Grant No. 60974004)the Natural Science Foundation of Jilin Province,China (Grant No. 201115222)
文摘The global stability problem of Takagi-Sugeno（T-S） fuzzy Hopfield neural networks（FHNNs） with time delays is investigated.Novel LMI-based stability criteria are obtained by using Lyapunov functional theory to guarantee the asymptotic stability of the FHNNs with less conservatism.Firstly,using both Finsler＇s lemma and an improved homogeneous matrix polynomial technique,and applying an affine parameter-dependent Lyapunov-Krasovskii functional,we obtain the convergent LMI-based stability criteria.Algebraic properties of the fuzzy membership functions in the unit simplex are considered in the process of stability analysis via the homogeneous matrix polynomials technique.Secondly,to further reduce the conservatism,a new right-hand-side slack variables introducing technique is also proposed in terms of LMIs,which is suitable to the homogeneous matrix polynomials setting.Finally,two illustrative examples are given to show the efficiency of the proposed approaches.
基金Sate Education Committee's Doctoral Fund under GRANT 3961403National"Eighth Five-Year"Key Project under GRANT 85-703-02-03
文摘By use of Hopfield model and basis solution of homogeneous linear equations which are established in accordance with consistent state, a practical decision method for the existence of optimal Hopfield model of combinational circuits is provided. Finally, an example is given.
基金The"985 Project"and"211 Project"of Jilin Universitythe Basis Scientific Research Fund(200903286)of Ministry of Education of China+1 种基金the NSF(11126044,11071097)of ChinaShandong Postdoctoral Science Foundation(201003054),Innovation Program
文摘In this paper, we improve the algorithm and rewrite the function make- Pairing for computing a Gorni-Zampieri pair of a homogeneous polynomial map. As an application, some counterexamples to PLDP （dependence problem for power lin- car maps） are obtained, including one in the lowest dimension （n = 48） in all suchcounterexamples one has found up to now.
文摘In this parer, applications of the fractional calculus to the form (Az 2+Bz+C)ψ 2+(Dz+G)ψ 1+Eψ=f and the partial differential equation 2μz 2(Az 2+Bz+C)+(Dz+G)μz+δμ(z,t)=M 2μT 2+NμT, where ψ 1= d ψ d z and ψ 2= d 2ψ d z 2 are presented.
基金by Hunan Provincial Science and Technology Department'Key Field Research and Development Project'(No.2019WK2011)。
文摘To develop a larger in-line plasma enhanced chemical vapor deposition(PECVD)device,the length of the linear microwave plasma source needs to be increased to 1550 mm.This paper proposes a solution to the problem of plasma inhomogeneity caused by increasing device length.Based on the COMSOL Multiphysics,a multi-physics field coupling model for in-line PECVD device is developed and validated.The effects of microwave power,chamber pressure,and magnetic flux density on the plasma distribution are investigated,respectively,and their corresponding optimized values are obtained.This paper also presents a new strategy to optimize the wafer position to achieve the balance between deposition rate and film quality.Numerical results have indicated that increasing microwave power and magnetic flux density or decreasing chamber pressure all play positive roles in improving plasma homogeneity,and among them,the microwave power is the most decisive influencing factor.It is found that the plasma homogeneity is optimal under the condition of microwave power at 2000 W,chamber pressure at 15 Pa,and magnetic field strength at 45 mT.The relative deviation is within−3.7%to 3.9%,which fully satisfies the process requirements of the equipment.The best position for the wafer is 88 mm from the copper antenna.The results are very valuable for improving the quality of the in-line PECVD device.
基金Supported in part by the Basic Science and the Front Technology Research Foundation of Henan Province of China under Grant No.092300410179the Doctoral Scientific Research Foundation of Henan University of Science and Technology under Grant No.09001204
文摘The discrete complex cubic Ginzburg-Landau equation is an important model to describe a number of physical systems such as Taylor and frustrated vortices in hydrodynamics and semiconductor laser arrays in optics. In this paper, the exact solutions of the discrete complex cubic Ginzburg-Landau equation are derived using homogeneous balance principle and the GI/G-expansion method, and the linear stability of exact solutions is discussed.
文摘The mechanical behavior of geomaterials is studied using an XFEM （extended finite element method）. Usually, the modeling of such heterogeneous material is performed either through an analytical homogenization approach, or numerically, especially for complex microstructures. For comparison, the effective properties are obtained using a classical finite element analysis （through the so-called unit cell method） and an analytical homogenization approach. The use of XFEM proposed here retains the accuracy oftbe classical finite element approach, allowing one to use meshes that do not necessarily match the physical boundaries of the material constituents. Thanks to such methods, it is then possible to study materials with complex microstructures that have non-simplified assumptions commonly used by other methods, as well as quantify the impact of such simplification. The versatility of XFEM in dealing with complex microstructures, including polycrystalline-like microstructures, is also shown through the role of shape inclusions on the overall effective properties o fan argillite rock. Voronoi representation is used to describe the complex microstructure of argillite.
