A formulation of a differential equation as projection and fixed point pi-Mem alloivs approximations using general piecnvise functions. We prone existence and uniqueness of the up proximate solution* convergence in th...A formulation of a differential equation as projection and fixed point pi-Mem alloivs approximations using general piecnvise functions. We prone existence and uniqueness of the up proximate solution* convergence in the L2 norm and nodal supercnnvergence. These results generalize those obtained earlier by Hulme for continuous piecevjise polynomials and by Delfour-Dubeau for discontinuous pieceuiise polynomials. A duality relationship for the two types of approximations is also given.展开更多
The Cauchy problem for some parabolic fractional partial differential equation of higher orders and with time delays is considered. The existence and unique solution of this problem is studied. Some smoothness propert...The Cauchy problem for some parabolic fractional partial differential equation of higher orders and with time delays is considered. The existence and unique solution of this problem is studied. Some smoothness properties with respect to the parameters of these delay fractional differential equations are considered.展开更多
The aim of this paper is to get the decomposition of distributional derivatives of functions with bounded variation in the framework of Carnot-Caratheodory spaces (C-C spaces in brievity) in which the vector fields ar...The aim of this paper is to get the decomposition of distributional derivatives of functions with bounded variation in the framework of Carnot-Caratheodory spaces (C-C spaces in brievity) in which the vector fields are of Carnot type. For this purpose the approximate continuity of BV functions is discussed first, then approximate differentials of L1 functions are defined in the case that vector fields are of Carnot type and finally the decomposition Xu = (?)u ·Ln + X2 u is proved, where u ∈ BVx(?) and (Ω)u denotes the approximate differential of u.展开更多
This paper establishes the following pointwise result for simultancous Lagrange imterpolating approxima- tion:,then |f^(k)(x)-P_n^(k)(f,x)|=O(1)△_n^(q-k)(x)ω where P_n(f,x)is the Lagrange interpolating potynomial of...This paper establishes the following pointwise result for simultancous Lagrange imterpolating approxima- tion:,then |f^(k)(x)-P_n^(k)(f,x)|=O(1)△_n^(q-k)(x)ω where P_n(f,x)is the Lagrange interpolating potynomial of deereeon the nodes X_nUY_n(see the definition of the next).展开更多
Free convection of a viscous electrically conducting liquid past a vertical stretching surface is investigated in the presence of a transverse magnetic field.Natural convection is driven by both thermal and solutal bu...Free convection of a viscous electrically conducting liquid past a vertical stretching surface is investigated in the presence of a transverse magnetic field.Natural convection is driven by both thermal and solutal buoyancy.The original partial differential equations governing the problem are turned into a set of ordinary differential equations through a similar variables transformation.This alternate set of equations is solved through a Differential Transform Method(DTM)and the Pade approximation.The response of the considered physical system to the non-dimensional parameters accounting for the relative importance of different effects is assessed considering different situations.展开更多
This paper deals with the approximate controllability of semilinear neutral functional differential systems with state-dependent delay. The fractional power theory and α-norm are used to discuss the problem so that t...This paper deals with the approximate controllability of semilinear neutral functional differential systems with state-dependent delay. The fractional power theory and α-norm are used to discuss the problem so that the obtained results can apply to the systems involving derivatives of spatial variables. By methods of functional analysis and semigroup theory, sufficient conditions of approximate controllability are formulated and proved. Finally, an example is provided to illustrate the applications of the obtained results.展开更多
The Lin-Reissner-Tsien equation describes unsteady transonic flows under the transonic approximation. In the present paper, the equation is reduced to an ordinary differential equation via a similarity transformation....The Lin-Reissner-Tsien equation describes unsteady transonic flows under the transonic approximation. In the present paper, the equation is reduced to an ordinary differential equation via a similarity transformation. The resulting equation is then solved analytically and even exactly in some cases. Numerical simulations are provided for the cases in which there is no exact solution. Travelling wave solutions are also obtained.展开更多
Let ξn-1<ξn-2 <ξn-2 <… < ξ1 be the zeros of the the (n -1)-th Legendre polynomial Pn-1(x) and - 1 = xn < xn-1 <… < x1 = 1 the zeros of the polynomial W n(x) =- n(n - 1) Pn-1(t)dt = (1 -x2)P&...Let ξn-1<ξn-2 <ξn-2 <… < ξ1 be the zeros of the the (n -1)-th Legendre polynomial Pn-1(x) and - 1 = xn < xn-1 <… < x1 = 1 the zeros of the polynomial W n(x) =- n(n - 1) Pn-1(t)dt = (1 -x2)P'n-1(x). By the theory of the inverse Pal-Type interpolation, for a function f(x) ∈ C[-1 1], there exists a unique polynomial Rn(x) of degree 2n - 2 (if n is even) satisfying conditions Rn(f,ξk) = f(∈ek)(1≤ k≤ n - 1) ;R'n(f,xk) = f'(xk)(1≤ k≤ n). This paper discusses the simultaneous approximation to a differentiable function f by inverse Pal-Type interpolation polynomial {Rn(f,x)} (n is even) and the main result of this paper is that if f ∈ C'[1,1], r≥2, n≥ + 2> and n is even thenholds uniformly for all x ∈ [- 1,1], where h(x) = 1 +展开更多
A robust SQP method, which is analogous to Facchinei’s algorithm, is introduced. The algorithm is globally convergent. It uses automatic rules for choosing penalty parameter, and can efficiently cope with the possibl...A robust SQP method, which is analogous to Facchinei’s algorithm, is introduced. The algorithm is globally convergent. It uses automatic rules for choosing penalty parameter, and can efficiently cope with the possible inconsistency of the quadratic search subproblem. In addition, the algorithm employs a differentiable approximate exact penalty function as a merit function. Unlike the merit function in Facchinei’s algorithm, which is quite complicated and is not easy to be implemented in practice, this new merit function is very simple. As a result, we can use the Facchinei’s idea to construct an algorithm which is easy to be implemented in practice.展开更多
Abstract We study the fleet size and mix vehicle routing problem with constraints on the capacity of each vehicle. The objective is to minimize the total cost including fixed utilization cost of vehicles and traveling...Abstract We study the fleet size and mix vehicle routing problem with constraints on the capacity of each vehicle. The objective is to minimize the total cost including fixed utilization cost of vehicles and traveling cost by vehicles. We give differential approximation algorithms for the fleet size and mix vehicle routing problem （FSMVRP） with two kinds of vehicles, the capacities of which are respectively nlk and n2k, n2 〉 nl ≥ 1, k ≥ 1. Using existing theories for vehicle routing problems and feature of the algorithms represented in the paper, we also prove that the algorithms give（1-6n＋3/（n＋1）2k＋n＋1）differential approximation ratio for （k, nk） VRP, n 〉 1and （1-6n2＋3n/n1k＋n2k）2k）differential approximation ratio for （nlk, n2k）VRP, n2 〉 nl 〉 1.展开更多
A 14-bit low power self-timed differential successive approximation（SAR） ADC with an on-chip multisegment bandgap reference（BGR） is described.An on-chip multi-segment BGR,which has a temperature coefficient of 1.3...A 14-bit low power self-timed differential successive approximation（SAR） ADC with an on-chip multisegment bandgap reference（BGR） is described.An on-chip multi-segment BGR,which has a temperature coefficient of 1.3 ppm/℃and a thermal drift of about 100μV over the temperature range of -40 to 120℃is implemented to provide a high precision reference voltage for the SAR ADC.The Gray code form is utilized instead of binary form mode control to reduce substrate noise and enhance the linearity of the whole system.Self-timed bit-cycling is adopted to enhance the time efficiency.The 14-bit ADC was fabricated in a TSMC 0.13μm CMOS process. With the on-chip BGR,the SAR ADC achieves an SNDR of 81.2 dB（13.2 ENOB） and an SFDR of 85.2 dB with a conversion rate of 2 MS/s at room temperature and can keep an ENOB of more than 12 bits at a conversion rate of 2 MS/s over the temperature range from -40 to 120℃.展开更多
In this study, a collocation technique is presented for approximate solution of the fractional-order logistic population model. Actually, we develop the Bessel collocation method by using the fractional derivative in ...In this study, a collocation technique is presented for approximate solution of the fractional-order logistic population model. Actually, we develop the Bessel collocation method by using the fractional derivative in the Caputo sense to obtain the approximate solutions of this model problem. By means of the fractional derivative in the Caputo sense, the collocation points, the Bessel functions of the first kind, the method transforms the model problem into a system of nonlinear algebraic equations. Numerical applications are given to demonstrate efficiency and accuracy of the method. In applications, the reliability of the scheme is shown by the error function based on the accuracy of the approximate solution.展开更多
基金This research has been supported in part by the Natural Sciences and Engineering Research Council of Canada(Grant OGPIN-336)and by the"Ministere de l'Education du Quebec"(FCAR Grant-ER-0725)
文摘A formulation of a differential equation as projection and fixed point pi-Mem alloivs approximations using general piecnvise functions. We prone existence and uniqueness of the up proximate solution* convergence in the L2 norm and nodal supercnnvergence. These results generalize those obtained earlier by Hulme for continuous piecevjise polynomials and by Delfour-Dubeau for discontinuous pieceuiise polynomials. A duality relationship for the two types of approximations is also given.
文摘The Cauchy problem for some parabolic fractional partial differential equation of higher orders and with time delays is considered. The existence and unique solution of this problem is studied. Some smoothness properties with respect to the parameters of these delay fractional differential equations are considered.
文摘The aim of this paper is to get the decomposition of distributional derivatives of functions with bounded variation in the framework of Carnot-Caratheodory spaces (C-C spaces in brievity) in which the vector fields are of Carnot type. For this purpose the approximate continuity of BV functions is discussed first, then approximate differentials of L1 functions are defined in the case that vector fields are of Carnot type and finally the decomposition Xu = (?)u ·Ln + X2 u is proved, where u ∈ BVx(?) and (Ω)u denotes the approximate differential of u.
基金The second named author was supported in part by an NSERC Postdoctoral Fellowship,Canada and a CR F Grant,University of Alberta
文摘This paper establishes the following pointwise result for simultancous Lagrange imterpolating approxima- tion:,then |f^(k)(x)-P_n^(k)(f,x)|=O(1)△_n^(q-k)(x)ω where P_n(f,x)is the Lagrange interpolating potynomial of deereeon the nodes X_nUY_n(see the definition of the next).
文摘Free convection of a viscous electrically conducting liquid past a vertical stretching surface is investigated in the presence of a transverse magnetic field.Natural convection is driven by both thermal and solutal buoyancy.The original partial differential equations governing the problem are turned into a set of ordinary differential equations through a similar variables transformation.This alternate set of equations is solved through a Differential Transform Method(DTM)and the Pade approximation.The response of the considered physical system to the non-dimensional parameters accounting for the relative importance of different effects is assessed considering different situations.
基金supported by the National Natural Science Foundation of China(Nos.11171110,11371087)the Science and Technology Commission of Shanghai Municipality(No.13dz2260400)the Shanghai Leading Academic Discipline Project(No.B407)
文摘This paper deals with the approximate controllability of semilinear neutral functional differential systems with state-dependent delay. The fractional power theory and α-norm are used to discuss the problem so that the obtained results can apply to the systems involving derivatives of spatial variables. By methods of functional analysis and semigroup theory, sufficient conditions of approximate controllability are formulated and proved. Finally, an example is provided to illustrate the applications of the obtained results.
文摘The Lin-Reissner-Tsien equation describes unsteady transonic flows under the transonic approximation. In the present paper, the equation is reduced to an ordinary differential equation via a similarity transformation. The resulting equation is then solved analytically and even exactly in some cases. Numerical simulations are provided for the cases in which there is no exact solution. Travelling wave solutions are also obtained.
文摘Let ξn-1<ξn-2 <ξn-2 <… < ξ1 be the zeros of the the (n -1)-th Legendre polynomial Pn-1(x) and - 1 = xn < xn-1 <… < x1 = 1 the zeros of the polynomial W n(x) =- n(n - 1) Pn-1(t)dt = (1 -x2)P'n-1(x). By the theory of the inverse Pal-Type interpolation, for a function f(x) ∈ C[-1 1], there exists a unique polynomial Rn(x) of degree 2n - 2 (if n is even) satisfying conditions Rn(f,ξk) = f(∈ek)(1≤ k≤ n - 1) ;R'n(f,xk) = f'(xk)(1≤ k≤ n). This paper discusses the simultaneous approximation to a differentiable function f by inverse Pal-Type interpolation polynomial {Rn(f,x)} (n is even) and the main result of this paper is that if f ∈ C'[1,1], r≥2, n≥ + 2> and n is even thenholds uniformly for all x ∈ [- 1,1], where h(x) = 1 +
基金This research is supportedin part by the National Natural Science Foundation ofChina(Grant No. 39830070).
文摘A robust SQP method, which is analogous to Facchinei’s algorithm, is introduced. The algorithm is globally convergent. It uses automatic rules for choosing penalty parameter, and can efficiently cope with the possible inconsistency of the quadratic search subproblem. In addition, the algorithm employs a differentiable approximate exact penalty function as a merit function. Unlike the merit function in Facchinei’s algorithm, which is quite complicated and is not easy to be implemented in practice, this new merit function is very simple. As a result, we can use the Facchinei’s idea to construct an algorithm which is easy to be implemented in practice.
基金supported by the project of Central University Basic Research Fund(HEUCF150903)the project of the major research task,institute of Policy and Management,Chinese Academy of Sciences(Y201181z01)the National Natural Science Foundation of China(71273072)
文摘Abstract We study the fleet size and mix vehicle routing problem with constraints on the capacity of each vehicle. The objective is to minimize the total cost including fixed utilization cost of vehicles and traveling cost by vehicles. We give differential approximation algorithms for the fleet size and mix vehicle routing problem （FSMVRP） with two kinds of vehicles, the capacities of which are respectively nlk and n2k, n2 〉 nl ≥ 1, k ≥ 1. Using existing theories for vehicle routing problems and feature of the algorithms represented in the paper, we also prove that the algorithms give（1-6n＋3/（n＋1）2k＋n＋1）differential approximation ratio for （k, nk） VRP, n 〉 1and （1-6n2＋3n/n1k＋n2k）2k）differential approximation ratio for （nlk, n2k）VRP, n2 〉 nl 〉 1.
文摘A 14-bit low power self-timed differential successive approximation（SAR） ADC with an on-chip multisegment bandgap reference（BGR） is described.An on-chip multi-segment BGR,which has a temperature coefficient of 1.3 ppm/℃and a thermal drift of about 100μV over the temperature range of -40 to 120℃is implemented to provide a high precision reference voltage for the SAR ADC.The Gray code form is utilized instead of binary form mode control to reduce substrate noise and enhance the linearity of the whole system.Self-timed bit-cycling is adopted to enhance the time efficiency.The 14-bit ADC was fabricated in a TSMC 0.13μm CMOS process. With the on-chip BGR,the SAR ADC achieves an SNDR of 81.2 dB（13.2 ENOB） and an SFDR of 85.2 dB with a conversion rate of 2 MS/s at room temperature and can keep an ENOB of more than 12 bits at a conversion rate of 2 MS/s over the temperature range from -40 to 120℃.
文摘In this study, a collocation technique is presented for approximate solution of the fractional-order logistic population model. Actually, we develop the Bessel collocation method by using the fractional derivative in the Caputo sense to obtain the approximate solutions of this model problem. By means of the fractional derivative in the Caputo sense, the collocation points, the Bessel functions of the first kind, the method transforms the model problem into a system of nonlinear algebraic equations. Numerical applications are given to demonstrate efficiency and accuracy of the method. In applications, the reliability of the scheme is shown by the error function based on the accuracy of the approximate solution.
