In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality o...In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality of the Lagrangian function with respect to the primary variables of the problem, decomposes the solution process into two independent ones, in which the primary variables are solved for independently, and then the secondary variables, which are the Lagrange multipliers, are solved for, afterward. This is an innovation that leads to solving independently two simpler systems of equations involving the primary variables only, on one hand, and the secondary ones on the other. Solutions obtained for small sized problems (as preliminary test of the method) demonstrate that the new method is generally effective in producing the required solutions.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
The sulfide-based solid-state electrolytes(SEs)reactivity toward moisture and Li-metal are huge barriers that impede their large-scale manufactu ring and applications in all-solid-state lithium batteries(ASSLBs).Herei...The sulfide-based solid-state electrolytes(SEs)reactivity toward moisture and Li-metal are huge barriers that impede their large-scale manufactu ring and applications in all-solid-state lithium batteries(ASSLBs).Herein,we proposed an Al and O dual-doped strategy for Li_(3)PS_(4)SE to regulate the chemical/electrochemical stability of anionic PS_(4)^(3-)tetrahedra to mitigate structural hydrolysis and parasitic reactions at the SE/Li interface.The optimized Li_(3.08)A_(10.04)P_(0.96)S_(3.92)O_(0.08)SE presents the highestσLi+of 3.27 mS cm^(-1),which is~6.8 times higher than the pristine Li_(3)PS_(4)and excellently inhibits the structural hydrolysis for~25 min@25%humidity at RT.DFT calculations confirmed that the enhanced chemical stability was revealed to the intrinsically stable entities,e.g.,POS33-units.Moreover,Li_(3.08)Al_(0.04)P_(0.96)S_(3.92)O_(0.08)SE cycled stably in Li//Li symmetric cell over 1000 h@0.1 mA cm^(-2)/0.1 mA h cm^(-2),could be revealed to Li-Al alloy and Li_(2)Oat SE/Li interface impeding the growth of Li-dendrites during cycling.Resultantly,LNO@LCO/Li_(3.08)Al_(0.04)P_(0.96)S_(3.92)O_(0.08)/Li-In cell delivered initial discharge capacities of 129.8 mA h g^(-1)and 83.74%capacity retention over 300 cycles@0.2 C at RT.Moreover,the Li_(3.08)Al_(0.04)P_(0.96)S_(3.92)O_(0.08)SE presented>90%capacity retention over 200 and 300 cycles when the cell was tested with LiNi_(0.8)Co_(0.15)Al_(0.05)O_(2)(NCA)cathode material vs.5 and 10 mg cm^(-2)@RT.展开更多
We study some approximation properties of Lagrange interpolation polynomial based on the zeros of （1-x^2）cosnarccosx. By using a decomposition for f（x） ∈ C^τC^τ＋1 we obtain an estimate of ‖f（x） -Ln＋2（f, ...We study some approximation properties of Lagrange interpolation polynomial based on the zeros of （1-x^2）cosnarccosx. By using a decomposition for f（x） ∈ C^τC^τ＋1 we obtain an estimate of ‖f（x） -Ln＋2（f, x）‖ which reflects the influence of the position of the x＇s and ω（f^（r＋1）,δ）j,j = 0, 1,... , s,on the error of approximation.展开更多
This paper solves the two dimensional linear Fredholm integral equations of the second kind by combining the meshless barycentric Lagrange interpolation functions and the Gauss-Legendre quadrature formula. Inspired by...This paper solves the two dimensional linear Fredholm integral equations of the second kind by combining the meshless barycentric Lagrange interpolation functions and the Gauss-Legendre quadrature formula. Inspired by this thought, we convert the equations into the associated algebraic equations. The results of the numerical examples are given to illustrate that the approximated method is feasible and efficient.展开更多
This paper deals with the description and the representation of polynomials defined over n-simplices, The polynomials are computed by using two recurrent schemes: the Neville-Aitken one for the Lagrange interpolating ...This paper deals with the description and the representation of polynomials defined over n-simplices, The polynomials are computed by using two recurrent schemes: the Neville-Aitken one for the Lagrange interpolating operator and the De Casteljau one for the Bernstein-Bezier approximating operator. Both schemes fall intothe framework of transformations of the form where the F iare given numbers (forexample, at the initial step they coincide with the values of the function on a given lattice), and the coefficients (x) are linear polynomials valued in x and x is fixed. A general theory for such sequence of transformations can be found in [2] where it is also proved that these tranformations are completely characterized in term of a linear functional, reference functional. This functional is associated with a linear space., characteristic space.The concepts of reference functionals and characteristic spaces will be used and we shall prove the existence of a characteristic space for the reference functional: associated with these operators.展开更多
文摘In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality of the Lagrangian function with respect to the primary variables of the problem, decomposes the solution process into two independent ones, in which the primary variables are solved for independently, and then the secondary variables, which are the Lagrange multipliers, are solved for, afterward. This is an innovation that leads to solving independently two simpler systems of equations involving the primary variables only, on one hand, and the secondary ones on the other. Solutions obtained for small sized problems (as preliminary test of the method) demonstrate that the new method is generally effective in producing the required solutions.
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).
基金supported by the National Natural Science Foundation of China(Nos.21203008,21975025,12274025)the Hainan Province Science and Technology Special Fund(Nos.ZDYF2021SHFZ232,ZDYF2023GXJS022)the Hainan Province Postdoctoral Science Foundation(No.300333)。
文摘The sulfide-based solid-state electrolytes(SEs)reactivity toward moisture and Li-metal are huge barriers that impede their large-scale manufactu ring and applications in all-solid-state lithium batteries(ASSLBs).Herein,we proposed an Al and O dual-doped strategy for Li_(3)PS_(4)SE to regulate the chemical/electrochemical stability of anionic PS_(4)^(3-)tetrahedra to mitigate structural hydrolysis and parasitic reactions at the SE/Li interface.The optimized Li_(3.08)A_(10.04)P_(0.96)S_(3.92)O_(0.08)SE presents the highestσLi+of 3.27 mS cm^(-1),which is~6.8 times higher than the pristine Li_(3)PS_(4)and excellently inhibits the structural hydrolysis for~25 min@25%humidity at RT.DFT calculations confirmed that the enhanced chemical stability was revealed to the intrinsically stable entities,e.g.,POS33-units.Moreover,Li_(3.08)Al_(0.04)P_(0.96)S_(3.92)O_(0.08)SE cycled stably in Li//Li symmetric cell over 1000 h@0.1 mA cm^(-2)/0.1 mA h cm^(-2),could be revealed to Li-Al alloy and Li_(2)Oat SE/Li interface impeding the growth of Li-dendrites during cycling.Resultantly,LNO@LCO/Li_(3.08)Al_(0.04)P_(0.96)S_(3.92)O_(0.08)/Li-In cell delivered initial discharge capacities of 129.8 mA h g^(-1)and 83.74%capacity retention over 300 cycles@0.2 C at RT.Moreover,the Li_(3.08)Al_(0.04)P_(0.96)S_(3.92)O_(0.08)SE presented>90%capacity retention over 200 and 300 cycles when the cell was tested with LiNi_(0.8)Co_(0.15)Al_(0.05)O_(2)(NCA)cathode material vs.5 and 10 mg cm^(-2)@RT.
基金Supported by the National Nature Science Foundation.
文摘We study some approximation properties of Lagrange interpolation polynomial based on the zeros of （1-x^2）cosnarccosx. By using a decomposition for f（x） ∈ C^τC^τ＋1 we obtain an estimate of ‖f（x） -Ln＋2（f, x）‖ which reflects the influence of the position of the x＇s and ω（f^（r＋1）,δ）j,j = 0, 1,... , s,on the error of approximation.
文摘This paper solves the two dimensional linear Fredholm integral equations of the second kind by combining the meshless barycentric Lagrange interpolation functions and the Gauss-Legendre quadrature formula. Inspired by this thought, we convert the equations into the associated algebraic equations. The results of the numerical examples are given to illustrate that the approximated method is feasible and efficient.
文摘This paper deals with the description and the representation of polynomials defined over n-simplices, The polynomials are computed by using two recurrent schemes: the Neville-Aitken one for the Lagrange interpolating operator and the De Casteljau one for the Bernstein-Bezier approximating operator. Both schemes fall intothe framework of transformations of the form where the F iare given numbers (forexample, at the initial step they coincide with the values of the function on a given lattice), and the coefficients (x) are linear polynomials valued in x and x is fixed. A general theory for such sequence of transformations can be found in [2] where it is also proved that these tranformations are completely characterized in term of a linear functional, reference functional. This functional is associated with a linear space., characteristic space.The concepts of reference functionals and characteristic spaces will be used and we shall prove the existence of a characteristic space for the reference functional: associated with these operators.
