In this paper, the Adomian＇s decomposition method （ADM） is presented for finding the exact solutions of a more general biological population models. A new solution is constructed in power series. The fractional der...In this paper, the Adomian＇s decomposition method （ADM） is presented for finding the exact solutions of a more general biological population models. A new solution is constructed in power series. The fractional derivatives are described in the Caputo sense. To illustrate the reliability of the method, some examples are provided.展开更多
The kinetics of the decomposition of dimethylhexane-1,6-dicarbamate to 1,6-hexamethylene diisocyanate was studied. A consecutive reaction model was established and the reaction orders for the two steps were confirmed ...The kinetics of the decomposition of dimethylhexane-1,6-dicarbamate to 1,6-hexamethylene diisocyanate was studied. A consecutive reaction model was established and the reaction orders for the two steps were confirmed to be 1 and 1.3 by the integral test method and the numerical differential method, respectively. The activation energies of the two steps were （56.94 4±5.90） kJ·mol^-1 and （72.07±3.47） kJ·mol^-1 with the frequency factors exp（ 12.53±1.42） min^- 1 and （ 14.254±0.84） tool^-0.33. L^0.33·min^-1, respectively. Based on the kinetic model obtained, the progress of the reaction can be calculated under given conditions.展开更多
In this paper, we propose a new variation of the Adomian polynomials, which we call the degenerate Adomian polynomials, for the power series solutions of nonlinear ordinary differential equations with nonseparable non...In this paper, we propose a new variation of the Adomian polynomials, which we call the degenerate Adomian polynomials, for the power series solutions of nonlinear ordinary differential equations with nonseparable nonlinearities. We establish efficient algorithms for the degenerate Adomian polynomials. Next we compare the results by the Adomian decomposition method using the classic Adomian polynomials with the results by the Rach-Adomian-Meyers modified decomposition method incorporating the degenerate Adomian polynomials, which itself has been shown to be a confluence of the Adomian decomposition method and the power series method. Convergence acceleration techniques including the diagonal Pade approximants are considered, and new numeric algorithms for the multistage decomposition are deduced using the degenerate Adomian polynomials. Our new technique provides a significant advantage for automated calculations when computing the power series form of the solution for nonlinear ordinary differential equations. Several expository examples are investigated to demonstrate its reliability and efficiency.展开更多
It is widely known that the equation 2xx= has and only has two roots 0 and 1. Jiglevich A.B. and Petrov N. N. discovered that equation has two other roots, i.e. infinite place’s numbers (called super numbers): 821289...It is widely known that the equation 2xx= has and only has two roots 0 and 1. Jiglevich A.B. and Petrov N. N. discovered that equation has two other roots, i.e. infinite place’s numbers (called super numbers): 8212890625X=L and 1787109376Y=L, and obtained 4 (super number) roots of the equation2xx=. For progressing to wider conditions, with the way of exactly divisible and mutually orthogonal Latin squares, three attractive results are obtained: 1) A kind of polynomial 1()()niiPxxa==P-, ,1,2,,iain?KZ has and only has different n2 super number roots; 2) When n>2 and n 6, those n2 roots of the polynomial ()Px can be arranged in an n-order square matrix, of which n roots of every row and every column satisfy Vieta Formula of roots and coefficients; 3) In *Z ring of super number, the polynomial1()()niiPxxa==P-, ,1,2,,iain?KZ has n! different factorizations.展开更多
文摘In this paper, the Adomian＇s decomposition method （ADM） is presented for finding the exact solutions of a more general biological population models. A new solution is constructed in power series. The fractional derivatives are described in the Caputo sense. To illustrate the reliability of the method, some examples are provided.
基金the National Key Technology R&D Program(2013BAC11B03)the Knowledge Innovation Fund of Chinese Academy of Science(KGCX2-YW-215-2)the National Natural Science Foundation of China(21476244)
文摘The kinetics of the decomposition of dimethylhexane-1,6-dicarbamate to 1,6-hexamethylene diisocyanate was studied. A consecutive reaction model was established and the reaction orders for the two steps were confirmed to be 1 and 1.3 by the integral test method and the numerical differential method, respectively. The activation energies of the two steps were （56.94 4±5.90） kJ·mol^-1 and （72.07±3.47） kJ·mol^-1 with the frequency factors exp（ 12.53±1.42） min^- 1 and （ 14.254±0.84） tool^-0.33. L^0.33·min^-1, respectively. Based on the kinetic model obtained, the progress of the reaction can be calculated under given conditions.
文摘In this paper, we propose a new variation of the Adomian polynomials, which we call the degenerate Adomian polynomials, for the power series solutions of nonlinear ordinary differential equations with nonseparable nonlinearities. We establish efficient algorithms for the degenerate Adomian polynomials. Next we compare the results by the Adomian decomposition method using the classic Adomian polynomials with the results by the Rach-Adomian-Meyers modified decomposition method incorporating the degenerate Adomian polynomials, which itself has been shown to be a confluence of the Adomian decomposition method and the power series method. Convergence acceleration techniques including the diagonal Pade approximants are considered, and new numeric algorithms for the multistage decomposition are deduced using the degenerate Adomian polynomials. Our new technique provides a significant advantage for automated calculations when computing the power series form of the solution for nonlinear ordinary differential equations. Several expository examples are investigated to demonstrate its reliability and efficiency.
文摘It is widely known that the equation 2xx= has and only has two roots 0 and 1. Jiglevich A.B. and Petrov N. N. discovered that equation has two other roots, i.e. infinite place’s numbers (called super numbers): 8212890625X=L and 1787109376Y=L, and obtained 4 (super number) roots of the equation2xx=. For progressing to wider conditions, with the way of exactly divisible and mutually orthogonal Latin squares, three attractive results are obtained: 1) A kind of polynomial 1()()niiPxxa==P-, ,1,2,,iain?KZ has and only has different n2 super number roots; 2) When n>2 and n 6, those n2 roots of the polynomial ()Px can be arranged in an n-order square matrix, of which n roots of every row and every column satisfy Vieta Formula of roots and coefficients; 3) In *Z ring of super number, the polynomial1()()niiPxxa==P-, ,1,2,,iain?KZ has n! different factorizations.
