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
Natural hay pastures in semi-arid pastoral areas produce the highest yields of hay in northern China.However, long-term continuous hay harvesting with no rest interval has resulted in severe degradation across widespr...Natural hay pastures in semi-arid pastoral areas produce the highest yields of hay in northern China.However, long-term continuous hay harvesting with no rest interval has resulted in severe degradation across widespread areas of these natural hay pastures. In addition, no clear data exist on the spatial distribution or degree of degradation occurring in natural hay pastures primarily because a nationally unified and normative evaluation standard is lacking. In view of the above problems, we employed an analytic hierarchy process to carry out screening and accuracy validation of evaluation indicators for natural hay pastures in north China grasslands(temperate meadow steppes, temperate steppes, mountain meadows, and lowland meadows). Our study identified seven easily measured indicators that reflect the state of natural hay pastures(average height, aboveground biomass, coverage, proportion of medium grasses, litter biomass, proportion of degradation-indicative plants, and proportion of bare spots and saline-alkali spots). A five-level scoring method was employed to delineate the threshold range for these indicators, The results of this study show that this method effectively solved the technical bottleneck for graded evaluation of degradation in natural hay pastures. This provides a theoretical basis for the scientific assessment of natural hay pasture degradation as well as important technical support for sustainable use of natural hay pastures and livestock production.展开更多
The author constructs unitary intertwiners for degenerate C*-algebraic universal principal series of SL(n + 1) over a local field by explicitely normalizing standard intertwining integrals at the level of Hilbert modu...The author constructs unitary intertwiners for degenerate C*-algebraic universal principal series of SL(n + 1) over a local field by explicitely normalizing standard intertwining integrals at the level of Hilbert modules.展开更多
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.
基金National Key Research and Development Program of China(2017YFC0503805,2016YFC0500603,2017YFE0104500)China Agriculture Research System(CARS-34)National Nonprofit Institute Research Grant of CAAS(821-32)
文摘Natural hay pastures in semi-arid pastoral areas produce the highest yields of hay in northern China.However, long-term continuous hay harvesting with no rest interval has resulted in severe degradation across widespread areas of these natural hay pastures. In addition, no clear data exist on the spatial distribution or degree of degradation occurring in natural hay pastures primarily because a nationally unified and normative evaluation standard is lacking. In view of the above problems, we employed an analytic hierarchy process to carry out screening and accuracy validation of evaluation indicators for natural hay pastures in north China grasslands(temperate meadow steppes, temperate steppes, mountain meadows, and lowland meadows). Our study identified seven easily measured indicators that reflect the state of natural hay pastures(average height, aboveground biomass, coverage, proportion of medium grasses, litter biomass, proportion of degradation-indicative plants, and proportion of bare spots and saline-alkali spots). A five-level scoring method was employed to delineate the threshold range for these indicators, The results of this study show that this method effectively solved the technical bottleneck for graded evaluation of degradation in natural hay pastures. This provides a theoretical basis for the scientific assessment of natural hay pasture degradation as well as important technical support for sustainable use of natural hay pastures and livestock production.
文摘The author constructs unitary intertwiners for degenerate C*-algebraic universal principal series of SL(n + 1) over a local field by explicitely normalizing standard intertwining integrals at the level of Hilbert modules.
