扩充设计在生物制药,化学化工等领域运用广泛。Gao在2020年构造了一类范围固定二三混水平扩充设计。本文从设计的均匀性角度出发,研究了范围固定水平扩充设计在可卷型L2-偏差下的均匀型。首先建立水平扩充设计的可卷型L2-偏差与二水平...扩充设计在生物制药,化学化工等领域运用广泛。Gao在2020年构造了一类范围固定二三混水平扩充设计。本文从设计的均匀性角度出发,研究了范围固定水平扩充设计在可卷型L2-偏差下的均匀型。首先建立水平扩充设计的可卷型L2-偏差与二水平基石设计的相遇数之间的解析联系,并获得其下界。其次基于距离分布和字长型模式分别建立水平扩充设计与基石设计之间的解析联系。最后通过数值例子解释所获得理论结果。Augmented designs are widely applied in biological pharmacy, chemistry and chemical engineering, and so on. Gao constructed a class of range-fixed level-augmented designs in 2020. The article, starting from the perspective of design uniformity, investigates the uniformity of range-fixed level-augmented designs under the condition of wrap L2-discrepancy. Firstly, the analytical connection between the wrap L2-discrepancy of the range-fixed level-augmented designs of mixed two and three levels and the coincidence number of the footstone-designs with two levels is established, and its lower bound is obtained. Secondly, based on distance distribution and wordlength pattern, the analytical connections between the level-augmented designs and the footstone-designs are built respectively. Finally, the obtained theoretical results are explained by some numerical examples.展开更多
The Bingham fluid model has been successfully used in modeling a large class of non-Newtonian fluids. In this paper, the authors extend to the case of Bingham fluids the results previously obtained by Chipot and Marda...The Bingham fluid model has been successfully used in modeling a large class of non-Newtonian fluids. In this paper, the authors extend to the case of Bingham fluids the results previously obtained by Chipot and Mardare, who studied the asymptotics of the Stokes flow in a cylindrical domain that becomes unbounded in one direction, and prove the convergence of the solution to the Bingham problem in a finite periodic domain, to the solution of the Bingham problem in the infinite periodic domain, as the length of the finite domain goes to infinity. As a consequence of this convergence, the existence of a solution to a Bingham problem in the infinite periodic domain is obtained, and the uniqueness of the velocity field for this problem is also shown. Finally, they show that the error in approximating the velocity field in the infinite domain with the velocity in a periodic domain of length 2l has a polynomial decay in , unlike in the Stokes case （see [Chipot, M. and Mardare, S., Asymptotic behaviour of the Stokes problem in cylinders becoming unbounded in one direction, Journal de Mathgmatiques Pures et Appliqudes, 90（2）, 2008, 133-159]） where it has an exponential decay. This is in itself an important result for the numerical simulations of non-Newtonian flows in long tubes.展开更多
文摘扩充设计在生物制药,化学化工等领域运用广泛。Gao在2020年构造了一类范围固定二三混水平扩充设计。本文从设计的均匀性角度出发,研究了范围固定水平扩充设计在可卷型L2-偏差下的均匀型。首先建立水平扩充设计的可卷型L2-偏差与二水平基石设计的相遇数之间的解析联系,并获得其下界。其次基于距离分布和字长型模式分别建立水平扩充设计与基石设计之间的解析联系。最后通过数值例子解释所获得理论结果。Augmented designs are widely applied in biological pharmacy, chemistry and chemical engineering, and so on. Gao constructed a class of range-fixed level-augmented designs in 2020. The article, starting from the perspective of design uniformity, investigates the uniformity of range-fixed level-augmented designs under the condition of wrap L2-discrepancy. Firstly, the analytical connection between the wrap L2-discrepancy of the range-fixed level-augmented designs of mixed two and three levels and the coincidence number of the footstone-designs with two levels is established, and its lower bound is obtained. Secondly, based on distance distribution and wordlength pattern, the analytical connections between the level-augmented designs and the footstone-designs are built respectively. Finally, the obtained theoretical results are explained by some numerical examples.
基金supported by the University of Rouen and the Fédération Normandie Mathématiques, respectively
文摘The Bingham fluid model has been successfully used in modeling a large class of non-Newtonian fluids. In this paper, the authors extend to the case of Bingham fluids the results previously obtained by Chipot and Mardare, who studied the asymptotics of the Stokes flow in a cylindrical domain that becomes unbounded in one direction, and prove the convergence of the solution to the Bingham problem in a finite periodic domain, to the solution of the Bingham problem in the infinite periodic domain, as the length of the finite domain goes to infinity. As a consequence of this convergence, the existence of a solution to a Bingham problem in the infinite periodic domain is obtained, and the uniqueness of the velocity field for this problem is also shown. Finally, they show that the error in approximating the velocity field in the infinite domain with the velocity in a periodic domain of length 2l has a polynomial decay in , unlike in the Stokes case （see [Chipot, M. and Mardare, S., Asymptotic behaviour of the Stokes problem in cylinders becoming unbounded in one direction, Journal de Mathgmatiques Pures et Appliqudes, 90（2）, 2008, 133-159]） where it has an exponential decay. This is in itself an important result for the numerical simulations of non-Newtonian flows in long tubes.
