It is well known that resultant elimination is an effective method of solving multivariate polynomial equations. In this paper, instead of computing the target resultants via variable by variable elimination, the auth...It is well known that resultant elimination is an effective method of solving multivariate polynomial equations. In this paper, instead of computing the target resultants via variable by variable elimination, the authors combine multivariate implicit equation interpolation and multivariate resultant elimination to compute the reduced resultants, in which the technique of multivariate implicit equation interpolation is achieved by some high probability algorithms on multivariate polynomial interpolation and univariate rational function interpolation. As an application of resultant elimination, the authors illustrate the proposed algorithm on three well-known unsolved combinatorial geometric optimization problems. The experiments show that the proposed approach of resultant elimination is more efficient than some existing resultant elimination methods on these difficult problems.展开更多
Elimination theory is central in differential and difference algebra. The Wu-Ritt characteristic set method, the resultant and the Chow form are three fundamental tools in the elimination theory for algebraic differen...Elimination theory is central in differential and difference algebra. The Wu-Ritt characteristic set method, the resultant and the Chow form are three fundamental tools in the elimination theory for algebraic differential or difference equations. In this paper, the authors mainly present a survey of the existing work on the theory of characteristic set methods for differential and difference systems,the theory of differential Chow forms, and the theory of sparse differential and difference resultants.展开更多
This paper presents the stress resultants of hyperbolic paraboloidal shells using higher order shear deformation theory recently developed by Zannon [1]-[3]. The equilibrium equations of motion use Hamilton’s minimum...This paper presents the stress resultants of hyperbolic paraboloidal shells using higher order shear deformation theory recently developed by Zannon [1]-[3]. The equilibrium equations of motion use Hamilton’s minimum energy principle for a simply supported cross-ply structure by Zannon (TSDTZ) [2] [3]. The results are calculated for orthotropic, two-ply unsymmetrical [90/0] shells. The extensional, bending and coupling stiffness parameters are calculated using MATLAB algorithm for laminated composite hyperbolic paraboloidal shells. A comparison of the present study with other researchers in the literature is given, and is in good agreement.展开更多
Among several implicitization methods, the method based on resultant computation is a simple and direct one, but it often brings extraneous factors which are difficult to remove. This paper studies a class of rational...Among several implicitization methods, the method based on resultant computation is a simple and direct one, but it often brings extraneous factors which are difficult to remove. This paper studies a class of rational space curves and rational surfaces by implicitization with univaxiate resultant computations. This method is more efficient than the other algorithms in finding implicit equations for this class of rational curves and surfaces.展开更多
Post-stroke Antihypertensive Treatment Study (PATS) was a randomized, double-blind and placebo-controlled trial, which aimed at determining whether antihypertensive treatment could reduce the risk of fatal and nonfata...Post-stroke Antihypertensive Treatment Study (PATS) was a randomized, double-blind and placebo-controlled trial, which aimed at determining whether antihypertensive treatment could reduce the risk of fatal and nonfatal stroke incidence in patients with a history of stroke or transient ischemic attack (TLA). 5 665 patients were randomized by a sealed envelope system. Systolic blood pressure (SBP) ranged from 80 to 280 mm Hg and diastolic (DBP) from 50 to 150 mmHg. The average SBP was 154 mmHg and average DBP 93 mmHg. The mean age was 60 years. Among the patients, women accounted for 28%. In 71% the latest stroke was ischemic. Average follow-up approximated to 2 years. The three-year average SBP was 149 mmHg for the placebo group and 144 mmHg for the indapamide treatment group, and the three-year DBP was 89 mmHg and 87 mmHg respectively. The three-year first incidence of fatal and nonfatal stroke was 12.3 per 100 patients placebo treatment and 9.4 per 100 with indapamide. The relative risk by proportional hazards regression analysis was 0.71 (P=0.0009). For deaths from all causes, the relative risk was 0.91. (P>0.05). The findings of this trial indicate that in patients with a history of stroke or TLA, blood pressure reduction of 5 / 2 mmHg with 2.5 mg indapamide reduced the first incidence of fatal and nonfatal stroke by 29%, with three-year absolute benefit of 29 events per 1000 participants.展开更多
基金supported in part by the National Natural Science Foundation of China under Grant Nos.11471209,61321064 and 61361136002the Innovation Program of Shanghai Municipal Education Commission under Grant No.14ZZ046
文摘It is well known that resultant elimination is an effective method of solving multivariate polynomial equations. In this paper, instead of computing the target resultants via variable by variable elimination, the authors combine multivariate implicit equation interpolation and multivariate resultant elimination to compute the reduced resultants, in which the technique of multivariate implicit equation interpolation is achieved by some high probability algorithms on multivariate polynomial interpolation and univariate rational function interpolation. As an application of resultant elimination, the authors illustrate the proposed algorithm on three well-known unsolved combinatorial geometric optimization problems. The experiments show that the proposed approach of resultant elimination is more efficient than some existing resultant elimination methods on these difficult problems.
基金supported by the National Natural Science Foundation of China under Grant Nos.11688101,11301519,11671014
文摘Elimination theory is central in differential and difference algebra. The Wu-Ritt characteristic set method, the resultant and the Chow form are three fundamental tools in the elimination theory for algebraic differential or difference equations. In this paper, the authors mainly present a survey of the existing work on the theory of characteristic set methods for differential and difference systems,the theory of differential Chow forms, and the theory of sparse differential and difference resultants.
文摘This paper presents the stress resultants of hyperbolic paraboloidal shells using higher order shear deformation theory recently developed by Zannon [1]-[3]. The equilibrium equations of motion use Hamilton’s minimum energy principle for a simply supported cross-ply structure by Zannon (TSDTZ) [2] [3]. The results are calculated for orthotropic, two-ply unsymmetrical [90/0] shells. The extensional, bending and coupling stiffness parameters are calculated using MATLAB algorithm for laminated composite hyperbolic paraboloidal shells. A comparison of the present study with other researchers in the literature is given, and is in good agreement.
基金supported by the Natural Science Foundation of China under Grant No. 10901163the Knowledge Innovation Program of the Chinese Academy of Sciences
文摘Among several implicitization methods, the method based on resultant computation is a simple and direct one, but it often brings extraneous factors which are difficult to remove. This paper studies a class of rational space curves and rational surfaces by implicitization with univaxiate resultant computations. This method is more efficient than the other algorithms in finding implicit equations for this class of rational curves and surfaces.
文摘Post-stroke Antihypertensive Treatment Study (PATS) was a randomized, double-blind and placebo-controlled trial, which aimed at determining whether antihypertensive treatment could reduce the risk of fatal and nonfatal stroke incidence in patients with a history of stroke or transient ischemic attack (TLA). 5 665 patients were randomized by a sealed envelope system. Systolic blood pressure (SBP) ranged from 80 to 280 mm Hg and diastolic (DBP) from 50 to 150 mmHg. The average SBP was 154 mmHg and average DBP 93 mmHg. The mean age was 60 years. Among the patients, women accounted for 28%. In 71% the latest stroke was ischemic. Average follow-up approximated to 2 years. The three-year average SBP was 149 mmHg for the placebo group and 144 mmHg for the indapamide treatment group, and the three-year DBP was 89 mmHg and 87 mmHg respectively. The three-year first incidence of fatal and nonfatal stroke was 12.3 per 100 patients placebo treatment and 9.4 per 100 with indapamide. The relative risk by proportional hazards regression analysis was 0.71 (P=0.0009). For deaths from all causes, the relative risk was 0.91. (P>0.05). The findings of this trial indicate that in patients with a history of stroke or TLA, blood pressure reduction of 5 / 2 mmHg with 2.5 mg indapamide reduced the first incidence of fatal and nonfatal stroke by 29%, with three-year absolute benefit of 29 events per 1000 participants.
