1) Fermat's method of descent
Fermat下降法
2) Fermat method of infinite descent
Fermat无穷递降法
1.
We use elementary theory of number and Fermat method of infinite descent,some necessary conditions if the Diophantine equations x 4+mx 2y 2+ny 4=z 2 has positive integer solutions that fit (x,y) =1m.
利用Fermat无穷递降法 ,证明了方程x4 +mx2 y2 +ny4 =z2 在 (m ,n) =(± 18,5 4 ) ,(36 ,- 10 8) ,(± 36 ,10 8) ,(± 18,- 10 8) ,(- 18,10 8) ,(± 36 ,75 6 )时均无正整数解 ,并且获得了方程在 (m ,n) =(± 6 ,-2 4 ) ,(± 12 ,132 ) ,(- 36 ,- 10 8) ,(18,10 8)时无穷多组正整数解的通解公式 。
2.
We make use elementary theory of number and Fermat method of infinite descent,somenecessary conditions if the diophantine equations x 4+mx 2y 2+ny 4=z 2 has positive Integer solutions that fir (x,y) =1
Fermat无穷递降法 ,证明了方程x4 +mx2 +ny4 =z2 =z2 在 (m ,n) =± (6,-3 3 ) ,(6,3 3 ) ,(-3 ,-6) ,(± 1 2 ,1 68) ,(-6,-1 2 ) ,(1 2 ,84)均无正整数解 ,并且获得了方程在 (-3 ,6) ,(6,-1 5 ) ,(± 3 ,-3 )时的无穷多组正整数解的通解公式 ,从而完善了Aubry等人的结
3.
With the help of the elementary theory of number and Fermat method of infinite descent,some necessary conditions have been proved provided that the Diophantine equations x 4+mx 2y 2+ny 4=z 2 has positive Integer solutions that fit (x,y) =1 m.
利用数论方法及Fermat无穷递降法 ,证明了丢番图方程x4 +mx2 y2 +ny4 =z2 在 (m ,n) =(± 6,-3 ) ,(6,3 ) ,(± 3 ,3 ) ,(-12 ,2 4) ,(± 12 ,-2 4) ,(± 6,15 ) ,(-6,-15 ) ,(3 ,6)仅有平凡整数解 ,并且获得了方程在 (-6,3 ) ,(12 ,2 4) ,(3 ,-6) ,(-6,3 3 )时的无穷多组正整数解的通解公式 ,从而完善了Aubry等人的结
3) Bridgman method
下降法
1.
Large-sized of φ100 mm CaF2 single crystals were grown by the Bridgman method.
采用坩埚下降法成功生长了φ100mmCaF2晶体,研究了不同条件生长单晶的缺陷和光谱性能。
2.
CaF_2 single crystals were grown by Bridgman method in different growing conditions.
采用坩埚下降法生长了CaF2单晶体,研究了不同条件生长的单晶缺陷和光谱性能。
3.
The high temperature phase barium metaborate α-BaB2O4 single crystal with 25mm in diameter, 100mm in height was grown by the Bridgman method.
采用坩埚下降法生长出了新型双折射晶体高温相偏硼酸钡α-BaB2O4单晶,尺寸为φ25mm×100mm,在He-Ne激光照射下无散射颗粒和生长条纹,在可见光区用复式宝石折射仪粗略测得该晶体的双折射率△n=0。
4) descent algorithm
下降算法
1.
Global convergence of a conjugate descent algorithm;
一种共轭下降算法的全局收敛性
2.
A descent algorithm for global optimization;
全局最优化问题的下降算法
3.
A new descent algorithm for solving the nonlinear complementarity problems are presented.
提出了非线性互补问题的一个下降算法 ,并在一定条件下证明了该算法的收敛性定理 ,同时给出了一些数值例子 ,得到很好的数值结
5) descent method
下降法
1.
After observing two types of nonsmooth optimization methods,subgradient method and Bundle method,and the descent method briefly,a new idea on solving nondifferentiable problems is brought for- ward and then the new method is presented.
在分析了非光滑优化两类基本算法以及最速下降法要素的基础上,提出了一种求解非光滑优化问题的思路,形成了算法。
2.
Finally, wo present a descent method for solving VIP and study a global error bound for unconstrained optimization reformulation in order to discuss the convergence of itinerative method.
最后给出了一个求解的下降法，并考察了最优化问题的误差界问题，以分析叠代法的收敛性。
6) descent method
下降算法
1.
We consider the convergence properties of descent methods with errors proposed by Solodov and Svaiter.
本文考虑了Solodov和Svaiter提出的带误差项的下降算法的收敛性。
2.
This paper presents a class of descent method for unconstrained optimization problem, and proves its global convergence under Armijo s line search and wolfe s line search.
提出一类无约束优化下降算法 ,证明了Armijo搜索和Wolfe搜索下的全局收敛性 。
补充资料：[3-(aminosulfonyl)-4-chloro-N-(2.3-dihydro-2-methyl-1H-indol-1-yl)benzamide]
分子式：C16H16ClN3O3S
分子量：365.5
CAS号：26807-65-8
性质：暂无
制备方法：暂无
用途：用于轻、中度原发性高血压。
分子量：365.5
CAS号：26807-65-8
性质：暂无
制备方法：暂无
用途：用于轻、中度原发性高血压。
说明：补充资料仅用于学习参考，请勿用于其它任何用途。
参考词条