proof n. 1.证明;证据;【法律】证件;【法律】(口头或书面)证词,证言。 2.检验,考验;验算;检定的品质[强度等]。 3.试管。 4.【印刷】校样,印样。 5.(酒精的)标准强度。 6.(甲胄等的)耐力,坚牢强度,不贯穿性。 7.【摄影】样片;样张。 8.[Scot.] 审问。 9.【数学】证,证明,证法。 The proof of the pudding is in the eating. 布丁好坏一吃即知;空谈不如实验。 Here is proof positive. 有确实证据。 a foul proof 错字很多的校样。 a foundry proof (压型前的)清样。 an artist's [engraver's] proof 版面印样。 stand a severe proof 经受严格的考验。 afford proof of 提供证据。 armour of proof 戳不通的坚牢的铠甲。 below proof 不合格。 bring [put] to the proof 试,试验。 have proof of shot 能防弹,能避弹。 in proof of 作…的证据。 proof positive of his intention 他的企图的确证。 read the proof 校对。 adj. 1.试验过的,有保证的;(酒)合标准的,规定的。 2.校样的。 3.(子弹等)不入的,耐…的,防…的。 a proof coin 标准货币,制钱。 a proof sample 样品。 proof against the severest weather 经得起任何酷烈天气的。 proof against the pricks of all temptations 不为任何诱惑所动的。 vt. 使经得住,使(布等)耐久[不漏水(等)]。 proofed cloth 防水布。 adj. -less 无证据的。
A new method of proof on the distance formula from the point to the plane 点到平面距离公式的一种新证法
A necessary and sufficient condition for coexistence of positive periodic solutions is obtained . the result we get can be seen an extension of [ 30 ] . in this paper , we partially bring new ideas in the model establishing and some methods of proof 我们利用周期抛物型算子理论l ” ,解耦方法皿1 , schauder估计舶和分歧理论山‘ ’解决了周期捕食食饵系统的正解的共存态,得到了系统正周期解存在的一个充要条件
Chapter 2 of this paper , by using a new method of proof , we obtain the weak ergodic convergence theorem for general semigroups of asymptotically nonexpansive type semigroups in reflexive banach space . by theorem 2 . 1 of chapter 1 we get the weak ergodic convergence theorem of almost orbit for general semigroups of asymptotically nonexpansive type semigroups in reflexive banach space . by this method of proof , we give the weak ergodic convergence theorems for right reversible semigroups . by theorem 2 . 1 of chapter l , we generalize the result to almost orbit case . so we can remove a key supposition that almost orbit is almost asymptotically isometric . it includes all commutative semigroups cases . baillon [ 8 ] , hirano and takahashi [ 9 ] gave nonlinear retraction theorems for nonexpansive semigroups . recently mizoguchi and takahashi [ 10 ] proved a nonlinear ergodic retraction theorem for lipschitzian semigroups . hirano and kido and takahashi [ 11 ] , hirano [ 12 ] gave nonlinear retraction theorems for nonexpansive mappings in uniformly convex banach spaces with frechet differentiable norm . . in 1997 , li and ma [ 16 ] proved the ergodic retraction theorem for general semitopological semigroups in hilbert space without the conditions that the domain is closed and convex , which greatly extended the fields of applications of ergodic theory . chapter 2 of this paper , we obtain the ergodic retraction theorem for general semigroups and almost orbits of asymptotically nonexpansive type semigroups in reflexive banach spaces . and we give the ergodic retraction theorem for almost orbits of right reversible semitopological semigroups 近年来, bruck [ 5 ] , reich [ 6 ] , oka [ 7 ]等在具frechet可微范数的一致凸banach空间中给出了非扩张及渐近非扩张映射及半群的遍历收敛定理。 li和ma [ 13 ]在具frechet可微范数的自反banach空间中给出了一般交换渐近非扩张型拓扑半群的遍历收敛定理,这是一个重大突破。本文第二章用一种新的证明方法在自反banach空间中,研究了扬州大学硕士学位论文2一般半群上的( r )类渐近非扩张型半群的弱遍历收敛定理,即:定理3 . 1设x是具性质( f )的实自反banach空间, c是x的非空有界闭凸子集, g为含单位元的一般半群, s =仕工, 。