A new method of proof on the distance formula from the point to the plane 點到平面距離公式的一種新證法
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 我們利用周期拋物型算子理論l ” ,解耦方法皿1 , schauder估計舶和分歧理論山‘ ’解決了周期捕食食餌系統(tǒng)的正解的共存態(tài),得到了系統(tǒng)正周期解存在的一個充要條件
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 近年來, bruck [ 5 ] , reich [ 6 ] , oka [ 7 ]等在具frechet可微范數(shù)的一致凸banach空間中給出了非擴張及漸近非擴張映射及半群的遍歷收斂定理。 li和ma [ 13 ]在具frechet可微范數(shù)的自反banach空間中給出了一般交換漸近非擴張型拓撲半群的遍歷收斂定理,這是一個重大突破。本文第二章用一種新的證明方法在自反banach空間中,研究了揚州大學(xué)碩士學(xué)位論文2一般半群上的( r )類漸近非擴張型半群的弱遍歷收斂定理,即:定理3 . 1設(shè)x是具性質(zhì)( f )的實自反banach空間, c是x的非空有界閉凸子集, g為含單位元的一般半群, s =仕工, 。
method: n. 1.方法,方式;順序。 2.(思想、言談上的)條理 ...proof: n. 1.證明;證據(jù);【法律】證件;【法律】(口頭或書面 ...proof method: 驗證法, 證明方法indirect method of proof: 間接證明法inductive proof method: 歸納證明法synthetic method of proof: 綜合證貓systematic proof method: 系統(tǒng)證明法-proof: 后綴 表示“耐,防(等)”:acid-proof 耐酸的。Air-proof 密封的。 Dust-proof 防塵的。 Fire-proof 防火的。 Radar-proof 反雷達的。 Slander-proof 聽了壞話不會生氣的。 Sound-proof 隔音的。 Water-proof 防水的。 a proof: 防原子的a-proof: 防原子的in proof of: 作...的證據(jù)proof: n. 1.證明;證據(jù);【法律】證件;【法律】(口頭或書面)證詞,證言。 2.檢驗,考驗;驗算;檢定的品質(zhì)[強度等]。 3.試管。 4.【印刷】校樣,印樣。 5.(酒精的)標準強度。 6.(甲胄等的)耐力,堅牢強度,不貫穿性。 7.【攝影】樣片;樣張。 8.[Scot.] 審問。 9.【數(shù)學(xué)】證,證明,證法。 The proof of the pudding is in the eating. 布丁好壞一吃即知;空談不如實驗。 Here is proof positive. 有確實證據(jù)。 a foul proof 錯字很多的校樣。 a foundry proof (壓型前的)清樣。 an artist's [engraver's] proof 版面印樣。 stand a severe proof 經(jīng)受嚴格的考驗。 afford proof of 提供證據(jù)。 armour of proof 戳不通的堅牢的鎧甲。 below proof 不合格。 bring [put] to the proof 試,試驗。 have proof of shot 能防彈,能避彈。 in proof of 作…的證據(jù)。 proof positive of his intention 他的企圖的確證。 read the proof 校對。 adj. 1.試驗過的,有保證的;(酒)合標準的,規(guī)定的。 2.校樣的。 3.(子彈等)不入的,耐…的,防…的。 a proof coin 標準貨幣,制錢。 a proof sample 樣品。 proof against the severest weather 經(jīng)得起任何酷烈天氣的。 proof against the pricks of all temptations 不為任何誘惑所動的。 vt. 使經(jīng)得住,使(布等)耐久[不漏水(等)]。 proofed cloth 防水布。 adj. -less 無證據(jù)的。 proof of will: 遺囑證明, 遺囑認證flame proof = flame-proof: 防火的proof sheet; proof: 紅樣a documentory proof: 用文件來證實日期abrasion proof: 耐磨的abrasion-proof: 防磨的; 耐磨的absolute proof: 絕對證明abundant proof: 充分的證據(jù)accident proof: 安全的acid proof: 耐防酸的; 耐酸,抗酸; 耐酸的; 酎酸的acid-proof: adj. 耐酸的。 actor-proof: 有戲劇效果的admission of proof: 墊付款項; 接納債權(quán)證明; 接納債權(quán)證實; 預(yù)付款帳戶; 預(yù)支款項