In this paper , by using the theories of semigroups as basis and using the generalized solution space as a inportant tool , we investigate the abstract cauchy problem and the fc - times integrated abstract cauchy problem and their relationships between fc - times integrated c - semigroups 许多作者在这些方面确实也取得了丰富的研究成果本文把研究抽象cauchy问题时通常讨论的banach空间扩大到frech ? t空间,主要以广义解空间为工具,以半群理论为基础。
In the third chapter , we derive a new family of deformed halley methods without the evaluation of the second frechet - derivative to approximate the roots of nondifferentiable equations in banach space . we also provided a existence - uniqueness theorem and a new system of recurrence relations 在第三章中,构造了一族避免二阶fre chet导数的修正halley迭代,用其去逼近banach空间中非线性算子方程的解,同时给出了存在唯一性定理和一种新型的递归关系。
3 . as for the existence of positive solutions , the cone theory and the fixed point index of condensing mapping are employed , and the results of the existence of positive solutions are obtained in the case of superlinear and sublinear . the conclusions extend and improve the existence theorem which lou ben - dong extablished in 1996 about the question of sturm - liouville of banach spaces 三、对于正解存在性问题,我们应用凝聚映射的不动点指数理论,分别在超线性与次线性情形下进行讨论,获得了一些正解存在的结果,主要结果推广和改进了1996年louben - dong对banach空间sturm - liouville问题所建立的存在性定理。
In this paper , by recalling the developping history of variational inequalities and by using many other authors " results in this field , especially by using the concept of generalized m - accretive mappings in banach spaces and the relevant results which was first introduced and studied by huang and fang , we introduce and study a new class of parametric nonlinear variational inclusions involving generalized m - accretive mappings in banach spaces and prove the existence theorems of solutions . at last , we also analyze the sensitivity of solutions for this kind of nonlinear variational inclusions . 通过变分不等式的引入和发展历史的回顾,借用前人对有限维空间和hilbert空间中(广义)变分不等式问题解的存在性和灵敏性分析的已知结果,特别是, huang和fang最近引入的广义m -增生的概念以及其相应的结果,我们研究并分析了banach空间中一类具广义m -增生映象的含参非线性变分包含问题。
( 1 ) the paper has studied the contractive mapping genetic algorithm , which can be converged to a global optimal solution proved by fixed - point theorem of banach space . it remedies the shortage of standard genetic algorithm . furthermore , the paper discusses the genetic operation in the algorithm such as the coding , select , cross over and mutation etc . it will be help to the next work about fusion with the neural network 本文融合神经网络技术和遗传算法,对轨道交通引起的地面振动进行了正分析和反演,并利用计算机技术实现了地面振动的三维动画模拟,这主要包括: ( 1 )研究了压缩映射遗传算法,利用banach空间的不动点定理证明了压缩映射遗传算法可以收敛到全局最优值,弥补了标准遗传算法不能收敛至全局最优值的不足。
The arrangement of the article is : in the second section the properties of existence , uniqueness , global attractivity are discussed ; in the third section , the properties of asmptotic periodic function are proved ; in the fourth and the fifth section , on one dimention and multiple - dimention , asmptotic periodic function space are banach space 本文的具体安排如下:第二节给出渐近周期解存在唯一性和全局吸引性;第三节证明了在某些适当的条件下,渐近周期函数的性质;第四,五节分别证明了在一维和高维下,渐近周期函数空间是banach空间
In this paper , we have proved that an anti - bounded c _ ( 0 ) - group in infinite - dimensional reflexive banach spaces is not exponentially stable under generating compact perturbation , and that a c _ ( 0 ) - isometric semigroup in infinite - dimensional hilbert spaces has the same property . so , we have extended and improved russell theorem 在本文中,我们分别证明了无限维自反banach空间中的反有界c _ 0 -群和无限维hilbert空间中的c _ 0 -等距半群在生成的紧扰动下一定不具指数稳定性,从而推广和改进了russell定理。
It is noticed that the definitions of limit and difference of waveforms reflect path sensitization in a circuit . it is interesting to note the consistency between this theory and the reality . to deduce the properties and applications of converse operations or generalized converse operations of waveform operations in waveform space 主要表现在:定义了波形空间;在波形空间中定义了与实际问题相符合的距离,极限,延迟算子;运用布尔运算推导出了波形空间是banach空间;波形的极限和差分的定义反映了电路中的通路敏化;推导出了波形空间中常见波形运算的逆运算或广义逆运算及其在电路中的性质并在通路敏化方面得到了一些应用。
By using bruck ' s lemma [ 10 ] , passty [ 31 ] extended the results of [ 1 , 16 ] to uniformly convex banach space with a frechet differentiable norm . however , there existed more or less limitations in their methods adopted . by using new techniques , chapter2 of this paper discussed the weak convergence theorem for right reversible semigroup of asymptotically nonexpansive type semigroup and the corresponding theorem for its almost - orbit in the reflexive banach space with a frechet differentiable norm or opial property Feattieranddotson 16 ]和bose [ l ]通过使用opial引理17 }在具弱连续对偶映照的一致凸b ~ h空间中证明了渐近非扩张映照的弱收敛定理, passty 31通过使用bruck引理10 ]把1 , 16 ]的结果推广到具freehet可微范数的一致凸banach空间,然而,他们的证明存在着种种局限性。
Secondly , the concept of ordinary brown motion is given and the relationship between ordinary brown motion and ordinary martingale is discussed ; furthermore , the conclusion that an ordinary brown motion is an ordinary martingale is proven . through banach space embedding theory , the definition of the normality of set - valued variable is given and the increment of set - valued stochastic process is given . through the independency of a - algebra , the independency of the increment of set - valued stochastic process is given 接着给出了一般的布朗运动的定义,讨论了一般的布朗运动与一般的鞅之间的关系,指出一般的布朗运动是一个一般的鞅,通过banach空间的嵌入理论,给出了集值随机变量正态性的定义和集值随机过程的增量的定义;用过代数的独立性得到了集值随机过程的增量的独立性的定义,最后给出了集值布朗运动的定义并且类似于一般的布朗运动,给出了集值布朗运动的表示。