查询词典 locally bounded function

Firstly, we get the necessary and sufficient conditions for Toeplitz operators that commutes with another such operator whose symbol is a monomial, meanwhile, we completely characterize when the mellin transform of the bounded function on the interval 0,1 is a rational function.

首先得到了以有界函数为符号的Toeplitz算子和以单项式函数为符号的Toeplitz算子可交换的充要条件，同时给出了0，1区间上的有界函数的Mellin变换为有理函数的充要条件。

From [1], Every transition function is a positive strongly continuous semigroup of contractions on l\, but it isnt a strongly continuous semigroup on l_∞- In fact, the sufficient and necessary condition for a transition function to be a strongly continuous semigroup on l_∞ is that the q—matrix Q is an uniformly bounded q—matrix on l_∞- This is the trivial case.

由Anderson[1]知道转移函数P是l_1空间上正的强连续压缩半群，但P一般来说不是l_∞空间上的强连续半群，而P是l_∞上强连续半群的充要条件是q—矩阵Q是l_∞。

According to the structured element representation theorem of fuzzy number and fuzzy-valued function, we obtained one-to-one isometric mapping from the family of standard bounded monotone function with same monotonic formal on [-1, 1] to the fuzzy number space, and proved they are homeomorphic.

在模糊值函数的模糊结构元表述理论的基础上，利用[-1，1]上同序标准单调函数类上的距离诱导出模糊值函数空间上的距离，证明了模糊实数空间与[-1，1]上同序单调函数类同胚。

In chapter 4,we consider the existence of harmonic function in negative sectional curvature manifolds.we get that,if Ricci ≥-C(1 + r~2)r =ρ(O.x, then there have non-canstant bounded harmnic function in negative sectional curvature manifolds.

第四章考虑负曲率流形上调和函数，得到了在Ricci≥-C(1+r~2)其中r=ρ的负曲率流形的调和函数的存在性。

For the Riemann boundary value problems for the first order elliptic systems , we translates them to equivalent singular integral equations and proves the existence of the solution to the discussed problems under some assumptions by means of generalized analytic function theory , singular integral equation theory , contract principle or generaliezed contract principle ; For the Riemann-Hilbert boundary value problems for the first order elliptic systems , we proves the problems solvable under some assumptions by means of generalized analytic function theory , Cauchy integral formula , function theoretic approaches and fixed point theorem ; the boundary element method for the Riemann-Hilbert boundary value problems for the generalized analytic function , we obtains the boundary integral equations by means of the generalized Cauchy integral formula of the generalized analytic function , introducing Cauchy principal value integration , dispersing the boundary of the area , and we obtains the solution to the problems using the boundary conditions .

对于一阶椭圆型方程组的Riemann边值问题，是通过把它们转化为与原问题等价的奇异积分方程，利用广义解析函数理论、奇异积分方程理论、压缩原理或广义压缩原理，证明在某些假设条件下所讨论问题的解的存在性；对于一阶椭圆型方程组的Riemann-Hilbert边值问题，利用广义解析函数理论、Cauchy积分公式、函数论方法和不动点原理，证明在某些假设条件下所讨论问题的可解性；广义解析函数的Riemann-Hilbert边值问题的边界元方法是利用广义解析函数的广义Cauchy积分公式，引入Cauchy主值积分，通过对区域边界的离散化，得到边界积分方程，再利用边界条件得到问题的解。

We prove the equivalent conditions of completely monotone function, we also discuss the relationship of positive definite function, semi-positive definite function and completely monotone function when the function take values in a commutitive von Neumann algebras.

我们证明了完全单调函数的几个等价条件，并且讨论了取值于交换von Neumann代数的正定函数，半正定函数及完全单调函数之间的关系。

Properties of efficient portfolios and the efficient frontier to the model are systematically analyzed. Our main results concerning the properties are: every efficient portfolio can be solved by minimizing portfolio risk under a given level of portfolio return or by maximizing portfolio return under a given level of portfolio risk; on the efficient frontier, the risk is a convex and strictly increasing function of the return and the return is a concave and strictly increasing function of the risk; the utility function on the efficient frontier can be expressed as a quasi-concave function of the risk or the return if the investor's utility function is quasi-concave.

从理论上系统地对该模型下的有效投资组合和有效前沿的性质进行了分析，结果表明：每一个有效投资组合可通过在给定期望收益水平的条件下最小化投资组合风险来获得，或者在给定风险水平的条件下最大化期望投资组合收益来获得；在有效前沿上，风险是收益的严格单调递增凸函数，收益是风险的严格单调递增凹函数；当投资者的效用函数是拟凹函数时，则有效前沿上的效用可表达成风险或收益的拟凹函数。

The convex function develeped so many years that convex functionals are now a class of very universal functionals.The kinetic energy in the classical is the most natural convex function.Others like entropy and so on are convex functions.The economic core is closely connected with the convex function.The western economic core question is the optimized question.The optimized theory has something to do with the convex function and the concave function.

凸函数的发展经年已相当完善其应用非常广泛，在古典力学中的动能，就是最自然直接的凸函数，其他如熵……等均是，连经济学的核心都与之有极密切相关，西方经济学的核心问题是最优化问题，最优化理论又与凸函数与凹函数密切相关。

The decreasing conditions of an energy function are investigated by the use of convex function. By utilization of the primal convex function, the conditions are analyzed under which its conjugate function minus a quadratic function is also convex.

利用凸函数的定义研究了能量函数下降的条件，根据凸函数的性质分析它的共轭函数减去二次函数之差仍为凸函数的条件。

The paper uses precise step to produce the continuity function of water hammer mathematic model, not only gains more precise water hammer pressure function and water hammer wave speed functionbut also founds correct water hammer mathematic modelContinuity EquationMovement EquationAfter ignoring subordinate facts, function (1) and (2) translate into the current applied water hammer pressure function and water hammer wave speed function.

本论文对水击数学模型中的连续性方程重新进行了严谨的推导，不仅得到了更加准确的水击压强和水击波速的计算公式也建立了正确的水击数学模型连续性方程运动方程当忽略次要因素以后，公式(1)和(2)即可转化为当前应用的水击压强计算公式和水击波速计算公式。

This was not understood at the time, and therefore went unaddressed, until ascension became so distorted that we chose to stop ascending and wait for a time when all records would be revealed.

这在当时没有被了解，因此进行着无改编，直到提升变得如此扭曲，我们选择去停止提升并等待所有记录能被揭示的那一天。

The attack＇s nuisance value is increased because mobile phone networks also send notifications of new voicemail by sms,so an attacked phone may stop advising of new voice messages too,it warned.

它警告：这种攻击的危害增长是因为移动电话网络也会通过短信发送新语音邮件的通知。所以受到攻击的手机可也以停止新的语音信息的提示。