查询词典 integer valued function

Association with complex function in this study, mathematical thought in this phase inspires the later integer theory of analytic function.

通过与复变函数关联度的考察，强调了这一阶段蕴含的数学思想对后来整体解析函数理论具有一定的思想启发力。5。

For any positive integer n, about the Smarandache LCM dual function SL*, the main purpose of the fifth Chapter is using the elementary method to study the calculating problem of a Dirichlet series involving the Smarandache LCM dual function SL* and the mean value distribution property of SL*, obtain an exact calculating formula and a sharper asymptotic formula for it.

对于给定的自然数n，关于Smarandache LCM对偶函数SL~*，本文第五章利用初等方法研究了一个包含SL~*的Dirichlet级数计算问题及SL~*的均值性质，分别给出了精确计算公式和一个较强的渐近公式。

Under the concave transaction costs function, using the variance of profolio return rate to express profolio risk, and taking the risk-return combination difference as the objective function, we propose Mean-variance D.C- integer optimization model under concave transaction costs and minimal transaction unit constraints.

2考虑凹交易费用函数，用投资组合收益率的方差反映组合风险，以风险-收益的组合差作为目标函数，提出了考虑交易费用及最小交易量的均值—方差D.C-整数优化模型。

Then a filled function method for the integer programming problem is proposed,which tries to find a better discrete local minimal solution of the problem by minimizing a filled function.

该方法通过寻找填充函数的离散局部极小解以期找到整数规划问题的比当前离散局部极小解好的解。该文的算法是直接法，数值试验表明算法是有效的。

Firstly,the mixed-integer bi-level programming is transformed into a single level continuous optimization problem by virtue of penalty function concept and optimal value function tool.

利用罚函数思想和最优值函数的概念将混合整数双层规划转化为连续变量的单层非线性规划，然后用事先确定步长的凸组合算法迭代求解此单层非线性规划，进而得到原双层规划的局部最优解

The results indicated that the piecewise linear function approach was easy to model nonlinear unit consumptions with a higher accuracy without regressing any parameter, and the related model could be solved quickly for a medium size problem.Meanwhile, the piecewise linear function approach could simultaneously handle nonlinearities of multi raw materials in a unit without adding any new integer variable.

案例结果表明，分段线性函数不需要回归参数，建模简单，精度较高，对于中等规模问题求解时间短，能够同时处理装置的多种原料非线性单耗，而不需要增加新的整数变量，多项式函数则不具有这些优点。

The constructing process of the algorithms itself indicate that they are brevity and have definite geometric meaning, scientific iterative terminal criterions and no strict requirement to function. Finally, some digital experimentation is presented to indicate the algorithms application in solving the problem of maximum of function, transcendental equation,integer programming and so on. The results indicate that the algorithms have more global and more adaptability compared to traditional algorithms and have more calculating efficiency and more scientific iterative terminal criterions compared to some present popular artificial intelligence algorithms.

算法的构造过程本身表明了该算法简单明了、几何意义明确、迭代终止准则科学、对函数的要求较低；最后举了几个数值试验的例子以说明该类算法在求函数的最值，解超越方程以及整数规划等问题中的应用；数值试验的结果标明该算法比单纯由"微分"思想演化而来的传统算法有更好的全局性和对问题的更广泛的适应性，比现在流行的一些人工智能方法有更高的运算效率和更适当的迭代中止准则。

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。

Many will continue to choose to live in duality and in conflict.

许多人将继续选择活在二元对立性和冲突中。

I find that students of the University of Physical Education all wear sportswear at first sight.

我发现：体育大学的学生乍一看，都是穿运动衣，大家都一样