查询词典 formula transformation

Some well-known results on area transformation formula and variant transformation formula of double integral are improved and generalized.

对现有的有关面积变换公式和二重积分变量变换公式的结果作了相应的改进和推广。

Tz summation formula and an extension formula of Sears\' terminating balanced _4Φ_3 series transformation formula and an extension involving multiple sum about finite Heine\'s _2Φ_1 transformation formula are given.

应用推广后的算子，我们给出了q-Paff-Salschütz和公式的推广、Sears终止型的4Φ3变换公式的推广以及多重的有限(来源：a5ABd7C论文网www.abclunwen.com)Heine 2Φ1变换公式。

The main content of this thesis is to find and prove some summation and transformation formulae of basic hypergeometric series by the modified Cauchy method,operator method and inversion techniques,which include many well-known results as special cases,for example,q-Saalschiitz summation formula,Baileys _6ψ_6 summation formula,non-terminating Watson transformation formula and Rogers-Ramanujan identities etc.

本文的主要内容是利用修正的Cauchy方法、算子方法和组合反演技巧来发现和证明一些基本超几何级数求和公式和变换公式，其中包含一些著名的公式，如q-Saalschüz求和公式、Bailey的_6ψ_6求和公式和非终止的Watson变换公式等作为其特殊情况。

By using this method we obtain two gen-eralized transformation formulae of q-integral form,two identities of basic hypergeometric series,as well as formal extensions for q-Pfaff-Saalschütz formula,q-Chu-Vandermonde identity and a three-term transformation formula of _3φ_2-series.

我们推广了两个q-积分形式的变换公式和两个有关基本超几何级数的恒等式，还得到q-Pfaff-Saalschütz公式、q-Chu-Vandermonde恒等式和基本超几何级数中一个有关_3φ_(2~-)级数的三项变换公式等的形式推广。

Now by using Dai's exact solution formula and studying the asymptotical behavior controlcondition and using the series expression of the famous Riemann Zeta-function in number theory,after introducing and proving a new representation theory of inverse Laplace transformation wedirectly obtained Chen's solution formulae and their unique existence condition without usingLaplace transformation and〓 inverse formula.

本文从带消发散参数的严格解出发，通过研究渐近行为控制条件，利用数论中著名的Riemann-Zeta函数的级数表示，引入并证明一个逆Laplace变换的新的表示定理，直接导出了陈等发展的级数解，并得到了级数解的存在、唯一性条件。

Methods By using Lebesgue integral and Fouries series, area transformation formula of planar domain and variant transformation formula of double integral are discussed.

利用勒贝格积分和傅立叶级数讨论平面区域面积变换公式和二重积分变量变换公式。

In this paper, Newton iteration formula for computing normal depth and critical depth was put forward by mathematical transformation of uniform flow equation and critical flow equation of circular section tunnel. Then, the relationship between the corresponding central angle and the introduced parameters was analyzed. An approximate formula for angle was obtained according to optimal uniform approximation principle. Using this approximate formula as initial value of iteration formula, a direct formula for calculating normal depth and critical depth of circular section tunnel was established after its first iterative.

该文通过对圆形断面均匀流方程与临界流方程的数学变换，分别得到其正常水深与临界水深的牛顿迭代公式，同时，通过对正常水深与临界水深对应的中心角与引入参数之间关系的分析及数值计算，利用最优一致逼近原理分别得到了正常水深与临界水深对应中心角的近似计算式，并以此近似计算式为初值，用迭代方程进行一次迭代得到了圆形断面均匀流水深与临界流水深的直接计算公式。

Via generalizing the Cauchy method we obtain a new method,called the modified Cauchy method.By means of this method we establish two bilateral _3ψ_3 and _4ψ_4 series summation formulae,two four-term summation and transformation formulae for unilateral _3φ_2-series and bilateral _3ψ_3-series,and two five-term summation and transformation formulae for unilateral _3φ_2-series and bilateral _3φ_3-series,which contain many known results as their special cases,such as non-terminating q-Saalschütz summation formula,Bilateral _6ψ_6 series summation formula of Bailey,non-terminating Watson transformation formula and some transformations of _3φ_2-series etc.

通过对Cauchy方法的推广，我们得到修正的Cauchy方法，采用这个方法分别得到两个双边的_3ψ_3和_4ψ_4基本超几何级数的求和公式、单边_3φ_~(2-)级数和双边_3ψ_(3~-)级数的两个四项求和变换公式和两个五项求和变换公式，它们包括许多已有的结果为特例，如非终止的q-Saalschütz求和公式、Bailey的very-well-poised双边级数_6ψ_6求和公式、非终止的Watson变换公式和一些关于单边_3φ_(2~-)级数的变换公式等。

Then the structure unit of hexangular lattice is found according to the principle of invariable symmetry. Renormalization transformation is processed when we regard the structure unit and the growth model as graphs before and after transformation respectively. After choosing the11thermodynamic function fugacity as parameter, we can write out the partition functions before and after transformation and the formula of renormalization transformation. At the same time, we also work out the fixed points of transformation.

然后根据对称性不变的原则，从整体晶格中选取结构单元，把结构单元和生长模型分别作为重整化变换前、后的图形来进行重整化变换，选取热力学函数易逸度为参量，写出了重整化变换前后的配分函数和重整化变换关系式，求出了这一变换的不动点。

Chapter one of this text has recommended the foreign insurance to apply financial economy to the products pricing method of insurance company, but these methods have not explained how to determine the fair premium of the multiple-line insurance company .In order to solve many business line insurance company pricing problem, chapter two introduce an very important model in insurance company capital allocation field - MR capital allocation model, through deriving capital allocation formula and simulation analysis indicate MR model allocate multiple- line insurance company capital scientifically. In order to apply MR model to non-life insurance pricing, chapter three will extend MR model to introduce loss 3 and layer P . Since the premise of MR model is a certain market price of loss, the chapter four will use the risk-neutral probability transformation technique to get the market value of loss. Under lognormal distribution, we will use location parameter shift and proportional PH transformation to illuminate the technique. The final chapter combines the prior sections result to deduce out the fair premium formula, and apply it to price the catastrophe insurance.

本文的第一章介绍了国外保险业将财务经济学应用到保险公司产品定价的方法，但是这些方法都没有说明如何确定多业务线保险公司的公平保费；为了解决多业务线保险公司定价问题，第二章引入保险公司资本配置领域非常重要的一个模型—MR资本配置模型，通过推导资本配置公式及模拟分析表明MR模型科学地配置了多业务线公司的资本；为了将MR模型应用到非寿险公司的定价中去第三章扩展了MR模型，引入了损失β和层β的概念：由于MR模型的前提条件是有一个确定的损失市场价值，第四章利用风险中性转化方法获得损失的市场价值，在损失为对数正态分布的条件下，通过位置参数转化和比例危险转化方法给出了实例说明；第五章结合前几章的结果给出非寿险公司公平保费的定价公式，并运用它给出了巨灾保险价格的模拟分析。

They weren't aggressive, but I yelled and threw a rock in their direction to get them off the trail and away from me, just in case.

他们没有侵略性，但我大喊，并在他们的方向扔石头让他们过的线索，远离我，以防万一。

In slot 2 in your bag put wrapping paper, quantity does not matter in this case.

在你的书包里槽2把包装纸、数量无关紧要。