hyperbolic function 中文意思是什麼

hyperbolic function 解釋
雙曲函數
  • hyperbolic : adj. 【數學】雙曲線的。adv. -ically adj. 誇張法的。
  • function : n 1 功能，官能，機能，作用。2 〈常 pl 〉職務，職責。3 慶祝儀式；（盛大的）集會，宴會。4 【數學】...
  1. Firstly we deduce hyperbolic function transformation and then apply to a class of reaction diffusion equation and brusselator reaction diffusion model which has physics, chemistry and biology significance. thus we obtain many new exact and explicit solutions ( including solitary wave soluiton, peoiodic wave solution and rational functions solutions ) to above equations

    推導出了雙曲函數變換，利用此方法探討了一類反應擴散方程， brusselator反應擴散方程這些具有物理、化學、生物意義的方程的精確解（包括奇性孤波解，周期解和有理函數解） 。
  2. We have calculated and plotted the curves of the refractive index, group velocity index, lowest - order and second - order dispersion indexes as a function of wavelength. the lowest - order and higher - order dispersion - induced broadening and deforming of light pulses is analyzed for various pulse shapes, such as gaussian, super - gaussian and hyperbolic secant pulses

    給出了折射率、群速指數、低階和二階色散系數隨波長變化的關系曲線，研究了高斯脈沖、超高斯脈沖和雙曲正割脈沖等超短脈沖在clbo晶體中傳播時，由於低階色散和高階色散引起的脈沖展寬和形變。
  3. The mostly conclusion of this part is as follows, on the conditon of travelling wave, the exact solitary wave solutions to some nonlinear wave equations such as sawada - kotera equation, kaup - kupershmidt equation, the fifth order kdv equation, fisher - kolmogorov equation, on the help of the computer algebraic system ( maple ), are explicitly established by making use of the hyperbolic function method. this part is maken up of three sections

    本部分的主要結論如下，利用雙曲函數展開法，在行波條件下，對sawada - kotera方程， kaup - kupershmidt方程，五階kdv方程， fisher - kolmogorov方程，等幾類非線性波動方程求解，將其孤立波表示為雙曲函數的多項式，從而將非線性波方程的求解問題轉化為非線性代數方程組的求解問題，並藉助于計算機代數系統求解非線性代數方程組，最終獲得了這些非線性波動方程的若干精確孤立波解。
  4. The asinh ( ) function returns the inverse hyperbolic sine of a number

    函數的作用是：返回至各指定數值所對應的反雙曲正弦值。
  5. A theoretical model for predicting ground displacement and deformation due to mining of phosphate body in wenjiaping by using hyperbolic tangent function was given in this paper

    摘要針對文家坪磷礦地下開采巖體移動變形問題，給出了用於預測分析地下開采引起地表移動變形的雙曲正切函數模型。
  6. Secondly, in this part, we will introduce the notation of average geodesic curvature for curves in the hyperbolic plane, and investigate the relationship between the embeddedness of the curve and its average geodesic curvature. finally, we will employ the minkowski ' s support function to construct a new kind of non - circular smooth constant breadth curves in order to attack some open problems on the constant width curves ( for example, whether there is a non - circular polynomial curve of constant width, etc. ) in the second part, we will first follow the ideas of gage - hamilton [ 28 ], gage [ 26 ] and the author ' s dissertation [ 47 ] to present a perimeter - preserving closed convex curve flow in the plane, which is from physical phenomena

    其次，對雙曲平面上的曲線引入平均測地曲率的概念，並討論雙曲平面上凸曲線的嵌入性與它的平均測地曲率之間的關系，其目的是為了將雙曲平面上曲線的性質與歐氏平面中曲線的性質作一些對比；最後，我們利用minkowski支撐函數構造了一類新的非圓的光滑常寬曲線，其目的是想回答有關常寬曲線的一些未解決問題（如是否存在非圓的多項式常寬曲線
  7. Explicit solutions for the optimal consumption and portfolio of the hyperbolic absolute risk aversion function family

    雙曲型絕對風險厭惡函數的最優消費與投資組合的顯示解
  8. The mathematics - mechanization method is applied the field of differential equations. many algorithm for constructing solitary wave solutions for a class of nonlinear wave equations are given, and implemented in a computer algebraic system, such as the hyperbolic tangent function method and the hyperbolic function method etc. exact solitary wave solutions of a great deal of nonlinear equations are gained

    將機械化數學方法應用於偏微分方程領域，建立了構造一類非線性波方程的精確孤立波解的許多演算法，如，雙曲正切函數展開法，雙曲函數方法等，並在計算機數學系統上加以實現，因而推導出了一批非線性波方程的精確孤立波解。
  9. This feature reflects the physical phenomenon of breaking of waves and development of shock waves. in the fields of fulid dynamics, ( 0. 2. 1 ) is an approximation of small visvosity phenomenon. if viscosity ( or the diffusion term, two derivatives ) are added to ( 0. 2. 1 ), it can be researched in the classical way which say that the solutions become very smooth immediately even for coarse inital data because of the diffusion of viscosity. a natural idea ( method of regularity ) is obtained as follows : solutions of the viscous convection - diffusion pr oblem approachs to the solutions of ( 0. 2. 1 ) when the viscosity goes to zeros. another method is numerical method such as difference methods, finite element method, spectrum method or finite volume method etc. numerical solutions which is constructed from the numerical scheme approximate to the solutions of the hyperbolic con - ervation laws ( 0. 2. 1 ) as the discretation parameter goes to zero. the aim of these two methods is to construct approximate solutions and then to conside the stability of approximate so - lutions ( i, e. the upper bound of approximate solutions in the suitable norms, especally for that independent of the approximate parameters ). using the compactness framework ( such as bv compactness, l1 compactness and compensated compactness etc ) and the fact that the truncation is small, the approximate function consquence approch to a function which is exactly the solutions of ( 0. 2. 1 ) in some sense of definiton

    當考慮粘性后，即在數學上反映為（ 0 . 1 . 1 ）中多了擴散項（二階導數項） ，即使很粗糙的初始數據，解在瞬間內變的很光滑，這由於流體的粘性擴散引起，這種對流-擴散問題可用古典的微分方程來研究。自然的想法就是當粘性趨于零時，帶粘性的對流-擴散問題的解在某意義下趨于無粘性問題（ 0 . 1 . 1 ）的解，這就是正則化方法。另一辦法從離散（數值）角度上研究僅有對流項的守恆律（ 0 . 1 . 1 ） ，如構造它的差分格式，甚至更一般的有限體積格式，有限元及譜方法等，從這些格式構造近似解（常表現為分片多項式）來逼近原守恆律的解。
  10. A general class of solutions to nonlinear scalar equations with static cylindrical symmetry is obtained in the form of a hyperbolic function series. these solutions can be used to describe a long. straight global string

    利用雙曲函數級數的技術，研究了靜態軸對稱非線性標量方程的解析解.在物理上.這些解描述了無限長的直整體弦
  11. One of most effectively straightforward methods to construct travelling solitary wave solutions is tanh - function method. the algorithm is based on the fact that the solitary wave solutions are essentially of a localized nature. seeking solitary wave solutions which are in terms of hyperbolic tangent function gives a nonlinear system of algebraic equation

    尋求非線性演化方程孤波解的雙曲正切方法是直接代數方法中最為有效的方法之一，其基本原理是利用非線性演化方程孤波解的局部性特點，將孤波解表示為雙曲正切函數的多項式，從而將非線性演化方程的求解問題轉化為非線性代數方程組的求解問題。
  12. Chapter5 : the recently developed method of hyperbolic tangent function expansion is extended and new function transformation is applied to construct some new solitary solutions of kdv equation and klein - gordon equation and the jacobi elliptic function expansion method, which is advanced in 2001, and the extended method of doubly jacobi function expansion are used to construct the exact solutions of a kind of nonlinear evolution equations

    第五章對近年來發展起來的雙曲正切函數展開法加以改進，採用新的變換函數，得到了kdv方程和非線性klein - gordon方程的一些新的孤立波解。其次，分別採用2001年提出的jacobi橢圓函數展開法和本文由此擴展而來的雙橢圓函數展開法，求解了一大類非線性發展方程，得到了一系列新的周期解。
  13. To deblur edge after image magnifying, an adaptie edge sharpness presering image magnification is put forword, which can fit edges of any direction, gradient and amplitude, utilizing the gradient imgormation of the image and the properties of the hyperbolic tangent function haing reiewing the character of a typical edge

    針對圖像放大后出現邊緣模糊的現象，論文考察了典型邊緣的特徵，利用圖像的梯度信息和雙曲正切函數的性質，提出了一種較好地擬合任意方向、陡度和幅度的邊緣，因此能夠保持邊緣銳度的自適應圖像放大演算法。
  14. Arc hyperbolic function

    反雙曲函數
  15. The atanh ( ) function returns the inverse hyperbolic tangent of an angle

    函數的作用是：返回一個指定角度參數所對應的反雙曲正切值。
  16. In this paper, depending on the enormous 356 pile testing date detailed with soil and pile parameters and p ~ s curves, covering xi ' an and adjacent areas, we analyzed the load transmission mechanism of pile in loess foundation, and proposed a kind of hyperbolic load transmission function between pile and it ' s neighboring soil. meanwhile, we created a mathematical model to predict p ~ s curve and bearing capacity of single pile. by analyzing the compacting effect caused by pile - sinking of pressed pile in loess and it ' s influence on bearing capacity and settlement, two parameters, kc and ke are introduced to modify the soil cohesive c and deformation modulus es

    本文利用現己收集到的西安及其周邊地區356根打入樁、靜壓樁、灌注樁的現場試樁資料（其中打入樁67根，靜壓樁121根，鉆孔灌注樁168根，並有詳細的地層勘探資料，樁深資料，荷載沉降?曲線）對西安黃土地基中的打入樁、靜壓樁、灌注樁的荷載傳遞機理進行了分析研究，認為用雙曲線型的荷載傳遞函數模擬樁土之間的荷載傳遞函數是合適的，並用荷載傳遞分析的方法建立了計算p s曲線的數學模型及極限承載力的確定方法。
  17. In section 1, some nonlinear wave equations of this part discussing are recommended ; in section 2, the elementary tool of this part utilizing is mentioned, namely, the hyperbolic function method ; in section 3, seme exact solitary wave solutions to these nonlinear wave equations are attained

    本部分由三節組成，第一節介紹了所討論的幾類非線性波動方程；第二節介紹了本部分所使用的基本工具，即，雙曲函數方法；第三節給出了這些非線性波動方程的若干精確孤立波解。
  18. Chapter 4 gives hyperbolic function transformation method and its applications

    第四章討論了雙曲函數變法及其應用
  19. Extended hyperbolic function method and new exact solitary wave solutions of zakharov equations

    方程組的新精確孤立波解
  20. Modified hyperbolic function method and exact solutions to nonlinear evolution equations

    修正雙曲函數法與非線性發展方程的精確解
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