infinite boundary 中文意思是什麼
infinite boundary
解釋
無窮遠邊界-
Firstly, in spherical coordinate system, the sovp formulation for the time - harmonic electromagnetic fields of the current dipole in conductive infinite - space is derived, using reciprocity theorem and transforming relations between special functions. then, selecting appropriate coordinate system, using superposition principle, the boundary - value problem of modified magnetic vector potential on the problem of a time - harmonic current dipole in spherical conductor is solved and analytical solution is obtained. finally, by means of the addition formulas of legendre polynomial and spherical harmonics function of degree n and order 1, the analytical solution in spherical coordinate system specially located is transformed into that in spherical coordinate system arbitrarily located
首先利用特殊函數間的轉化關系和互易定理推導得到了無限大導體空間中球坐標下時諧電流元電磁場的二階矢量位形式：然後利用疊加原理，選擇合適坐標系，求解了導體球中時諧電流元的修正磁矢量位邊值問題，得到了問題的解析解；最後依據不同坐標系下電磁場解的轉化原理，藉助勒讓德多項式和n次1階球諧函數的加法公式，將坐標系特殊安放時的電磁場解析解變換到坐標系一般安放時的解析解，給出了球內電場和球外磁場的並矢格林函數。 -
The study indicate that the surface form has no effect on kl, but has obvious effect on kll, and will affect the breaking angle and mode ; in finite plate, the boundary condition has effect on the sif and the k is bigger than in infinite plate ; the effect of the distance and the angle between cracks are all have obvious effects on the multiple crack interaction, and the interactions between cracks also have obvious effects on the sif, which can be neglect only when the distance is bigger enough
研究表明：裂面狀態對k _的大小沒有影響，而對k _的影響卻很大，相同應力條件下，裂面狀態會影響裂紋的開裂角和開裂方式；有限板的邊界對應力強度因子有一定的影響，其k比無限板中的k略大；裂紋間的距離、夾角等因素對裂紋間的干涉效應均有較大影響，裂紋間的干涉效應對應力強度因子的影響非常顯著，只有當裂紋間的距離充分大時，干涉效應才可忽略。 -
To draw this boundary, physicists and mathematicians use a distorted length scale similar to escher ' s, squeezing an infinite distance into a finite one
為了畫出這個邊界，物理學家和數學家利用了類似於艾雪所用的扭曲尺度，將無窮大的距離壓縮成有限的長度。 -
The markov chains ' analysis results show that the expected casualty of the former form is the same as one of the latter form at unknown or infinite mine - field boundary, the expected casualty of the former form is less than one of the latter form at known or finite mine - field boundary
根據馬爾可夫過程理論的分析，可以比較出2種清掃模式下掃雷艇期望損失在雷區邊界未知或無限時是相同的，而對邊界已知的有限雷區，邊緣漸進模式的期望損失比中心航道模式小。 -
In this paper, through the idea of domain decomposition method and the theory of natural boundary reduction, we study overlapping domain decomposition method and non - overlapping domain decomposition method for elliptic boundary value problems in an infinite domain
本文藉助區域分解思想並基於自然邊界歸化理論，研究無窮凹角區域橢圓邊值問題的重疊型和非重疊型區域分解演算法。 -
Using this scattered wave function and moving coordinate system, the problem can be summarized to scattering of sh - wave by multiple circular cavities in infinite space and the boundary conditions can be satisfied
利用這一波函數，則可將該問題轉化成為一個對無限空間中相鄰多個圓形孔洞對sh波散射的求解問題。 -
In the section 2, firstly based on the diffusion approximation theory, the temporal characteristics of the reflectance and the transmittance were theoretically analyzed in turbid tissues ; secondly, the curves were simulated that the intensity and the pulse shape of the time resolved reflectance and transmittance versus the absorption a, the scattering s and the anisotropy coefficient g in two different boundary conditions : semi - infinite turbid media and homogeneous slab ; at last, the optical properties can be derived from the curves ; in the section 3, the conditions of ultra short laser pulses of different pulse - width and shapes has been theoretical analyzed and calculated, besides, the simulated the curves of the intensity and pulse shapes of the reflectance and transmittance in a homogeneous slab are obtained for use and future studying
第二章中首先根據漫射近似理論對超短脈沖在以生物組織為典型的混濁介質中傳輸進行了理論分析，然後對兩種邊界條件下產生的漫反射、漫透射光脈沖強度和形狀隨各光學特性參數的變化情況進行了數值模擬，最後得到了混濁介質的光學特性參數與漫反射、透射脈沖強度與形狀的關系曲線。第三章對不同形狀和脈寬的脈沖光源入射到混濁介質中產生的漫反射、漫透射脈沖的強度和形狀進行了理論分析和數值模擬，並將高斯脈沖與方波脈沖情況進行了對比，得到了各種情況的漫反射、漫透射脈沖強度、形狀與各光學特性參數的關系曲線，這對從分析脈沖形狀中提取介質的光學特性參數的信息有重要的意義。 -
The various medium parameters have different influence on the reflection of the laser pulse. based on the diffusion approximation theory, the boundary condition of semi - infinite homogeneous media, the influence of the absorption a, the scattering s and the anisotropy coefficient g on the ultra short laser pulse of different pulse - width and shapes has been researched
論文對超短脈沖在混濁介質中的傳輸進行了理論分析和數值模擬，並在不同脈寬的高斯脈沖和方波脈沖入射到混濁介質的漫反射、漫透射脈沖強度和形狀進行了理論分析和數值模擬，得到了它們與各光學特性參數的關系曲線。 -
Firstly, the paper introduces the principle of instituting contact interface element and the format of integral method for element stiffness matrix ; secondly, because of the zero of displacement and load of soil in the infinite boundary, the unique shape of element stiffness matrix is obtained for coupling the three different elements
文中首先闡述了接觸元建立的方法以及單元剛度矩陣的積分方法；由於無限遠處的土場位移、地震作用力皆為零，計算中對該單元剛度矩陣的形式不同於四節點等參元，文中推導了平行無限元的單元剛度拒陣方，並介紹了無限元單元剛度矩陣組裝原理。 -
There are two problems in simulating sh - wave issue by finite element method. the first is establishing artificial boundary problem, because of simulating the infinite field from the finite field in which intercept from the infinite field, so we introduce artificial boundary
用有限元模擬波動問題，其首要問題是人工邊界的設置問題，由於要從無限域中截取有限區域來模擬無限域，所以要引入人工邊界。 -
By comparison, it was clear that the bem could solve the problem not only effectively but also precisely. in the second chapter the theory of weighted residual technique is illustrated and the boundary integral function of the potential problem is deduced by it. methods of obtaining green ' s function fundamental solutions in infinite region and semi - infinite region are presented
第二章首先說明了加權余量法的原理，並由此推出了勢問題的邊界積分方程，還介紹了無限域和半無限域中格林函數基本解的求法，以及多介質域和第三類邊界條件的處理方法，最後說明了邊界積分方程的數值解法。 -
This thesis in theory deals with electromagnetic wave scattering by multilayered confocal and non - confocal spheroidal particles illuminated by gaussian beams, in which the main contributions are as follows : 1. in the case of multilayered confocal spheroidal particles, the scattered fields as well as the fields within each layer are obtained in terms of infinite series with spheroidal vector wave functions by using an appropriate expansion of the incident gaussian beam. by virtue of the boundary conditions, we write the set of equations for determining the unknown expansion coefficients and then solve it
本文從理論上研究了多層共焦和非共焦橢球粒子對高斯波束的散射，主要成果如下： 1 .我們研究了多層共焦橢球粒子對高斯波束的散射，把入射高斯光，散射場，各層橢球內的電場和磁場用適當的橢球矢量波函數展開，應用電磁場邊界條件，寫出確定各展開系數的方程組，求出散射場系數，進而求出散射場及散射截面。 -
Especially, when the isocline of x is monotone decreasing in 0 < x < 1, the svstem has no limit cycle and is globally stable ; next, we construct a saddle bifurcation at the boundary equilibrium and a degenerated bogdanov - takens bifurcation at the interior equilibrium by choosing appropriate parameter values in the following two sections, where our work are based on the theory of central manifolds and normal torms. we prove that is a codimention 3 focus - type equilibrium. system ( 6. 1 ) will have two limit cycles at some appropriate bifurcation parameter values, and have homoclinic or double - homoclinic orbits at some other appropriate bifurcation parameter values ; at last, we study the qualitative properties of the system at infinite in the poincare sphere
因為系統在（ 0 ， 0 ）點處沒有定義，這給研究其在（ 0 ， 0 ）附近的動力學性質帶來了困難，我們應用文獻[ 17 ]中關于研究非線性方程奇點的系列理論和方法，圓滿解決了這一問題，給出了第一象限內當t +或t -時，在全參數狀態下系統的軌線趨于（ 0 ， 0 ）點的所有可能情況，其相圖也得以描繪；並且，系統不存在極限環的幾個充分條件我們也予以列出，當x的等傾線在0 x 1范圍內遞減時，系統不存在極限環，全局漸近穩定；然後，我們以中心流形定理和正規型方法為主要工具，巧妙選擇參數，分別構造了一個余維2的鞍點分岔和一個余維3退化bogdanov - takens分岔，證明了平衡點是余維3的焦點型平衡點，存在參數， m ，的值使得系統（ 6 . 1 ）有兩個極限環，還存在參數， m ，的另外值使得系統（ 6 . 1 ）有同宿軌或雙同宿軌。 -
In this article, we study the infinite boundary value problems for first order nonlinear impulsive differential equations with " supremum " by means of the upper and lower solution method and the monotone iterative technique, and obtain the existence theorems for their extremal solutions
摘要應用上下解方法和單調迭代技術研究了帶有上確界的一階非線性脈沖微分方程無窮邊值問題，並獲得了其極值解的存在性結果。 -
At the same time, the problem described above was solved in the frequency domain and the analytical solution for lateral steady response of single pile with finite length or with infinite length was developed under different boundary conditions
同時，對上述同一問題在頻域內進行求解，得到了各種邊界條件下的有限長樁和無限長樁水平穩態振動解。 -
Infinite boundary value problems for nonlinear impulsive differential equations with quot; supremum quot
的非線性脈沖微分方程無窮邊值問題 -
Multiple positive unbounded solutions of infinite boundary value problem of a class of nonlinear second order differential equation
一類非線性二階微分方程無窮邊值問題的多重正無界解 -
In this paper, by constructing a special cone and using fixed point theorem on cone, the existence of at least one positive unbounded solutions of infinite boundary value problem of a class of singular differential equations is obtained
摘要通過構造一個特殊的錐，利用錐上的不動點定理討論了一類二階奇異微分方程無窮邊值問題正無界解的存在性。 -
In this paper, by constructing a special cone and using krasnoselskii fixed point theorem, the existence of two positive unbounded solutions of infinite boundary value problem of a class of nonlinear second order differential equation is proved
摘要本文通過構造一個特殊的錐，利用錐拉壓不動點定理，證明了一類非線性二階微分方程無窮邊值問題的兩個正無界解的存在性。 -
In this pattern a new kind of infinite boundary element is developed to reduce wave reflection on the boundary. by this method, a simple and convenient numerical way is worked out and dissipation of the pore press, damping can be taken into account. it can not only solve the problem of material nonlinearity, but also be suitable for the problem of large deformation
考慮到反射波在計算區域內經多次反射、透射和散射對計算結果可能產生較大的影響，在上述飽和砂土有限元模型的基礎上，建立了一種新的動力無限元計算模型，該模型能滿足工程計算的要求。
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