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multipole

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multipole adj.,n.【物理學】多極(的),復極(的)。

adj.,n. 【物理學】多極(的),復極(的)。 “electric multipole“ 中文翻譯：   電多極子“magnetic multipole“ 中文翻譯：   磁多極“multipole configuration“ 中文翻譯：   多極位形“multipole emission“ 中文翻譯：   多極發射“multipole expansion“ 中文翻譯：   多極擴散; 多極展開“multipole field“ 中文翻譯：   多極場“multipole fields“ 中文翻譯：   多極場“multipole interaction“ 中文翻譯：   多極相互作用“multipole magnet“ 中文翻譯：   多極磁鐵“multipole moment“ 中文翻譯：   多極矩“multipole moments“ 中文翻譯：   多極矩“multipole potentiality“ 中文翻譯：   多極的潛能性“multipole radiation“ 中文翻譯：   多極輻射“multipole switch“ 中文翻譯：   多刀開關; 多端開關; 多極開關“multipole transition“ 中文翻譯：   多極躍遷“universal multipole“ 中文翻譯：   通用多極“electric multipole field“ 中文翻譯：   電多極場“electric multipole moment“ 中文翻譯：   電多極矩“electric multipole radiation“ 中文翻譯：   電多極輻射“electromagnetic field of multipole“ 中文翻譯：   多極電磁場“electromagnetic multipole radiation“ 中文翻譯：   電磁多極輻射“high-order multipole radiation“ 中文翻譯：   高次多極輻射“magnetic multipole field“ 中文翻譯：   磁多極場“magnetic multipole radiation“ 中文翻譯：   磁多極輻射“multipole acoustic log“ 中文翻譯：   多極聲波測井“multipolarmultipole“ 中文翻譯：   多極的

multipolymer

The content of this thesis can be reduced to two parts , the first part expounds the boundary integral equation theory for composite metallic and dielectric structures and its resolving technique based on method of moments , the second part expounds the multilevel fast multipole algorithm and its stand - alone and parallel implements technique 論文的內容可分為兩大部分,第一部分主要闡述了用于分析“金屬與介質混合結構”的邊界積分方程理論及其基于矩量法的求解技術;第二部分闡述了用于加速計算的快速多極算法理論及其串行與并行實現技術。

It regards the master of knowledge as its sole objective and ignores the vitality of teacher and student ; it pursues unified requirements and ignores students “ differences and potential development ; it emphasizes linear and static control and ignores dynamics and synthetic aspects of teaching ; it stresses one - way subject - object structure and ignores subjects “ multipole interaction , social interaction , two - way structure and dual conformity in subject - object - subject structure in educational communication 它以知識的掌握作為教育的唯一追求，忽視教師、學生的生命性；追求統一要求，忽視學生的差異性、潛在發展性；強調線性的、靜態的控制，忽視動態的非線性的動態生成性和綜合滲透性；強調單向度的主體一客體，忽視教育交往中主體?客體?主體結構中主體的多極性、社會交往性以及雙向建構和雙重整合性。

Applying the method studied in this thesis , theoretical calculation of certain container ship in regular wave has been done on ship motion and hydrodynamic pressure . it also has the results compared with those obtained under multipole conditions in the model tests . as a consequence , we abstract some characteristics of the distribution of instantaneous hydrodynamic pressure on ship wet surface , and the distribution changes with forward speed and wave parameters 利用本文方法對某集裝箱船進行了規則波中的船舶運動和水動壓力的理論計算，并與船模水池試驗所提供的多狀態的壓力分布數據相比較，得出船體表面瞬時壓力的分布及其隨航速和波浪參數變化的某些規律。

The major work is as follows : solution of two dimensional radiation or diffraction fluid field . this thesis extends multipole expansion method to adapt to disturbed fluid fields of 2d floating bodies with asymmetric forms , which is applied with symmetric forms originally . and given the solution of potential velocity and hydrodynamic pressure of radiation and diffraction fluid fields , which is incited by a 2d arbitrary form , actual application field of the multipole expansion method has been enlarged 關于二維擾動流場的求解：將通常僅適宜求解具有對稱形狀二維物體擾動流場的多極展開法(保角變換方法)擴展至非對稱形狀二維物體，給出了任意形狀二維物體的輻射和繞射流場的速度勢及水動壓力的頻域解，進一步擴大了多極展開法的實際應用范圍。

Through the event horizon temperature of a kind of manko black hole with mass multipole moment can derive that the value is a constant except singular points , near which the temperature values are irregular . as one of the novel conclusions , such phenomena about the distribution has been paid reasonable explanation 本文對一類具有質量多極矩的manko黑洞的視界溫度進行了研究，準確地計算出此類黑洞的熱輻射溫度在視界上除內稟奇點處外是常數，而在黑洞視界面的內稟奇點附近的視界溫度出現異常值，并對這種溫度分布的現象作了合理的解釋。

Finally the paper emphatically introduces the mlfma ( multilevel fast multipole algorithm ) . based on hybrid field integral equation the formulation of computation for the electromagnetic scattering of three - dimensional object is derivated . then the optimization of invariant terms and the expression of every child cube is analyzed during the electromagnetic scattering calculation when using the mlfma 文章最后引入多層快速多極子法，從混合場的積分方程出發，推導出多層快速多極子法計算三維物體電磁散射的公式，分析了多層快速多極子法計算三維物體電磁散射過程中不變項計算的優化和編程時每個小立方體的表示方法。

People also have made a series of researching theoretical work on black hole ' s radiation etc . , while relative issues need being studied furtherly . in this paper , researches on black hole ' s radiation effect and relative issues including the nonthermal effect of the black hole with mass multipole moment , there exists a new kind of dirac energy levels and the crossing region of dirac energy levels 其中，通過對一類具有質量多極矩的黑洞的非熱輻射效應的研究得到了一些有意義的新結果，發現了一類新的dirac能級和一類新的dirac能級交錯區，這種新的dirac能級交錯區的出現導致非熱輻射的發生，在一些方向上出現輻射能量很大的非熱輻射。

In the paper , the new electromagnetic scattering algorithms have been introduced - recursive aggregate t - matrix algorithm ( ratma ) and fast multipole algorithm ( fma ) . two kinds of methods are precise and efficient and have advantages over conventional method of moment in computational speed and requirement for storage space 本文研究了基于積分方程的電磁散射計算方法，主要研究了兩種算法：遞推t矩陣法和快速多極子法，這兩種算法都有計算量小、所需內存少和精度高的優點。

Research on electromagnetic scattering of complex targets has been received much attention for a long time , the fast inhomogeneous plane wave algorithm ( fipwa ) in this paper performs well in this purpose , and the computation complexity of its multilevel version ( mlfipwa ) is of the same order as the multilevel fast multipole algorithm ( mlfma ) 復雜目標電磁散射研究長期以來廣受關注,本文研究的快速非均勻平面波算法,可以快速精確的求解任意復雜目標的電磁散射問題,其多層形式的計算復雜度與多層快速多極子相當。

From the exact expression of the field , we obtain a multipole polynomial expansion , and under the paraxial condition we furthermore obtain the approximate expression . the loffe trap , consisting of two coils with parallel currents and four straight conductors with currents in alternating directions , is one of the most important traps . we specially study the field structure of it by using both the exact expression and a multipole polynomial expansion that facilitates studies of classical or quantum orbits . if the region near the origin is of interest , we may obtain a simple expression of the field and this configuration may be called idealized loffe trap 若只討論阱中的近原點區域時，阱中的磁場可以呈現出一種簡潔的形式，人們把它稱為理想ioffe阱。磁矩反平行于磁場的中性粒子在阱中與磁場發生相互作用，借助相互作用勢，可以獲得粒子在阱中的經典運動方程。在一定的近似條件下，我們可以采用逐次近似的方法，使方程簡化，其中三個分量式中關于z的方程比較容易求解，而關于x 、 y的方程則演化為我們熟悉的馬丟方程的形式。

After solution of radiational and diffractional fluid field of asymmetrical sections by applying the multipole expansion method , wave loads on damaged ships are calculated by the linear strip theory under the non - upright floating condition , taking the effect on the heel angle and trimming angle caused by the damaged tank inundation below waterline into account 然后采用線性切片理論，計及水線以下破損后船舶由于艙室進水產生的橫傾角與縱傾角的影響，利用多級展開法求解非對稱剖面的二維輻射和繞射流場，計算了破損船體非正浮狀態條件下的波浪載荷。

A new approach , the multipole theory ( mt ) method , is briefly described for analysis of waveguide eigenvalue problems . the essential concept is to represent the solution of the waveguide partial differential equation by the generalized mt formula of 2 - d helmholtz equation . the applied rules and the procedure of the mt method are also introduced . by calculating and analyzing some engineering problems , it is shown that the mt method is an effective approach for analysis of waveguide eigenvalue problems 本文利用多極理論分析波導本征值問題.給出用多極理論分析波導本征值問題的使用規則和實施方法.實例計算結果表明，用多極理論分析波導本征值問題，不僅具有較高的計算精度，而且可以很方便地應用于波導工程問題的設計與計算，多極理論是一種有效的波導本征值分析方法

For these proposes , we chose electromagnetic boundary integral equation ( bie ) theory as the theoretical foundation , method of moments ( mom ) as numerical process and the multilevel fast multipole algorithm ( mlfma ) to accelerate the solving process and reduce memory requirement 為此,我們選擇了電磁場邊界積分方程( bie )理論作為理論基礎,以矩量法( mom )作為數值求解方法,并使用多層快速多極算法( mlfma )來加速求解過程和降低存儲需求。

The results indicate that the effects of the dirac sea states are pronounced in the collective multipole excitations for nuclei , especially on the isoscalar giant modes , but become weaker for light nuclei , while the contributions on the isovector modes are negligible 在核的同位旋標量激發模式中， dirac海負能核子態在不同的共振模式中的貢獻程度不一。對于同一種激發模式， dirac海負能核子態的貢獻隨著核子數的減少而變弱。

Here are some references for nrqcd & nrqed : renormalization group scaling in nonrelativistic qcd on the multipole expansion , the qcd heavy quark potential to order v * * 2 : one loop matching conditions on matching calculations 11下面是非相對論性量子色動力學和非相對論性量子電動力學的一些參考資料：關于多極展開的非相對論性量子色動力學中的重整化群定標，關于匹配計算的v * * 2階的量子色動力學重夸克勢：單圈匹配條件。

To further speed up the solution of scattering from three dimensional electrically large object by multilevel fast multipole algorithm ( mlfma ) , a local multilevel fast multipole algorithm ( lmlfma ) based on local interactions is proposed to evaluate matrix - vector multiplication 摘要為了進一步加速多層快速多極子算法求解電大尺寸目標電磁散射，提出了一種基于局部耦合技術計算矩陣矢量相乘的多層快速多極子方法。

Combining the homogeneous matrix transformation theory of space mechanism and computer graphics , we raise the general principle and motion simulation ' s method of complicated mechanism , which is represented by spacial multipole structure of open chain 通過將空間機構學齊次矩陣變換原理和計算機圖形學原理相結合，提出了以空間多桿開式鏈機構為代表的復雜機械系統運動三維圖形仿真的一般原理和方法。

Van der waals ( vdw ) complexes are weak bonding complexes formed by atoms or molecules through interaction of electric multipole moments and dispersion forces . these complexes are characterized by their comparatively low binding energy ( 100 - 1000cm - 1 ) 范德瓦爾斯( vdw )復合物是原子或分子間通過多極矩和色散相互作用形成的弱鍵能復合物，它們的鍵能比較弱，一般為100 1000cm ~ ( - 1 ) 。

Using the fully consistent rrpa method , we have studied the properties of collective multipole excitations for several closed - shell and closed sub - shell nucleus in the isoscalar modes and isovector modes 計算結果顯示，從fermi海核子態到dirac海負能核子態形成的對激發在核的集體激發中的貢獻很重要，尤其是對核的同位旋標量激發模式。