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orthogonality
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  正交性
     In this paper we have proved the orthogonality principle in L2 space and come to the conclusion that the principle is equivalent to Linear Minimum Mean - Square Error Estimation or Wiener Filtering. The continuous Wiener - Holf equation and error formula are derived from the principle.
     证明了L2空间中的正交性原理,得到正交性原理与线性最小均方误差估计与维纳滤波是等价的结论,并用正交性原理推导出连续型的维纳—霉夫方程及误差表达式。
短句来源
     An accurate method of computing phase samples making use of the orthogonality of complex impulse response is presented.
     提出了利用复脉冲响应的正交性精确计算相位抽样的方法。
短句来源
     Adding some lower terms in the remainder of orthogonal expansion in an element so that the remainder satisfies more orthogonality conditions in the element, and obtain a desired superclose function to finite element solution, thus several new superconvergence results for the initial value problem of ordinary differential equation are derived.
     在单元正交展开的余项中添加若干待定低次项,使此余项在一个单元上满足更多的正交性条件,得到所需的超接近于有限元解的逼近函数,由此对常微分方程初值问题导出了一些新的超收敛结果.
短句来源
     Let H be a complex Hilbert space, B(H) denote the algebra of all linear bounded operators on H. In this note, the additive maps on B(H) preserving orthogonality and the additive maps on von Neumann algebra commuting with | ? |k are characterized.
     设H是复Hilbert空间,B(H)表示H上所有有界线性算子构成的代数. 本文刻划了B(H)上保正交性的可加映射和von Neumann代数上与运算|·|k交换的可加映射.
短句来源
     First, we give the relation of Birkhoff orthogonality and functionals in Banach space, then use functionals as a tool to investigate the relations of Birkhoff orthogonality and underling Banach space.
     首先,建立了Banach空间中两个元素的Birkhoff正交性和线性泛函的关系,然后以线性泛函为主要工具,讨论了Birkhoff正交性和Banach空间结构的关系。
短句来源
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  正交
     Through orthogonality optimization experiment,the best prescription constituents of peptone and MgSO4·7 H2O and KH2PO4 and red sugar which were added to solid medium to mycelium growth of edible mushroom white Flammulina velutipes F3,They were 0.10% peptone,0.10% MgSO4·7 H2O,0.20% KH2PO4 and 2.0% red sugar,respectively.
     通过正交优化试验得出固体培养基配方中添加蛋白胨、MgSO4.7 H2O、KH2PO4、赤砂糖的最佳配比浓度分别为0.10%、0.10%、0.20%、2.0%,此时白金针菇F3菌丝生长速度最快,且菌丝浓密。
短句来源
     The orthogonality experiment was used to optimize cultural conditions, and the result showed that the optimal cultural conditions were pH6.0, temperature 33℃, K_2HPO_4 0.2%, yeast cream 0.1%, MgSO_4 0.2%, peptone 2.5%, dissolubility starch 2.5%.
     经过培养条件优化的正交实验,发现诱变后的S2菌株最佳培养条件为初始pH6.0,培养温度33℃,K_2HPO_4 0.2%,酵母膏0.1%,MgSO_4 0.2%,蛋白胨2.5%,可溶性淀粉2.5%。
短句来源
     Walsh's orthogonality code is the ideal choice.
     沃尔什(Walsh)正交码是一种理想选择。
短句来源
     Based on the analysis of the two-way multirate filter bank,orthogonality,regularity and symmetry of orthogonal,biorthogonal and symlets wavelets are examined.
     从双通道多采样率滤波器组出发,分析了正交小波、双正交小波以及折中的symlets小波的正交性、正则性、对称性等特性.
短句来源
     The platform is made up of A/D ( AD6640 12bit 65 MSPS ) , orthogonality transform , digital filtering and DSP, etc.
     该平台由高速A/D变换器(AD6640 12位65MSPS)、正交变换、数字滤波器、DSP等部分构成。
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  “orthogonality”译为未确定词的双语例句
     CONDITIONS OF ORTHOGONALITY AND STABILITY ASSOCIATED WITH THE GENERAL REFINEMENT EQUATION
     CONDITIONS OF ORTHOGONALITY AND STABILITY ASSOCIATED WITH THE GENERAL REFINEMENT EQUATION
短句来源
     The optimum enrichment medium obtained by orthogonality test consist of adding 0.5% Soya peptone,0.5% Yeast Extract,1% Beef Extract,0.2% K_2HPO_4 in the 10% wort medium.
     t-3的麦芽复合汁增菌培养基最佳配比为:在10%的麦芽汁中添加0.5%大豆蛋白胨、0.5%酵母膏、1%牛肉膏、0.2%K2HPO4; 在麦芽复合汁增菌培养基中,S.
短句来源
     This method has 4 advantages: 1) The experiment scheme is simple and satisfies the orthogonality condition.
     该方法有4个特点:1)实验方案的构造方法简单,而且得到的实验方案具有各特征参数搭配均衡的特点;
短句来源
     An optimal localization of the canonical molecular orbitals of molecules CH4, C2H6, C2H4, C,H, was successfully performed by means of projection operator method, so for as the restriction of orthogonality is given up.
     本文应用投影算子方法,放弃了正变化条件的限制,成功地将CH4、C2H6、C2H4、C2H2分子的正则分子轨道实现了最佳定域化。
短句来源
     In Banach spaces l_S~P and C_p, we give some properties Birkhoff orthogonality.
     其次,在特殊的Banach空间l_S~p和C_p中,给出了两个元素Birkhoff正交的充要条件。
短句来源
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  orthogonality
Orthogonality conditions for ?1, …, ?q naturally impose constraints on the scaling coefficients, which are then called the wavelet matrix.
      
Furthermore, we generalize the sufficient and necessary conditions of orthogonality given by Lawton and Cohen to the case of several dimensions and arbitrary dilation matrix A.
      
We extend to general finite groups a well-known relation used for checking the orthogonality of a system of vectors as well as for orthogonalizing a nonorthogonal one.
      
Orthogonality criteria for compactly supported refinable functions and refinable function vectors
      
In this paper we give a comprehensive set of necessary and sufficient conditions for the orthogonality of compactly supported refinable functions and refinable function vectors.
      
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In this paper we studied the Maxwell's equations in imhomogeneous and anisotropic media as an operator. It is defined in a bounded region, which can be comprehended as a resonant cavity in micro-wave technique. But these cavities are filled with ferrite, plasma or other gyrotropic medium, all these new media become more and more important in practice. We proved that under some concrete conditions imposed on μ, e and restrictions on the boundary value, the operator of Maxwell's equations becomes a symmetric one....

In this paper we studied the Maxwell's equations in imhomogeneous and anisotropic media as an operator. It is defined in a bounded region, which can be comprehended as a resonant cavity in micro-wave technique. But these cavities are filled with ferrite, plasma or other gyrotropic medium, all these new media become more and more important in practice. We proved that under some concrete conditions imposed on μ, e and restrictions on the boundary value, the operator of Maxwell's equations becomes a symmetric one. The symmetry and self-adjoint property give much convenience in eigenfunction expansion problems. Besides, we derived the orthogonality of characteristic oscillation and reciprocity theorem in general.

在本文中,把在不均匀各向异性介质中的麦克斯韦方程看作算符,它定义在一个有界区域,可以被理解为微波技术中的谐振腔。但在这腔中充填着铁氧体,等离子体或其他各向异性介质,这些介质在应用中日益重要。文中证明了在某些、边界条件下,算符成为对称。而对称性和自伴性在本征函数展开中带来很多方便;此外我们推导了本征振动的正变性和互易定理。 如果不满足对称性,引入伴谐振腔的概念,所谓伴谐振腔在几何形状上和原来的腔相同,但、和边界条件不一样。它和自伴谐振腔在正交性和互易定理上有某些相似之处。

A new approximate method for treating nn and pp pairing force in nuclei is presented. In this method the difficulties connected with the application of BCS-Bogolubov method to nuclei such as the non-conservation of the number of particles, the apperance of spurious states, and non-orthogonality between wave functions of different excited states are avoided. But the method can be conviently adopted only when the number of particles n and the number of levels Ω considered are small (n ≤10, Ω≤10 ). Also the...

A new approximate method for treating nn and pp pairing force in nuclei is presented. In this method the difficulties connected with the application of BCS-Bogolubov method to nuclei such as the non-conservation of the number of particles, the apperance of spurious states, and non-orthogonality between wave functions of different excited states are avoided. But the method can be conviently adopted only when the number of particles n and the number of levels Ω considered are small (n ≤10, Ω≤10 ). Also the approximation of this method is good onlv under such conditions. In this method the many-body nature of the excitation is displayed explicitly without introducing the conception of quasi-particles. The excitation of the system can be divided into two classes. The first class of excitation is a kind of single particle excitation embedded in a many-body system under the action of the pairing force. This would correspond to the excitation of a single quasi-particle a_v~+av0 or to two quasi-particle excitation of the type α_v~+β_(v')~+,α_v~+α_v'~+(v'±v) etc. in the BCS-Bogolubov method. The second class of excitation is a pair excitation in which the distribution of the conjugated pairs of particles among the levels is altered. This type of excitation would correspond to superposition of quasi-particle excitations of the type α_v~+β_v~+,α_v~+β_v~+α_μ~+β_μ~+, Also examined is the effect of pairing force on the β- and γ-transition probability in the new formalism. In general, β-transition is retarded by the pairing force while in γ-transition the effect of pairing force varies according to the nature of the relative excitation between the initial and final states. When the relative excitation is of the first class, the transition is retarded to various extent, depending on the nature of the γ-transition. If the relative excitation is of the second class, the transition is forbidden when the pairing force is not in action, and is allowed only for electric transition arising from the charge-current distribution when the pairing force is present. Finally this method is applied to investigate the effect of pairing force on the intrinsic spectra and β-transition in 72Hf178 as an example.

本文提出了一个处理原子核中nn及pp对力的近似方法。这个方法避免了通常将方法应用于原子核所引起的困难,例如粒子数不守恒,假态的出现以及不同激发态波函数不正交等。但这个方法只有在所需考虑的粒子数n及能级数Ω不太大时(n≤10,Ω≤10)才能较方便地被应用,近似程度才比较好。在这个方法中,毋须引入准粒子的概念,激发的多体性质被明显地表示出来。系统的激发可分为两大类型。第一类型激发是一种以多体系为背景的单粒子跃迁,相应于一个准粒子的跃迁α_ν~+α_ν,或两个准粒子的激发α_v~+β_v′~+,α_v~+α_v′~+(vv′)。第二类型激发是对激发,在这种激发中,各能级上共轭粒子对的填充几率改变了,相应于共轭的准粒子对的激发α_v~+β_v~+,α_v~+β_v~+α_μ~+β_μ~+,…. 本文还考察了对力在r及β跃迁中的影响。在β跃迁中,对力一般是使跃迁受阻。在r跃迁中,对力的效应随初末态间的相对激发类型不同而异,如相对激发属于第一类型,则跃迁受阻,受阻程度随跃迁的电磁性质不同而有所差别,如相对跃迁属于第二类型,则在无对力作用时跃迁是禁戒的,在对力作用下也只有由电荷电流所产生的电跃迁是允许的。 最后本文以Hf~...

本文提出了一个处理原子核中nn及pp对力的近似方法。这个方法避免了通常将方法应用于原子核所引起的困难,例如粒子数不守恒,假态的出现以及不同激发态波函数不正交等。但这个方法只有在所需考虑的粒子数n及能级数Ω不太大时(n≤10,Ω≤10)才能较方便地被应用,近似程度才比较好。在这个方法中,毋须引入准粒子的概念,激发的多体性质被明显地表示出来。系统的激发可分为两大类型。第一类型激发是一种以多体系为背景的单粒子跃迁,相应于一个准粒子的跃迁α_ν~+α_ν,或两个准粒子的激发α_v~+β_v′~+,α_v~+α_v′~+(vv′)。第二类型激发是对激发,在这种激发中,各能级上共轭粒子对的填充几率改变了,相应于共轭的准粒子对的激发α_v~+β_v~+,α_v~+β_v~+α_μ~+β_μ~+,…. 本文还考察了对力在r及β跃迁中的影响。在β跃迁中,对力一般是使跃迁受阻。在r跃迁中,对力的效应随初末态间的相对激发类型不同而异,如相对激发属于第一类型,则跃迁受阻,受阻程度随跃迁的电磁性质不同而有所差别,如相对跃迁属于第二类型,则在无对力作用时跃迁是禁戒的,在对力作用下也只有由电荷电流所产生的电跃迁是允许的。 最后本文以Hf~(178)为例,应用上述方法,初步分析了对力对偶偶核的内部激发能谱及β衰变的影响。

We shall attempt to study an interesting phenomenon in the theory of best approximation. We begin by some concepts which will be used below. 1. Let be a Hilbert space, h_n∈, and let (h_,h_k)=η_r),n,k=0,1,2,...; (1) (ⅰ) If η_(nk)=1 (n=0,1,2…), (2) η_(nk)→0 (for n≠k, as n,k→∞) (3) and η_(nk)→0 (for any fixed k, as n→∞; for any fixed n, as k→∞),(4) then we say that the sequence {h_n} is a quasi-orthonormal system (QONS)of 1st kind. (ⅱ) If (2) and (4) are satisfied, we say that {h_n} is a QONS of 2nd klnd. (ⅲ) If...

We shall attempt to study an interesting phenomenon in the theory of best approximation. We begin by some concepts which will be used below. 1. Let be a Hilbert space, h_n∈, and let (h_,h_k)=η_r),n,k=0,1,2,...; (1) (ⅰ) If η_(nk)=1 (n=0,1,2…), (2) η_(nk)→0 (for n≠k, as n,k→∞) (3) and η_(nk)→0 (for any fixed k, as n→∞; for any fixed n, as k→∞),(4) then we say that the sequence {h_n} is a quasi-orthonormal system (QONS)of 1st kind. (ⅱ) If (2) and (4) are satisfied, we say that {h_n} is a QONS of 2nd klnd. (ⅲ) If (2) and (3) are satisfied, we say that {h_m} is a QONS of 3rd kind. 2. Let f(x)∈C_(-1,1), p(x)∈C_(-1,1) be a non-negative weight function, and let P_n(x)=P_n(f,x) be the (nth) best approximation polynomials or simply the minimum polynomials of f with the weight p on [—1,1. We say simply that ψ_n(x)=f(x)-p_m(x) is the minimum sequence of functions for f. 3. Let f∈C_(-1,1)~′ (the class of functions with 1st derivative belonging to C_(-1,1), L_n=‖(f—P_n)p‖y_n=(f—P_n)P, where P_n are the minimum polynomials, the functions Q_n(x)=(y_n~(′2))/(L_n~2-y_n~2) (5) are called the (nth) associate functions of f. Concerning these definitions and reserving the sense of the above symbols, we proved the following theorems. Let A be a certain class of real irreducible proper fractions and let the positive weight p(x) take the form Ⅰ. {C_0+…+c_vx~v}~(1/2) or Ⅱ. {C_0+…+c_vx~v}~(-1/2); Then under certain restrictions (see the begInning of §2) we have THEOREM 1. Let R_n(x)={Q_m(x)((1-x~2)/((n±v/2)~2))}~(-1) where="±" corespond to p taking Ⅰ or Ⅱ, respectively. (ⅰ) If L_m=O(1),‖1—R_m‖=o(1/n), ‖R_n~′‖=o(1/n), then the normal minimum sequence of functions λ_n {f—P_n} is a QONS of 1st kind in space L_(-1,1)~2((p~2(x)/(1-x~2)~(1/2)) (ⅱ) If L_m=o(1),‖1—R_m‖=O(1/n), ‖R_n~′‖=O(1/n), the conclusion of (ⅰ) also holds. (ⅲ) If L_m=O(1), ‖1—R_n‖=o(1), ‖R_n~′‖=o(1), the same sequence λ_n{f—P_n} is a QONS of 2nd kind in L_(-1,1)~2((p~2(x)/(1-x~2)~(1/2)). THEOREM 2. Let p(x) be of the form Ⅱ, the associate functions of f be of the form Q_n(x)=((n-v/2)~2)/(1-x~2){1+sum from n=1 to 1,μ B_l/(x-β_l)+sum from n=1 to 1,v C_j/(x-y)}~2 (U_(μ-1)~2)/(V_(2μ-2)), where B,C,β,γ are constants, U,V are some μ—1 th and 2μ—2 th order polynomials, respectively. If (ⅰ) (?) (U_(μ-1)~2(x))/(V_(2μ-2)(x))=1 (—∞orthogonality.

文中引进伪直交性(quasi-orthogonality)概念,它是平常直交性概念的一种推广。受到了古典切彼曉夫多項式等的提示,我們指出对於連續函数的某一子类,其最小元列在某內积空間中具有第一种、第二种或第三种伪直交性。这些結果可以看成一种嵌入性质(embedding property)。文中有若干例子說明伪直交系的存在,还給出定理的特例,即在某些情形最小元列具有(真)直交性。

 
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