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an associative
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  联想
     An Associative Memory Neural Network Based on Classifying Thought
     基于分类思想的联想记忆神经网络
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     AN ASSOCIATIVE THINKING AND LEARNING NN MODEL BASED ON HOPFIELD NET
     基于Hopfield网的自学习联想思维神经网络模型
短句来源
     Analysis of an Associative Memory Model Based on Matched Filters
     对基于匹配滤波器的联想记忆模型的分析
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     Discussing the differentia of Medical- Diagnostic Expert System(MDES), this paper gives an Associative Memory Neural Network(AMNN) appropriative to the inference engine of MDES.
     本文探讨了医疗诊断专家系统(MDES)的特殊性,提出了适合于MDES推理机的联想记忆神经网络(AMNN)。
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     Hence, an associative interpolation algorithm is proposed in this paper for improving the learning accuracy of CMAC. Meanwhile, a simulation experiment is described.
     该文提出了一种改进 CMAC学习精度的联想插补算法 ,同时给出了一个仿真实验 .
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  “an associative”译为未确定词的双语例句
     It is an associative algebra over R, with parameters Ω = {ω_a ∈ R | a ≥ 0} and u = (u_1,··· , u_m) ∈ R~m.
     这是一类依赖于参数Ω={ω_α∈R|α≥0}以及参数u=(u_1,…,u_m)∈R~m的结合R-代数。
短句来源
     Suppose R is an associative ring with an identity, _RP is a progenerator and E= End _RP.
     设R是带恒等元的结合环,_RP是投射生成元,E=End_RP.
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     A#_σH is an associative algebra with identity element 1_A#1_H if and only if the following two conditions are satisfied: 1. A is a twisted H-module.
     x所在的类,且得到了交叉积A#_σH是一个单位元为1_A#1_H的结合代数的充要条件: 1.A是扭H-模.
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     An Associative Study of the Expression of Fas、Bcl-2 in the Pulpy Nucleus Tissue of Lumbar Discs and the Apoptosis of Nuclei Pulposus
     腰椎间盘髓核组织Fas、Bcl-2的表达与髓核细胞凋亡的相关研究
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     Su Yucai and Zhao Kaiming introduced the Weyl type algebra A[D] and proved that A[D], as an associative algebra, is simple if and only if A is D-simple and κ1 [D] acts faithfully on A.
     苏育才与赵开明引进Weyl型代数A[D]并且证明了结合代数A[D]是单代数当且仅当A是D-单的且κ1[D]在A上的作用为忠实的.
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  相似匹配句对
     An E.
     建议了一种E .
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     An.
     An.
短句来源
     Let R be an associative ring.
     设R为结合环。
短句来源
     Let R be an associative ring with identity.
     设R是有单位元的结合环,J是R的Jacobson根。
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  an associative
Implications for the polymerization mechanism are discussed; the process follows an associative interchange (Ia) pathway.
      
It is shown that any neutral polyverbal subgroup W is generated as a subgroup by the set of its fully neutral polywords, and a necessary and sufficient condition is given for an associative neutral polyverbal operation to be verbal.
      
It is proved that ifR is an associative algebra with identity element over an infinite fieldF, then the algebraR(-) is nilpotent of lengthc if and only if the semigroupM(R) (orA(R)) is nilpotent of lengthc (in the sense of A.
      
Let R be an associative ring with unit, let S be a semigroup with zero, and let RS be a contracted semigroup ring.
      
Infinite Independent Systems of Identities of an Associative Algebra over an Infinite Field of Characteristic Two
      
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In this paper we first give a definition for a module over a non-assoeiative and non-distributive ring (briefly NAD-ring). It can easily be seen that the notion of module over NAD-ring contains the notion of module over an associative ring in usual sense. However, we have constructed an example which shows that the module over NAD-ring can not be always an usuat module over an associative ring. Using this notion of module over an NAD-ring we can introduce the notion of primitive NAD-ring. Then we...

In this paper we first give a definition for a module over a non-assoeiative and non-distributive ring (briefly NAD-ring). It can easily be seen that the notion of module over NAD-ring contains the notion of module over an associative ring in usual sense. However, we have constructed an example which shows that the module over NAD-ring can not be always an usuat module over an associative ring. Using this notion of module over an NAD-ring we can introduce the notion of primitive NAD-ring. Then we define Jacobson-radical of NAD-ring. It can be proved that the Jacobson-radical J of an NAD-ring R can be expressed as the intersection of all maximal normal regular right ideals of R and that the Jacobson-radical of the residue NAD-ring R/J is O. Therefore we can introduce the notion of semi-simple NAD-ring. In this paper we give a method of characterizing the Jacobson-radical. Using this characterization we obtain the following main results:Structure theorem. Let R be a semi-simple non-associative and non-distrlbutivering, satisfying the minimal condition for right ideals of R, then(ⅰ) R has a finite number of dimple ideals (a_1), (a_2),…, (a_n) of R such that R is a direct sam of these.(ⅱ) Every ideal A of R is a direct sam of (a_i_1), (a_i_2),…, (a_i_5) which are some of (a_1), (a_2),…, (a_n). If the ideal A of R is considered as a ring, then every (right) ideal of A is also a (right) ideal of R. Moreover, R has exactly 2~n number of non-zero ideals of R.(ⅲ) Every right ideal of R is a direct sum of a finite number of minimal right ideals of R.(ⅳ) Every prime ideal of R must be maximal and the number of prime ideals of R is n exactly, n being the number of (a_1),…, (a_n) given by (ⅰ). Moreover every prime ideal p_i is the form p_i=(a_1)+…+(a_(i-1)) + (a_(i+1))+…+ (a_n).In particular, if our NAD-rings are the usual associative rings then our results are consistent with the well-known results.

本文对非结合非分配环(以下简称两非环)引进Jacobson根概念,同时证明了它是文中意义下的极大合格正则右理想之交,并且通过一系列概念及结果,主要来建立两非环的结构定理,任何满足右理想极小条件的半单纯两非环R只有有限多个单纯理想,并且R是这些单纯理想之直和,这些单纯理想都是满足右理想极小条件的单纯半单纯两非环,它们中的每一个都可分解成有限多个极小右理想之直和,特别两非环取为通常结合环时,本文的结果包含通常结合环所熟知的结果。

In the literature, only the tensor product SL of a right R module S and a left R module L is defined and considered, where R is a ring. The theory of such tensor products is very important in the theory of rings, modules, categories and homology. However, such a tensor product is not a ring module, neither a left R module, nor a right R module. In this paper, the tensor product L_1L_2 of two left ring modules is defined, where L_i is a left R_i module, i=1, 2, R_1 and R_2 are K-rings, may not equal. Thus, if...

In the literature, only the tensor product SL of a right R module S and a left R module L is defined and considered, where R is a ring. The theory of such tensor products is very important in the theory of rings, modules, categories and homology. However, such a tensor product is not a ring module, neither a left R module, nor a right R module. In this paper, the tensor product L_1L_2 of two left ring modules is defined, where L_i is a left R_i module, i=1, 2, R_1 and R_2 are K-rings, may not equal. Thus, if is a category of a class of lelt ring madules L_μ, associated with morphisms H (L_μ, L_λ), L_μ, being left R_μ module and if L' is a left R' module, then—L' is a functor of . A part of the results obtained are the following: Let K be a commutative ring with unity. In §2, we considered the tensor product of some well-known K rings (wrt. K). Some of them are. If R_1 and R_2 are division rings, K is a field, and if a∈R_1, β∈R_2, such that they have the same minimum polynomial, over K, then R_1R_2 can't be a division ring. Let R_1 and R_2 be simble rings over a field K, with centrum ∑_1 and ∑_2 resp. Let F=K(∑_1,∑_2), then R_1R_2 is simple, if and only if for any finitely many elements t_1, t_2…, t_n ∈∑_2, whenever they are linear ind. over K, they are lin. ind. over ∑_1. This improves a theorem of Azumaya and Nakayama obtained in 1944. Let R_i be K-rings, and L_i be left R_i modules, i=1, 2, in §3, we first define a R_1R_2 mapping φ of L_1×L_2 into a left R_1R_2 module S being multiliner, if Φ(sum from i to u_i a_i, sum from to v_j β_j)=sum from ij(u_iv_j)Φ(a_i, β_j). A left R_1R_2 module S is called a tensor product of L_1 and L_2 written S=L_1L_2, if (1) φ: L_1×L_2 →→ S being multlilinear, and (2) whenever ψ: L_1×L_2 → V being multilinrear, f: S → V, f φ=ψ. The existence, uniqueness, and some fundamental properties of such tensor products are proved. In §4, We considered the functor—L'. Suppose L_μ and L'_R are left R_μ and R'_λ modules. Let σ: R_1 → R'_1 be a K homorphism, f_σ: L_1 → L'_1 be a mapping, such that f_σ(ua+vβ)=uf_σa+vf_σβ∈L'_1, u, v∈R'_1, β∈L_1, we then have the commutative diagram and whenever f_σ.g_τ are isomorbhisms, f_σg_τ is an isomorphism. Some properties of flat modules are considered. If L_μ and L' are projective left R_μ and R' modules, then L_μL' is also projective. If L_μL' is projective, and L' is a projective K module, then L_μ must be projective. Let R be an associative ring, L a left R module, its dual module is a right R module. We then have: if L_μ and L'_λ are finitely generated projective modules, then L_μ~*L'_λ~*≌(L_μL_λ)~*. 20

本文首先在§2中讨论了几种常见的环的张量积,在§3中,对于一个左Rl模L_1与一个左R_2模L_2定义了它们的多重线性映射,从而定义了它们的张量积L_1L_2证明了这种张量积的存在性,唯一性,与一些基本性质。在§4中,对一类左环模所构成的范畴,考虑了函子——L′的几个初步性质,这里L′也是一个左环模。

In the literature, only the tensor product SL of a right R module S and a left R module L is defined and considered, where R is a ring. The theory of such tensor products is very important in the theory of rings, modules, categories and homology, However, such a tensor product is not a ring module, neither a left R module, nor a right R module. In this paper, the tensor product L_1L_2 of two left ring modules is defined, where L_i is a left R_i module, i=1, 2, R_1 and R_2 are K-rings, may not equal. Thus, if...

In the literature, only the tensor product SL of a right R module S and a left R module L is defined and considered, where R is a ring. The theory of such tensor products is very important in the theory of rings, modules, categories and homology, However, such a tensor product is not a ring module, neither a left R module, nor a right R module. In this paper, the tensor product L_1L_2 of two left ring modules is defined, where L_i is a left R_i module, i=1, 2, R_1 and R_2 are K-rings, may not equal. Thus, if is a category of a class of left ring madules L_μ, associated with morphisms H (L_μ, L_λ). L_μ being left R_μ module and if L′is a left R′ module, then —L′ is a functor of. A part of the results obtained are the following: Let K be a commutative ring with unity. In §2, we considered the tensor product of some well-known K rings (wrt. K). Some of them are. If R_1 and R_2 are division rings, K is a field, and ifα∈R_1, β∈R_2, such that they have the same minimum polynomial, over K, then R_1R_2 can′t be a division ring. Let R_1 and R_2 be simble rings over a field K, with centrum ∑_1 and ∑_2 resp. Let F=K(∑_1,∑_2), then R_1R_2 is simple, if and only if for any finitely many elements t_1.t_2…,t_n ∈∑_2, whenever they are linear ind. over K, they are lin. ind. over ∑_1. This improves a theorem of Azumaya and Nakayama obtained in 1944. Let R_i be K-rings, and L_i be left R_1 modules, i=1, 2, in §3, we first define a R_1R_2 mapping φ of L_1×L_2 into a left R_1R_2 module S being multilinear, if A left R_1R_2 module S is calied a tensor product of L_1 and L_2, written S= L_1L_2, if(1) φ:L_1×L_2 →→ S being multilinear, and (2) whenever φ: L_1×L_2 →V being multilinrear, f: S→V, fφ=φ. The exisience, uniqueness, and some fundamental properties of such tensor products are proved. In §4, We considered the functor —L′. Suppose L_μ and L_R are left R_μ and R_λ modules. Let σ:R_1→R_1 be a K homorphism, f_σ:L_1→L_1 be a mapping, such that we then have the commutative diagram and whenever f_σ g)τ are isomorbhisms, f_σg_τ is an isomorphism. Some properties of flat modules are considered. If L_μ and L' are projective left R_μ, and R' modules, then L_μL' is also projective. If L_μL' is projective, and L' is a projective K module, then L_μ must be projective. Let R be an associative ring, L a left R module, its dual module is a right R module. We then have: if L_μ and L'_λ are finitely generated projective modules, then L_μ~*L'_λ~*(L_μL_λ)~*.

本文首先在§2中讨论了几种常见的环的张量积,在§3中,对于一个左R_1模L_1与一个左R_2模L_2定义了它们的多重线性映射,从而定义了它们的张量积L_1L_2证明了这种张量积的存在性,唯一性,与一些基本性质。在§4中,对一类左环模所构成的范畴,考虑了函子——L~′的几个初步性质,这里L~′也是一个左环模。

 
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