An extended multi-valued exponential bi-directional associative memory (EMV-eBAM) model is presented in this paper based on Wang抯 MV-eBAM model, which is a special case of EMV-eBAM (extended MV-eBAM).

An algorithm ispresented for finding a 3-indepondent set of Qn,and 2n-[log2n]-1≤I3(n)≤[2n/(n+1)] is shown. These results are applied to the design of neural associative memories.

(2)For any x∈X, {(x*h)*h|h∈H} is denoted by H x and {H x|x∈X} is denoted by X/H 2 , * operation is X/H 2 is defined by H x*H y=H x*y . Then (X/H 2,*,H 0) is a generalized associative BCI_algebra.

They are: (1) Let φ be a representation on a finite dimensional associative algebra A, its representative matrix is T_(a) (=aφ∈ F_n, n>1) for any a∈A, and there exists an element a∈Z(A), a≠0, so that T_(a)≠0 and det T_(a) =0, then φ is reducible.

Using an In∶Fe∶LN crystal with an n(Li)/n(Nb) ratio of 1.38 as the recorder medium and an In∶Fe∶LN crystal with an n(Li)/n(Nb) ratio of 1.05 as the phase conjugate mirror, holographic associative storage experiments were conducted.

Using Cu∶Co∶SBN crystal as a storage element and using Mg∶Fe∶LiNbO 3 crystal as a phase conjugate reflector to gain the feedback system, the associative storage experiment is realized.

This paper proposes an improved version of the associative memory learning control system (AMLCS) for industrial processes with almost completely unknown but slowly time-varying dynamics.

A new embedded cache structure called X-way set associative cache was proposed. Through an instance of FFT,its principle and structure were introduced and its validity was discussed.

Invariant Theory for Non-Associative Real Two-Dimensional Algebras and Its Applications

The set ${\mathcal A}$ of all non-associative algebra structures on a fixed 2-dimensional real vector space $A$ is naturally a ${\mbox{\rm GL}}(2,{\mbox{\bf R}})$-module.

We show that the absolute invariants (i.e.,the ${\mbox{\rm GL}}(2, {\mbox{\bf R}})$-invariants in the field of fractions of ${\mathcal P}$) distinguish the isomorphism classes of 2-dimensional non-associative real division algebras.

Infinitesimal multiplication of a graded associative algebra is defined and the integrability of infinitesimal multiplication is discussed through the Massey F-product.

Coordinates and automorphisms of polynomial and free associative algebras of rank three

In this paper We have discussed the relation between the solvabilityfor all beR (a ring)and the uniqueness of the equation ax = b determined byan element aeR. The above—mentioned R is a general (associative) ring,and in particular, a ring With descending (or ascending) chain conditionfor right—ideals. Thus, We have obtained the relation betWeen the surjectivity and the injectivity of the left multiplication a1 determined by anelement aeR.

With the rapid development of the semiconductor integrated circuit technology, the cellular computer becomes an important trend for giant computers. There is no doubt that multiprocessor systems, array processor systems and associative array processor systems may be cellulated. But what will be with the more preferable giant vector computers for which the language may be expanded on the basis of the standard languages, the operating rules are similar to the conventional rules, and the efficiency is higher?Can...

With the rapid development of the semiconductor integrated circuit technology, the cellular computer becomes an important trend for giant computers. There is no doubt that multiprocessor systems, array processor systems and associative array processor systems may be cellulated. But what will be with the more preferable giant vector computers for which the language may be expanded on the basis of the standard languages, the operating rules are similar to the conventional rules, and the efficiency is higher?Can they be cellulated? this is what the present article will discuss in detail and the answer is positive. In this paper, some vector expansion of the standard language and an architecture of the vector computer of vertical and horizontal processing are described.Furthermore, the architecture of the normal cellular vector computer, and the architecture of cellular vector computer of vertical and horizontal processing are discussed.Finally, the advantages and the limitations due to which the number of cell-elements of vector computers can't be very large are described.

This paper continues to study the theory of the first paper by the author with symbols and notions appearing in this paper the same as in the first one if not specially stated. In order to state our main results, we first introduce some notions.An ideal a is called hypernilpotent, if there exists a finite number of positive intergers n_1, n_2,…, n_r such that a~(n1,n2,…,nr)=0.It is proved that a is hypernilpotent if and only if a is solvable, i.e. there exists an integer m ≥0 such that a~((m)) = 0.From the concept...

This paper continues to study the theory of the first paper by the author with symbols and notions appearing in this paper the same as in the first one if not specially stated. In order to state our main results, we first introduce some notions.An ideal a is called hypernilpotent, if there exists a finite number of positive intergers n_1, n_2,…, n_r such that a~(n1,n2,…,nr)=0.It is proved that a is hypernilpotent if and only if a is solvable, i.e. there exists an integer m ≥0 such that a~((m)) = 0.From the concept of hypernilpotent we can now define a radieal as follows: First, we can see easily that the union of all the hypernilpotent ideals of a non-associative and non-distributive ring R (briefly NAD-ring) may not be hypernilpotent. Furthermore, R may have hypernilpotent ideals. Let be the ideals of R such that is the union of all the hypernilpotent ideals of R In general, for every ordinal a which is not a limit ordinal, we define to be the ideal of R such that is the union of all the hypernilpotent ideals of R if a is a limit ordinal, we define In this way we obtain an ascending chain of ideals We may consider the smallest ordinal τ such that This ideal we shall call the radical of R.Definition 1: An NAD-ring R is called semi-simple,if the radicalThen we can state the following structure theorem.Theorem i: Let R be an NAD-ring with ascending chain condition (briefly a.e.e.) of ideals. Suppose that every prime ideal of R is maximal and R~2= R. ThenR is semi-simple if and only if R = R_1⊕R_2⊕... ⊕R_r,where R_i are non-nilpotent ideals which are simple rings.Theorem 2: Let R be a semi-simple NAD-ring with a. c.c. on ideals of R, then the following conditions are equivalent (i) R can be expressed uniquely as R= R_1⊕R_2⊕... ⊕R_r apart from the order of the R_i, where R_i are n on-nilpotent ideals which are simple rings.(ii) R~2= R, and every prime ideal is maximal.(iii) R~2= R, and every principle ideal (a) of R can be expressed uniquely as R_(i1)⊕R_(i2)⊕…⊕R_(is),where R_(ij) are non-nilpotent ideals, which are simple rings.If one of these prepositions holds, then so does the following.(i) every ideal a of R is principal and a~2 = a.(ii) every prime ideal p can be expressed uniquely as P_i = R_1⊕R_2⊕…⊕R_(i-1) ⊕R_(i+1)⊕…⊕R_r,i = i, 2…, r.(iii) the number of ideals of R is precisely(1r)+ (2r)+…+(rr)while the number of proper prime ideals of R is precisely r.Definition 2: The W-ascending chain conidtion (briefly w- a.c.c.) on ideals of R is said to hold in R, if for a given ascending chain on ideals a_1 a_2 …a_n … there exists a finite number of positive integers n_1,…,n-r and n such that W~(n1,…,nr)∩a_n= W~(n1,…,nr,)∩a_(n+1)=… where W = ∪ a_i.It is clear that every ring satisfying a. c.c. on ideals also satisftes w- a. c.c. on ideals.Theorem 3: The conclusions of theorems 1 and 2 are still valid, if NAD-ring satisfies w-a.c.c, on ideals and a.c.c. (i.e. descending chain condition) on ideals of R instead of a.c.c, on ideals of R.Definition 3: Let m be an ideal of R. An ideal a is called m-hypernilpotent,if there exists a finite number of positive integers n_,…,n_r such that a~(n1,…,nr)m. Otherwise a is called m-nonhypernilpotent.Theorem 4 : Let R be an NAD-ring with w- a. c. c. on ideals then we have the following results: (i) If m is an ideal, then there exists a semi-prime ideal p containing m such that every principal ideal (a) contained in p is m-hypernilpotent. Hence every semiprime ideal p containing m must cantain p.In this case we will say that p is m-semiprime.(ii) If a is an m-nonhypernilpotent ideal, then there exexists at least one anonhypernilpotent prime ideal p_a such that p_a m and that p_a≥p≥m implies p_a=p, where p is prime.In this case we will say that p_a is m-prime.(iii) every m-semiprime ideal p can be expressed as an intersection of m-prime ideals. If R satisfies a.c.c, on ideals, then p=p_1 ∩…∩ p_r where p_i are prime ideals, and then there exist two finite sets of positive integers n_1,…,m_t and k_(1,…,) k_s respectively such that p~(m1,…,m_t) m p~(k,…,k_s