The Q&A (Question & Answer) knowledge base of an organization is important for knowledge management. It can provide experience and knowledge for a questioner. This paper applies a Fuzzy-Neural Network (FNN) model to construct Q&A knowledge base automatically. The FNN computes the important degree with sentences and infers the strength of each sentence for question properties. In addition, the b...

In the previous lecture we proved the Kronecker-Weber theorem: every abelian extension L of Q lies in a cyclotomic extension Q(ζm)/Q. The isomorphism Gal(Q(ζm)/Q) ' (Z/mZ)× allows us to view Gal(L/Q) as a quotient of (Z/mZ)×. Conversely, for each quotient H of (Z/mZ)×, there is a subfield L of Q(ζm) for which H ' Gal(L/Q). We now want make the correspondence between H and L explicit, and then g...

Let E be an elliptic curve over Q of conductor N = Mp, having a prime p‖N of multiplicative reduction. Because E is modular, it corresponds to a normalised weight two eigenform on Γ0(N), whose q-expansion is denoted f = ∑n anq . LetX := hom(Z×p ,Z×p ) Z/(p−1)Z×Zp, which contains Z as a dense subset by associating to k ∈ Z the character x → xk−2. Denote by A(U) the ring of Cp-valued p-adic analy...

Let G be a bounded domain in R" and Q = G X (0, T). We consider the solution^«) of the pseudo-parabolic initial-value problem (1 + M(x))y,(u) + L(x)y(u) = u in L2(Q), y(-,0;u) = 0 in L2(G), to be the state corresponding to the control u. Here M(x) and L{x) are symmetric uniformly strongly elliptic second-order partial differential operators. The control problem is to find a control un in a fixe...

Three interior point methods are proposed for sufficient horizontal linear complementarity problems (HLCP): a large update path following algorithm, a first order corrector-predictor method, and a second order corrector-predictor method. All algorithms produce sequences of iterates in the wide neighborhood of the central path introduced by Ai and Zhang. The algorithms do not depend on the handi...

A first order affine scaling method and two mth order affine scaling methods for solving monotone linear complementarity problems (LCP) are presented. All three methods produce iterates in a wide neighborhood of the central path. The first order method has O(nL2(lognL2)(log lognL2)) iteration complexity. If the LCP admits a strict complementary solution then both the duality gap and the iterati...

In this paper the concept of S-neighborhoods is introduced and we give a new characterization of L-topological vector spaces in terms of S-neighborhood base of θλ(λ ∈ M(L)). As an application, we obtain a necessary and sufficient condition of a vector Ltopology determined by its level topologies. Copyright c ©2003 Yang’s Scientific Research Institute, LLC. All rights reserved.

Abstract. Von Neumann’s addition method adds two numbers given in q-ary representation by forming a number consisting of the added digits, reduced modulo q, and another number, representing the carries and repeating this until the string of carries consists only of zeros. The average number of iterations was studied by Knuth. We extend these results by considering the (q, d) system, with base q...