A novel decomposition of NTT blocklengths is proposed using repeated applications of Rader’s algorithm to reduce the problem to that of realising a single small-length NTT. An efficient implementation of this small-length NTT is achieved by an initial basis conversion of the data, so that the new basis corresponds to the kernel of the small-length NTT. Multiplication by powers of the kernel bec...

Susumu TANABÉ Abstract. This is a review article on the Gauss-Manin system associated to the complete intersection singularities of projection. We show how the logarithmic vector fields appear as coefficients to the Gauss-Manin system (Theorem 2.7). We examine further how the multiplication table on the Jacobian quotient module calculates the logarithmic vector fields tangent to the discriminan...

where we use the notation dxI for (1.4) dxI = dxi1 ∧ dxi2 ∧ ... ∧ dxik for I = {i1, i2, ..., ik} with i1 < i2 < ... < ik. So ΩX is a free module over C ∞(X) generated by dxI . Obviously, Ω k X = 0 for k > n and ⊕ΩX is a graded ring (noncommutative without multiplicative identity) with multiplication defined by the wedge product (1.5) ∧ : (ω1, ω2)→ ω1 ∧ ω2. Note that (1.6) ω1 ∧ ω2 = (−1)12ω2 ∧ ω...

1. Background 2. Residue number system 2.1. Encoding 2.2. Decoding 2.3. Scaling 3. Basis for numerical methods 4. Processor design concepts 4.1. Cyclic phase implementation 4.2. Mapping with beam position control 4.3. Multipurpose arithmetic module 5. Extended computing applications 5.1. Polynomial evaluation 5.2. Matrix multiplication and transforms 6. Concluding remarks 7. References Abstract...

Let A and B be two Hopf algebras and R ∈ Hom(B ⊗ A, A ⊗ B), the twisted tensor product Hopf algebra A#RB was introduced by S. Caenepeel et al in [3] and further studied in our recent work [6]. In this paper we give the necessary and sufficient conditions for A#RB to be a Hopf algebra with a projection. Furthermore, a braided Hopf algebra A is constructed by twisting the multiplication of A thro...

For any rank 2 Drinfeld module ρ defined over an algebraic function field, we consider its period matrix Pρ, which is analogous to the period matrix of an elliptic curve defined over a number field. Suppose that the characteristic of the finite field Fq is odd and that ρ does not have complex multiplication. We show that the transcendence degree of the field generated by the entries of Pρ over ...

1. The construction of T(A) is motivated by dualizing the fundamental group 7Ti(X) of a differentiable manifold X with a base point Xo. Let A be the -R-algebra of C functions on X equipped with the derivation d, which is the usual differentiation from A into the Amodule M = ÛA of C 1-forms on X. Recall that the shuffle algebra Sh(M) consists of the i£-module of the tensor algebra TR(M) and the ...

Susumu TANABÉ Abstract. This is a review article on the Gauss-Manin system associated to the complete intersection singularities of projection. We show how the logarithmic vector fields appear as coefficients to the Gauss-Manin system (Theorem 2.7). We examine further how the multiplication table on the Jacobian quotient module calculates the logarithmic vector fields tangent to the discriminan...

The operations in the set of fuzzy numbers are usually obtained bythe Zadeh extension principle. But these definitions can have some disadvantagesfor the applications both by an algebraic point of view and by practicalaspects. In fact the Zadeh multiplication is not distributive with respect tothe addition, the shape of fuzzy numbers is not preserved by multiplication,the indeterminateness of t...

the objective of this study was to develop a new optimal parallel algorithm for matrix multiplication which could run on a fibonacci hypercube structure. most of the popular algorithms for parallel matrix multiplication can not run on fibonacci hypercube structure, therefore giving a method that can be run on all structures especially fibonacci hypercube structure is necessary for parallel matr...