FPGAs are increasingly being used in the high performance and scientific computing community to implement floating-point based hardware accelerators. We present FPGA floating-point multiplication. Such circuits can be extremely useful in the FPGA implementation of complex systems that benefit from the reprogramability and parallelism of the FPGA device but also require a general purpose multipl...

This paper deals with the problem of existence of compromise decisions and conditions for a compromise decision to be weakly Pareto-optimal, i.e., to be a weak Pareto-maximizer, Pareto-maximizer, or strong Pareto-maximizer. The concept of compromise decision is generalized by adopting triangular norms. Further, a concept of fuzzy interval is introduced. Suucient conditions for the existence of ...

First we show that continuous piecewise-affine systems are equivalent to max-minplus-scaling systems (i.e., systems that can be modeled using maximization, minimization, addition and scalar multiplication). Next, we consider model predictive control for these systems. In general, this leads to nonlinear non-convex optimization problems. However, we present a method based on canonical forms for ...

We show that two important quantities from two disparate areas of complexity theory — Strassen’s exponent of matrix multiplication ω and Grothendieck’s constant KG — are intimately related. They are different measures of size for the same underlying object — the matrix multiplication tensor, i.e., the 3-tensor or bilinear operator μl,m,n : Fl×m × Fm×n → Fl×n, (A,B) 7→ AB defined by matrix-matri...

A healthy lifestyle is an important focus in today's society. The physical benefits of regular exercise are abundantly clear, but physical fitness is also associated with better cognitive performance. How these two factors together relate to characteristics of the brain is still incompletely understood. By applying mathematical concepts from 'network theory', insights in the organization and dy...

Polynomial multiplication is the most computationally expensive part of lattice-based cryptography algorithm. However, existing acceleration schemes have problems, such as low performance and high hardware resource overhead. Based on polynomial number theoretic transformation (NTT), this paper proposed a simple element Montgomery module reduction with pipeline structure to realize fast multipli...

Let A be a finite dimensional Hopf algebra, D(A) = A ⊗A its Drinfel’d double and H(A) = A#A its Heisenberg double. The relation between D(A) and H(A) has been found by J.-H. Lu in [24] (see also [33], p. 196): the multiplication of H(A) may be obtained by twisting the multiplication of D(A) by a certain left 2-cocycle which in turn is obtained from the R-matrix of D(A). It was also obtained in ...

The centralizer algebra of the action of U(n) on the real tensor powers ⊗RV of its natural module, V = Cn, is described by means of a modification in the multiplication of the signed Brauer algebras. The relationships of this algebra with the invariants for U(n) and with the decomposition of ⊗RV into irreducible submodules is considered.

The basic arithmetic operations (i.e. addition, multiplication, and inversion) in finite fields, GF (q), where q = p k and p is a prime integer, have several applications in cryptography, such as RSA algorithm, Diffie-Hellman key exchange algorithm [1], the US federal Digital Signature Standard [2], elliptic curve cryptography [3, 4], and also recently identity based cryptography [5, 6]. Most p...

Let G be a finite group and k a fixed algebraically closed field of characteristic p>0 . If p is odd, let H(; be the subring of H*(G,k) consisting of elements of even degree; following [20-22] we take H~=H*(G,k) if p=2, though one could just as well use the subring of elements of even degree for all p. H a is a finitely generated commutative k-algebra [13], and we let Va denote its associated a...