A hybrid radix-4/radix-8 architecture targeted for high bit, general purpose, digital multipliers is presented as a compromise between the high speed of a radix-4 multiplier architecture and the low power dissipation of a radix-8 multiplier architecture. In this hybrid radix4/radix-8 multiplier architecture, the performance bottleneck of a radix-8 multiplier, the generation of three times the m...

Lagrange multipliers for distributed parameter systems with mixed control-state constraints may exhibit better regularity properties than those for problems with pure pointwise state constraints, (1), (2), (4). Under natural assumptions, they are functions of certain L-spaces, while Lagrange multpliers for pointwise state constraints are, in general, measures. Following an approach suggested in...

An exact analysis of the N-dimensional blackbody radiation process in a nonextensivè a la Tsallis scenario is performed for values of the nonextensive's index in the range (0 < q < 1). The recently advanced " Optimal Lagrange Multipliers " (OLM) technique has been employed. The results are consistent with those of the extensive, q = 1 case. The generalization of the celebrated laws of Planck, S...

We now consider the family of operators Tλ, λ ≥ 0, defined on Rn by T̂λ f (ξ) = mλ f̂ (ξ), where mλ(ξ) = (1− |ξ|)+. These are the Bochner-Riesz multipliers, which can be viewed as an attempt to smooth out the singularity of the disc multiplier to see if we can obtain boundedness on a wider range of Lp spaces. Note that when λ = 0 we obtain S1, and that as λ increases, the multiplier mλ becomes sm...

Some extensions of an inequality from IMO’2001 are proven by means of the Lagrange multiplier criterion.

We show, in two different ways, that the Tsallis’ partition function and its derivatives are related to thermodynamic quantities such as entropy, internal energy, etc., in the same way as in Boltzmann-Gibbs’ formalism, with the Lagrange multiplier β replaced by its value 1 kBT . They are obtained within the finite heat bath canonical ensemble approach. Furthermore, we discuss the meaning of the...