We show that a 3-valued current mode CMOS 2-input BSC adder can be converted into a CMOS binary 4-2 counter or into a 1-digit Azivienis-like adder using a redundant number representation. Using a current mode algorithm to derive binary CMOS implementations of these arithmetic operators leads to equivalent or faster circuit implementation that the typical implementations that have been used unti...

This paper describes how a modular machine description, which specifies the functionality and the binary representation of an instruction set, can be transformed into a hardware model. This model is built from few generic hardware entities (registers, memories, arithmetic/logic operators, selectors and connections) and may eventually serve as an input to high-level hardware synthesis tools. The...

We survey techniques to compute the action of the Hecke operators on the cohomology of arithmetic groups. These techniques can be seen as generalizations in different directions of the classical modular symbol algorithm, due to Manin and Ash-Rudolph. Most of the work is contained in papers of the author and the author with Mark McConnell. Some results are unpublished work of Mark McConnell and ...

The next steps after this prehistoric Part I will be directed to a description of the Howe operators introduced by Kudla and Millson and their special Schwartz forms and classes. This has as attractor the fact that the modular and automorphic forms arising naturally in context with these classes find very nice geometric interpretations of their Fourier coefficients and thus lead to an intriguin...

Lipschitzian and kernel aggregation operators with respect to the natural T indistinguishability operator ET and their powers are studied. A t-norm T is proved to be ET -lipschitzian, and is interpreted as a fuzzy point and a fuzzy map as well. Given an archimedean t-norm T with additive generator t, the quasi-arithmetic mean generated by t is proved to be the more stable aggregation operator w...

the concept of geometric-arithmetic indices (ga) was put forward in chemical graph theoryvery recently. in spite of this, several works have already appeared dealing with these indices.in this paper we present lower and upper bounds on the second geometric-arithmetic index(ga2) and characterize the extremal graphs. moreover, we establish nordhaus-gaddum-typeresults for ga2.

continuing the work k. c. das, i. gutman, b. furtula, on second geometric-arithmetic indexof graphs, iran. j. math chem., 1(2) (2010) 17-28, in this paper we present lower and upperbounds on the third geometric-arithmetic index ga3 and characterize the extremal graphs.moreover, we give nordhaus-gaddum-type result for ga3.

Let G be a reductive algebraic group associated to a self-adjoint homogeneous cone defined over Q, and let Γ ⊂ G be a appropriate neat arithmetic subgroup. We present two algorithms to compute the action of the Hecke operators on H(Γ;Z) for all i. This simultaneously generalizes the modular symbol algorithm of Ash-Rudolph [7] to a larger class of groups, and provides techniques to compute the H...

In their paper, Recht and Ré have presented conjectures and consequences of noncommutative variants of the arithmetic mean-geometric mean (AM-GM) inequality for positive definite matrices. Let A1, . . . , An be a collection of positive semidefinite matrices and i1, . . . , ik be random indices in {1, . . . , n}. To avoid symmetrization issues that arise since matrix products are non-commutative...

Let G be a reductive algebraic group associated to a self-adjoint homogeneous cone defined over Q, and let Γ ⊂ G be a appropriate neat arithmetic subgroup. We present two algorithms to compute the action of the Hecke operators on H(Γ;Z) for all i. This simultaneously generalizes the modular symbol algorithm of Ash-Rudolph [7] to a larger class of groups, and provides techniques to compute the H...