We introduce a new implementation of a three-input multiplier. This multiplier is capable of accepting three binary inputs, and producing the product, a*b*c. Although this implementation requires more space, it reduces the number of clock cycles required to multiply three numbers. In this paper, we present the front end 4-bit partial product array that can be incorporated into a typical multipl...

A nilpotent quotient algorithm for finitely presented Lie rings over Z (LIENQ) is described. The paper studies the graded and non-graded cases separately. The algorithm computes the so-called nilpotent presentation for a finitely presented, nilpotent Lie ring. A nilpotent presentation consists of generators for the abelian group and the products expressed as linear combinations for pairs formed...

In the framework of usual superfield approach, we derive the exact local, covari-ant, continuous and off-shell nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the U(1) gauge field (A µ) and the (anti-)ghost fields ((¯ C)C) of the Lagrangian density of a four (3 + 1)-dimensional QED by exploiting the horizontality condition defined on the six (4 + 2)-dimensi...

It is known that the generator of a strictly continuous one parameter unitary group in the multiplier algebra of a C∗ -algebra is affiliated to that C∗ -algebra . We show that under natural non degeneracy conditions, this self adjoint unbounded operator lies indeed in the (unbounded) multiplier algebra of the Pedersen’s ideal of the C∗ -algebra .

Two’s complement multipliers are performance and power-critical components for wireless baseband signal processing applications. Parallel clusters of multiplier, multiply-add, multiply-accumulate cores are required to perform complex filter operations in Fast Fourier Transform (FFT) accelerators while consuming ultra low energy/operation [1]. A 12x9b single-cycle two’s complement twiddle multip...

As the heat kernel plays an important role in many problems in harmonic analysis, an explicit usable expression is very much desirable. An explicit expression for the heat kernel for the Heisenberg group Hn = C ×R was obtained by Hulanicki [9] and by Gaveau [7]. Gaveau [7] also obtained the heat kernel for free nilpotent Lie groups of step two. Cygan [4] obtained the heat kernel for all nilpote...

We develop methods for computing with matrix groups defined over a range of infinite domains, and apply those methods to the design of algorithms for nilpotent groups. In particular, we provide a practical nilpotency testing algorithm for matrix groups over an infinite field. We also provide algorithms to answer a number of structural questions for a nilpotent matrix group.The main algorithms h...

We show that group C*-algebras of finitely generated, nilpotent groups have finite nuclear dimension. It then follows, from a string of deep results, that the C*-algebra A generated by an irreducible representation of such a group has decomposition rank at most 3. If, in addition, A satisfies the universal coefficient theorem, another string of deep results shows it is classifiable by its Ellio...

Abstract The Bogomolov multiplier of a group is the unramified Brauer associated with quotient variety faithful representation group. This object an obstruction for to be stably rational. purpose this paper study these multipliers nilpotent pro-$p$ groups by transporting them their Lie algebras. Special focus set on case $p$-adic nilpotency class $2$, where we analyse moduli space. then applied...