In this paper, we prove results concerning the large scale geometry of connected, simply connected nilpotent Lie groups equipped with left invariant Riemannian metrics. Precisely, we prove that there do not exist quasi-isometric embeddings of such a nilpotent Lie group into either a CAT0 metric space or an Alexandrov metric space. The main technical aspect of this work is the proof of a limited...

We study the connection between the Goodwillie tower of the identity and the lower central series of the loop group on connected spaces. We define the simplicial theory of homotopy n-nilpotent groups. This notion interpolates between infinite loop spaces and loop spaces. We prove that the set-valued algebraic theory obtained by applying π0 is the theory of ordinary n-nilpotent groups and that t...

Let c ≥ 0, d ≥ 2 be integers and N (d) c be the variety of groups in which every dgenerator subgroup is nilpotent of class at most c. N.D. Gupta posed this question that for what values of c and d it is true that N (d) c is locally nilpotent? We prove that if c ≤ 2 d + 2 − 3 then the variety N (d) c is locally nilpotent and we reduce the question of Gupta about the periodic groups in N (d) c to...

Formal and informal modifications to the US-Japan Alliance have expanded value operational structure delivers in support of US Japanese national combined naval activities Southeast Asia. This article analyzes how now serves as an increasingly powerful force multiplier which magnifies capabilities, efficiency, impact two allies’ Unlike previous studies on role United States or Japan region, it f...

The floating-point multiplication is one of the most basic and frequent digital signal processing operations, and its accuracy and throughput greatly decide the overall accuracy and throughput of the digital signal processors. Based on vectorizing a conventional double precision multiplier, we propose a multiple precision floating-point multiplier. It supports either one double precision multip...

A bit parallel systolic multiplier in the finite field GF(2) over the polynomial basis where irreducible polynomial generate the field GF(2) is presented. The complexity of the proposed multiplier is compared in terms of area, latency and speed. The proposed multiplier has high throughput as compared with the traditional systolic multiplier. Moreover, this multiplier is highly regular, modular,...

In this paper we describe an efficient implementation of an IEEE 754 single precision floating point multiplier targeted for Xilinx Virtex-5 FPGA. VHDL is used to implement a technology-independent pipelined design. The multiplier implementation handles the overflow and underflow cases. Rounding is not implemented to give more precision when using the multiplier in a Multiply and Accumulate (MA...