nine organic substrates viz., rice grains, sorghum grains, wheat grains, millet grains, wheat straw, rice husk, cow dung, sawdust, and poultry manure were used for mass multiplication of trichoderma harzianum. of these,sorghum grains followed by millet grains were the best substrates. the poultry manure appeared to be the most unsuitable substrate, whereas rice grains, wheat grains, wheat straw...

in this paper, we propose a new definition of intuitionistic fuzzyquasi-metric and pseudo-metric spaces based on intuitionistic fuzzy points. weprove some properties of intuitionistic fuzzy quasi- metric and pseudo-metricspaces, and show that every intuitionistic fuzzy pseudo-metric space is intuitionisticfuzzy regular and intuitionistic fuzzy completely normal and henceintuitionistic fuzzy nor...

This paper presents a review with numerical example and complexity analysis of the fast multiplication algorithms to help embedded system designers to improve the hardware performance for many applications such as cryptosystems design. The paper presented two practical multiplication algorithms: Karatsuba multiplication algorithm with time complexity O(n ) and Schönhage–Strassen multiplication ...

We present a design of an IEEE oating-point multiplier capable of performing either a double-precision multiplication or a single-precision multiplication. In single-precision the la-tency is two clock cycles and in double-precision the latency is three clock cycles, where each pipeline stage contains roughly fteen logic levels. A single-precision multiplication can be followed immediately by a...

We show that the multiplication operation c = a br ,1 in the eld GF2 k can be implemented signiicantly faster in software than the standard multiplication, where r is a special xed element of the eld. This operation is the nite eld analogue of the Montgomery multiplication for modular multiplication of integers. We give the bit-level and word-level algorithms for computing the product, perform ...

we study umbilic (space-like) submanifolds of pseudo-riemannian space forms, then define totally semi-umbilic space-like submanifold of pseudo euclidean space and relate this notion to umbilicity. finally we give characterization of total semi-umbilicity for space-like submanifolds contained in pseudo sphere or pseudo hyperbolic space or the light cone.a pseudo-riemannian submanifold m in (a ps...