Desdanine inhibited the plaque formation of male-specific coliphages but not that of other coliphages tested. Desdanine also suppressed the multiplication of both RNA phage Q beta and filamentous DNA phage f1 at the concentration of 3.13 approximately 6.25 mug/ml which had no influence on the growth of their host cells. However, the inhibitory effect on the phage multiplication was not due to t...

a. N1 = {(i1, i2, . . . , in) : ik ∈ Ik for all k ∈ {1, 2, . . . , n}} and b. N2 = {(x1, x2, . . . , xn) : ∑n k=1 xk = 0}. Proof. To prove (a), it suffices to show, by Proposition 1, that N1 is nonempty and x + ry ∈ N1 for all r ∈ R and all x, y ∈ N1. For the first condition, (0, 0, . . . , 0) ∈ N1 since Ik is a subgroup of R containing the additive identity 0 for all k ∈ {1, 2, . . . , n}. Tha...

7 Rings Definition. A ring consists of a set R on which are defined operations of addition and multiplication satisfying the following axioms: • x+ y = y + x for all elements x and y of R (i.e., addition is commutative); • (x+ y) + z = x+ (y + z) for all elements x, y and z of R (i.e., addition is associative); • there exists an an element 0 of R (known as the zero element) with the property th...

This paper is devoted for the design and implementation of a 32bit Arithmetic module it is used for vedic Mathematics algorithms. We have various arithmetic multiplication techniques like Urdhva, Tiryakbhyam, Nikhilam, and Anurupye has been thoroughly analyzed. A 32 x 32 bit multiplier using Urdhava Tiryakbhyam, it has been designed and using this multiplier, a MAC unit has been designed. An Ar...

let r be a g-graded ring and m be a g-graded r-module. in this article, we introduce the concept of graded weakly classical prime submodules and give some properties of such submodules.

We show that the multiplication operation c = a · b · r −1 in the field GF(2 k) can be implemented significantly faster in software than the standard multiplication, where r is a special fixed element of the field. This operation is the finite field analogue of the Montgomery multiplication for modular multiplication of integers. We give the bit-level and word-level algorithms for computing the...

We study multiplication modules. The rings are not assumed to be commutative. Several criteria with some applications given for a direct sum of modules module.

The Hardy space H(D) can be viewed as a module over the polynomial ring C[z, w] with module action defined by multiplication of functions. The core operator is a bounded self-adjoint integral operator defined on submodules of H(D), and it gives rise to some interesting numerical invariants for the submodules. These invariants are difficult to compute or estimate in general. This paper computes ...

We consider the class of algebras of rank 4 equipped with a standard involution over an arbitrary base ring. In particular, we characterize quaternion rings, those algebras defined by the construction of the even Clifford algebra. A quaternion algebra is a central simple algebra of dimension 4 over a field F . Generalizations of the notion of quaternion algebra to other commutative base rings R...