binary operation

By utilizing the idea of neutrosophic theory, Vasantha Kandasamy and Florentin Smarandache studied neutrosophic algebraic structures in [4,5,6] by inserting an indeterminate element "I" in the algebraic structure and then combine "I" with each element of the structure with respect to corresponding binary operation *.

Topological materials would form a transistor's active, 'channel' component, accomplishing the binary operation used in computing, switching between open (0) and closed (1).

* the binary operation * is closed on S (taking any two elements x, y from G and applying the binary operation, the result is still an element from S)

As a tool in the proof of this fact, we point out a kind of compatibility relation between the original binary operation of a given Hom-Maltsev algebra and the ternary operation mentioned above (Lemma 13).

Ultimately, the chapter appropriately concludes by admitting that the play of gender, with "either extreme versions of gay macho masculinity or excessive femininity" (55), simply reinforces the concept that gender is a binary operation. Indeed, the very concept of gender here remains entrenched in a decidedly cisgendered construct.

From now on, if * is a binary operation on a set X, k is a positive integer, and x [member of] X, then we denote [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] by ([*.sub.k])x.

If we denote [A.sub.[alpha]] = [[a.sub.1[alpha]]; [a.sub.2[alpha]]] and [B.sub.[alpha]] = [[b.sub.1[alpha]]; [b.sub.2[alpha]]] then the extended binary operation for increasing binary operation * is

A set (Eq.) with a binary operation addition " " and a ternary multiplication "" , denoted by juxtaposition, is said to be a ternary semiring S if it satisfies the following conditions:

For this purpose a binary operation in the space of bounded functions on an interval is established.