**References in periodicals archive**?

For convenience, we can simply use N = <[??], A > to represent an element N in neutrosophic cubic set and the element N can be called a neutrosophic cubic number (NCN).

[58] developed a strategy for ranking of neutrosophic cubic numbers (NCNs) based on the score and accuracy functions.

The 13 papers explore such topics as automorphic Galois representations and the inverse Galois problem, from Galois to Hopf Galois: theory and practice, a space weight one modular forms attached to totally real cubic number fields, the characterization of gaps and elements of a numerical semigroup using Groebner bases, fractional p-adic differentiability under the Amice transform, and when the modular world become non-holomorphic.

The purpose of this paper is to provide some results in that direction for cubic number fields.

We will restrict our attention to finding elements in the rings of integers of pure cubic number fields Q([cube root of d]),where d is even, that cannot be written as a difference of two squares.

My guess: they would have seized on the fact that 8 is the first cubic number (after 1), implying a secret message of completion and wholeness.

We introduce a neutrosophic cubic number aggregation operator and prove its basic properties.

For obtaining group decision, we aggregate all the individual decision matrices ([DM.sup.p], p = 1, 2, ..., M) to an aggregated decision matrix (DM) using the neutrosophic cubic numbers weighted aggregation (NCNWA) operator as follows:

We have employed linguistic variables to present criteria weights and presented conversion of linguistic variables into neutrosophic cubic numbers. We have also proposed a conversion formula for neutrosophic cubic number into fuzzy number.

The decision makers' weights and criteria (attributes) weights are described by neutrosophic cubic numbers using linguistic variables.

Nichomachus also considered the connections between numbers and three-dimensional geometrical patterns, such as the cubic numbers and the pyramidal numbers.

We have defined arithmetic average operator for neutrosophic cubic numbers. We have employed information entropy scheme to calculate unknown weights of the attributes.

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