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If we know the determinate and sub-indeterminate part(s) of an argument a0 + a1I1 + a2I2 + ... +anIn how do we similarly find the determinate and sub-indeterminate part(s) of a function (or operation) of this argument f (a0 + a1I1 + a2I2 + ... +anIn)? The AH-Isometry is designed to do just that. The function f may be of one or more variables (arguments), it may also be some unary or n-ary operation. Real examples are presented in this paper of such arguments and functions. We now present for the first time the most general form, the n-Refined AH-Isometry. [ABSTRACT FROM AUTHOR]

In this paper we present the symbolic neutrosophic and plithogenic Marshall-Olkin type I class of distributions. We derive the formal form of the cumulative distribution function and probability density function of neutrosophic and plithogenic Marshall-Olkin Type I class of distributions. As a special case of the mentioned class of distributions we study the generalized uniform distribution in both neutrosophic and plithogenic forms, we derive its PDF and CDF then present an algorithm of random numbers generation according to it, then we estimate its parameters using maximum likelihood estimation and support the results with a simulation study to show the efficiency of the calculated parameters and study its asymptotic properties including unbiasedness and consistency.

In this article, the definition of literal neutrosophic stochastic processes is presented for the first time in the form 𝒩𝑡 = 𝜉𝑡 + 𝜂𝑡𝐼 ;𝐼 2 = 𝐼 where both {𝜉(𝑡),𝑡 ∈ 𝑇} and {𝜂(𝑡),𝑡 ∈ 𝑇} are classical real valued stochastic processes. Characteristics of the literal neutrosophic stochastic process are defined and its formulas are driven including neutrosophic ensemble mean, neutrosophic covariance function and neutrosophic autocorrelation function. Concept of literal neutrosophic stationary stochastic processes is well defined and many theorems are presented and proved using classical neutrosophic operations then using the one-dimensional AH-Isometry. Some solved examples are presented and solved successfully. We have proved that studying the literal neutrosophic stochastic process {𝒩(𝑡),𝑡 ∈ 𝑇} is equivalent to studying two classical stochastic processes which are {𝜉(𝑡),𝑡 ∈ 𝑇} and {𝜉 𝑡 + 𝜂𝑡 ,𝑡 ∈ 𝑇}.

The objective of this paper is to study and define some algebraic curves with neutrosophic variables in neutrosophic real field 𝑅(𝐼), where we study what are the relationships between classical algebraic curves and neutrosophic algebraic curves depending on the geometric isometry (AH-Isometry).

The objective of this paper is to study and define some algebraic curves with neutrosophic variables in neutrosophic real field R(I), where we study what are the relationships between classical algebraic curves and neutrosophic algebraic curves depending on the geometric isometry (AH-Isometry). [ABSTRACT FROM AUTHOR]

In this article, the definition of literal neutrosophic stochastic processes is presented for the first time in the form Nt = 𝜉t + ηt I; I² = I where both {𝜉(t), t ∈ T} and {η(t), t ∈ T} are classical real valued stochastic processes. Characteristics of the literal neutrosophic stochastic process are defined and its formulas are driven including neutrosophic ensemble mean, neutrosophic covariance function and neutrosophic autocorrelation function. Concept of literal neutrosophic stationary stochastic processes is well defined and many theorems are presented and proved using classical neutrosophic operations then using the one-dimensional AH-Isometry. Some solved examples are presented and solved successfully. We have proved that studying the literal neutrosophic stochastic process {N(t), t ∈ T} is equivalent to studying two classical stochastic processes which are {𝜉(t), t ∈ T} and {𝜉t + ηt, t ∈ T}. [ABSTRACT FROM AUTHOR]

In this paper, we study the algebraic relationships between n-refined neutrosophic modules by using semi-module homomorphisms. On the other hand, this work shows the relationship between neutrosophic geometrical AH-isometry and semimodule isomorphisms. [ABSTRACT FROM AUTHOR]