Genetic Algebras Research Articles

Multi-objective optimization of FCC separation system based on NSGA-Ⅱ

Based on the industrial production data, the simulation of the separation process of a 2 million tons/year FCC unit including the fractionation and the absorption-stabilization systems were conducted on Aspen Plus software. To optimize the operation process, multi-objective optimization was performed integrating the Aspen Plus platform and MATLAB environment utilizing the improved non-dominated sorting genetic algorithm (NSGA-Ⅱ). The established multi-objective optimization model was used for the operating variable screening, the genetic algebra selection and the optimal solution determination. During the optimization, the total yield of LPG and stable gasoline was aimed as the first optimization objective while the energy consumption of the whole system as the second objective. Five expressions were applied as the constraint functions and nine operating variables were conducted as the decision variables. The results showed that the performances of FCC separation system have been greatly improved after optimization. Some optimization strategies are advised for the whole system. The total yield of LPG and stabilized gasoline increases by 2. 44 %, and the energy consumption of the separation system decreases by 41. 79 %. In addition, the CO2 emission is reduced by 23.59 t/h and the total annual cost (TAC) is reduced by $0.89 million/year. It has been revealed that the multi-objective optimization method based on NSGA-Ⅱ algorithm is useful for the guidance of the optimization of industrial petrochemical process.

Axial view on pseudo-composition algebras and train algebras of rank 3

We show that pseudo-composition algebras and train algebras of rank 3 generated by idempotents are characterized as axial algebras with fusion laws derived from the Peirce decompositions of idempotents in these classes of algebras. The corresponding axial algebras are called [Formula: see text]-axial algebras, where [Formula: see text] is an element of the ground field. As a first step toward their classification, we describe the [Formula: see text]- and [Formula: see text]-generated subalgebras of such algebras.

Functional Train Algebras of Rank ≤ 3

Functional Train Algebras of Rank ≤ 3

Genetic algebras associated with permuted Lotka-Volterra operators

The aim of this paper is to examine the structure of genetic algebras associated with permuted Lotka-Volterra operators on a finite-dimensional simplex. Furthermore, three dimensional permuted Lotka-Voltarra algebras are considered and the description of their derivations are given as well.

Implementation of Algebra Structure in The Field of Biology in Blood Group Inheritance


 
 
 
 Genetics is a branch of biology that scientifically studies heredity (heredity). One of the inherited genetic identities is blood type. The most commonly used blood group systems are the ABO and Rhesus blood group systems. This blood group inheritance can be analyzed using any antigen from the blood group system. The antigei are then used as the basis for the vector space affecting the field. Binary operations were defined for each blood group system and analyzed using gamete and zygotic algebra. We derive equations that are used as axioms to form the algebraic structure of any blood group system. After the ABO blood group and Rhesus algebra were determined, the ABO binary function was determined and supplemented with the Rhesus blood group system (ABOi Rh). This binomial operation is used to derive equations that act as axioms to form the algebraic structure of the ABO Rh blood group system.
 
 
 

Algebraic structure of plenary train algebras of rank 4

In this paper, we study plenary train algebras of rank 4 admitting an idempotent. We obtain the Peirce decomposition of these algebras relative to an idempotent and the product of the associated Peirce components. The effect of changing an idempotent is discussed under the e-stability hypothesis. We show that a back-crossing algebra is a plenary train algebra of rank 4 if and only if it is a principal train algebra of rank 4. Finally, we study the particular case of monogenic back-crossing train algebras.

Algebras Satisfying Polynomial Identity of Degree Six that are Principal Train

In this paper we study the class of algebras satisfying a polynomial identity of degree six that are principal train algebras of rank $3$ or $4$, for which we give the explicit form of the train equation. If the rank of $A$ is $n\geq 5$ in general, we provide the form of the train equation in some cases.

Genetic Algebras Associated with ξ(a)-Quadratic Stochastic Operators.

The present paper deals with a class of ξ(a)-quadratic stochastic operators, referred to as QSOs, on a two-dimensional simplex. It investigates the algebraic properties of the genetic algebras associated with ξ(a)-QSOs. Namely, the associativity, characters and derivations of genetic algebras are studied. Moreover, the dynamics of these operators are also explored. Specifically, we focus on a particular partition that results in nine classes, which are further reduced to three nonconjugate classes. Each class gives rise to a genetic algebra denoted as Ai, and it is shown that these algebras are isomorphic. The investigation then delves into analyzing various algebraic properties within these genetic algebras, such as associativity, characters, and derivations. The conditions for associativity and character behavior are provided. Furthermore, a comprehensive analysis of the dynamic behavior of these operators is conducted.

A flow of quantum genetic Lotka-Volterra algebras on [formula omitted

In the present paper, we define a quantum analog of Lotka-Volterra algebras using a coalgebra scheme. This new framework provides a fresh perspective for the treatment of generic algebras. Additionally, a flow of quantum analogs of Lotka-Volterra genetic algebras is investigated. It's worth mentioning that such types of algebras are first introduced in this work. We observe that a flow of algebras is a particular type of continuous-time dynamical system, with states that are algebras and a structural constant matrix that depends on time and satisfies certain analogs of the Kolmogorov-Chapman equations. Using quantum quadratic operators, it is constructed a flow of quantum Lotka-Volterra algebras for the given multiplication. Furthermore, time-dependent behavior properties of these flow algebras are examined. The algebraic properties of the introduced flows are also studied, such as finding idempotents and examining an algebra generated by a pair of idempotents. It is shown that the later one is associative, while the flow is not associative. Additionally, derivations of the flow of the algebras are described.

Genetic Algebras generated by b−bistochastic Quadratic Stochastic Operators: The Character and Associativity

In the present paper we consider a genetic algebra induced by b−bistochastic Quadratic Stochastic Operators (QSOs) which is called b−bistochastic genetic algebra. First, we characterize their nontrivial character function on Rn. It turns out that, the given character function is not unique, hence full descriptions of such functions on R1 and R2 are established. Moreover, the defined algebra is commutative but not associative in general, hence, the associativity of b−bistochastic genetic algebras defined on R1 and R2 are described. In this work, the existence of non-trivial derivations on such algebras are given.

Bernstein algebras that are algebraic and the Kurosh problem

We study the class of Bernstein algebras that are algebraic, in the sense that each element generates a finite-dimensional subalgebra. Every Bernstein algebra has a maximal algebraic ideal, and the quotient algebra is a zero-multiplication algebra. Several equivalent conditions for a Bernstein algebra to be algebraic are given. In particular, known characterizations of Bernstein train algebras in terms of nilpotency are generalized to the case of locally train algebras. Along the way, we show that if a Banach Bernstein algebra is algebraic (respectively, locally train), then it is of bounded degree (respectively, train).Then we investigate the Kurosh problem for Bernstein algebras: whether a finitely generated Bernstein algebra which is algebraic of bounded degree is finite-dimensional. This problem turns out to have a closed link with a question about associative algebras. In particular, when the bar-ideal is nil, the Kurosh problem asks whether a finitely generated Bernstein train algebra is finite-dimensional. We prove that the answer is positive for some specific cases and for low degrees, and construct counter-examples in the general case.On the other hand, by results of Yagzhev the Jacobian conjecture is equivalent to a certain statement about Engel and nilpotence identities of multioperator algebras. We show that the generalized Jacobian conjecture for quadratic mappings holds for Bernstein algebras.

Classification of Four Dimensional Train Algebras of Degree 2 and Exponent 4

This paper is devoted to the classification of train algebras of degree 2 and exponent 4. This classification is made in dimension at most four and according to the type of the algebra. We first show that in four dimension, the type of algebra can only be of (2,0,1,1), (2,1,0,1) or (2,1 ,1,0).

On train algebras of degree 2 and exponent 4

In this paper, we deal with a class of nonassociative algebras called train algebras of degree 2 and exponent 4; Thus we give some results on algebras verifying a train identity of degree 2 and exponent 4. The structure of this class of algebras is studied through Peirce decomposition relative to a non zero idempotent. We give the necessary and sufficient conditions for an algebra verifying a train identity of degree 2 and exponent 4 to be Bernstein or train algebra of rank less than or equal to 3. Finally, we give some necessary conditions that must be verified by a train algebra of degree 2 and exponent 4, mainly in dimension four.

Representations of power-associative train algebras of rank 4

This paper is devoted to the study of four-dimensional commutative power-associative non-Jordan train algebras. The existence of a unique orthogonal idempotent element in such kind of algebras enables us to define a non-zero algebra homomorphism over their ground field, which gives rise to train algebras of rank 4. We describe the irreducible representations over an algebraically closed field of characteristic prime to 30 by means of multilinear identities which define it. Furthermore, we provide sufficient conditions to guarantee whenever a representation is decomposable.

Predicting Business Risks of Commercial Banks Based on BP-GA Optimized Model

To further explore the influence path of internet finance on the risk prevention and management of commercial banks, the backpropagation neural network optimization algorithm was used to predict the risk value and the change of the risk level of commercial banks under the background of internet environment was empirically studied and analyzed. The results showed that the maximum size of genetic algebra and the number of individuals significantly impacted the algorithm’s optimization performance when the genetic algorithm was used for parameter optimization. Through continuous attempts, the prediction effect was the best when the genetic algebra was 62, and the individual number was 45. The training network showed that the test set’s fitting degree was 96.07%, and the prediction error was 0.84%, which was much better than those before optimization. When the predicted risk value was more significant than 0.39, the bank should be vigilant and strengthen risk prevention. The development of internet finance can reduce commercial banks’ business risk levels, reduce their dependence on traditional business, and decrease commercial banks’ business risk levels. It can be seen that commercial banks can effectively improve risk management ability and efficiency promoted by technological development, so the level of business risk they undertake can be reduced.

Evolution algebras and dynamical systems of a worm propagation model

ABSTRACT We consider an evolution algebra identifying the coefficients of SIS–SIR worm propagation models as the structure constants of the algebra. The basic properties of this algebra are studied. We prove that it is a commutative (and hence flexible), not associative and baric algebra. We describe the full set of idempotent elements and the full set of absolute nilpotent elements. We find all the fixed points of the dynamical systems. We also study several properties of the algebra connecting them to dynamical systems.

The universality of one half in commutative nonassociative algebras with identities

In this paper we will explain an interesting phenomenon which occurs in general nonassociative algebras. More precisely, we establish that any finite-dimensional commutative nonassociative algebra over a field satisfying an identity always contains 12 in its Peirce spectrum. We also show that the corresponding 12-Peirce eigenspace satisfies the Jordan type fusion laws. The present approach is based on an explicit representation of the Peirce polynomial for an arbitrary algebra identity. To work with fusion rules, we develop the concept of the Peirce symbol and show that it can be explicitly determined for a wide class of algebras. We also illustrate our approach by further applications to genetic algebras and algebra of minimal cones (the so-called Hsiang algebras).

On evolution operators in characteristic 2

We are interested in the evolution operators defined on commutative and non-associative algebras when the characteristic of the scalar field is 2. We distinguish four types: nilpotent, quasi-constant, ultimately periodic, and plenary train operators. They are studied and classified for non-baric and for baric algebras.

Peirce-evanescent baric identities

Peirce-evanescent baric identities are polynomial identities verified by baric algebras such that their Peirce polynomials are the null polynomial. In this paper procedures for constructing such homogeneous and non homogeneous identities are given. For this we define an algebraic system structure on the free commutative nonassociative algebra generated by a set T which provides for classes of baric algebras satisfying a given set of identities similar properties to those of the varieties of algebras. Rooted binary trees with labeled leaves are used to explain the Peirce polynomials. It is shown that the mutation algebras satisfy all Peirce-evanescent identities, it results from this that any part of the field K can be the Peirce spectrum of a K-algebra satisfying a Peirce-evanescent identity. We end by giving methods to obtain generators of homogeneous and non-homogeneous Peirce-evanescent identities that are applied in several univariate and multivariate cases.

Determining When an Algebra Is an Evolution Algebra

Evolution algebras are non-associative algebras that describe non-Mendelian hereditary processes and have connections with many other areas. In this paper, we obtain necessary and sufficient conditions for a given algebra A to be an evolution algebra. We prove that the problem is equivalent to the so-called SDC problem, that is, the simultaneous diagonalisation via congruence of a given set of matrices. More precisely we show that an n-dimensional algebra A is an evolution algebra if and only if a certain set of n symmetric n×n matrices {M1,…,Mn} describing the product of A are SDC. We apply this characterisation to show that while certain classical genetic algebras (representing Mendelian and auto-tetraploid inheritance) are not themselves evolution algebras, arbitrarily small perturbations of these are evolution algebras. This is intringuing, as evolution algebras model asexual reproduction, unlike the classical ones.