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This paper purports to study the optical solitons solutions regarding the nonlinear schr¨odinger equation with dual power law of nonlinearity along with self steeping and repercussion. The optical solutions mostly comprise of singular solitons with nonlinear chirping. The adopted solitary wave ansatz and the importance of the obtained chirped soliton pulses are also discussed. [ABSTRACT FROM AUTHOR]

To store voluminous data of the enterprises and organizations opt for cloud storage. Outsourcing data in the cloud allows many autho- rized users to access the data from different geographical locations. The service provider stores the users data in data centers at remote lo- cations. Cloud Service provides infrastructure and web services to the users retrieving an unlimited data and paying the service consumed by the user. The cryptographic primitives use digital signatures for data integrity checking on the remote data. The client is unable to download the whole data stored in data center to validate its integrity. Therefore, efficient techniques required to prove the integrity of their outsourced data with least amount of communication, and computa- tion cost. This paper describes the digital signature schemes used in auditing techniques at client and its performance. [ABSTRACT FROM AUTHOR]

It is commonly claimed that emerging technologies, including Augmented Reality (AR), open up new perspectives for education. Today, the finding of this research is that few objective data support the hypotheses that are made about the interest, effectiveness, usability and acceptability of these technologies that are based on interaction and immersion in real time. In this article, we present a review of some of the ergonomic problems of AR in teaching surfaces and volumes of 3D geometric shapes. In this approach, AR is considered and evaluated as an educational resource that helps with the activity and briefly explains the concept of AR and the envisaged interests of this technology for teaching. [ABSTRACT FROM AUTHOR]

In this paper we study the controllability for the 1D-Heat equation with a Dirichlet boundary condition, in the presence of a scale-invariant parameter. First, we construct the scale-invariant solutions for the one-dimensional heat equation. Then we present our problem statement. We finally prove the Dirichlet boundary controllability. [ABSTRACT FROM AUTHOR]

The Oracle database is widely acknowledged for its high level of trustworthiness. This paper elucidates the manner in which Oracle DB provides an automated methodology for the identification and optimization of performance issues. The capacity for self-tuning is an essential element in the development of a dependable and trustworthy self-directed database. This paper offers a comprehensive examination of Oracle's self-tuning capabilities, focusing on the Automatic Database Diagnostic Monitor (ADDM) as a prominent automatic tuning solution. The discussion encompasses an overview of these capa- bilities and a thorough presentation of ADDM's features and functionalities. The ADDM (Automatic Database Diagnostic Monitor) is a tool that systematically evaluates and scrutinizes the data obtained from the Automatic Workload Repository (AWR) in order to detect and assess possible performance concerns within the Oracle Database. To assess the efficacy of ADDM, we formulated a program to replicate substantial server workloads and effectively implemented ADDM suggestions to address the identified issues, thereby ensuring a trustworthy resolution. [ABSTRACT FROM AUTHOR]

In this paper, we present a new analytical scheme to generate atomic solutions of partial differential equations. The theory of tensor product in Banach spaces coupled with some features of atomics operators are utilized to attain our results. Some demonstrative examples are given for completeness. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of (τ1, τ2)-extremally disconnected spaces. Moreover, we establish some characterizations of (τ1, τ2)-extremally disconnected spaces. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to use the notion of the general-ized quadrangle (Ω, L) of type O-6(2) to show that NE(A(B)) induces SL(A(B)) on A(B), where B is a coclique of Ω, A(B) = 〈ex | x ∈ B〉 is the space spanned by ex, x ∈ B and NE(A(B)) is the stabilize of A(B) in the Chevalley group E = E6(K) of type E6 over a field K of characteristic 2, and to show that E acts transitively on the family V2 of all 2-dimensional singular subspaces of the 27-dimensional module A over K, we also compute |V2|, the order of V2. Next, we compute the action of the subgroup H = 〈UΔ, UΔσ 〉 of E on the 27-dimensional module A over K, where UΔ,UΔσ are two root subgroups of E and we prove that H acts completely reducibly on A with H &#8780 SL2(K). It is important to mention that the motivation behind this work is the challenging nature of the investigation of Chevalley groups, in particular E6, over fields of characteristic 2, and also that this work could lead to more understanding of this type of group. [ABSTRACT FROM AUTHOR]

The modified RSA provides high efficiency against attacks and, as a result, it is considered the ideal choice for many applications. In this paper, we introduce an alternative to the modified RSA key encryption system called TPRSA, based on Tri-Cartesian algebra and polynomials, by modifying the mathematical structure of text encryption and decryption keys to obtain a high level of security. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and investigate a class of bi-univalent functions associated with Gegenbauer Polynomials. For functions in this class, we derive the estimations for the initial Taylor-Maclaurin coefficients |a2| and |a3|. Moreover, we obtain the classical Fekete-Szegö inequality of functions belonging to this class. [ABSTRACT FROM AUTHOR]

In this paper, a new family of iterative methods for the simultane-ous approximation of simple complex polynomial zeros is presented. The proposed family of simultaneous methods is constructed on the basis of the well-known third order Ehrlich iteration, combined with an iterative correction from the sixth order Neta's method for nonlinear equations. It is proved that the use of this iterative correction allows to increase the convergence order of the basic method from three to eight. Numerical examples are given to illustrate the convergence and effectiveness of the proposed combined method. [ABSTRACT FROM AUTHOR]

In this paper, we prove that the Diophantine equation 147x + 741y = z² has no non-negative integer solution. [ABSTRACT FROM AUTHOR]

The fuzziness approach is useful when trying to solve programming problems with a degree of ambiguity. In recent years, various approaches to the difficulties of fuzzy linear programming have developed. Many papers use the features of fuzzy sets as a method to find the best solutions to fuzzy programming problems, and some of these papers deal with fully fuzzy linear programming problems in which all variables are triangular fuzzy numbers or trapezoidal fuzzy numbers. For the fully fuzzy linear programming (FFLP) problems, where all the variables and parameters are of the same type as decagonal fuzzy numbers, this study provides a new ranking function technique and a new membership function of decagonal fuzzy numbers. Using the arithmetic decagonal fuzzy numbers and the proposed ranking function technique, a new algorithm for a fully fuzzy simplex (FFS) method is offered to obtain the optimal fuzzy solution. In the paper's applied section, we provide a working example of how to establish a fuzzy optimal solution to the given problem. [ABSTRACT FROM AUTHOR]

This paper is concerned with the notion of θ(Λ, p)-continuous functions. Moreover, some characterizations and several properties concerning θ(Λ, p)-continuous functions are investigated. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new class of functions called strongly θ(Λ, p)-continuous functions. Moreover, we investigate several characterizations and some properties concerning strongly θ(Λ, p)-continuous functions. [ABSTRACT FROM AUTHOR]

This paper is concerned with the concept of weakly δ(Λ, p)-closed functions. Moreover, several characterizations of weakly δ(Λ, p)-closed functions are established. [ABSTRACT FROM AUTHOR]

In 2019, Burshtein [1] showed that the equation px+py = z² has no positive integer solution, except for p = 2, 3. For p = 2, all solutions of the equation in the Fibonacci and Lucas numbers was investigated by Hashim [2]. In this paper, we prove that (x, y, z) = (F5,L3,L6) is the unique solution of the equation, when p = 3. [ABSTRACT FROM AUTHOR]

The objective of this research paper is to justify that an additive mapping F from a semiprime ring R to itself will be ϕ-centralizer having a suitable torsion restriction on R if it satisfies certain algebraic equations. [ABSTRACT FROM AUTHOR]

Let X be a nonempty set and let T(X) denote the semigroup of transformations from X to itself under the composition of functions. For a fixed subset Y of a nonempty set X, let Fix(X, Y) be the set of all self-maps on X which fix all elements in Y. Then Fix(X, Y) is a regular subsemigroup of T(X). In this paper, we characterize coregular elements of Fix(X, Y) and give necessary and sufficient conditions for Fix(X, Y) to be coregular. Moreover, we study some properties of regularity on Fix(X, Y) and give necessary and sufficient conditions for the set of all left regular (right regular and completely regular) elements to be a subsemigroup of Fix(X, Y). [ABSTRACT FROM AUTHOR]

In this paper, we present a simple numerical technique based on optical frequency domain reflectometry. Nonlinear Schrödinger having anti-cubic equation is suggested for computing a new solitons-solutions propagation. The dispersion is to be calculated from variations in the frequency chirp rate, when frequency-chirped light is utilized as the light source. We utilize an accurate model of the average dispersion, in fibers up to several tens of kilometers. The numerical simulation is obtained by applying variable perturbation theory on the group velocity dispersion term in nonlinear Schrödinger having anti-cubic equation. The proposed model is used with some particular conditions; to be significantly more accurate for links with strong nonlinearities and high dispersion. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new concept called T-Hopfian modules, which is a generalization of the notion of Hopfian modules. We show that if a module M satisfies the ACC on non-T-small submodules, then it is T-Hopfian. We explore additional properties of T-Hopfian modules and provide examples for illustration. [ABSTRACT FROM AUTHOR]

Due to the wide variety of distant information transmission, data encryption has become an absolute necessity for practically all data transaction applications. Sensitive data gets uploaded to the cloud every day through many methods. AES algorithm is now the best option for many applications that require security services. Because of this, a lot of research has been carried out to improve the performance and efficiency of the algorithm. This paper's main goal is to propose an improved method for encrypting and decrypting data. As key sharing was a significant problem in the symmetric approach, we generate the key using the ECC and will encrypt and decrypt data using the AES using this key. The suggested algorithm, which is simpler than ECC and solely utilized for key generation-not data encryption or decryption-is more secure than AES because it circumvents the key-sharing issue that plagued AES. [ABSTRACT FROM AUTHOR]

In this paper, we define the bi-periodic k-Pell sequence. We obtain Binet's formula, some identities of the bi-periodic k-Pell sequences like Catalan, Cassini and D'Ocagne's identities as well as some related summation formulas. [ABSTRACT FROM AUTHOR]

An R-moduleM is called δ-weakly Hopfian if any δ-small surjective endomorphism of M is an automorphism. In this paper we explore various properties of δ-weakly Hopfian modules, shedding light on their distinct characteristics. Additionally, we examine the δ-weakly Hopficity of modules over polynomial and truncated polynomial rings. [ABSTRACT FROM AUTHOR]

In this paper, absolute g*ωα-continuous functions in bigeneralized topological spaces is introduced and characterized. [ABSTRACT FROM AUTHOR]

In this paper we investigate the parameter estimation of solar photovoltaic (PV) models using the self-adaptive differential evolution algorithm with dynamic fitness-ranking mutation and pheromone strategy (SDE-FMP). The dynamic mutation divides the population into three groups according to fitness values and selects groups and their vectors with adaptive probabilities to create a mutant vector. The algorithm also encodes scaling factor and crossover rate values into target vectors to use in mutation and crossover operations and adjusts them with pheromones in the selection process. Experimental results show that the SDE-FMP algorithm can give the solutions with the lowest errors and is overall competitive with the compared methods regarding the mean errors. [ABSTRACT FROM AUTHOR]

Due to the importance of the NTRU public key cryptosystem, many improvements have been made to it by increasing security or speed to keep pace with the process of technological development in exchanging various data. In this paper, we construct a public key cryptosystem called HAQTR using non-commutative quaternion algebra with the change of the mathematical structure. [ABSTRACT FROM AUTHOR]

The reliability of computing the Complex Network using probability theory as a complex system is the main topic of this paper. The reliability assignment and optimization issue was dealt with using the Genetic Algorithm (GA), which has the ability to deal with complex issues that are typical in engineering systems. A higher number of duplicates are frequently necessary when the cost of execution is significant. In addition to GA, we use the particle swarm optimization (PSO) technique. This method is based on how accumulating organisms behave. In order to compare the resilience and durability of the algorithms that aid in determining the fitness of a particular system, two algorithms will be used in this paper. [ABSTRACT FROM AUTHOR]

This paper deals with a perturbed nonlinear system of fractional order differential equations (FrODEs) with Caputo derivative. The purpose of the paper is to discuss uniform stability (US), asymptotic stability (AS), Mittag-Leffer stability (MLS) of zero solution and boundedness at infinity of non-zero solutions of this perturbed nonlinear system of FrODEs with Caputo derivative. We obtain four new theorems on these mathematical concepts via a Lyapunov function (LF) and its Caputo derivative. For illustration, an example is provided which satisfies assumptions of the four new results and, in particular, shows their applications. The new results of this paper generalize and improve some recent ones in the literature and they have contributions to theory of FrODEs. [ABSTRACT FROM AUTHOR]

Let G be a simple connected graph. A dominating set S ⊆ V (G) of G is a restrained dominating set in G if for every v ∈ V (G)S there exists u ∈ V (G)S such that uv ∈ E(G). A restrained dominating set S of G is a 1-movable restrained-dominating set of G if for every v ∈ S either S {v} is a restrained dominating set of G or there exists u ∈ (V(G)S) ∩ N(v) such that (S{v}) ∪ {u} is a restrained dominating set of G. The minimum cardinality of a 1-movable restrained-dominating set in G, denoted by γ¹mr(G), is the 1-movable restrained-domination number of G. In this paper, the 1-movable restrained-dominating sets in the corona of graphs are characterized. Also, the 1-movable restrained-dominationnumbers of these graphs are determined. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the concept of regular generalized (τ1, τ2)-closed sets. First, we introduce the notion of regular generalized (τ1, τ2)-closed sets. Next, we study some properties of regular generalized (τ1, τ2)-closed sets and regular generalized (τ1, τ2)-open sets. Finally, we consider some characterizations of (τ1, τ2)-T1/2-spaces. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the notion of (τ1, τ2)-R1 bitopological spaces. Moreover, some characterizations of (τ1, τ2)-R1 bitopological spaces are investigated. [ABSTRACT FROM AUTHOR]

In this paper, we show that the Diophantine equation 3x +121y = z² has precisely two solutions in non-negative integers; namely, (1, 0, 2) and (5, 2, 122). [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of (τ1, τ2)-T1/2-spaces. We also investigate some characterizations of (τ1, τ2)-T1/2-spaces. [ABSTRACT FROM AUTHOR]

In 2022, Bantaojai et al. [3] introduced an algebra structure called Bd-algebras. In this paper, we define a new notion called fuzzy Bd-ideals of Bd-algebras and study some of its basic properties. Moreover, we characterize fuzzy Bd-ideals by the different types of their level subsets in Bd-algebras. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to introduce the structure space of uniformly strongly prime ideals of an ordered semigroup and to study the separation axioms and the compactness property. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the notion of generalized (τ1, τ2)-closed sets. First, we introduce the notion of generalized (τ1, τ2)-closed sets. Next, we study some properties of generalized (τ1, τ2)-closed sets. Finally, we investigate some properties of generalized (τ1, τ2)-open sets. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of (τ1, τ2)*-closed sets. Moreover, we investigate some properties of (τ1, τ2)*-closed sets and (τ1, τ2)*-open sets. [ABSTRACT FROM AUTHOR]

Clustering is an essential data exploration technique applied to many disciplines and applications such as data mining, image processing, bioinformatics, and machine learning. A clustering method identifies hidden patterns in a dataset and combines similar data points into clusters. The problems are challenging when they have many data points, attributes, and cluster partitions. In this paper, we propose an adaptive differential evolution with an archive strategy (ADEAS) to find candidate centroids and minimize their intra-cluster distance for solving partitional clustering problems. The archiving strategy stores inferior solutions during the selection operation to increase population diversity and create directions for guiding the search. We validate the proposed algorithm with several well-known methods using the UCI datasets. The results show that ADEAS outperforms the compared methods. [ABSTRACT FROM AUTHOR]

In this paper, we establish a new eight-dimensional algebra callked KAH-Octo. Moreover, we study subalgebras aand give some properties of the algebra such as division, isomorphism, simple, semi-simple, Jordan, Malcev, among others. Furthermore, we give some applications to some interesting areas of mathematics such as cryptography. [ABSTRACT FROM AUTHOR]

In this paper, we focus on terms with fixed variables count, terms under which the total numbers of occurrences of variables in each position are equal. Moreover, we determine conditions for which the set of terms with fixed variables count is closed under the generalized superposition. Furthermore, we form the partial algebras of such terms satisfying certain axioms as weak identities. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new property of rings called the f(x), g(x)-clean property, which is a generalization of the g(x)-clean property. We prove that a commutative ring Q is feebly clean if and only if it is f(x), f(x)-clean, where f(x) is a suitable quadratic polynomial. We prove additional results of this property and include examples for clarity. [ABSTRACT FROM AUTHOR]

In this paper, we study counting perfect matchings in linear chain graphs, focusing on identically colored and alternatingly colored odd faces, using recurrence relations. Our primary objective is to derive explicit formulas for the numbers of perfect matchings in linear chain graphs with identically colored odd faces. Furthermore, we establish a relationship between the numbers of perfect matchings in linear chain graphs with identically colored odd faces and strip snake chain graphs. This relationship provides us with an alternative way of validating the numbers of perfect matchings in linear chain graphs with the same colored odd faces. [ABSTRACT FROM AUTHOR]

A positive integer n is called a t-co-cobalancing number if n is a solution of the equation 1+2+3+...+(n+1) = (n+1+t)+(n+2+t)+...+(n+r+t) for some positive integer r and fixed positive integer t. In this paper, we present a function and recurrence relations for t-co-cobalancing numbers. Moreover, we give some interesting properties of t-co-cobalancing numbers. [ABSTRACT FROM AUTHOR]

Let G be a simple connected graph. The geodetic independence polynomial G, denoted by g(G; x), is the polynomial whose coefficients correspond to the number of geodetic independent subsets of V (G). In this paper, we apply the Chuh-Shih-Chieh's Identity to establish the geodetic independence polynomial of cycles. [ABSTRACT FROM AUTHOR]

In this paper, we investigate r-ideals in commutative ordered semigroups with zero and identity. Moreover, we study some properties of r-ideals. Furthermore, we give several characterizations of r-ideals. [ABSTRACT FROM AUTHOR]

In this paper, we establish the induced path polynomials of graphs resulting from the join and corona of two connected graphs. [ABSTRACT FROM AUTHOR]

In this paper, we model a network obtained by sequential total linear interactions of independent sequence of finite networks. We determined the connectivity of the nodes and the proximity of every pair of nodes of the resulting network structure. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to compute the probability Pr(G) that two elements of the group G, drawn at random with replacement, commute; that is, Pr(G) = Number of ordered pairs (x, y) ∈ G × G such that xy = yx/|G × G| = |G|² In particular, we compute Pr(G) for some groups such as the extraspecial groups of order p³, p prime, for the permutation groups G = Sn and G = An, n ≥ 5, for 10 non-abelian groups of order p4 and for simple groups of certain type. [ABSTRACT FROM AUTHOR]

In this paper, we call the module N the Goldie supplement extending module (GSCS-module) which is a new generalization weaker than the Goldie extending module and stronger than the Goldie weakly supplement extending module. We discuss the relation between Goldie supplement extending module and other notions such as the Goldie extending module and the supplement extending module. Moreover, we explain when the submodule of Goldie supplement extending is a Goldie supplement extending module. Furthermore, we show that the direct sum of GSCS-module holds only under certain conditions. [ABSTRACT FROM AUTHOR]