This research investigates the relationship between algebra and graph theory, specifically how algebra facilitates graph theory. Associating matrices with graphs introduces the concept of graph energies. A new energy formula of non-commuting graphs for dihedral groups using closeness Laplacian and closeness signless Laplacian matrices is investigated in this paper. It is found that both energies are always equivalent and are categorized as hyperenergetic.
A study of the local and the semilocal convergence is carried out for the Chebyshev-Halley-type iterative methods under ω-type condi tions. The conditions are imposed only on the first-order derivatives. In both cases, the convergence region and the region of uniqueness of the solution is established. The new technique is a usefull alternative to expensive Taylor series used to study the convergence of iterative methods requiring high order derivatives not on the methods. The re sults of a numerical experiment are presented to check the convergence conditions.
We study iterative methods for solving common fixed point prob lems in the presence of summable computational errors.
The purpose of this paper is to introduce and examine two classes of quartic real polynomials P having the same Euclidean norm as their Lagrange resolvent, respectively, having the square of the Euclidean norm equal to the height of the Lagrange resolvent. The reduced form of the polynomial P is provided, which eliminates the cubic term. Find ing such polynomials with integer coefficients is always of interest. The Lagrange resolvent associates a cubic curve with each of these polyno mials as a cubic polynomial. It highlights the situations in which these cubic curves are elliptic curves.
In the framework of CAT(0) spaces, we prove that the mean of iterations of an asymptotically nonexpansive mapping with nonempty f ixed point set converges weakly to a fixed point. The result extends the similar previous result for nonexpansive mappings in CAT(0) spaces [13] and generalizes the results of [11] from Hilbert spaces to Hadamard spaces.
In the current digital era, information security is a top priority and outdated algorithms must be updated or replaced. This article presents a novel method that combines encryption and steganography to conceal secret text messages in color graphics. Using a chaotic pseudorandom generator, the position and arrangement of the picture pixels used for information embedding are chosen at pseudorandom. Another layer of protection is to encrypt the secret message before embedding it. This issue will deter attackers from looking for signs of steganography. The suggested indiscernible stegoalgorithm is being evaluated. We perform randomness tests, histograms, peak signal-to-noise ratio analysis, and other tests using conventional statistical and empirical methods. The novel results are presented and analyzed in the current article.
In this paper, we propose the concept of ρ-strong convergence for difference sequences of fractional order, denoted by ∆α-ρ-strong con vergence, in a q-rung orthopair fuzzy normed space. We establish the uniqueness of this convergence and provide its algebraic characteriza tion. A convergence criterion for subsequences is derived, and the rela tionship between ∆α-strong convergence and ∆α-ρ-strong convergence is examined under conditions on liminf s ρs . Moreover, an inclusion re sult is obtained by employing a positive non-decreasing sequence µs satisfying ρs µs under suitable assumptions. Finally, we introduce the notion of ρ-strongly Cauchy difference sequences of fractional order and investigate their connection with ∆α-ρ-strong convergence.
The usual equation for the motion of electrons in the deterministic Rutherford-Bohr atomic model is conservative with a singular potential at the origin. When a dissipation is added, new phenomena appear, mainly a contraction of orbits for large time. A special model is studied in which the dissipation coefficient varies as the inverse of the square of the distance to the nucleus, and it is shown that this equation has contraction properties similar to the case of a linear damping, but the backward equation shows affine growth of the orbits for large time, which is more realistic than the exponential growth in the case of linear damping.
We use the theory of the dynamical systems to study the dynamics of the ΛCDM model of the universe. A three-dimensional autonomous dynamical system of a class of Lotka-Volterra dynamical systems, with density parameters of the universe’s constituents as dependent vari ables is inferred. It is assumed that the matter content in our universe consists of barotropic perfect fluids without mutual interaction (ex cept gravitational). The appropriate physical interpretation, as well as parametrization between the scale expansion factor of the universe and cosmological density parameters is presented.
In this paper, we construct a new class of bicomplex sequences whose components are Fibonacci finite operator sequences. A sys tematic study of their structural properties is carried out within the framework of the idempotent decomposition of bicomplex numbers. We derive explicit recurrence relations, polynomial representations, and matrix formulations for these bicomplex Fibonacci finite opera tor sequences. Several identities are established using the associated matrix representation.
This paper introduces the spectral properties of positive linear op erators under the framework of lacunary statistically relatively uniform convergence. We define the concept of lacunary statistically relatively uniform and establish inclusion and stability results for sequences of positive linear operators. Furthermore, we examine the convergence of spectral radii and provide illustrative examples using classical opera tors. This work extends both Korovkin-type approximation theory and spectral theory into the lacunary statistical relatively uniform setting.
This paper extends the foundational work on Roegenian Economics by developing a rigorous mathematical framework for the thermo dynamic-economic correspondence initiated by Georgescu-Roegen. We provide an enhanced dictionary between thermodynamic and economic state variables. The main contributions include: (i) a formal proof of the existence and uniqueness of the economic triple point; (ii) charac terization theorems for critical phenomena; (iii) derivation of Maxwell type relations for economic potentials; and (iv) stability analysis via Legendre transforms. We present empirical validation using World Bank Governance Indicators and IMF inflation data for 2022-2023, demonstrating that the phase diagram captures the relationship be tween institutional stability and price dynamics. The analysis iden tifies candidates for triple point behavior (Venezuela, Zimbabwe) and supercritical regimes (Switzerland, Singapore).
Some newclasses of general triequilibrium inclusions are introduced and investigated. We establish the equivalence between the general triequilibrium inclusions and the fixed point problems, which is used to discuss the existence of the unique solution. Using various techniques such as resolvent methods and dynamical systems coupled with finite difference approach, we suggest and analyze a number of new multi step methods for solving triequilibrium inclusions. Convergence analysis of these methods is investigated under suitable conditions. Sensitivity analysis is also investigated. Various special cases are discussed as applications of the main results. Several open problems are suggested for future research.
Let A and B be non-empty subsets of a metric space (X,d). Let T : A∪B → A∪B be a map such that T(A) ⊆ B and T(B) ⊆ A satisfying a certain contractive condition called cyclic orbital proximal contraction. We give the necessary conditions for the existence of a unique point ξ ∈ A such that d(ξ,Tξ) is equal to the distance between A and B. Our main result generalizes the main result of [A.A. Eldred and P. Veeramani, Existence and convergence of best proximity points, J. Math. Anal. Appl., 323 (2006), 1001-1006].
A Steiner triple system (STS) of order v is a 3-uniform hypergraph with v vertices in which every 2-subset of vertices has degree 1. A Kirkman triple system (KTS) is a resolvable Steiner triple system, that is, a partition of the blocks of the triple system into classes which are themselves partitions of the set of vertices into disjoint blocks. In this paper we give a construction of KTS of order v = 3h much simpler and less technical than previously known constructions.
In this paper, we present new fixed point results for multivalued maps on extension spaces with respect to a map.
We introduce the notion of α-ψ-R contractive mappings that act on a metric space. We establish the existence and uniqueness of fixed points for this class of mappings and provide a sequence of iterates which approximate their fixed points. Some examples are presented and the relationships with some previous results are described.
We establish a generalization of Ekeland’s variational principle for submonotone maps defined on a preordered pseudometric space and with values in a preordered monoid. The proof relies on an ordering principle for more general preordered sets.
The existence and location of solutions are established for an elliptic system with full gradient dependence and intrinsic operators. The abstract results are applied to a system with convolution products.
The order topology has been historically defined only for totally ordered sets. Here, the order topology in partially ordered sets will be constructed. Several attempts have been provided in the recent litera-ture on partially ordered groups, rings and modules. This manuscript contains a full construction that provides solid foundational ground to the previous attempts and serves to pay tribute to the topological trajectory of Prof. Ricceri.
