Bulletin of the Transilvania University of Brasov. Series III: Mathematics and Computer Science

Solving split equality fixed point problem of generalized demimetric mapping and certain optimization problem via dynamic step-size technique

H.A. Abass — 2025-01-14

In this article, we study the split equality problem of certain optimization problem in real Hilbert spaces. We propose a new viscosity iterative algorithm for approximating solution for finite families of split equality variational inequality and split equality fixed point problems of generalized demi metric mapping in real Hilbert spaces. Using our iterative method, we establish a strong convergence result for finding a common element for finite families of variational inequality and fixed point problems of generalized demimetric mapping. We present some consequences and application to the convex minimization problem to validate our main result. Our result complements and generalizes some related results in literature.

Eta-Ricci solitons on Lorentzian para-Kenmotsu manifolds

P. Almia — 2025-01-14

This work introduces the investigation of ETA(η)-Ricci solitons on a Lorentzian para-Kenmotsu manifold. In this study, we investigate η-Ricci solitons on Lorentzian para-Kenmotsu manifolds satisfying the condition C.D=0. Additionally, we have constructed and thoroughly shown the findings about the harmonic and Weyl harmonic curvature tensor. Furthermore, our study focuses on the outcomes obtained by investigating Lorentzian para-kenmotsu manifolds that possess a η-Ricci soliton meeting the curvature requirement N•ψ=0. Finally, we provide an illustrative case of a manifold that demonstrates the presence of proper η-Ricci solitons.

Projectile motion under quadratic air resistence via multistep-differential transformation method

J. Asad — 2025-01-14

The projectile motion system was examined in this study when air resistance was present (we only looked at the situation of quadratic air resistance). First, we used Newtonian mechanics to derive the equation governing the system. Second, the study focused on the projectile motion’s characteristics, namely its maximum height and maximum horizontal range. Additionally, we used simulation plots to apply the Differential Transform Method (DTM) and the Multistep Differential Transform Method (Ms-DTM) to solve the equations found. This allowed us to discuss the projectile’s trajectory. We computed the flying time and the maximum range by comparing our findings with experimental data from published research. In the end, the absolute errors were computed to find the optimal numerical approach to solve this problem.

A note on Stancu operators with three parameters

Gulen Bascanbaz-Tunca — 2025-01-14

In this paper, we consider the sequence of positive linear operators L^α,β_n,r depending on three non-negative parameters; an integer r and two reals α and β such that α ≤ β, constructed by Stancu. We consider a Kantorovich-type generalization of Stancu’s operators and investigate their convergence properties in Lp-norm. Finally, we observe variation detracting property for the Stancu operator and its Kantorovich modification. Moreover, we show that the Stancu operator satisfies an inequality that we call variation detracting when the attached function is of bounded p-variation in the sense of Riesz.

Generalization of some inequalities using Lidstone interpolation via diamond integrals

M. Bilal — 2025-01-14

In present paper, several inequalities involving Csisz´ar divergence are established by utilizing diamond integrals and Lidstone interpolation polynomials. Consequently, new and generalized inequalities are yields. The functions involved in these inequalities are higher order convex functions. Inequalities involving Shannon entropy, Kullback-Leibler discrimination, triangle distance and Jeffrey’s distance, are studied as particular instances with the help of specially chosen convex functions. The main findings are also discussed for some special time scales (both discrete and continuous). Many existing results are also obtained which established the link with existing literature.

Exponential decay for thermoelasticity with two porous structures

Adina Chirila — 2025-01-14

The paper is about the spatial behaviour of an elastic continuum with two porous structures in the one-dimensional case. The equilibrium of the continuum is studied without the presence of an external body force or extrinsic equilibrated body forces.

A note on geometric construction of spectrally arbitrary zero-nonzero pattern matrices

R.P. Deore — 2025-01-14

In this paper, we give a geometric construction for spectrally arbitrary zero-nonzero pattern matrices. The geometric construction also deals with computation of a matrix realization for a given characteristic polynomial.

Bounds of curvatures for submanifolds of product spaces

Z. Jabeen — 2025-01-14

The paper is devoted to the study of bounds for the normalized scalar curvature and the generalized normalized δ-Casorati curvatures for submanifolds of product spaces.

Maps on matrices preserving idempotency of a triadic relation

Mahdi Karder — 2025-01-14

Let M_n be the algebra of all n×n real or complex matrices. In this paper, we give a full description of continuous maps on M_n such that Φ(A)(Φ(B)− Φ(C)) is idempotent if and only if A(B − C) is idempotent for all A, B, C ∈ M_n.

Warped product pointwise PR-semi-slant immersions in para-Kähler manifolds

A. Kumar — 2025-01-14

This study investigates the geometry of warped product pointwise PR-semi- slant immersions M in para-Kahler manifolds M̄^2m that naturally englobes the warped product PR and semi-slant immersions. We first derive the non-existence of warped product M_λ ×_f M_T, and then by presenting a numerical example examine the presence of warped product M such that M = M_T ×_fM_λ in M̄^2m. Finally, we derive some characterizations for pointwise PR-semi-slant submanifolds to be locally warped product M_T ×_f M_λ in terms of shape operator and endomorphisms. The mixed totally geodesic case is also discussed.

Generalization of Gaussian Mersenne numbers and their new families

M. Kumari — 2025-01-14

In this article, we present the generalized Gaussian Mersenne numbers with arbitrary initial values and discuss two particular cases, namely, Gaussian Mersenne and Gaussian Mersenne-Lucas numbers. We present their various algebraic properties such as Binet’s formula, negatively subscripted elements, Catalans’s, Cassini’s, and d’Ocagne’s identities, partial sum, binomial sum, generating and exponential generating functions, etc. In addition, we study a new generalized sequence arising from the explicit expression made with the characteristic roots and refer to them as the k-generalized Gaussian Mersenne numbers. We present various identities of them and show their connections with the generalized Gaussian Mersenne numbers.

An altenative proof of the Catalan conjecture

C. Liu — 2025-01-14

The original proof [5] of Catalan’s conjecture uses real binomial power series expansions and annihilation of real class groups, based on a Theorem of Thaine. In this paper we provide a simplified approach to this proof, which uses Stickelberger annihilation of the minus part of the class group, and thus does not require the Theorem of Thaine. The approach is based on proving the existence of a character connecting Galois exponents of roots of unity.

Almost periodically unitary solutions to stochastic differential equations

O. Mellah — 2025-01-14

In this paper, we consider a class of stochastic differential equations with almost periodic coefficients. In the one-dimensional case, by using the unitary group of operators associated to the stationary increments of the Brownian motion, we show the unitary almost periodicity of the solution. We also prove that the tightness is a property of almost periodically unitary processes. Some examples are given.

Convergence of third orderNewton-like method in Riemannian manifolds

P.K. Parida — 2025-01-14

In this article, we present semilocal convergence of third order Newton-like method in Riemannian manifolds. We study convergence analysis with Lipschitz continuity condition and by using recurrence relations of the method. Finally, two numerical examples are given to illustrate the effectiveness of our results.

A general fixed point theorem for a pair of mappings satisfying a mixed implicit relation in S-metric spaces

A.-M. Patriciu — 2025-01-14

The purpose of this paper is to extend the notion of mixed implicit relation by [19] to S - metric spaces and to prove a general fixed point theorem for a pair of mappings in S - metric spaces, generalizing some results by [3], [10], [15] and other papers.

Some new results on normal BH-algebras

Daniel Abraham Romano — 2025-01-14

The concept of BH-algebra was introduced in 1998 by Y. B. Jun, E. H. Roh, and H. S. Kim as a generalization of BCH/BCI/BCK-algebras. The same authors launched the idea of a normal BH-algebra at the end of the last century. This paper discusses the concept of atoms in normal BH-algebras. Thus, some conditions were found that they ensure the existence of such elements. Also, the extension of a normal BH-algebra A to the normal BHalgebra A ∪ {a} is considered so that the element a is an atom in A ∪ {a}.

Feistel inspired novel hybrid cryptosystem for information secure processing

N. Aydin — 2025-01-14

In this paper, we propose a novel hybrid encryption algorithm that enhances security by integrating DNA encoding, the Rabin algorithm, a one-time pad (OTP), and a Feistel-inspired structure. The algorithm begins with the application of a DNA-based OTP key, used exclusively for a single secure communication session. In the second step, it combines public and private keys to generate a Rabin key. By incorporating a Feistel-inspired scheme and leveraging the inherent randomness of DNA sequences, the resulting ciphertext achieves a high level of security, making it significantly more challenging to decrypt without the private key.

Exploiting cellular automata and linear regression to predict disease spread

A. Baicoianu — 2025-01-14

The Covid-19 epidemic has significantly impacted the world, highlighting the urgent need to understand and anticipate its mechanisms of spread. This essential knowledge is necessary to plan and conduct an immediate and adequate public health response. This study presents an approach to modeling the spread of Covid-19 using non-uniform cellular automata. The paper extends the application of a previously developed model that uses cellular automata and the SIRD epidemiological model for predicting the evolution of Covid-19. Originally developed for a different context, the model is now adapted to assess the progression of the pandemic in Germany and Italy, considering the potential impact of neighboring countries on the spread of the epidemic. Additionally, this approach expands the prediction model to countries lacking infection data (Switzerland) by using estimated parameters from neighboring countries and randomly initialized parameters for the target country. The study demonstrates the model’s precision in tracking infection rates over time by employing reliable public data sources such as the World Health Organization and existing information from national health websites. The study not only furnishes valuable insights into the regional distribution of the epidemic’s impact but also makes a significant contribution by extending the model’s application beyond the borders of a single country. It introduces a strategy for extrapolating patterns of infection spread across borders, marking it as the first study of its kind with substantial importance in the field.

A new approach to construct basic probability assignment and its applications in data classification

M. Kaur — 2025-01-14

In the present work, we have proposed a classification algorithm that uses Dempster Shafer (D-S) evidence theory since it has emerged as an effective tool in handling data classification problems. As basic probability assignment (BPA) is a pre-requisite for applying D-S theory, how to generate it is a hot issue. This paper proposes a novel method for generating basic probability assignments (BPAs) from training data. Dempster Shafer’s (D-S) rule of Combination is utilized for the unification of these BPAs and finally, classify each data item using these unified BPAs. Testing is carried out using some popular benchmark data sets consisting of three classes. Evaluated results show that the classification accuracy is comparatively high.