<abstract><title style='display:none'>Abstract</title>In this paper, inspired by recent articles of A. Szynal-Liana &amp; I. Włoch and F. T. Aydin &amp; S. Yüce (see [26] and [2]), we will introduce the ̄<italic>h</italic>-Jacobsthal quaternions and the ̄<italic>h</italic>-Jacobsthal–Lucas sequences and their associated quaternions. The new results that we have obtained extend most of those obtained in [26].</abstract>

On ̄h-Jacobsthal and ̄h-Jacobsthal–Lucas sequences, and related quaternions

A review of leadership

<abstract><title style='display:none'>Abstract</title> N. Palaniappan et. al [20, 28] have investigated the concept of intuitionistic fuzzy normal subrings in associative rings. In this study we extend these notions for a class of non-associative rings</abstract>

Department of Mathematics, Quaid-i-Azam University Islamabad-Pakistan

Department of Mathematics, COMSATS, Institute of Information Technology, Abbottabad-Pakistan

Intuitionistic Fuzzy Normal subrings over a non-associative ring

<abstract><title style='display:none'>Abstract</title>We deduce exact integral formulae for the coefficients of Gaussian, multinomial and Catalan polynomials. The method used by the authors in the papers [2, 3, 4] to prove some new results concerning cyclotomic and polygonal polynomials, as well as some of their extensions is applied.</abstract>

A new formula for the coefficients of Gaussian polynomials

<abstract><title style='display:none'>Abstract</title> All rings are commutative with 1 ≠ 0, and all modules are unital. The purpose of this paper is to investigate the concept of 2-absorbing primary submodules generalizing 2-absorbing primary ideals of rings. Let M be an R-module. A proper submodule N of an R-module M is called a 2-absorbing primary submodule of M if whenever a; b ∈ R and m ∈ M and abm ∈ N, then am ∈ M-rad(N) or bm ∈ M-rad(N) or ab ∈(N :R M). It is shown that a proper submodule N of M is a 2-absorbing primary submodule if and only if whenever I1I2K ⊆ N for some ideals I1; I2 of R and some submodule K of M, then I1I2 ⊆ (N :R M) or I1K ⊆ M-rad(N) or I2K ⊆ M-rad(N). We prove that for a submodule N of an R-module M if M-rad(N) is a prime submodule of M, then N is a 2-absorbing primary submodule of M. If N is a 2-absorbing primary submodule of a finitely generated multiplication R-module M, then (N :R M) is a 2-absorbing primary ideal of R and M-rad(N) is a 2-absorbing submodule of M. </abstract>

On 2-Absorbing Primary Submodules of Modules over Commutative Rings

<abstract><title style='display:none'>Abstract</title> In this paper we develop a new β-method applied to the resolution of homogeneous transmission lines. A comparison with conventional methods used for this type of problems like FDTD method or classical β-method is also given. Furthermore, various numerical experiments are presented to confirm the accuracy, efficiency and stability of our proposed method. In particular, these simulations show that our new scheme is unconditionally stable and fourth-order accurate in space and time. </abstract>

Numerical Analysis of Transmission Lines Equation by new β-method Schemes

<abstract><title style='display:none'>Abstract</title>
In this paper, the unknown parameters of a SEIRS mathematical model for the dynamics of COVID-19 are estimated by the least squares approach using data of Trkiye. In the considered model, the infective group is divided into two classes consisting of diagnosed and undiagnosed individuals. Since the data for undiagnosed infective individuals in the community is unknown, three di erent scenarios are proposed. The numerical solutions of the model using the estimated parameter values and the actual data are demonstrated with graphs.
</abstract>

Parameter estimation for a SEIRS model with COVID-19 data of Türkiye

<abstract><title style='display:none'>Abstract</title>
The filled function method has recently become very popular in optimization theory, as it is an e cient and e ective method for finding the global minimizer of multimodal functions. However, the fact that the existing filled functions in the literature generally have exponential or logarithmic terms and/or parameter sensitivity reduces the e ectiveness of this method. In this study, we propose a new non parameter and without exponential/logarithmic terms filled function, which is numerically stable, and is successfully used to solve global optimization problems. Furthermore, we have demonstrated how successful this new filled function method in terms of e ciency with numerical experiments and comparisons.
</abstract>

A New Filled Function for Global Optimization

<abstract>
<title style='display:none'>Abstract</title>
In this paper, a special kind of curve pair associated with each other by the linear dependency between the principal normal vector of the first curve (called Mannheim curve) and the binormal vector of the second curve (called Mannheim partner curve) is considered. A connection with the coupled dispersionless equation and Mannheim curve pair is established. Also, the Lax pair of the obtained coupled dispersionless equation from the motions of any Mannheim curve pair is given. This gives us a significant condition based on the curvature and torsion of any Mannheim curve for its integrability since it is well-known that the Lax pair provides the integrability of di erential equations.
</abstract>

Geometry of coupled dispersionless equations with Mannheim curves

<abstract><title style='display:none'>Abstract</title>
In this study, we have examined <italic>q− </italic>central Delannoy numbers and their Cauchy products. We have given some related equalities using the properties of recurrence relations. Moreover, using quantum integers, we have obtained the fundamental identities provided by Cauchy products of central Delannoy numbers.
</abstract>

On Cauchy Products of <italic>q−</italic>Central Delannoy Numbers

<abstract><title style='display:none'>Abstract</title>
In this study, generalized rectifying ruled surfaces of Frenet-type framed base curves in the three-dimensional Euclidean space are introduced. These surfaces are a generalization of not only the tangent and binormal surfaces of Frenet-type framed base curves, but also the tangent and binormal surfaces of regular curves. Additionally, we present some geometric characterizations and properties of these surfaces. Then, the singular point classes of the surface are scrutinized and the conditions for being a cross-cap surface are stated. Moreover, generalized rectifying surfaces are examined as framed surfaces by using the framed surface theory, and we investigate the basic invariants and curvatures of them. Then, several illustrative examples with figures are given to support the theorems and results.
</abstract>

Generalized Rectifying Ruled Surfaces of Special Singular Curves

<abstract><title style='display:none'>Abstract</title>
In the geometry of curves in 𝔼3, if the principal normal vector field of a given space curve <italic>ϕ</italic> with non-zero curvatures is the principal normal vector field of another space curve <italic>ϕ</italic>*, then the curve <italic>ϕ</italic> is called a Bertrand curve and <italic>ϕ</italic>* is called Bertrand partner of <italic>ϕ</italic>. These curves have been studied in di erent space over a long period of time and found wide application in di erent areas. Therefore, we have a great knowledge of geometric properties of these curves. In this paper, revested results for spacelike Bertrand curves with non-null normal vectors will be given with the previous studies on Bertrand curves in 𝔼13. Follow this revested results, the Bertrand curve conditions of a spacelike curve are obtained in 𝔼13. In addition, new curve samples that meet the obtained conditions are constructed and the graphs of these curves are given.
</abstract>

Spacelike Bertrand curves in Minkowski 3-space revisited

<abstract><title style='display:none'>Abstract</title>In this paper, we introduce the notion of interpolative Rus-Reich-Ćirić type 𝒵- contractions in the setting of complete metric space. We also consider some immediate consequences of our main results.</abstract>

Interpolative Rus-Reich-Ćirić Type Contractions via Simulation Functions

<abstract><title style='display:none'>Abstract</title>We consider a porous thermoelastic body, including voidage time derivative among the independent constitutive variables. For the initial boundary value problem of such materials, we analyze the temporal behaviour of the solutions. To this aim we use the Cesaro means for the components of energy and prove the asymptotic equipartition in mean of the kinetic and strain energies.</abstract>

Department of Mathematics and Computer Sciences, Transilvania University of Brasov, Bdul Iuliu Maniu, nr. 50, Brasov, Romania.

On Temporal Behaviour of Solutions in Thermoelasticity of Porous Micropolar Bodies

<abstract><title style='display:none'>Abstract</title> We review the superiorization methodology, which can be thought of, in some cases, as lying between feasibility-seeking and constrained minimization. It is not quite trying to solve the full edged constrained minimization problem; rather, the task is to find a feasible point which is superior (with respect to an objective function value) to one returned by a feasibility-seeking only algorithm. We distinguish between two research directions in the superiorization methodology that nourish from the same general principle: Weak superiorization and strong superiorization and clarify their nature.</abstract>

Weak and Strong Superiorization: Between Feasibility-Seeking and Minimization

<abstract><title style='display:none'>Abstract</title>In this paper, the notion of closed cubic intuitionistic ideals, cubic intuitionistic <italic>p</italic>-ideals and cubic intuitionistic <italic>a</italic>-ideals in <italic>BCI</italic>-algebras are introduced, and several related properties are investigated. Relations between cubic intuitionistic subalgebras, closed cubic intuitionistic ideals, cubic intuitionistic <italic>q</italic>-ideals, cubic intuitionistic <italic>p</italic>-ideals and cubic intuitionistic <italic>a</italic>-ideals are discussed. Conditions for a cubic intuitionistic ideal to be a cubic intuitionistic <italic>p</italic>-ideal are provided. Characterizations of a cubic intuitionistic <italic>a</italic>-ideal are considered. The cubic intuitionistic extension property for a cubic intuitionistic <italic>a</italic>-ideal is established.</abstract>

Cubic Intuitionistic Structures Applied to Ideals of <italic>BCI</italic>-Algebras

<abstract><title style='display:none'>Abstract</title>The problem of reflection and transmission of plane waves at an imperfect boundary between two thermally conducting micropolar elastic solid half spaces with two temperature is investigated. Amplitude ratio of various reflected and transmitted waves are presented when a set of coupled longitudinal wave (LD-wave) and thermal wave (T-wave) and a set of coupled transverse wave and microrotation waves (CDI, CDII) is made incident. The expressions for reflection and transmission coefficients which are the ratios of the amplitudes of reflected and transmitted waves at different angles of incident wave are obtained. The corresponding expressions for the normal force stiffness, transverse force stiffness, transverse couple stiffness and perfect bonding has also been included. Stiffness and two temperature e ects on these amplitude ratios with angle of incidence have been depicted graphically. Some special and particular cases are also discussed.</abstract>

Department of Mechanical Engineering, NIT Kurukshetra, Kurukshetra 136119, India

Reflection and transmission of waves from imperfect boundary between two heat conducting micropolar thermoelastic solids

<abstract><title style='display:none'>Abstract</title>Let (X; d) be a metric space endowed with a graph G such that the set V (G) of vertices of G coincides with X. We define the notion of G-Kannan maps and obtain a fixed point theorem for such mappings</abstract>

Fixed points of Kannan mappings in metric spaces endowed with a graph

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