<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> 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>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> 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>
Let <italic>n, m</italic> ∈ ℕ, <italic>n</italic> ≥ 3 and <italic>n</italic> ≥ <italic>m</italic> ≥ 2. In this paper, we study some properties of the unrestricted virtual singular braid of braid monoid <italic><bold>UVSB</bold>mn</italic> and group <bold><italic>UVSG</italic></bold><italic>mn</italic>. These properties emerged by studying the analogous properties of the unrestricted virtual singular pseudosymmetric braid of braid monoid and group. These mathematical objects are submonoids and subgroups of the virtual singular braid group <italic>VSGn</italic>. For many of these quotients, we have obtained reduced presentations.
</abstract>

On the unrestricted virtual singular braid

<abstract>
<title style='display:none'>Abstract</title>
In this article, we study the existence of mild solutions of a non-instantaneous integrodi erential equations on unbounded domain via resolvent operators in Banach space. For our proofs, we employ the semigroups theory and Schauder’s fixed point theorem. Moreover, we show that solutions of our problem are attractive. Finally, an example is given to validate the theory part.
</abstract>

Existence and attractivity results on semi-infinite intervals for integrodifferential equations with non-instantaneous impulsions in Banach spaces

<abstract>
<title style='display:none'>Abstract</title>
Let Ω ⊂ ℝ<italic>N</italic>, <italic>N</italic> ≥ 2, be a bounded domain with smooth boundary ∂Ω. Consider the following generalized Robin-Steklov eigenvalue problem associated with the operator 𝒜<italic>u</italic> = <italic>−</italic> Δ<italic>pu −</italic> Δ<italic>qu</italic>
<disp-formula>
<alternatives>
<graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_auom-2024-0003_eq_001.png"/>
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="block"><mml:mrow><mml:mrow><mml:mo>{</mml:mo> <mml:mrow><mml:mtable><mml:mtr><mml:mtd><mml:mrow><mml:mi>𝒜</mml:mi><mml:mi>u</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>ρ</mml:mi></mml:mrow><mml:mn>1</mml:mn></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>|</mml:mo> <mml:mi>u</mml:mi> <mml:mo>|</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mi>p</mml:mi><mml:mo>-</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mi>u</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>ρ</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>|</mml:mo> <mml:mi>u</mml:mi> <mml:mo>|</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mi>q</mml:mi><mml:mo>-</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mi>u</mml:mi><mml:mo>=</mml:mo><mml:mi>λ</mml:mi><mml:mi>α</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>|</mml:mo> <mml:mi>u</mml:mi> <mml:mo>|</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mi>r</mml:mi><mml:mo>-</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mi>u</mml:mi><mml:mo>,</mml:mo><mml:mi> </mml:mi><mml:mi> </mml:mi><mml:mi> </mml:mi><mml:mi>x</mml:mi><mml:mo>∈</mml:mo><mml:mi mathvariant="normal">Ω</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr><mml:mtr><mml:mtd><mml:mrow><mml:mfrac><mml:mrow><mml:mo>∂</mml:mo><mml:mi>u</mml:mi></mml:mrow><mml:mrow><mml:mo>∂</mml:mo><mml:msub><mml:mrow><mml:mi>v</mml:mi></mml:mrow><mml:mi>A</mml:mi></mml:msub></mml:mrow></mml:mfrac><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>γ</mml:mi></mml:mrow><mml:mn>1</mml:mn></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>|</mml:mo> <mml:mi>u</mml:mi> <mml:mo>|</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mi>p</mml:mi><mml:mo>-</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mi>u</mml:mi><mml:mo>+</mml:mo><mml:msub><mml:mrow><mml:mi>γ</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>|</mml:mo> <mml:mi>u</mml:mi> <mml:mo>|</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mi>q</mml:mi><mml:mo>-</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mi>u</mml:mi><mml:mo>=</mml:mo><mml:mi>λ</mml:mi><mml:mi>β</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mi>x</mml:mi><mml:mo>)</mml:mo></mml:mrow><mml:msup><mml:mrow><mml:mrow><mml:mrow><mml:mo>|</mml:mo> <mml:mi>u</mml:mi> <mml:mo>|</mml:mo></mml:mrow></mml:mrow></mml:mrow><mml:mrow><mml:mi>r</mml:mi><mml:mo>-</mml:mo><mml:mn>2</mml:mn></mml:mrow></mml:msup><mml:mi>u</mml:mi><mml:mo>,</mml:mo><mml:mi> </mml:mi><mml:mi> </mml:mi><mml:mi>x</mml:mi><mml:mo>∈</mml:mo><mml:mo>∂</mml:mo><mml:mi mathvariant="normal">Ω</mml:mi><mml:mo>,</mml:mo></mml:mrow></mml:mtd></mml:mtr></mml:mtable></mml:mrow> </mml:mrow></mml:mrow></mml:math>
<tex-math>\left\{ {\matrix{ {\mathcal{A}u + {\rho _1}\left( x \right){{\left| u \right|}^{p - 2}}u + {\rho _2}\left( x \right){{\left| u \right|}^{q - 2}}u = \lambda \alpha \left( x \right){{\left| u \right|}^{r - 2}}u,\,\,\,x \in \Omega ,} \cr {{{\partial u} \over {\partial {v_A}}} + {\gamma _1}\left( x \right){{\left| u \right|}^{p - 2}}u + {\gamma _2}\left( x \right){{\left| u \right|}^{q - 2}}u = \lambda \beta \left( x \right){{\left| u \right|}^{r - 2}}u,\,\,x \in \partial \Omega ,} \cr } } \right.</tex-math>
</alternatives>
</disp-formula>
where <italic>p, q, r</italic> ∈ (1, ∞), <italic>p &lt; q</italic>; α, <italic>ρi </italic>∈ <italic>L</italic>∞(Ω) and β, <italic>γi </italic>∈ <italic>L</italic>∞(∂Ω) are nonnegative functions satisfying ∫Ω <italic>α dx</italic> + ∫∂Ω β <italic>dσ &gt;</italic> 0 and ∫Ω ρ<italic>i dx</italic> + ∫∂Ω γ<italic>i dσ</italic> &gt; 0, <italic>i</italic> = 1, 2.
We show that, if either <italic>r &lt; p</italic> or <italic>r &gt; q</italic> with <italic>r &lt; q</italic>(<italic>N −</italic> 1)<italic>/</italic>(<italic>N − q</italic>) in case <italic>q &lt; N</italic>, then the eigenvalue set (spectrum) of the above problem is precisely (0, ∞). If <italic>r</italic> ∈ {<italic>p, q</italic>} then the corresponding spectrum is a smaller interval (<italic>d,</italic> ∞), <italic>d &gt;</italic> 0. On the other hand, if <italic>r</italic> ∈ (<italic>p, q</italic>) with <italic>r &lt; p</italic>(<italic>N −</italic> 1)<italic>/</italic>(<italic>N − p</italic>) in case <italic>p &lt; N</italic>, then we are able to identify an interval of eigenvalues [λ*, ∞), where λ* is a positive number depending on <italic>r</italic>.
Obviously, the spectrum of the above problem coincides with the spectra of the Neumann-like, Robin-like, and Steklov-like eigenvalue problems corresponding to the cases when some of the functions α, β, γ<italic>i </italic>vanish.
</abstract>

andreea.laura.burlacu@365.univ-ovidius.ro

On an eigenvalue problem associated with the (<italic>p, q</italic>) − Laplacian

<abstract>
<title style='display:none'>Abstract</title>
To extent the notion of the MP weak group inverse for square matrices, we introduce the concept of the weighted MP weak group inverse for rectangular matrices. A number of different representations and characterizations are derived for the weighted MP weak group inverse as well as limit and integral expressions. Applying the weighted MP weak group inverse, we solve some linear equations and give their solutions.
</abstract>

Weighted MP weak group inverse

<abstract>
<title style='display:none'>Abstract</title>
After introducing the definition of hypergroups by Marty, the study of hyperstructures and its connections with other fields has been of great importance. In this paper, we continue the investigation between hyperstructure theory and number theory. More precisely, we define an <italic>Hv</italic>-module of complex valued functions over the <italic>Hv</italic>-ring of arithmetics, classify its complete parts, the strongly regular relations on it and identify its fundamental module.
</abstract>

<italic>Hv</italic>-module of functions over <italic>Hv</italic>-ring of arithmetics and it’s fundamental module

<abstract>
<title style='display:none'>Abstract</title>
In this paper, we introduce the basic notions of the fractional summation, difference and <italic>q</italic>-difference with the quaternionic fractional order for the quaternion-valued functions and establish some of their basic properties. Based on this, the summation representations of solutions for the nonlinear quaternion-valued fractional difference equation and <italic>q</italic>-difference equation are obtained. In addition, several examples are provided to illustrate the feasibility of our obtained results in each section.
</abstract>

Quaternion Fractional Difference with Quaternionic Fractional Order and Applications to Fractional Difference Equation

<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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Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

The Journal of "Ovidius" University of Constanta

This journal is devoted to pure and applied mathematics. Papers from other fields of science may be accepted if they present interesting original mathematical results. Starting 2008 the journal...

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This journal is devoted to pure and applied mathematics. Papers from other fields of science may be accepted if they present interesting original...