rss_2.0Sciendo RSS Feed for Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematicăhttps://sciendo.com/journal/AUOMhttps://www.sciendo.comhttps://sciendo-parsed.s3.eu-central-1.amazonaws.com/6470c48671e4585e08aa4fff/cover-image.jpghttps://sciendo.com/journal/AUOM140216https://sciendo.com/article/10.2478/auom-2024-0016<abstract> <title style='display:none'>Abstract</title> <p>In the past few decades, researchers have found that studying modules using endomorphisms is a powerful and useful tool. This has led to valuable works in this field. Recently, the study of (dual) Rickart modules has become an important approach as they are deeply connected to endomorphisms. Building on this work, the authors introduce a new perspective on (dual) Rickart modules using isomorphism. We also define virtually (dual) Rickart modules. It is shown that rings with all modules virtually Rickart are semisimple rings. The paper includes various examples to illustrate the concepts presented.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/auom-2024-00162024-07-10T00:00:00.000+00:00https://sciendo.com/article/10.2478/auom-2024-0025<abstract> <title style='display:none'>Abstract</title> <p>The fundamental aim of this research is to analyze the configuration of 𝔽₄<italic>R</italic> submodules, skew cyclic codes over 𝔽₄<italic>R</italic> and establish their connection with DNA codes, where 𝔽₄ is a field of order 4 and <italic>R</italic> = 𝔽₄ + <italic>u</italic>𝔽₄ + <italic>v</italic>𝔽₄ + <italic>w</italic>𝔽₄ with <italic>u</italic>² = <italic>u, v</italic>² = <italic>v, w</italic>² = <italic>w, uv</italic> = <italic>vu</italic> = 0, <italic>vw</italic> = <italic>wv</italic> = 0, <italic>wu</italic> = <italic>uw</italic> = 0 is a finite ring. This is achieved by examining particular subclasses like reversible codes. Ultimately, this study aims to utilize Gray maps to derive codes that possess the characteristics of DNA structures. At the end of this paper, we have provided the necessary and sufficient condition for skew cyclic codes to be reversible complement.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/auom-2024-00252024-07-10T00:00:00.000+00:00https://sciendo.com/article/10.2478/auom-2024-0023<abstract> <title style='display:none'>Abstract</title> <p>In this article, we introduce the Boyd-Wong type multivalued contractions and demonstrate that such mappings have a fixed point. Additionally, we look at the solvability of a few (<italic>k – ~</italic>)-Hilfer initial value fractional differential inclusions of order <italic>n −</italic> 1 <italic>&lt; α &lt; n</italic> (<italic>n</italic> ≥ 2). To demonstrate the usability of our result, an example is provided.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/auom-2024-00232024-07-10T00:00:00.000+00:00https://sciendo.com/article/10.2478/auom-2024-0017<abstract> <title style='display:none'>Abstract</title> <p>Let ℙ be the set of prime numbers, ℙ the union ℙ ∪ {0}, and for any field <italic>E</italic>, let char(<italic>E</italic>) be its characteristic, ddim(<italic>E</italic>) the Diophantine dimension of <italic>E</italic>, <italic>𝒢</italic>_E the absolute Galois group of <italic>E</italic>, and cd(<italic>𝒢</italic>_E) the Galois cohomological dimension <italic>𝒢</italic>_E. The research presented in this paper is motivated by the open problem of whether cd(<italic>𝒢</italic>_E) ≤ ddim(<italic>E</italic>). It proves the existence of quasifinite fields Φ_q : <italic>q</italic> ∈ ℙ, with ddim(Φ_q) infinity and char(Φ_q) = <italic>q</italic>, for each <italic>q</italic>. It shows that for any integer <italic>m &gt;</italic> 0 and <italic>q ∈</italic> ℙ, there is a quasifinite field Φ_m,q such that char(Φ_m,q) = <italic>q</italic> and ddim(Φ_m,q) = <italic>m</italic>. This is used for proving that for any <italic>q</italic> ∈ ℙ and each pair <italic>k</italic>, <italic>ℓ ∈</italic> (𝕅 ∪ {0, ∞}) satisfying <italic>k</italic> ≤ <italic>ℓ</italic>, there exists a field <italic>E</italic>_k,ℓ;q with char(<italic>E</italic>_k,ℓ;q) = <italic>q</italic>, ddim(<italic>E</italic>_k,ℓ;q) = <italic>ℓ</italic> and cd(<italic>𝒢</italic>_{E_k,ℓ;q}) = <italic>k</italic>. Finally, we show that the field <italic>E</italic>_k,ℓ;q can be chosen to be perfect unless <italic>k</italic> = 0 ≠ = <italic>ℓ</italic>.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/auom-2024-00172024-07-10T00:00:00.000+00:00https://sciendo.com/article/10.2478/auom-2024-0020<abstract> <title style='display:none'>Abstract</title> <p>In this study, we examine osculating-type curves with Frenet-type frame in Myller configuration for Euclidean 3-space <italic>E</italic>₃. We present the necessary characterizations for a curve to be an osculating-type curve. Characterizations originating from the natural structure of Myller configuration are a generalization of osculating curves according to the Frenet frame. Also, we introduce some new results that are not valid for osculating curves. Then, we give an illustrative numerical example supported by a figure.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/auom-2024-00202024-07-10T00:00:00.000+00:00https://sciendo.com/article/10.2478/auom-2024-0022<abstract> <title style='display:none'>Abstract</title> <p>This paper presents Leray–Schauder alternatives and a topological transversality (homotopy) theorem for compact upper semicontinuos maps having (strongly) convexly totally bounded ranges.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/auom-2024-00222024-07-10T00:00:00.000+00:00https://sciendo.com/article/10.2478/auom-2024-0021<abstract> <title style='display:none'>Abstract</title> <p>We consider a generalization of the coupon collector problem with unequal probabilities, such that there are two additional coupons in the coupon set: one that speeds up the coupon collection process, and the one that slows it down. We derive some upper and lower bounds on the distribution function of the waiting time until a subcollection or a full collection of coupons is sampled.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/auom-2024-00212024-07-10T00:00:00.000+00:00https://sciendo.com/article/10.2478/auom-2024-0018<abstract> <title style='display:none'>Abstract</title> <p>Recent results in mathematical modeling predicting crack behavior under various load conditions in human bones as anisotropic elastic composite materials are presented in this survey. New and interesting challenges in theoretical models of fracture were proposed and had significant importance for fracture mechanics. Our goal is to present an overview of the use and limitations of existing relevant theories. The present study aims to introduce mathematical models to researchers unfamiliar with the concepts, to improve and provide new insights into bone fracture mechanics.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/auom-2024-00182024-07-10T00:00:00.000+00:00https://sciendo.com/article/10.2478/auom-2024-0024<abstract> <title style='display:none'>Abstract</title> <p>Ideals and filters are important notions with different meanings in the study of algebraic structures related to logical systems. In this paper we establish new connections between these concepts in residuated lattices.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/auom-2024-00242024-07-10T00:00:00.000+00:00https://sciendo.com/article/10.2478/auom-2024-0019<abstract> <title style='display:none'>Abstract</title> <p>Let <italic>G</italic> and <italic>H</italic> be two graphs, each one of them being a path, a cycle or a star. In this paper, we determine the <italic>b</italic>-chromatic number of every subdivision-vertex neighbourhood corona <italic>G</italic> ⊡ <italic>H</italic> or <italic>G</italic> ⊡ <italic>K</italic>_n, where <italic>K</italic>_n is the complete graph of order <italic>n</italic>. It is also established for those graphs <italic>K</italic>_n ⊡ <italic>G</italic> having <italic>m</italic>-degree not greater than <italic>n</italic> + 2. All the proofs are accompanied by illustrative examples.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/auom-2024-00192024-07-10T00:00:00.000+00:00https://sciendo.com/article/10.2478/auom-2024-0002<abstract> <title style='display:none'>Abstract</title> <p>Let <bold>S</bold> = ℤ<italic>_p</italic>[<italic>u, v</italic>]<italic>/〈u</italic>², <italic>v</italic>², <italic>uv − uv〉</italic> be a semi-local ring, where <italic>p</italic> is a prime number. In the present article, we determine the generating sets of <bold>S</bold> and use them to construct the structures of ℤ<italic>_p</italic><bold>S</bold>-additive cyclic and constacyclic codes. The minimal polynomials and spanning sets of ℤ<italic>_p</italic><bold>S</bold>-additive cyclic and constacyclic codes are also determined. These codes are identified as <bold>S</bold>[<italic>y</italic>]-submodules of the ring <bold>S</bold>_{β₁, β₂} = ℤ<italic>_p</italic>[<italic>y</italic>]<italic>/〈y</italic>^{<italic>β</italic>₁} <italic>−</italic> 1<italic>〉 ×</italic> <bold>S</bold>[<italic>y</italic>]<italic>/〈y</italic>^{<italic>β</italic>₂} <italic>−</italic> 1<italic>〉</italic>. Some results that represent the relationship between the minimal polynomials of ℤ<italic>_p</italic><bold>S</bold>-additive cyclic codes and their duals have been obtained. Furthermore, optimal ℤ<italic>_p</italic><bold>S</bold>-additive codes and maximum distance separable codes have been evaluated (see Table 1). Finally, we use MAGMA software to find the parameters of Optimal and MDSS codes.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/auom-2024-00022024-05-27T00:00:00.000+00:00https://sciendo.com/article/10.2478/auom-2024-0014<abstract> <title style='display:none'>Abstract</title> <p>The use of the <italic>barycentre map</italic> between two copies of ℝ<italic>ⁿ</italic>, the first one with a metric without conjugate points, the second one with the canonical flat metric, allows to prove in a simplified way the fact that Riemannian tori without conjugate points are flat, as conjectured by Hopf in 1948 and proved definitively by Burago and Ivanov in 1994.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/auom-2024-00142024-05-27T00:00:00.000+00:00https://sciendo.com/article/10.2478/auom-2024-0007<abstract> <title style='display:none'>Abstract</title> <p>In this article we present a stochastic ordering verification algorithm between multivariate discrete distributions implemented in the C++ programming language. This algorithm is essential in problems of finding the optimal portfolio when dealing with discrete distributions.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/auom-2024-00072024-05-27T00:00:00.000+00:00https://sciendo.com/article/10.2478/auom-2024-0006<abstract> <title style='display:none'>Abstract</title> <p>An approximate inverse <italic>LU</italic> preconditioner is constructed based on the Sherman–Morrison formula. Applying recursively that inversion formula a multiplicative decomposition of the inverse of a matrix is obtained. This recursion in compact form is the base to build the proposed preconditioner that we call V–AISM. For nonsingular <italic>M</italic>-matrices and <italic>H</italic>-matrices of the invertible class the stability of the preconditioner is proved. Numerical results show that V–AISM is robust and competitive compared with other preconditioners.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/auom-2024-00062024-05-27T00:00:00.000+00:00https://sciendo.com/article/10.2478/auom-2024-0013<abstract> <title style='display:none'>Abstract</title> <p>The study of the linear methods of approximation, which are given by sequences of positive and linear operators, studied extremely, in relation to different subjects of analysis, such as numerical analysis. The principal objective of this manuscript is to develop a new and more comprehensive version of Gamma type operators and presented their approximation features. For this purpose, we benefit from two sequences of functions, which are α<italic>_n</italic>(<italic>x</italic>) and β<italic>_n</italic>(<italic>x</italic>), and from the function τ(<italic>x</italic>). To indicate how the function τ play a significant role in the construction of the operator, we reconstruct the mentioned operators which preserve exactly two test functions from the set {1, τ, τ²}. Then we established Voronovskaya type theorem and order of approximation properties of the newly defined operators utilizing weighted modulus of continuity to show that their approximation properties. At the end of this note, we present a series of numerical results to show that the new operators are an approximation technique.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/auom-2024-00132024-05-27T00:00:00.000+00:00https://sciendo.com/article/10.2478/auom-2024-0008<abstract> <title style='display:none'>Abstract</title> <p>This study is motivated through the interesting non-Arcchimedean stability results of ρ-inequalities and ρ-equations arising from linear, second power, third power and fourth power mappings. The aim of this paper is to determine the solutions of new multiplicative inverse <italic>µ-</italic>inequalities and <italic>µ</italic>-equations arising from multiplicative inverse mapping. Further, their stabilities involved with various superior limits are proved in the context of non-Archimedean complete normed spaces.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/auom-2024-00082024-05-27T00:00:00.000+00:00https://sciendo.com/article/10.2478/auom-2024-0005<abstract> <title style='display:none'>Abstract</title> <p>In this article, we study relationships between closure operators and hoops. We investigate the properties of closure operators and hoop-homomorphism on hoops. We show that the image of a closure operator on a hoop is isomorphic to a quotient hoop. In addition, we define the notion of closure operator on ideals of hoop and investigate some properties of it and some related results are proved. We define proper closer operators on ideals of hoop and we show that the set of all proper closure operators on hoops makes a bounded lattice by some operations.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/auom-2024-00052024-05-27T00:00:00.000+00:00https://sciendo.com/article/10.2478/auom-2024-0009<abstract> <title style='display:none'>Abstract</title> <p>We first introduce a notation for multiple (<italic>n</italic> ≥ 3) <italic>q</italic>-hypergeometric functions, where negative values of summation indices are allowed. Then we extend the notation for <italic>q</italic>-Horn functions to include tilde values corresponding to powers of 2. Karlssons reduction formulas are correspondingly <italic>q</italic>-deformed by using these notations. A formula for sums of inverse <italic>q</italic>-shifted factorials is used to find further formulas. The second part of the paper is devoted to convergence aspects for <italic>q</italic>-Horn functions and ’abnormal’ <italic>q</italic>-Horn functions. It turns out that some simple estimates for convergence can be made in the <italic>q</italic>-case, these are then supplemented with tables of numerical values. It is shown that the convergence regions are significantly increased in the <italic>q</italic>-case, and we compare with convergence regions in the ordinary case.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/auom-2024-00092024-05-27T00:00:00.000+00:00https://sciendo.com/article/10.2478/auom-2024-0011<abstract> <title style='display:none'>Abstract</title> <p>Let <italic>R</italic> be a commutative ring with identity, and let <italic>S</italic> be a multiplicative subset of <italic>R</italic>. Then R is called a nonnil-<italic>S</italic>-Noetherian ring if every nonnil ideal of <italic>R</italic> is <italic>S</italic>-finite. Also, <italic>R</italic> is called a u-<italic>S</italic>-Noetherian ring if there exists an element <italic>s</italic> ∈ <italic>S</italic> such that for each ideal <italic>I</italic> of <italic>R</italic>, <italic>sI</italic> ⊆ <italic>K</italic> for some finitely generated sub-ideal <italic>K</italic> of <italic>I</italic>. In this paper, we examine some new characterization of nonnil-<italic>S</italic>-Noetherian rings. Then, as a generalization of nonnil-<italic>S</italic>-Noetherian rings and u-<italic>S</italic>-Noetherian rings, we introduce and investigate the nonnilu-<italic>S</italic>-Noetherian rings class.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/auom-2024-00112024-05-27T00:00:00.000+00:00https://sciendo.com/article/10.2478/auom-2024-0012<abstract> <title style='display:none'>Abstract</title> <p>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.</p> </abstract>ARTICLEtruehttps://sciendo.com/article/10.2478/auom-2024-00122024-05-27T00:00:00.000+00:00en-us-1