rss_2.0Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică FeedSciendo RSS Feed for Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică Feed a relation between GAG codes and AG codes<abstract><title style='display:none'>Abstract</title> <p>In this paper, we first give a relationship between generalized algebraic geometry codes (GAG codes) and algebraic geometry codes (AG codes). More precisely, we show that a GAG code is contained (up to isomorphism) in a suitable AG code. Next we recall the concept of an <italic>N</italic><sub>1</sub><italic>N</italic><sub>2</sub>-automorphism group, a subgroup of the automorphism group of a GAG code. With the use of the relation we obtained between these two classes of codes, we show that the <italic>N</italic><sub>1</sub><italic>N</italic><sub>2</sub>-automorphism group is a subgroup of the automorphism group of an AG code.</p> </abstract>ARTICLEtrue Spatial Quaternionic b-lift Curves<abstract><title style='display:none'>Abstract</title> <p>This study is based on the discovered relationships between the quaternionic slant helix and the quaternionic general helix. In this direction, we first examined quaternions, spatial quaternionic curves and b-lift curves. Furthermore, we defined the spatial quaternionic b-lift curve and characterized of Frenet fields. Afterward, we found the curvatures of the b-lift curve and using them we obtained a result between the quaternionic slant helix and quaternionic general helix. Finally, we consolidated our results with an example and visualized our curves with the MATLAB program.</p> </abstract>ARTICLEtrue Fixed Point Results for Sehgal-Proinov Type Contractions in Modular Metric Spaces<abstract><title style='display:none'>Abstract</title> <p>In this paper, inspired by Proinov type contractions, we intend to acquire novel definitions and results that expand Sehgals [3] metric fixed point theory in the sense of modular <italic>b−</italic>metric space. To demonstrate the theorems, we employ a general form of (<italic>α, β</italic>) <italic>−</italic>admissible and multi-valued mappings and obtain some general results for single-valued mapping in the context of modular <italic>b−</italic>metric space.</p> </abstract>ARTICLEtrue characterization of operators via Berezin symbol and related questions<abstract><title style='display:none'>Abstract</title> <p>In this paper, we characterize the hyponormal operators with regard to Berezin symbol and reproducing kernel. Also, we demonstrate several Berezin number inequalities for bounded linear operators.</p> </abstract>ARTICLEtrue the dual quaternion geometry of screw motions<abstract><title style='display:none'>Abstract</title> <p>In this study, the screw motions are studied using dual quaternions with the help of di erent perspectives. Firstly, orthogonality definition of dual quaternions is given and geometric interpretation of orthogonality condition is made. Then, the definition of dual circle is given using orthogonal dual quaternions and it is proved that this dual circle can represent the set of all screw motions. Also, these given theorems are reinforced with some conclusions. In addition, it is seen that a dual quaternion represents a screw motions as a screw operator therefore, other dual quaternions derived from the same dual quaternion represent the same screw motions. Then, it is seen that a screw motions symbolized by a dual quaternion transforms one dual vector to another, and when the sign of the dual vectors changes, it provides the same screw motions. Consequently, the answer of the question “Which dual circles symbolizing screw motions are dual orthonormal to each other?” is given and an important conclusion is obtained regarding this.</p> </abstract>ARTICLEtrue relations and exponential of dual-generalized complex matrices<abstract><title style='display:none'>Abstract</title> <p>In this study, taking into account the fundamental properties of dual-generalized complex (DGC) matrices, various types of similarity relations are introduced considering coneigenvalues/coneigenvectors via di erent conjugates. The exponential version of DGC matrices are identified and then their theoretical characteristic theorems are obtained. Finally, examples for DGC matrix exponential are given.</p> </abstract>ARTICLEtrue study on magnetic curves in trans-Sasakian manifolds<abstract><title style='display:none'>Abstract</title> <p>In this paper, we focused on biharmonic, <italic>f</italic>-harmonic and <italic>f</italic>-biharmonic magnetic curves in trans-Sasakian manifolds. Moreover, we obtain necessary and su cient conditions for magnetic curves as well as Legendre magnetic curves to be biharmonic, <italic>f</italic>-harmonic and <italic>f</italic>-biharmonic. We investigate the states of these conditions in <italic>α</italic>-Sasakian, <italic>β</italic>-Kenmotsu and cosymplectic manifolds. Besides, we obtain some nonexistence theorems.</p> </abstract>ARTICLEtrue general helix and framed -slant helix in ℝ<abstract><title style='display:none'>Abstract</title> <p>In this paper, we focus on general and <italic>ζ</italic><sub>3</sub>-slant helices with any singular points in four-dimensional Euclidean space, which are called framed general and <italic>ζ</italic><sub>3</sub>-slant helices, respectively. Then, we state and prove the conditions of necessity and su ciency for any framed curves to be general helices or <italic>ζ</italic><sub>3</sub>-slant helices in ℝ<sup>4</sup>. Also, we give some characterizations for framed helices.</p> </abstract>ARTICLEtrue Point Index for Simulation Mappings and Applications<abstract><title style='display:none'>Abstract</title> <p>In this paper, we construct the fixed point index for a class of contractive mapping defined by a simulation mapping and a measure of noncompact-ness noted by <italic>Z</italic><italic><sub>µ</sub></italic><italic>− </italic>contraction maps. Then we establish some fixed point theorem for this mapping of the Krasnoselskii type. An Application to the integral equation is presented to support the results.</p> </abstract>ARTICLEtrue Cauchy Products of Central Delannoy Numbers<abstract><title style='display:none'>Abstract</title> <p>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.</p> </abstract>ARTICLEtrue Rectifying Ruled Surfaces of Special Singular Curves<abstract><title style='display:none'>Abstract</title> <p>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.</p> </abstract>ARTICLEtrue of coupled dispersionless equations with Mannheim curves<abstract> <title style='display:none'>Abstract</title> <p>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.</p> </abstract>ARTICLEtrue estimation for a SEIRS model with COVID-19 data of Türkiye<abstract><title style='display:none'>Abstract</title> <p>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.</p> </abstract>ARTICLEtrue New Filled Function for Global Optimization<abstract><title style='display:none'>Abstract</title> <p>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.</p> </abstract>ARTICLEtrue Bertrand curves in Minkowski 3-space revisited<abstract><title style='display:none'>Abstract</title> <p>In the geometry of curves in 𝔼<sup>3</sup>, 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><sup>*</sup>, then the curve <italic>ϕ</italic> is called a Bertrand curve and <italic>ϕ</italic><sup>*</sup> 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 𝔼<sub>1</sub><sup>3</sup>. Follow this revested results, the Bertrand curve conditions of a spacelike curve are obtained in 𝔼<sub>1</sub><sup>3</sup>. In addition, new curve samples that meet the obtained conditions are constructed and the graphs of these curves are given.</p> </abstract>ARTICLEtrue of reversible cyclic codes over 𝔽 + 𝔽 + 𝔽<abstract> <title style='display:none'>Abstract</title> <p>Let <italic>q</italic> be a power of prime <italic>p</italic>. In this article, we investigate the reversible cyclic codes of arbitrary length <italic>n</italic> over the ring <italic>R</italic> = 𝔽<italic><sub>q</sub></italic> +<italic>u</italic>𝔽<italic><sub>q</sub></italic> + <italic>u</italic><sup>2</sup>𝔽<italic><sub>q</sub></italic>, where <italic>u</italic><sup>3</sup> = 0 mod <italic>q</italic>. Further, we find a unique set of generators for cyclic codes over <italic>R</italic> and classify the reversible cyclic codes with their generators. Moreover, it is shown that the dual of reversible cyclic code over <italic>R</italic> is reversible. Finally, some examples of reversible cyclic codes are provided to justify the importance of these results.</p> </abstract>ARTICLEtrue for -dual mixed volumes<abstract> <title style='display:none'>Abstract</title> <p>In the paper, our main aim is to generalize the <italic>q</italic><sup>th</sup> dual volume to <italic>L<sub>p</sub></italic> space, and introduce <italic>pq</italic><sup>th</sup>-<italic>dual mixed volume</italic> by calculating the first order variation of <italic>q</italic><sup>th</sup> dual volumes. We establish the <italic>L<sub>pq</sub></italic>-Minkowski inequality for <italic>pq</italic><sup>th</sup>-dual mixed volumes and <italic>L<sub>pq</sub></italic>-Brunn-Minkowski inequality for the <italic>q</italic><sup>th</sup>-dual volumes, respectively. The new inequalities in special case yield some new dual inequalities for the <italic>q</italic><sup>th</sup>-dual volumes.</p> </abstract>ARTICLEtrue equations as -dimensional dynamical system<abstract> <title style='display:none'>Abstract</title> <p>In this paper we study dynamics of the standard cosmological model of the universe assuming that it is filled with <italic>n</italic> types of non-interacting barotropic perfect fluids. For that purpose, a dynamical system of a class of Lotka-Volterra dynamical systems is derived, that consists of <italic>n</italic> nonlinear differential equations of the first order, whose dependent variables are density parameters of the material in the universe. Analytical solution of that system represents new parametrization of density parameters. Moreover, we perceive the evolution of the universe in the frame of the linear stability theory.</p> </abstract>ARTICLEtrue Various 2-absorbing prime ideals in non commutative rings<abstract> <title style='display:none'>Abstract</title> <p>In this paper we analyze strongly 2-absorbing prime ideals (shortly strongly 2-API), strongly 2-absorbing weak prime ideals (shortly strongly 2-AWPI) and 2-absorbing weak prime ideals (shortly 2-AWPI) in a non-commutative ring, which represent generalization of prime ideals (shortly PI) in a non-commutative ring. The relationship between the strongly 2-API and the 2-absorbing prime ideal (shortly 2-API) is examined. We provide examples to illustrate the new concept of strongly <italic>m</italic><sub>a</sub><sub>1</sub>-system and strongly <italic>m</italic><sub>a</sub><sub>2</sub>-system as well as the relationships beween them. Let <italic>I</italic> be an ideal of <italic>𝒭</italic> and <italic>𝒨</italic> be a strongly <italic>m</italic><sub>a</sub><sub>1</sub>-system such that <italic>I ∩ 𝒨</italic> = ϕ. Then there exists a strongly 2-API <italic>𝒫</italic> of <italic>𝒭</italic> containing <italic>I</italic> such that <italic>𝒫 ∩ 𝒨</italic> = ϕ. We prove that <italic>𝒫</italic> is a strongly 2-API if and only if <italic>𝒜</italic><sub>1</sub><italic>𝒜</italic><sub>2</sub><italic>𝒜</italic><sub>3</sub> ⊆ <italic>𝒫</italic> implies that <italic>𝒜</italic><sub>1</sub> ⊆ <italic>𝒫</italic> or <italic>𝒜</italic><sub>2</sub> ⊆ <italic>𝒫</italic> or <italic>𝒜</italic><sub>3</sub> ⊆ <italic>𝒫</italic> for all ideals <italic>𝒜</italic><sub>1</sub><italic>, 𝒜</italic><sub>2</sub> and <italic>A</italic><sub>3</sub> of <italic>𝒭</italic>.</p> </abstract>ARTICLEtrue and Lucas Polynomials in -gon<abstract> <title style='display:none'>Abstract</title> <p>In this paper, we bring into light, study the polygonal structure of Fibonacci polynomials that are placed clockwise on these by a number corresponding to each vertex. Also, we find the relation between the numbers with such vertices. We present a relation for obtained sequence in an <italic>n</italic>-gon yielding the <italic>m</italic>-th term formed at <italic>k</italic> vertices. Also, we apply these situations to Lucas polynomials and find new recurrence relations. Then, the numbers obtained by writing the coefficients of these polynomials in step form are shown in OEIS.</p> </abstract>ARTICLEtrue