Abstract Bone is a complex material that can be regarded as an anisotropic elastic composite material. The problem of crack propagation in human bone is analyzed by using a generalization of the maximum tensile stress criterion (MTS). The results concern the critical stress for crack propagation and the direction of the crack path in Iliac bone.
{"title":"Mixed Mode Crack Propagation in Iliac Bone","authors":"E. Baesu, D. Iliescu, B. Radoiu, S. Halichidis","doi":"10.2478/auom-2021-0034","DOIUrl":"https://doi.org/10.2478/auom-2021-0034","url":null,"abstract":"Abstract Bone is a complex material that can be regarded as an anisotropic elastic composite material. The problem of crack propagation in human bone is analyzed by using a generalization of the maximum tensile stress criterion (MTS). The results concern the critical stress for crack propagation and the direction of the crack path in Iliac bone.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81866719","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The subject of this paper is an analytic approximate method for a class of stochastic functional differential equations with coefficients that do not necessarily satisfy the Lipschitz condition nor linear growth condition but they satisfy some polynomial conditions. Also, equations from the observed class have unique solutions with bounded moments. Approximate equations are defined on partitions of the time interval and their drift and diffusion coefficients are Taylor approximations of the coefficients of the initial equation. Taylor approximations require Fréchet derivatives since the coefficients of the initial equation are functionals. The main results of this paper are the Lp and almost sure convergence of the sequence of the approximate solutions to the exact solution of the initial equation. An example that illustrates the theoretical results and contains the proof of the existence, uniqueness and moment boundedness of the approximate solution is displayed.
{"title":"An approximate Taylor method for Stochastic Functional Differential Equations via polynomial condition","authors":"D. Djordjević, M. Milosevic","doi":"10.2478/auom-2021-0037","DOIUrl":"https://doi.org/10.2478/auom-2021-0037","url":null,"abstract":"Abstract The subject of this paper is an analytic approximate method for a class of stochastic functional differential equations with coefficients that do not necessarily satisfy the Lipschitz condition nor linear growth condition but they satisfy some polynomial conditions. Also, equations from the observed class have unique solutions with bounded moments. Approximate equations are defined on partitions of the time interval and their drift and diffusion coefficients are Taylor approximations of the coefficients of the initial equation. Taylor approximations require Fréchet derivatives since the coefficients of the initial equation are functionals. The main results of this paper are the Lp and almost sure convergence of the sequence of the approximate solutions to the exact solution of the initial equation. An example that illustrates the theoretical results and contains the proof of the existence, uniqueness and moment boundedness of the approximate solution is displayed.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90219526","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The aim of this paper is to consider the extensibility of the Diophantine triple {2, b, c}, where 2 < b < c, and to prove that such a set cannot be extended to an irregular Diophantine quadruple. We succeed in that for some families of c’s (depending on b). As corollary, for example, we prove that for b/2 − 1 prime, all Diophantine quadruples {2, b, c, d} with 2 < b < c < d are regular.
摘要考虑了2 < b < c的Diophantine三元组{2,b, c}的可拓性，并证明了该集合不能被扩展到不规则的Diophantine四重组。我们成功地证明了c的一些族(取决于b)。作为推论，例如，我们证明了对于b/2−1素数，所有2 < b < c < d的Diophantine四元组{2,b, c, d}都是正则的。
{"title":"The extensibility of the Diophantine triple {2, b, c}","authors":"Nikola Adžaga, A. Filipin, Ana Jurasic","doi":"10.2478/auom-2021-0016","DOIUrl":"https://doi.org/10.2478/auom-2021-0016","url":null,"abstract":"Abstract The aim of this paper is to consider the extensibility of the Diophantine triple {2, b, c}, where 2 < b < c, and to prove that such a set cannot be extended to an irregular Diophantine quadruple. We succeed in that for some families of c’s (depending on b). As corollary, for example, we prove that for b/2 − 1 prime, all Diophantine quadruples {2, b, c, d} with 2 < b < c < d are regular.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76615415","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this paper, we establish some basic results for quaternion combined impulsive matrix dynamic equation on time scales for the first time. Quaternion matrix combined-exponential function is introduced and some basic properties are obtained. Based on this, the fundamental solution matrix and corresponding Cauchy matrix for a class of quaternion matrix dynamic equation with combined derivatives and bi-directional impulses are derived.
{"title":"Fundamental solution matrix and Cauchy properties of quaternion combined impulsive matrix dynamic equation on time scales","authors":"Chao Wang, Zhien Li, R. Agarwal","doi":"10.2478/auom-2021-0021","DOIUrl":"https://doi.org/10.2478/auom-2021-0021","url":null,"abstract":"Abstract In this paper, we establish some basic results for quaternion combined impulsive matrix dynamic equation on time scales for the first time. Quaternion matrix combined-exponential function is introduced and some basic properties are obtained. Based on this, the fundamental solution matrix and corresponding Cauchy matrix for a class of quaternion matrix dynamic equation with combined derivatives and bi-directional impulses are derived.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78423776","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Over finite local Frobenius non-chain rings of length 5 and nilpotency index 4 and when the length of the code is relatively prime to the characteristic of the residue field of the ring, the structure of the dual of γ-constacyclic codes is established and the algebraic characterization of self-dual, reversible γ-constacyclic codes and γ-constacyclic codes with complementary dual are given.
{"title":"Self dual, reversible and complementary duals constacyclic codes over finite local Frobenius non-chain rings of length 5 and nilpotency index 4.","authors":"C. A. Castillo-Guillén, C. Álvarez-García","doi":"10.2478/auom-2021-0017","DOIUrl":"https://doi.org/10.2478/auom-2021-0017","url":null,"abstract":"Abstract Over finite local Frobenius non-chain rings of length 5 and nilpotency index 4 and when the length of the code is relatively prime to the characteristic of the residue field of the ring, the structure of the dual of γ-constacyclic codes is established and the algebraic characterization of self-dual, reversible γ-constacyclic codes and γ-constacyclic codes with complementary dual are given.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85215231","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In the paper, the concept of Lp-dual three-mixed quermassintegrals is introduced. The formula for the Lp-dual three-mixed quermassintegrals with respect to the p-radial addition is proved. Inequalities of Lp-Minkowski, and Brunn-Minkowski type for the Lp-dual three-mixed quermassintegrals are established. The new Lp-Minkowski inequality is obtained that generalize a family of Minkowski type inequalities. The Lp-Brunn-Minkowski inequality is used to obtain a series of Brunn-Minkowski type inequalities.
{"title":"Lp-dual three mixed quermassintegrals","authors":"Chang-Jian Zhao, M. Bencze","doi":"10.2478/auom-2021-0030","DOIUrl":"https://doi.org/10.2478/auom-2021-0030","url":null,"abstract":"Abstract In the paper, the concept of Lp-dual three-mixed quermassintegrals is introduced. The formula for the Lp-dual three-mixed quermassintegrals with respect to the p-radial addition is proved. Inequalities of Lp-Minkowski, and Brunn-Minkowski type for the Lp-dual three-mixed quermassintegrals are established. The new Lp-Minkowski inequality is obtained that generalize a family of Minkowski type inequalities. The Lp-Brunn-Minkowski inequality is used to obtain a series of Brunn-Minkowski type inequalities.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84025561","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We show a simple example for ordered semigroup 𝕊 = 𝕊 (+,⩽) that 𝕊 ⊆ℝ (ℝ denotes the real line) and ]a, b[ + ]c, d[ = ]a + c, b + d[ for all a, b, c, d ∈ 𝕊 such that a < b and c < d, but the intervals are no translation invariant, that is, the equation c +]a, b[ = ]c + a, c + b[ is not always fulfilled for all elements a, b, c ∈ 𝕊 such that a < b. The multiplicative version of the above example is shown too. The product of open intervals in the ordered ring of all integers (denoted by ℤ) is also investigated. Let Ix := {1, 2, . . ., x} for all x ∈ ℤ+ and defined the function g : ℤ+ → ℤ+ by g(x):=max{ y∈ℤ+|Iy⊆Ix⋅Ix } gleft( x right): = max left{ {y in {mathbb{Z}_ + }|{I_y} subseteq {I_x} cdot {I_x}} right} for all x ∈ ℤ+. We give the function g implicitly using the famous Theorem of Chebishev. Finally, we formulate some questions concerning the above topics.
{"title":"Sums and products of intervals in ordered semigroups","authors":"T. Glavosits, Zsolt Karácsony","doi":"10.2478/auom-2021-0025","DOIUrl":"https://doi.org/10.2478/auom-2021-0025","url":null,"abstract":"Abstract We show a simple example for ordered semigroup 𝕊 = 𝕊 (+,⩽) that 𝕊 ⊆ℝ (ℝ denotes the real line) and ]a, b[ + ]c, d[ = ]a + c, b + d[ for all a, b, c, d ∈ 𝕊 such that a < b and c < d, but the intervals are no translation invariant, that is, the equation c +]a, b[ = ]c + a, c + b[ is not always fulfilled for all elements a, b, c ∈ 𝕊 such that a < b. The multiplicative version of the above example is shown too. The product of open intervals in the ordered ring of all integers (denoted by ℤ) is also investigated. Let Ix := {1, 2, . . ., x} for all x ∈ ℤ+ and defined the function g : ℤ+ → ℤ+ by g(x):=max{ y∈ℤ+|Iy⊆Ix⋅Ix } gleft( x right): = max left{ {y in {mathbb{Z}_ + }|{I_y} subseteq {I_x} cdot {I_x}} right} for all x ∈ ℤ+. We give the function g implicitly using the famous Theorem of Chebishev. Finally, we formulate some questions concerning the above topics.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89391181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Let R be a commutative ring with identity and S be a multiplicative subset of R. In this paper, we introduce the concept of weakly S-prime ideals which is a generalization of weakly prime ideals. Let P be an ideal of R disjoint with S. We say that P is a weakly S-prime ideal of R if there exists an s ∈ S such that, for all a, b ∈ R, if 0 ≠ ab ∈ P, then sa ∈ P or sb ∈ P. We show that weakly S-prime ideals have many analog properties to these of weakly prime ideals. We also use this new class of ideals to characterize S-Noetherian rings and S-principal ideal rings.
{"title":"On weakly S-prime ideals of commutative rings","authors":"F. Almahdi, E. M. Bouba, M. Tamekkante","doi":"10.2478/auom-2021-0024","DOIUrl":"https://doi.org/10.2478/auom-2021-0024","url":null,"abstract":"Abstract Let R be a commutative ring with identity and S be a multiplicative subset of R. In this paper, we introduce the concept of weakly S-prime ideals which is a generalization of weakly prime ideals. Let P be an ideal of R disjoint with S. We say that P is a weakly S-prime ideal of R if there exists an s ∈ S such that, for all a, b ∈ R, if 0 ≠ ab ∈ P, then sa ∈ P or sb ∈ P. We show that weakly S-prime ideals have many analog properties to these of weakly prime ideals. We also use this new class of ideals to characterize S-Noetherian rings and S-principal ideal rings.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75305717","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this paper we establish some two point weighted Taylor’s expansions for analytic functions f : D ⊆ ℂ→ ℂ defined on a convex domain D. Some error bounds for these expansions are also provided. Examples for the complex logarithm and the complex exponential are also given.
{"title":"Two Points Taylor’s Type Representations for Analytic Complex Functions with Integral Remainders","authors":"S. Dragomir","doi":"10.2478/auom-2021-0022","DOIUrl":"https://doi.org/10.2478/auom-2021-0022","url":null,"abstract":"Abstract In this paper we establish some two point weighted Taylor’s expansions for analytic functions f : D ⊆ ℂ→ ℂ defined on a convex domain D. Some error bounds for these expansions are also provided. Examples for the complex logarithm and the complex exponential are also given.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83898728","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this article, two-dimensional nonlinear and multi-term time fractional diffusion equations are solved numerically by collocation method, which is used with the help of Lucas operational matrix. In the proposed method solutions of the problems are expressed in terms of Lucas polynomial as basis function. To determine the unknowns, the residual, initial and boundary conditions are collocated at the chosen points, which produce a system of nonlinear algebraic equations those have been solved numerically. The concerned method provides the highly accurate numerical solution. The accuracy of the approximate solution of the problem can be increased by expanding the terms of the polynomial. The accuracy and efficiency of the concerned method have been authenticated through the error analyses with some existing problems whose solutions are already known.
{"title":"Numerical solution of two-dimensional nonlinear fractional order reaction-advection-diffusion equation by using collocation method","authors":"Manpal Singh, S. Das, Rajeev, E. Crăciun","doi":"10.2478/auom-2021-0027","DOIUrl":"https://doi.org/10.2478/auom-2021-0027","url":null,"abstract":"Abstract In this article, two-dimensional nonlinear and multi-term time fractional diffusion equations are solved numerically by collocation method, which is used with the help of Lucas operational matrix. In the proposed method solutions of the problems are expressed in terms of Lucas polynomial as basis function. To determine the unknowns, the residual, initial and boundary conditions are collocated at the chosen points, which produce a system of nonlinear algebraic equations those have been solved numerically. The concerned method provides the highly accurate numerical solution. The accuracy of the approximate solution of the problem can be increased by expanding the terms of the polynomial. The accuracy and efficiency of the concerned method have been authenticated through the error analyses with some existing problems whose solutions are already known.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2021-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79320413","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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