Abstract In this paper, we study multi-level distance edge labeling for infinite rectangular, hexagonal and triangular grids. We label the edges with non-negative integers. If the edges are adjacent, then their color difference is at least 2 and if they are separated by exactly a single edge, then their colors must be distinct. We find the edge coloring number of these grids to be 9, 7 and 16, respectively so that we could color the edges of a rectangular, hexagonal and triangular grid with at most 10, 8 and 17 colors, respectively using this coloring technique. Repeating the sequence pattern for different grids, we can color the edges of a grid of larger size.
{"title":"On L′ (2, 1)–Edge Coloring Number of Regular Grids","authors":"D. Deepthy, J. V. Kureethara","doi":"10.2478/auom-2019-0034","DOIUrl":"https://doi.org/10.2478/auom-2019-0034","url":null,"abstract":"Abstract In this paper, we study multi-level distance edge labeling for infinite rectangular, hexagonal and triangular grids. We label the edges with non-negative integers. If the edges are adjacent, then their color difference is at least 2 and if they are separated by exactly a single edge, then their colors must be distinct. We find the edge coloring number of these grids to be 9, 7 and 16, respectively so that we could color the edges of a rectangular, hexagonal and triangular grid with at most 10, 8 and 17 colors, respectively using this coloring technique. Repeating the sequence pattern for different grids, we can color the edges of a grid of larger size.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82733953","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 Using a global inversion theorem we investigate properties of the following operator V(x)(⋅):=xΔ(⋅)+∫0⋅v(⋅,τ,x,(τ))Δτ, x(0)=0, matrix{matrix{ V(x)( cdot ): = {x^Delta }( cdot ) + int_0^ cdot {vleft( { cdot ,tau ,x,left( tau right)} right)} Delta tau , hfill cr ,,,,,,,,,,,,,,,,,,,,,,,,,,,x(0) = 0, hfill cr}cr {} cr } in a time scale setting. Under some assumptions on the nonlinear term v we then show that there exists exactly one solution xy∈W Δ,01,p([0,1]𝕋,N) {x_y} in W_{Delta ,0}^{1,p}left( {{{[0,1]}_mathbb{T}},{mathbb{R}^N}} right) to the associated integral equation { xΔ(t)+∫0tv(t,τ,x(τ))Δτ=y(t) for Δ-a.e. t∈[0.1]𝕋,x(0)=0, left{ {matrix{{{x^Delta }(t) + int_0^t {vleft( {t,tau ,xleft( tau right)} right)} Delta tau = y(t),,,for,Delta - a.e.,,,t in {{[0.1]}_mathbb{T}},} cr {x(0) = 0,} cr } } right. which is considered on a suitable Sobolev space.
{"title":"On the existence and uniqueness of solution to Volterra equation on a time scale","authors":"Bartłomiej Kluczyński","doi":"10.2478/auom-2019-0040","DOIUrl":"https://doi.org/10.2478/auom-2019-0040","url":null,"abstract":"Abstract Using a global inversion theorem we investigate properties of the following operator V(x)(⋅):=xΔ(⋅)+∫0⋅v(⋅,τ,x,(τ))Δτ, x(0)=0, matrix{matrix{ V(x)( cdot ): = {x^Delta }( cdot ) + int_0^ cdot {vleft( { cdot ,tau ,x,left( tau right)} right)} Delta tau , hfill cr ,,,,,,,,,,,,,,,,,,,,,,,,,,,x(0) = 0, hfill cr}cr {} cr } in a time scale setting. Under some assumptions on the nonlinear term v we then show that there exists exactly one solution xy∈W Δ,01,p([0,1]𝕋,N) {x_y} in W_{Delta ,0}^{1,p}left( {{{[0,1]}_mathbb{T}},{mathbb{R}^N}} right) to the associated integral equation { xΔ(t)+∫0tv(t,τ,x(τ))Δτ=y(t) for Δ-a.e. t∈[0.1]𝕋,x(0)=0, left{ {matrix{{{x^Delta }(t) + int_0^t {vleft( {t,tau ,xleft( tau right)} right)} Delta tau = y(t),,,for,Delta - a.e.,,,t in {{[0.1]}_mathbb{T}},} cr {x(0) = 0,} cr } } right. which is considered on a suitable Sobolev space.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72754757","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 present Leray–Schauder alternatives for a general class of Mönch type maps.
摘要本文给出了一类一般Mönch类型映射的Leray-Schauder替代。
{"title":"Leray–Schauder Alternatives for Maps Satisfying Countable Compactness Conditions","authors":"D. O’Regan","doi":"10.2478/auom-2019-0041","DOIUrl":"https://doi.org/10.2478/auom-2019-0041","url":null,"abstract":"Abstract In this paper we present Leray–Schauder alternatives for a general class of Mönch type maps.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82710591","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 manuscript we investigate the existence of mild solution for a abstract impulsive neutral integro-differential equation by using semi-group theory and Krasnoselskii-Schaefer fixed point theorem in different approach. At last, an example is also provided to illustrate the obtained results.
{"title":"Existence results for an impulsive neutral integro-differential equations in Banach spaces","authors":"V. Usha, D. Baleanu, M. Arjunan","doi":"10.2478/auom-2019-0043","DOIUrl":"https://doi.org/10.2478/auom-2019-0043","url":null,"abstract":"Abstract In this manuscript we investigate the existence of mild solution for a abstract impulsive neutral integro-differential equation by using semi-group theory and Krasnoselskii-Schaefer fixed point theorem in different approach. At last, an example is also provided to illustrate the obtained results.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82533501","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 study the split common fixed point problem in Hilbert spaces. We find a common solution of the split common fixed point problem for two demicontractive operators without a priori knowledge of operator norms. A strong convergence theorem is obtained under some additional conditions and numerical examples are included to illustrate the applications in signal compressed sensing and image restoration.
{"title":"Adaptive algorithm for solving the SCFPP of demicontractive operators without a priori knowledge of operator norms","authors":"D. Kitkuan, P. Kumam, V. Berinde, A. Padcharoen","doi":"10.2478/auom-2019-0039","DOIUrl":"https://doi.org/10.2478/auom-2019-0039","url":null,"abstract":"Abstract In this paper, we study the split common fixed point problem in Hilbert spaces. We find a common solution of the split common fixed point problem for two demicontractive operators without a priori knowledge of operator norms. A strong convergence theorem is obtained under some additional conditions and numerical examples are included to illustrate the applications in signal compressed sensing and image restoration.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89237803","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}
S. Bilal, O. Cârja, T. Donchev, N. Javaid, A. Lazu
Abstract We show here that the set of the integral solutions of a nonlocal differential inclusion is dense in the set of the solution set of the corresponding relaxed differential inclusion. We further define a notion of limit solution and show that the set of limit solutions is closed and is the closure of the set of integral solutions. An illustrative example is provided.
{"title":"Relaxation of nonlocal m-dissipative differential inclusions","authors":"S. Bilal, O. Cârja, T. Donchev, N. Javaid, A. Lazu","doi":"10.2478/auom-2019-0033","DOIUrl":"https://doi.org/10.2478/auom-2019-0033","url":null,"abstract":"Abstract We show here that the set of the integral solutions of a nonlocal differential inclusion is dense in the set of the solution set of the corresponding relaxed differential inclusion. We further define a notion of limit solution and show that the set of limit solutions is closed and is the closure of the set of integral solutions. An illustrative example is provided.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78436082","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 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.
{"title":"A new formula for the coefficients of Gaussian polynomials","authors":"D. Andrica, O. Bagdasar","doi":"10.2478/auom-2019-0031","DOIUrl":"https://doi.org/10.2478/auom-2019-0031","url":null,"abstract":"Abstract 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.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82107219","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 consider the absolute values of the Selberg zeta-function, associated to the compact Riemann surface, at places symmetric with respect to the line ℛ(s) = 1/2. We prove an inequality for the Selberg zeta-function, extending the result of R. Garunkštis and A. Grigutis.
{"title":"An inequality for the Selberg zeta-function, associated to the compact Riemann surface","authors":"I. Belovas","doi":"10.2478/auom-2019-0032","DOIUrl":"https://doi.org/10.2478/auom-2019-0032","url":null,"abstract":"Abstract We consider the absolute values of the Selberg zeta-function, associated to the compact Riemann surface, at places symmetric with respect to the line ℛ(s) = 1/2. We prove an inequality for the Selberg zeta-function, extending the result of R. Garunkštis and A. Grigutis.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78971840","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 main goal of this paper is to give some representations of MV-algebras in terms of derivations. In this paper, we investigate some properties of implicative and difference derivations and give their characterizations in MV-algebras. Then, we show that every Boolean algebra (idempotent MV-algebra) is isomorphic to the algebra of all implicative derivations and obtain that a direct product representation of MV-algebra by implicative derivations. Moreover, we prove that regular implicative and difference derivations on MV-algebras are in one to one correspondence and show that the relationship between the regular derivation pair (d, g) and the Galois connection, where d and g are regular difference and implicative derivation on L, respectively. Finally, we obtain that regular difference derivations coincide with direct product decompositions of MV-algebras.
{"title":"Study of MV-algebras via derivations","authors":"Jun Tao Wang, Yanhong She, Ting Qian","doi":"10.2478/auom-2019-0044","DOIUrl":"https://doi.org/10.2478/auom-2019-0044","url":null,"abstract":"Abstract The main goal of this paper is to give some representations of MV-algebras in terms of derivations. In this paper, we investigate some properties of implicative and difference derivations and give their characterizations in MV-algebras. Then, we show that every Boolean algebra (idempotent MV-algebra) is isomorphic to the algebra of all implicative derivations and obtain that a direct product representation of MV-algebra by implicative derivations. Moreover, we prove that regular implicative and difference derivations on MV-algebras are in one to one correspondence and show that the relationship between the regular derivation pair (d, g) and the Galois connection, where d and g are regular difference and implicative derivation on L, respectively. Finally, we obtain that regular difference derivations coincide with direct product decompositions of MV-algebras.","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89911154","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, inspired by recent articles of A. Szynal-Liana & I. Włoch and F. T. Aydin & S. Yüce (see [26] and [2]), we will introduce the ̄h-Jacobsthal quaternions and the ̄h-Jacobsthal–Lucas sequences and their associated quaternions. The new results that we have obtained extend most of those obtained in [26].
在本文中，受A. Szynal-Liana & I. Włoch和F. T. Aydin & S. y ce(参见[26]和[2])的最新文章的启发，我们将介绍h-Jacobsthal四元数和h-Jacobsthal - lucas序列及其相关的四元数。我们得到的新结果扩展了文献[26]中的大部分结果。
{"title":"On ̄h-Jacobsthal and ̄h-Jacobsthal–Lucas sequences, and related quaternions","authors":"Giuseppina Anatriello, G. Vincenzi","doi":"10.2478/auom-2019-0030","DOIUrl":"https://doi.org/10.2478/auom-2019-0030","url":null,"abstract":"Abstract In this paper, inspired by recent articles of A. Szynal-Liana & I. Włoch and F. T. Aydin & S. Yüce (see [26] and [2]), we will introduce the ̄h-Jacobsthal quaternions and the ̄h-Jacobsthal–Lucas sequences and their associated quaternions. The new results that we have obtained extend most of those obtained in [26].","PeriodicalId":55522,"journal":{"name":"Analele Stiintifice Ale Universitatii Ovidius Constanta-Seria Matematica","volume":null,"pages":null},"PeriodicalIF":0.6,"publicationDate":"2019-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83477433","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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