In this paper, we consider the multiple line detection problem on the basis of a data points set coming from a number of lines not known in advance. A new and efficient method is proposed, which is based upon center-based clustering, and it solves this problem quickly and precisely. The method has been tested on 100 randomly generated data sets. In comparison to the incremental algorithm, the method gives significantly better results. Also, in order to identify a partition with the most appropriate number of clusters, a new index has been proposed for the case of a cluster whose lines are cluster-centers. The index can also be generalized for other geometrical objects.
{"title":"A fast and efficient method for solving the multiple line detection problem","authors":"R. Scitovski, Una Radojicic, K. Sabo","doi":"10.21857/yvjrdcqq8y","DOIUrl":"https://doi.org/10.21857/yvjrdcqq8y","url":null,"abstract":"In this paper, we consider the multiple line detection problem on the basis of a data points set coming from a number of lines not known in advance. A new and efficient method is proposed, which is based upon center-based clustering, and it solves this problem quickly and precisely. The method has been tested on 100 randomly generated data sets. In comparison to the incremental algorithm, the method gives significantly better results. Also, in order to identify a partition with the most appropriate number of clusters, a new index has been proposed for the case of a cluster whose lines are cluster-centers. The index can also be generalized for other geometrical objects.","PeriodicalId":269525,"journal":{"name":"Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117276292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yoshi Kanno, Matea Puvaca, Z. Tomljanović, N. Truhar
This paper deals with damping optimization of the mechanical system based on the minimization of the so-called “average displacement amplitude”. Further, we propose three different approaches to solving this minimization problems, and present their performance on two examples.
{"title":"Optimization of damping positions in a mechanical system","authors":"Yoshi Kanno, Matea Puvaca, Z. Tomljanović, N. Truhar","doi":"10.21857/Y26KEC33Q9","DOIUrl":"https://doi.org/10.21857/Y26KEC33Q9","url":null,"abstract":"This paper deals with damping optimization of the mechanical system based on the minimization of the so-called “average displacement amplitude”. Further, we propose three different approaches to solving this minimization problems, and present their performance on two examples.","PeriodicalId":269525,"journal":{"name":"Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-06-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128310950","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Reordering the terms of a series is a useful mathematical device, and much is known about when it can be done without affecting the convergence or the sum of the series. For example, if a series of real numbers absolutely converges, we can add the even-indexed and odd-indexed terms separately, or arrange the terms in an infinite two-dimensional table and first compute the sum of each column. The possibility of even more intricate re-orderings prompts us to find a general underlying principle. We identify such a principle in the setting of Banach spaces, where we consider well-ordered series with indices beyond {omega}, but strictly under {omega}_1 . We prove that for every absolutely convergent well-ordered series indexed by a countable ordinal, if the series is rearranged according to any countable ordinal, then the absolute convergence and the sum of the series remain unchanged.
{"title":"Rearranging absolutely covergent well-ordered series in Banach spaces","authors":"Vedran vCavci'c, Marko Doko, M. Horvat","doi":"10.21857/yq32oh4qd9","DOIUrl":"https://doi.org/10.21857/yq32oh4qd9","url":null,"abstract":"Reordering the terms of a series is a useful mathematical device, and much is known about when it can be done without affecting the convergence or the sum of the series. For example, if a series of real numbers absolutely converges, we can add the even-indexed and odd-indexed terms separately, or arrange the terms in an infinite two-dimensional table and first compute the sum of each column. The possibility of even more intricate re-orderings prompts us to find a general underlying principle. We identify such a principle in the setting of Banach spaces, where we consider well-ordered series with indices beyond {omega}, but strictly under {omega}_1 . We prove that for every absolutely convergent well-ordered series indexed by a countable ordinal, if the series is rearranged according to any countable ordinal, then the absolute convergence and the sum of the series remain unchanged.","PeriodicalId":269525,"journal":{"name":"Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123656676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Let R be a ∗-ring containing a nontrivial self-adjoint idempotent. In this paper it is shown that under some mild conditions on R, if a mapping d : R → R satisfies d([U, V ]) = [d(U), V ] + [U, d(V )] for all U, V ∈ R, then there exists ZU,V ∈ Z(R) (depending on U and V ), where Z(R) is the center of R, such that d(U +V ) = d(U) + d(V ) +ZU,V . Moreover, if R is a 2-torsion free prime ∗-ring additionally, then d = ψ+ ξ, where ψ is an additive ∗-derivation of R into its central closure T and ξ is a mapping from R into its extended centroid C such that ξ(U + V ) = ξ(U) + ξ(V ) +ZU,V and ξ([U, V ]) = 0 for all U, V ∈ R. Finally, the above ring theoretic results have been applied to some special classes of algebras such as nest algebras and von Neumann algebras.
{"title":"Characterizations of ∗-Lie derivable mappings on prime ∗-rings","authors":"A. Alkenani, M. Ashraf, B. Wani","doi":"10.21857/y26kec3379","DOIUrl":"https://doi.org/10.21857/y26kec3379","url":null,"abstract":"Let R be a ∗-ring containing a nontrivial self-adjoint idempotent. In this paper it is shown that under some mild conditions on R, if a mapping d : R → R satisfies d([U, V ]) = [d(U), V ] + [U, d(V )] for all U, V ∈ R, then there exists ZU,V ∈ Z(R) (depending on U and V ), where Z(R) is the center of R, such that d(U +V ) = d(U) + d(V ) +ZU,V . Moreover, if R is a 2-torsion free prime ∗-ring additionally, then d = ψ+ ξ, where ψ is an additive ∗-derivation of R into its central closure T and ξ is a mapping from R into its extended centroid C such that ξ(U + V ) = ξ(U) + ξ(V ) +ZU,V and ξ([U, V ]) = 0 for all U, V ∈ R. Finally, the above ring theoretic results have been applied to some special classes of algebras such as nest algebras and von Neumann algebras.","PeriodicalId":269525,"journal":{"name":"Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132134354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we study a linear operator related to Hurwitz-Lerch zeta function and hypergeometric function in the punctured unit disk. A certain subclass of meromorphically univalent functions associated with the above operator defined by the concept of subordination is also introduced, and its characteristic properties are studied.
{"title":"A certain subclass of univalent meromorphic functions defined by a linear operator associated with the Hurwitz-Lerch zeta function","authors":"F. Ghanim, H. Al‐Janaby","doi":"10.21857/ygjwrcjjxy","DOIUrl":"https://doi.org/10.21857/ygjwrcjjxy","url":null,"abstract":"In this paper, we study a linear operator related to Hurwitz-Lerch zeta function and hypergeometric function in the punctured unit disk. A certain subclass of meromorphically univalent functions associated with the above operator defined by the concept of subordination is also introduced, and its characteristic properties are studied.","PeriodicalId":269525,"journal":{"name":"Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti","volume":"367 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134363486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we address an appealing and so far not completed combinatorial problem of difference set (DS) existence in groups of order 144. We apply our recently established method for DS construction which proves to be very efficient. The result is more than 5000 inequivalent (144, 66, 30) DSes obtained in 131 groups of order 144. The number of nonisomorphic symmetric designs rising from them is 1364. Using the obtained DSes as a source, new regular (144, 66, 30, 30) and (144, 65, 28, 30) partial difference sets are constructed, together with the corresponding strongly regular graphs. 43 non-isomorphic graphs of valency 66 are obtained and 78 of valency 65. The full automorphism groups of these graphs, as well as those of symmetric designs, are explored using the software package Magma.
{"title":"Hadamard difference sets and related combinatorial objects in groups of order 144","authors":"Tanja Vucicic","doi":"10.21857/ypn4oc88w9","DOIUrl":"https://doi.org/10.21857/ypn4oc88w9","url":null,"abstract":"In this paper we address an appealing and so far not completed combinatorial problem of difference set (DS) existence in groups of order 144. We apply our recently established method for DS construction which proves to be very efficient. The result is more than 5000 inequivalent (144, 66, 30) DSes obtained in 131 groups of order 144. The number of nonisomorphic symmetric designs rising from them is 1364. Using the obtained DSes as a source, new regular (144, 66, 30, 30) and (144, 65, 28, 30) partial difference sets are constructed, together with the corresponding strongly regular graphs. 43 non-isomorphic graphs of valency 66 are obtained and 78 of valency 65. The full automorphism groups of these graphs, as well as those of symmetric designs, are explored using the software package Magma.","PeriodicalId":269525,"journal":{"name":"Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114815156","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper is concerned with the resolvent operator of one dimensional singular Dirac operator with transmission conditions. We study the Titchmarsh-Weyl function of this problem. Later, we construct a Green function and a spectral function for regular and singular problems. With the help of these functions, we obtain an expansion into a Fourier series of resolvent in regular case. Furthermore, we give integral representations in terms of the spectral function for the resolvent of this operator with transmission conditions in singular case. Finally, we obtain a formula for the Titchmarsh-Weyl function in terms of the spectral function of the singular Dirac system.
{"title":"Resolvent operator of singular Dirac system with transmission conditions","authors":"B. Allahverdiev, H. Tuna","doi":"10.21857/mnlqgc00ny","DOIUrl":"https://doi.org/10.21857/mnlqgc00ny","url":null,"abstract":"This paper is concerned with the resolvent operator of one dimensional singular Dirac operator with transmission conditions. We study the Titchmarsh-Weyl function of this problem. Later, we construct a Green function and a spectral function for regular and singular problems. With the help of these functions, we obtain an expansion into a Fourier series of resolvent in regular case. Furthermore, we give integral representations in terms of the spectral function for the resolvent of this operator with transmission conditions in singular case. Finally, we obtain a formula for the Titchmarsh-Weyl function in terms of the spectral function of the singular Dirac system.","PeriodicalId":269525,"journal":{"name":"Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124153355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Complex networks are often used to model objects and their relations. Network descriptors are graph-theoretical invariants assigned to graphs that correspond to complex networks. Transmission and betweenness centrality are well known network descriptors and networkness and network surplus have been recently analyzed. All these four descriptors are based on the unrealistic assumption about equal communication between all vertices. Here, we amend this by assuming that vertices on the distance larger then one communicate less than those that are neighbors. We analyze network descriptors for all possible values of the factor α that measures reduction in the communication of the vertices that are not neighbors. We term these descriptors one-alpha descriptors and determine their extremal values.
{"title":"One-alpha weighted network descriptors","authors":"Tanja Vojkovic, D. Vukičević","doi":"10.21857/94kl4cxxjm","DOIUrl":"https://doi.org/10.21857/94kl4cxxjm","url":null,"abstract":"Complex networks are often used to model objects and their relations. Network descriptors are graph-theoretical invariants assigned to graphs that correspond to complex networks. Transmission and betweenness centrality are well known network descriptors and networkness and network surplus have been recently analyzed. All these four descriptors are based on the unrealistic assumption about equal communication between all vertices. Here, we amend this by assuming that vertices on the distance larger then one communicate less than those that are neighbors. We analyze network descriptors for all possible values of the factor α that measures reduction in the communication of the vertices that are not neighbors. We term these descriptors one-alpha descriptors and determine their extremal values.","PeriodicalId":269525,"journal":{"name":"Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127582800","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper we study isometries of ruled surfaces in the Lorentz-Minkowski space that preserve rulings. A special attention is given to the classes of surfaces having no Euclidean counterparts. We also construct some examples of isometric ruled surfaces with certain properties and rulings preserved.
{"title":"Minding isometries of ruled surfaces in Lorentz-Minkowski space","authors":"Ljiljana Primorac Gajčić, Željka Milin-Šipuš","doi":"10.21857/y54jofpplm","DOIUrl":"https://doi.org/10.21857/y54jofpplm","url":null,"abstract":"In this paper we study isometries of ruled surfaces in the Lorentz-Minkowski space that preserve rulings. A special attention is given to the classes of surfaces having no Euclidean counterparts. We also construct some examples of isometric ruled surfaces with certain properties and rulings preserved.","PeriodicalId":269525,"journal":{"name":"Rad Hrvatske akademije znanosti i umjetnosti. Matematičke znanosti","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117023140","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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