611 results
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2. The Clar and Fries structures of a fullerene I.
- Author
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Graver, Jack E. and Hartung, Elizabeth J.
- Subjects
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NUMBER theory , *MATCHING theory , *SET theory , *RING theory , *MATHEMATICAL analysis - Abstract
Given the Kekulé structure of a fullerene that gives its Clar structure, the Kekulé edges that do not lie on any benzene ring of the Clar structure lie on open chains that pair up the pentagonal faces and perhaps some closed chains. In this paper, we introduce Fries chains and show that given the Kekulé structure of a fullerene that gives its Fries structure, the Kekulé edges that do not lie on two benzene rings lie on the union of a set of these Fries chains. The edges that lie on exactly one benzene ring belong to exactly one of these chains while edges that lie on no benzene ring belong to exactly two of these chains. We will see that the Fries chains will include the Clar chains in some cases and will be quite distinct from the Clar chains in other cases. Examples of fullerenes with the property that the set of benzene rings that give its Clar number are not a subset of the benzene rings that give its Fries number have been known for a few years. However, in all of these known examples, almost all of the benzene rings of its Clar structure are among benzene rings of its Fries structure. In this paper, we describe a class of fullerenes with the property that the set of benzene rings of its Clar structure and the set of benzene rings of its Fries structure practically disjoint. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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3. Quantification of R-fuzzy sets.
- Author
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Khuman, Arjab Singh, Yang, Yingjie, and John, Robert
- Subjects
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FUZZY sets , *SET theory , *FUZZY algorithms , *MATHEMATICAL models , *MATHEMATICAL analysis - Abstract
The main aim of this paper is to connect R-fuzzy sets and type-2 fuzzy sets, so as to provide a practical means to express complex uncertainty without the associated difficulty of a type-2 fuzzy set. The paper puts forward a significance measure, to provide a means for understanding the importance of the membership values contained within an R-fuzzy set. The pairing of an R-fuzzy set and the significance measure allows for an intermediary approach to that of a type-2 fuzzy set. By inspecting the returned significance degree of a particular membership value, one is able to ascertain its true significance in relation, relative to other encapsulated membership values. An R-fuzzy set coupled with the proposed significance measure allows for a type-2 fuzzy equivalence, an intermediary, all the while retaining the underlying sentiment of individual and general perspectives, and with the adage of a significantly reduced computational burden. Several human based perception examples are presented, wherein the significance degree is implemented, from which a higher level of detail can be garnered. The results demonstrate that the proposed research method combines the high capacity in uncertainty representation of type-2 fuzzy sets, together with the simplicity and objectiveness of type-1 fuzzy sets. This in turn provides a practical means for problem domains where a type-2 fuzzy set is preferred but difficult to construct due to the subjective type-2 fuzzy membership. [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
- View/download PDF
4. Semi-transitive orientations and word-representable graphs.
- Author
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Halldórsson, Magnús M., Kitaev, Sergey, and Pyatkin, Artem
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GRAPH theory , *SET theory , *LINEAR statistical models , *MATHEMATICAL analysis , *ALGORITHMS - Abstract
A graph G = ( V , E ) is a word-representable graph if there exists a word W over the alphabet V such that letters x and y alternate in W if and only if ( x , y ) ∈ E for each x ≠ y . In this paper we give an effective characterization of word-representable graphs in terms of orientations. Namely, we show that a graph is word-representable if and only if it admits a semi-transitive orientation defined in the paper. This allows us to prove a number of results about word-representable graphs, in particular showing that the recognition problem is in NP, and that word-representable graphs include all 3-colorable graphs. We also explore bounds on the size of the word representing the graph. The representation number of G is the minimum k such that G is a representable by a word, where each letter occurs k times; such a k exists for any word-representable graph. We show that the representation number of a word-representable graph on n vertices is at most 2 n , while there exist graphs for which it is n / 2 . [ABSTRACT FROM AUTHOR]
- Published
- 2016
- Full Text
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5. When is [formula omitted]?
- Author
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Azarpanah, F., Ghirati, M., and Taherifar, A.
- Subjects
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COINCIDENCE theory , *INFINITY (Mathematics) , *MATHEMATICAL equivalence , *MODULES (Algebra) , *SET theory , *MATHEMATICAL analysis - Abstract
This short article is in fact an erratum to Theorem 2.5 in Ghirati and Taherifar (2014) [6] . In this paper, we prove that J ( C ( X ) / C F ( X ) ) = 0 or equivalently, the socle C F ( X ) of C ( X ) coincides with the intersection of all essential maximal ideals of C ( X ) if and only if every infinite subset of I ( X ) contains a closed infinite subset, if and only if every pseudocompact subset of X has at most a finite number of isolated points. This fact shows that part (2) of aforementioned Theorem 2.5 is not correct. Our results in this paper also amend Theorem 5.6 in Azarpanah et al. (2008) [2] . Examples are provided to illustrate and delimit our results. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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6. An integrated system for modeling hypervelocity interaction of solids.
- Author
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Meshkov, Vladimir V., Fedosov, Yuri A., and Filatova, Natalya N.
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HYPERVELOCITY , *FUZZY sets , *MEMBERSHIP functions (Fuzzy logic) , *SET theory , *MATHEMATICAL analysis , *SPACE debris - Abstract
The main purpose of the article is to show feasibility and efficiency of combining different types of simulating a hypervelocity impact interaction of solids within a single system. It allows effective application of new mathematical apparatus for analysis and comparison of experimental results. The paper considers the features of an integrated system that combines the results of experiments reproducing the high-velocity impact interaction of solids. The experiments included different types of modeling. System structure and the tasks solved within individual functional modulus were discussed. Based on the theory of fuzzy sets, new algorithms were proposed for comparing edges of the images obtained in the physical and computational experiment. Mathematical models were verified by such procedure. Differences in the shape and size of a cloud of particles that appears after penetrating a single barrier were estimated in the framework of designed models, as well as the differences in the sizes of punched holes using fuzzy variables and related membership functions. When analyzing experimental results, fuzzy sets enable switching from data structures to knowledge structures that are necessary to create an intelligent system for analyzing and predicting the effects of the interaction between space debris and spacecraft structures. • Types of simulating a hypervelocity impact interaction of solids can be combined. • This combining is efficient and feasible. • New algorithms were proposed for comparing edges of the images. • Fuzzy sets enable switching from data structures to knowledge structures. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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7. On bilateral matching between fuzzy sets.
- Author
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Kacprzyk, Janusz, Krawczak, Maciej, and Szkatuła, Grażyna
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FUZZY sets , *SET theory , *PERTURBATION theory , *MATHEMATICAL analysis , *STATISTICAL matching , *COMPARATIVE studies - Abstract
In the paper, we describe the new measure of matching fuzzy sets. The introduced measure of perturbation of one fuzzy set by another fuzzy set is considered instead of commonly used distance between two fuzzy sets. The operations known in the fuzzy set theory are used and the perturbation of one fuzzy set by another fuzzy set is understood as a measure describing changes of the first fuzzy set after adding the second one. Obviously, the opposite case can also be considered wherein the second fuzzy set is perturbed by the first one. In general, the new measure is asymmetric and can provide more information compare to a distance between fuzzy sets. The values of such measures of fuzzy sets’ perturbation are in range between 0 and 1. In this paper several mathematical properties of the measure of fuzzy sets’ perturbation are studied, and the measure of sets’ perturbation is compared to other selected measures. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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8. The effectiveness of three-way classification with interpretable perspective.
- Author
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Liu, Dun
- Subjects
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PROBLEM solving , *TWO-way communication , *CLASSIFICATION , *MATHEMATICAL analysis , *SET theory - Abstract
As a typical methodology to deal with uncertain issues, the three-way decision (3WD) has been developed rapidly in nearly ten years, both in theories and applications. Three-way classification is one of the important research fields of 3WD, which utilizes the idea of 3WD to solve classification problems. In this paper, we focus on investigating the effectiveness of three-way classification through two evaluation indicators: the classification quality (Precision , Recall , Accuracy and F 1 ) and the decision cost. The comparisons between two-way classification and three-way classification are concretely analyzed, some mathematical properties, judging conditions and decision criteria of these two classification methods are also discussed in detail. Finally, the experimental results on eight UCI data sets validate the mathematical analysis, which reveal the effectiveness of three-way classification. [ABSTRACT FROM AUTHOR]
- Published
- 2021
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9. The relationship between attribute reducts in rough sets and minimal vertex covers of graphs.
- Author
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Chen, Jinkun, Lin, Yaojin, Lin, Guoping, Li, Jinjin, and Ma, Zhouming
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ROUGH sets , *SET theory , *GRAPH theory , *MATHEMATICAL optimization , *MATHEMATICAL analysis - Abstract
The problems to find attribute reduction in rough sets and to obtain the minimal vertex cover for graphs are both NP-hard problems. This paper studies the relationship between the two problems. The vertex cover problem for graphs from the perspective of rough sets is first investigated. The attribute reduction of an information system is then studied in the framework of graph theory. The results in this paper show that finding the minimal vertex cover of a graph is equivalent to finding the attribute reduction of an information system induced from the graph. Conversely, the attribute reduction computation can be translated into the calculation of the minimal vertex cover of a derivative graph. Finally, a new algorithm for the vertex cover problem based on rough sets is presented. Furthermore, experiments are conducted to verify the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]
- Published
- 2015
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10. Lyapunov-type inequalities for a class of higher-order linear differential equations.
- Author
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Yang, Xiaojing, Kim, Yong-In, and Lo, Kueiming
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LYAPUNOV functions , *MATHEMATICAL inequalities , *SET theory , *LINEAR differential equations , *GENERALIZATION , *MATHEMATICAL analysis , *NUMERICAL analysis - Abstract
Abstract: In this paper, we obtain some Lyapunov-type inequalities for a class of higher-order linear differential equations. The results of this paper generalize and improve some earlier results on this topic. [Copyright &y& Elsevier]
- Published
- 2014
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11. On some Godbillon–Vey classes of a family of regular foliations.
- Author
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Ida, Cristian and Popescu, Paul
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FOLIATIONS (Mathematics) , *COHOMOLOGY theory , *MANIFOLDS (Mathematics) , *BOREL subsets , *SET theory , *MATHEMATICAL analysis - Abstract
Abstract: The aim of the paper is to construct some Godbillon–Vey classes of a family of regular foliations, defined in the paper. These classes are cohomology classes on the manifold or on suitable open subsets. Some examples are also considered. [Copyright &y& Elsevier]
- Published
- 2014
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12. Homogeneously non-idling schedules of unit-time jobs on identical parallel machines.
- Author
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Quilliot, Alain and Chrétienne, Philippe
- Subjects
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PARALLEL algorithms , *SCHEDULING , *SET theory , *FEASIBILITY studies , *MATHEMATICS , *MATHEMATICAL analysis - Abstract
Abstract: In this paper, we study the basic homogeneous -machine scheduling problem where weakly dependent unit-time jobs have to be scheduled within the time windows between their release dates and due dates so that, for any subset of machines, the set of the time units at which at least one machine is busy, is in interval. We first introduce the notions of pyramidal structure, -hole, -matching, preschedule, -schedule and schedule for this problem. Then we provide a feasibility criteria for a preschedule. The key result of the paper is then to provide a structural necessary and sufficient condition for an instance of the problem to be feasible. We conclude by giving the directions of ongoing works and by bringing open questions related to different variants of the basic non-idling -machine scheduling problem. [Copyright &y& Elsevier]
- Published
- 2013
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13. Sperner type theorems with excluded subposets.
- Author
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Katona, Gyula O.H.
- Subjects
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SPERNER theory , *PARTIALLY ordered sets , *SET theory , *GENERALIZATION , *MATHEMATICS , *MATHEMATICAL analysis - Abstract
Abstract: Let be a family of subsets of an -element set. Sperner’s theorem says that if there is no inclusion among the members of then the largest family under this condition is the one containing all -element subsets. The present paper surveys certain generalizations of this theorem. The maximum size of is to be found under the condition that a certain configuration is excluded. The configuration here is always described by inclusions. More formally, let be a poset. The maximum size of a family which does not contain as a (not-necessarily induced) subposet is denoted by . The paper is based on a lecture of the author at the Jubilee Conference on Discrete Mathematics [Banasthali University, January 11–13, 2009], but it was somewhat updated in December 2010. [Copyright &y& Elsevier]
- Published
- 2013
- Full Text
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14. Bijective soft set decision system based parameters reduction under fuzzy environments
- Author
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Gong, Ke, Wang, Panpan, and Xiao, Zhi
- Subjects
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SET theory , *BIJECTIONS , *ALGORITHMS , *FUZZY systems , *TIME series analysis , *MATHEMATICAL analysis - Abstract
Abstract: Gong et al. (2010) and Xiao et al. (2010) have proposed the notion of bijective soft set and exclusive disjunctive soft set, respectively, which is a subtype of soft set. On the basis of their work, this paper extends these notions to fuzzy environments, and formulates the concept of bijective fuzzy soft set, which can deal with more uncertain problems. Moreover, this paper proposes two parameters reduction algorithms: one (Algorithm 1) is based on bijective fuzzy soft system, and the other (Algorithm 2) takes weight of an element into consideration. Since the threshold plays an important role in these algorithms, we proposed an algorithm (Algorithm 3) to decide the optimal value of threshold specially. Afterwards, an example analysis of the two parameters reduction algorithms is given and the result shows that the two algorithms lead to the same parameters reduction of a bijective fuzzy soft system. Since Algorithm 2 considers the detail weights of elements, thus it can be used in more uncertain problems, such as time series analysis problems, than Algorithm 1. [Copyright &y& Elsevier]
- Published
- 2013
- Full Text
- View/download PDF
15. Interpolatory blending net subdivision schemes of Dubuc–Deslauriers type
- Author
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Conti, Costanza, Dyn, Nira, and Romani, Lucia
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INTERPOLATION , *SUBDIVISION surfaces (Geometry) , *CONTINUOUS functions , *STOCHASTIC convergence , *PERFORMANCE evaluation , *SET theory , *MATHEMATICAL analysis - Abstract
Abstract: Net subdivision schemes recursively refine nets of univariate continuous functions defined on the lines of planar grids, and generate as limits bivariate continuous functions. In this paper a family of interpolatory net subdivision schemes related to the family of Dubuc–Deslauriers interpolatory subdivision schemes is constructed and analyzed. The construction is based on Gordon blending interpolants to nets of univariate functions, and on a particular class of blending functions with properties related to the Dubuc–Deslauriers schemes. The general analysis tools for net subdivision schemes, developed in a previous paper by the authors, together with the properties of the blending functions, lead to the proof of the convergence of these schemes to limit functions having the same integer smoothness as the limits of the corresponding Dubuc–Deslauriers schemes. These results are proved for net subdivision schemes corresponding to the first 84 members of the Dubuc–Deslauriers family, and conjectured for the rest. A concrete example of a family of piecewise polynomial blending functions is considered, together with the corresponding family of net subdivision schemes. The performance of the first two net subdivision schemes in this family is demonstrated by two examples. [Copyright &y& Elsevier]
- Published
- 2012
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16. Coefficient estimates for a certain subclass of analytic and bi-univalent functions
- Author
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Xu, Qing-Hua, Gui, Ying-Chun, and Srivastava, H.M.
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ANALYTIC functions , *UNIVALENT functions , *MATHEMATICAL constants , *MATHEMATICAL analysis , *SET theory , *ALGEBRAIC functions - Abstract
Abstract: In this paper, we introduce and investigate an interesting subclass of analytic and bi-univalent functions in the open unit disk . For functions belonging to the class , we obtain estimates on the first two Taylor–Maclaurin coefficients and . The results presented in this paper would generalize and improve some recent work of Srivastava et al. [H.M. Srivastava, A.K. Mishra, P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (2010) 1188–1192]. [Copyright &y& Elsevier]
- Published
- 2012
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17. The categories of flows of Set and Top
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Echi, Othman
- Subjects
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CATEGORIES (Mathematics) , *SET theory , *MATHEMATICAL analysis , *DYNAMICS , *COMPACT spaces (Topology) , *ITERATIVE methods (Mathematics) , *MORPHISMS (Mathematics) - Abstract
Abstract: Following John Kennison, a flow (or discrete dynamical system) in a category C is a couple , where X is an object of C and is a morphism, called the iterator. If and are flows in C, then is a morphism of flows from to if . We let denote the resulting category of flows in C. This paper deals with and , where Set and Top denote respectively the categories of sets and topological spaces. By a Gottschalk flow, we mean a flow in Top satisfying the following conditions: [(i)] If is any almost periodic point of f, then the closure is a minimal set of f; [(ii)] All points in any minimal set of f are almost periodic points. As proven by Gottschalk, if X is a compact Hausdorff space and is a continuous function, then is a Gottschalk flow. In this paper, we prove that for any flow of Set, there is a topology on X for which is a Gottschalk flow in Top. This, actually, defines a covariant functor from into . The main result of this paper provides a characterization of spaces in the image of the functor in order-theoretical terms. Some categorical properties of and are also given. [Copyright &y& Elsevier]
- Published
- 2012
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18. Zero forcing sets and bipartite circulants
- Author
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Meyer, Seth A.
- Subjects
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SET theory , *BIPARTITE graphs , *GRAPH theory , *MATRICES (Mathematics) , *MATHEMATICAL analysis , *LINEAR algebra - Abstract
Abstract: In this paper we introduce a class of regular bipartite graphs whose biadjacency matrices are circulant matrices – a generalization of circulant graphs which happen to be bipartite – and we describe some of their properties. Notably, we compute upper and lower bounds for the zero forcing number for such a graph based only on the parameters that describe its biadjacency matrix. The main results of the paper characterize the bipartite circulant graphs that achieve equality in the lower bound and compute their minimum ranks. [Copyright &y& Elsevier]
- Published
- 2012
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19. On the spherical quasi-convexity of quadratic functions.
- Author
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Ferreira, O.P., Németh, S.Z., and Xiao, L.
- Subjects
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QUADRATIC forms , *ALGEBRAIC functions , *SET theory , *ALGEBRAIC logic , *MATHEMATICAL analysis - Abstract
Abstract In this paper the spherical quasi-convexity of quadratic functions on spherically convex sets is studied. Several conditions characterizing the spherical quasi-convexity of quadratic functions are presented. In particular, conditions implying spherical quasi-convexity of quadratic functions on the spherical positive orthant are given. Some examples are provided as applications of the obtained results. [ABSTRACT FROM AUTHOR]
- Published
- 2019
- Full Text
- View/download PDF
20. Granular Sets and its Properties.
- Author
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Deng, Shaobo and Li, Min
- Subjects
SET theory ,APPROXIMATION theory ,GRANULAR computing ,ROUGH sets ,MATHEMATICAL analysis ,MATHEMATICAL proofs - Abstract
Abstract: The paper introduced the definitions of the Granular Set,its lower approximation and its upper approximation,the positive region,the negative region and so on Granular sets expands the Rough Sets theory and has some important properties, This paper also proves them [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
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21. Soft groups and normalistic soft groups
- Author
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Sezgin, Aslıhan and Atagün, Akın Osman
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SET theory , *HOMOMORPHISMS , *GROUP theory , *MATHEMATICAL mappings , *MATHEMATICAL analysis , *NUMERICAL analysis , *MATHEMATICAL functions , *CONTINUOUS functions - Abstract
Abstract: Soft set theory, proposed by Molodtsov, has been regarded as an effective mathematical tool to deal with uncertainties. In this paper, first we correct some of the problematic cases in a previous paper by Aktaş and Çag˜man [H. Aktaş, N. Çag˜man, Soft sets and soft groups, Inf. Sci. 177 (2007) 2726–2735]. Moreover, we introduce the concepts of normalistic soft group and normalistic soft group homomorphism, study their several related properties, and investigate some structures that are preserved under normalistic soft group homomorphisms. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
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22. On operations of soft sets
- Author
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Sezgin, Aslıhan and Atagün, Akın Osman
- Subjects
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SET theory , *MATHEMATICAL logic , *UNCERTAINTY (Information theory) , *MATHEMATICAL proofs , *MATHEMATICAL analysis , *RELATION algebras - Abstract
Abstract: Soft set theory, proposed by Molodtsov, has been regarded as an effective mathematical tool to deal with uncertainties. In this paper, first we prove that certain De Morgan’s law hold in soft set theory with respect to different operations on soft sets. Then, we discuss the basic properties of operations on soft sets such as intersection, extended intersection, restricted union and restricted difference. Moreover, we illustrate their interconnections between each other. Also we define the notion of restricted symmetric difference of soft sets and investigate its properties. The main purpose of this paper is to extend the theoretical aspect of operations on soft sets. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
23. Test data compression using alternating variable run-length code
- Author
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Ye, Bo, Zhao, Qian, Zhou, Duo, Wang, Xiaohua, and Luo, Min
- Subjects
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DATA compression , *CODING theory , *SET theory , *MATHEMATICAL analysis , *MATHEMATICAL mappings , *TESTING - Abstract
Abstract: This paper presents a unified test data compression approach, which simultaneously reduces test data volume, scan power consumption and test application time for a system-on-a-chip (SoC). The proposed approach is based on the use of alternating variable run-length (AVR) codes for test data compression. A formal analysis of scan power consumption and test application time is presented. The analysis showed that a careful mapping of the don’t-cares in pre-computed test sets to 1s and 0s led to significant savings in peak and average power consumption, without requiring slower scan clocks. The proposed technique also reduced testing time compared to a conventional scan-based scheme. The alternating variable run-length codes can efficiently compress the data streams that are composed of both runs 0s and 1s. The decompression architecture was also presented in this paper. Experimental results for ISCAS''89 benchmark circuits and a production circuit showed that the proposed approach greatly reduced test data volume and scan power consumption for all cases. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
24. Matching polynomials for chains of cycles
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Bian, Hong, Zhang, Fuji, Wang, Guoping, and Yu, Haizheng
- Subjects
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POLYNOMIALS , *ALGEBRAIC cycles , *SET theory , *MATHEMATICAL analysis , *STATISTICAL matching - Abstract
Abstract: Došlić and Måløy (2010) obtained the extremal 6-cactus chains with respect to the number of matchings and of independent sets. Motivated by the prior paper, in this paper we give recurrences for matching polynomials of ortho-chains and meta-chains, and show that they are the -cactus chains with the most matchings. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
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25. A quasiseparable approach to five-diagonal CMV and Fiedler matrices
- Author
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Bella, T., Olshevsky, V., and Zhlobich, P.
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MATRICES (Mathematics) , *MATHEMATICAL transformations , *ORTHOGONAL polynomials , *SET theory , *SYSTEMS theory , *MATHEMATICAL analysis - Abstract
Abstract: Recent work in the characterization of structured matrices in terms of characteristic polynomials of principal submatrices is furthered in this paper. Some classical classes of matrices with quasiseparable structure include tridiagonal (related to real orthogonal polynomials) and banded matrices, unitary Hessenberg matrices (related to Szegö polynomials), and semiseparable matrices, as well as others. Hence working with the class of quasiseparable matrices provides new results which generalize and unify classical results. Previous work has focused on characterizing -quasiseparable matrices, matrices with order-one quasiseparable structure that are also upper Hessenberg. In this paper, the authors introduce the concept of a twist transformation, and use such transformations to explain the relationship between -quasiseparable matrices and the subclass of -quasiseparable matrices (without the upper Hessenberg restriction) which are related to the same systems of polynomials. These results generalize the discoveries of Cantero, Fiedler, Kimura, Moral and Velázquez of five-diagonal matrices related to Horner and Szegö polynomials in the context of quasiseparable matrices. [Copyright &y& Elsevier]
- Published
- 2011
- Full Text
- View/download PDF
26. Large sets of extended directed triple systems with odd orders
- Author
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Liu, Yuanyuan and Kang, Qingde
- Subjects
- *
MONADS (Mathematics) , *SET theory , *SPECTRAL theory , *INTEGERS , *MATHEMATICAL analysis , *EXISTENCE theorems - Abstract
Abstract: For three types of triples, unordered, cyclic and transitive, the corresponding extended triple, extended triple system and their large set are introduced. The spectrum of for even has been given in our paper (Liu and Kang (2009) ). In this paper, we shall discuss the existence problem of for odd and give the almost complete conclusion: there exists an for any positive integer except possible . [ABSTRACT FROM AUTHOR]
- Published
- 2010
- Full Text
- View/download PDF
27. Vertex-disjoint directed cycles of prescribed length in tournaments with given minimum out-degree and in-degree
- Author
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Lichiardopol, Nicolas
- Subjects
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PATHS & cycles in graph theory , *TOURNAMENTS (Graph theory) , *DIRECTED graphs , *SET theory , *MAXIMA & minima , *MATHEMATICAL analysis - Abstract
Abstract: In a recent paper, Bessy, Sereni and the author (see ) have proved that for , a tournament with minimum out-degree and in-degree both greater than or equal to contains at least vertex-disjoint directed triangles. In this paper, we generalize this result; more precisely, we prove that for given integers and , a tournament with minimum out-degree and in-degree both greater than or equal to contains at least vertex-disjoint directed cycles of length . We will use an auxiliary result established in , concerning a union of sets contained in another union of sets. We finish by giving a lower bound on the maximum number of vertex-disjoint directed cycles of length when only the minimum out-degree is supposed to be greater than or equal to . [Copyright &y& Elsevier]
- Published
- 2010
- Full Text
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28. Tree maps having chain movable fixed points
- Author
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Mai, Jie-Hua, Zhang, Geng-Rong, and Liu, Xin-He
- Subjects
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TREE graphs , *MATHEMATICAL mappings , *FIXED point theory , *SET theory , *TOPOLOGICAL entropy , *MATHEMATICAL analysis - Abstract
Abstract: In this paper we discuss some basic properties of chain reachable sets and chain equivalent sets of continuous maps. It is proved that if is a tree map which has a chain movable fixed point v, and the chain equivalent set is not contained in the set of periodic points of f, then there exists a positive integer p not greater than the number of points in the set such that is turbulent, and the topological entropy . This result generalizes the corresponding results given in Block and Coven (1986) , Guo et al. (2003) , Sun and Liu (2003) , Ye (2000) , Zhang and Zeng (2004) . In addition, in this paper we also consider metric spaces which may not be trees but have open subsets U such that the closures are trees. Maps of such metric spaces which have chain movable fixed points are discussed. [Copyright &y& Elsevier]
- Published
- 2010
- Full Text
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29. Lyapunov-type inequality for a class of odd-order differential equations
- Author
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Yang, Xiaojing, Kim, Yong-In, and Lo, Kueiming
- Subjects
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LYAPUNOV functions , *MATHEMATICAL inequalities , *SET theory , *DIFFERENTIAL equations , *GENERALIZATION , *MATHEMATICAL analysis - Abstract
Abstract: In this paper, we give a generalization of the well-known Lyapunov-type inequality for a class of odd-order differential equations, the result of this paper is new and generalizes some early results on this topic. [Copyright &y& Elsevier]
- Published
- 2010
- Full Text
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30. Differential subordination and superordination for certain subclasses of p-valent functions
- Author
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El-Ashwah, R.M. and Aouf, M.K.
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ORDINATION (Statistics) , *SET theory , *ANALYTIC functions , *MULTIPLIERS (Mathematical analysis) , *MATHEMATICAL transformations , *MATHEMATICAL analysis - Abstract
Abstract: In this paper we derive some subordination and superordination results for certain p-valent analytic functions in the open unit disc, which are acted upon by a class of extended multiplier transformations. Relevant connection of the results, which are presented in this paper with various known results are also considered. [Copyright &y& Elsevier]
- Published
- 2010
- Full Text
- View/download PDF
31. Large sets of extended directed triple systems with even orders
- Author
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Liu, Yuanyuan and Kang, Qingde
- Subjects
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SYSTEM analysis , *SET theory , *EXISTENCE theorems , *DIRECTED graphs , *COMBINATORICS , *MATHEMATICAL analysis - Abstract
Abstract: For three types of triples: unordered, cyclic and transitive, the corresponding extended triple, extended triple system and their large sets are introduced. The existence of and were completely solved. In this paper, we shall discuss the existence problem of and give the following conclusion: there exists an for any even except . The existence of with odd order will be discussed in another paper, we are working at it. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
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32. Pseudo-isochronicity in a class of septic differential systems
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Wu, Yusen and Li, Peiluan
- Subjects
- *
SET theory , *DIFFERENTIAL equations , *MATHEMATICAL transformations , *MATHEMATICAL analysis , *MATHEMATICS , *CALCULUS - Abstract
Abstract: This paper deals with the pseudo-isochronicity for a class of septic differential systems. In this paper, we transform infinity into the origin so that the properties of infinity can be investigated with the methods developed for finite critical points. By calculating the singular point quantities and period constants of the origin, the problem of infinity being a pseudo-isochronous center has been solved in this case. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
33. Set multi-covering via inclusion–exclusion
- Author
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Hua, Qiang-Sheng, Wang, Yuexuan, Yu, Dongxiao, and Lau, Francis C.M.
- Subjects
- *
COMBINATORIAL packing & covering , *SET theory , *ONLINE algorithms , *SIEVES (Mathematics) , *COMPUTATIONAL complexity , *MATHEMATICAL analysis - Abstract
Abstract: Set multi-covering is a generalization of the set covering problem where each element may need to be covered more than once and thus some subset in the given family of subsets may be picked several times for minimizing the number of sets to satisfy the coverage requirement. In this paper, we propose a family of exact algorithms for the set multi-covering problem based on the inclusion–exclusion principle. The presented ESMC (Exact Set Multi-Covering) algorithm takes time and space where is the maximum value in the coverage requirement set (The notation omits a factor). We also propose the other three exact algorithms through different tradeoffs of the time and space complexities. To the best of our knowledge, this present paper is the first one to give exact algorithms for the set multi-covering problem with nontrivial time and space complexities. This paper can also be regarded as a generalization of the exact algorithm for the set covering problem given in [A. Björklund, T. Husfeldt, M. Koivisto, Set partitioning via inclusion–exclusion, SIAM Journal on Computing, in: FOCS 2006 (in press, special issue)]. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
34. The unambiguity of segmented morphisms
- Author
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Freydenberger, Dominik D. and Reidenbach, Daniel
- Subjects
- *
MORPHISMS (Mathematics) , *MONOIDS , *SET theory , *COMBINATORICS , *COMPUTATIONAL mathematics , *MATHEMATICAL analysis - Abstract
Abstract: This paper studies the ambiguity of morphisms in free monoids. A morphism is said to be ambiguous with respect to a string if there exists a morphism which differs from for a symbol occurring in , but nevertheless satisfies ; if there is no such then is called unambiguous. Motivated by the recent initial paper on the ambiguity of morphisms, we introduce the definition of a so-called segmented morphism , which, for any , maps every symbol in an infinite alphabet onto a word that consists of distinct factors in , where and are different letters. For every , we consider the set of those finite strings over an infinite alphabet with respect to which is unambiguous, and we comprehensively describe its relation to any , . Thus, our work features the first approach to a characterisation of sets of strings with respect to which certain fixed morphisms are unambiguous, and it leads to fairly counter-intuitive insights into the relations between such sets. Furthermore, it shows that, among the widely used homogeneous morphisms, most segmented morphisms are optimal in terms of being unambiguous for a preferably large set of strings. Finally, our paper yields several major improvements of crucial techniques previously used for research on the ambiguity of morphisms. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
35. Existence of good large sets of Steiner triple systems
- Author
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Zhou, Junling and Chang, Yanxun
- Subjects
- *
STEINER systems , *EXISTENCE theorems , *SET theory , *BLOCK designs , *MATHEMATICAL analysis - Abstract
Abstract: The concept of good large set of Steiner triple systems (or GLS in short) was introduced by Lu in his paper “on large sets of disjoint Steiner triple systems”, [J. Lu, On large sets of disjoint Steiner triple systems, I–III, J. Combin. Theory (A) 34 (1983) 140-182]. In this paper a doubling construction for GLSs is displayed and some existence results are obtained. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
36. On minimal elements of upward-closed sets
- Author
-
Yen, Hsu-Chun and Chen, Chien-Liang
- Subjects
- *
SET theory , *COMPUTATIONAL complexity , *VECTOR analysis , *PETRI nets , *MATHEMATICAL analysis , *COMPUTER science , *DECIDABILITY (Mathematical logic) - Abstract
Abstract: Upward-closed sets of integer vectors enjoy the merit of having a finite number of minimal elements, which is behind the decidability of a number of Petri net related problems. In general, however, such a finite set of minimal elements may not be effectively computable. In this paper, we develop a unified strategy for computing the sizes of the minimal elements of certain upward-closed sets associated with Petri nets. Our approach can be regarded as a refinement of a previous work by Valk and Jantzen (in which a necessary and sufficient condition for effective computability of the set was given), in the sense that complexity bounds now become available provided that a bound can be placed on the size of a witness for a key query. The sizes of several upward-closed sets that arise in the theory of Petri nets as well as in backward-reachability analysis in automated verification are derived in this paper, improving upon previous decidability results shown in the literature. [Copyright &y& Elsevier]
- Published
- 2009
- Full Text
- View/download PDF
37. Substitution systems and the three versions of distributional chaos
- Author
-
Wang, Hui, Liao, Gongfu, and Fan, Qinjie
- Subjects
- *
GROUP theory , *DISTRIBUTION (Probability theory) , *MATHEMATICAL constants , *SET theory , *TOPOLOGY , *MATHEMATICAL analysis - Abstract
Abstract: There are three types of distributional chaos, namely DC1, DC2 and DC3. In this paper we present two constant-length substitution systems, one is DC2 but not DC1, and the other is DC3 but not DC2. (In this paper, chaos means existence of an uncountable scrambled set of the corresponding type while the existing examples deal with single pairs of points only.) [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
- View/download PDF
38. Two, more readily computable equivariant Nielsen numbers I. Nielsen theory for M-ads
- Author
-
Heath, Philip R.
- Subjects
- *
FIXED point theory , *MATHEMATICAL mappings , *SET theory , *TOPOLOGY , *COINCIDENCE theory , *MATHEMATICAL analysis - Abstract
Abstract: In this, the first of two papers outlining a Nielsen theory for “two, more readily computable equivariant numbers”, we define and study two Nielsen type numbers and , where f and k are M-ad maps. While a Nielsen theory of M-ads is of interest in its own right, our main motivation lies in the fact that maps of M-ads accurately mirror one of two fundamental structures of equivariant maps. Being simpler however, M-ad Nielsen numbers are easier to study and to compute than equivariant Nielsen numbers. In the sequel, we show our M-ad numbers can be used to form both upper and lower bounds on their equivariant counterparts. The numbers and , generalize the generalizations to coincidences, of Zhao''s Nielsen number on the complement , respectively Schirmer''s relative Nielsen number . Our generalizations are from the category of pairs, to the category of M-ads. The new numbers are lower bounds for the number of coincidence points of all maps and which are homotopic as maps of M -ads to f, respectively k firstly on the complement of the union of the subspaces in the domain M-ad X, and secondly on all of X. The second number is shown to be greater than or equal to a sum of the first of our numbers. Conditions are given which allow for both equality, and Möbius inversion. Finally we show that the fixed point case of our second number generalizes Schirmer''s triad Nielsen number . Our work is very different from what at first sight appears to be similar partial results due to P. Wong. The differences, while in some sense subtle in terms of definition, are profound in terms of commutability. In order to work in a variety of both fixed point and coincidence points contexts, we introduce in this first paper and extend in the second, the concept of an essentiality on a topological category. This allows us to give computational theorems within this diversity. Finally we include an introduction to both papers here. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
- View/download PDF
39. A study on optimality and duality theorems of nonlinear generalized disjunctive fractional programming
- Author
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Ammar, E.E.
- Subjects
- *
MATHEMATICAL optimization , *SET theory , *MATHEMATICAL analysis , *MAXIMA & minima - Abstract
Abstract: This paper is concerned with the study of necessary and sufficient optimality conditions for convex–concave generalized fractional disjunctive programming problems for which the decision set is the union of a family of convex sets. The Lagrangian function for such problems is defined and the Kuhn–Tucker Saddle and Stationary points are characterized. In addition, some important theorems related to the Kuhn–Tucker problem for saddle and stationary points are established. Moreover, a general dual problem is formulated and weak, strong and converse duality theorems are proved. Throughout the presented paper illustrative examples are given to clarify and implement the developed theory. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
- View/download PDF
40. A typed lambda calculus with intersection types
- Author
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Bono, Viviana, Venneri, Betti, and Bettini, Lorenzo
- Subjects
- *
MATHEMATICAL analysis , *MATHEMATICAL functions , *SET theory , *MATHEMATICS - Abstract
Abstract: Intersection types are well known to type theorists mainly for two reasons. Firstly, they type all and only the strongly normalizable lambda terms. Secondly, the intersection type operator is a meta-level operator, that is, there is no direct logical counterpart in the Curry–Howard isomorphism sense. In particular, its meta-level nature implies that it does not correspond to the intuitionistic conjunction. The intersection type system is naturally a type inference system (system à la Curry), but the meta-level nature of the intersection operator does not allow to easily design an equivalent typed system (system à la Church). There are many proposals in the literature to design such systems, but none of them gives an entirely satisfactory answer to the problem. In this paper, we will review the main results in the literature both on the logical interpretation of intersection types and on proposed typed lambda calculi. The core of this paper is a new proposal for a true intersection typed lambda calculus, without any meta-level notion. Namely, any typable term (in the intersection type inference) has a corresponding typed term (which is the same as the untyped term by erasing the type decorations and the typed term constructors) with the same type, and vice versa. The main idea is to introduce a relevant parallel term constructor which corresponds to the intersection type constructor, in such a way that terms in parallel share the same resources, that is, the same context of free typed variables. Three rules allow us to generate all typed terms. The first two rules, Application and Lambda-abstraction, are performed on all the components of a parallel term in a synchronized way. Finally, via the third rule of Local Renaming, once a free typed variable is bounded by lambda-abstraction, each of the terms in parallel can do its local renaming, with type refinement, of that particular resource. [Copyright &y& Elsevier]
- Published
- 2008
- Full Text
- View/download PDF
41. On the optimality of nonlinear fractional disjunctive programming problems
- Author
-
Ammar, E.E.
- Subjects
- *
MATHEMATICAL optimization , *SET theory , *LAGRANGIAN functions , *MATHEMATICAL analysis , *MAXIMA & minima , *OPERATIONS research - Abstract
Abstract: This paper is concerned with the study of necessary and sufficient optimality conditions for convex–concave fractional disjunctive programming problems for which the decision set is the union of a family of convex sets. The Lagrangian function for such problems is defined and the Kuhn–Tucker saddle and stationary points are characterized. In addition, some important theorems related to the Kuhn–Tucker problem for saddle and stationary points are established. Moreover, a general dual problem is formulated, and weak, strong and converse duality theorems are proved. Throughout the presented paper illustrative examples are given to clarify and implement the developed theory. [Copyright &y& Elsevier]
- Published
- 2007
- Full Text
- View/download PDF
42. On the 3BD-closed set
- Author
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Ji, L.
- Subjects
- *
SET theory , *ABSTRACT algebra , *NUMERICAL analysis , *MATHEMATICAL analysis - Abstract
Abstract: Let . For or , has been determined by Hanani. In this paper, we investigate the case of . It is easy to see that if , then . It is known that by Hanani and that by a previous paper of the author. We shall focus on the case of . It is proved that and . [Copyright &y& Elsevier]
- Published
- 2004
- Full Text
- View/download PDF
43. Unavoidable doubly connected large graphs
- Author
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Ding, Guoli and Chen, Peter
- Subjects
- *
RAMSEY numbers , *GRAPH theory , *SET theory , *MATHEMATICAL analysis - Abstract
A connected graph is doubly connected if its complement is also connected. The following Ramsey-type theorem is proved in this paper. There exists a function
h(n) , defined on the set of integers exceeding three, such that every doubly connected graph on at leasth(n) vertices must contain, as an induced subgraph, a doubly connected graph, which is either one of the following graphs or the complement of one of the following graphs:(1) Pn , a path onn vertices;(2) K1,ns , the graph obtained fromK1,n by subdividing an edge once;(3) K2,n&z.drule;e , the graph obtained fromK2,n by deleting an edge;(4) K2,n+ , the graph obtained fromK2,n by adding an edge between the two degree-n verticesx1 andx2 , and a pendent edge at eachxi .- Published
- 2004
- Full Text
- View/download PDF
44. Uniquely universal sets in [formula omitted] and [formula omitted].
- Author
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Krzeszowiec, Alicja
- Subjects
- *
UNIQUENESS (Mathematics) , *SET theory , *MATHEMATICAL formulas , *TOPOLOGICAL spaces , *MATHEMATICAL analysis - Abstract
Let X and Y be topological spaces. We say that X × Y satisfies the Uniquely Universal property (UU) iff there exists an open set U ⊆ X × Y such that for every open set W ⊆ Y there is a unique cross section of U with U ( x ) = { y ∈ Y : ( x , y ) ∈ U } = W . Arnold W. Miller in his paper [1] posed the following two questions: Problem 1 Does [ 0 , 1 ] × ω have UU? Problem 2 Does R × ω have UU? In this paper we present two constructions which give positive answers to both problems. [ABSTRACT FROM AUTHOR]
- Published
- 2015
- Full Text
- View/download PDF
45. Large-width bounds for learning half-spaces on distance spaces.
- Author
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Anthony, Martin and Ratsaby, Joel
- Subjects
- *
MATHEMATICAL bounds , *VECTOR spaces , *SET theory , *METRIC spaces , *MATHEMATICAL analysis - Abstract
A half-space over a distance space is a generalization of a half-space in a vector space. An important advantage of a distance space over a metric space is that the triangle inequality need not be satisfied, which makes our results potentially very useful in practice. Given two points in a set, a half-space is defined by them, as the set of all points closer to the first point than to the second. In this paper we consider the problem of learning half-spaces in any finite distance space, that is, any finite set equipped with a distance function. We make use of a notion of ‘width’ of a half-space at a given point: this is defined as the difference between the distances of the point to the two points that define the half-space. We obtain probabilistic bounds on the generalization error when learning half-spaces from samples. These bounds depend on the empirical error (the fraction of sample points on which the half-space does not achieve a large width) and on the VC-dimension of the effective class of half-spaces that have a large sample width. Unlike some previous work on learning classification over metric spaces, the bound does not involve the covering number of the space, and can therefore be tighter. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
46. The critical group of the Kneser graph on 2-subsets of an n-element set.
- Author
-
Ducey, Joshua E., Hill, Ian, and Sin, Peter
- Subjects
- *
SET theory , *GRAPH theory , *LAPLACIAN matrices , *MATHEMATICAL analysis , *MATHEMATICAL equivalence - Abstract
In this paper we compute the critical group of the Kneser graph K G ( n , 2 ) . This is equivalent to computing the Smith normal form of a Laplacian matrix of this graph. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
47. Remarks on selectively absolute star-Lindelöf spaces.
- Author
-
Song, Yan-Kui and Xuan, Wei-Feng
- Subjects
- *
MATHEMATICAL sequences , *TOPOLOGICAL spaces , *SET theory , *CARDINAL numbers , *MATHEMATICAL analysis - Abstract
A space X is selectively absolutely star-Lindelöf [1,3] if for each open cover U of X and any sequence ( D n : n ∈ ω ) of dense subsets of X , there are finite sets F n ⊆ D n ( n ∈ ω ) such that S t ( ⋃ n ∈ ω F n , U ) = X . In this paper, we continue to investigate topological properties of selectively absolute star-Lindelöf spaces, and show the following statements: (1) There exists a Tychonoff selectively a-star-Lindelöf, pseudocompact space X having a regular closed G δ subset which is not star-Lindelöf (hence not selectively a-star-Lindelöf); (2) Assuming 2 ℵ 0 = 2 ℵ 1 , there exists a normal selectively a-star-Lindelöf space X having a regular closed G δ subset which is not star-Lindelöf (hence not selectively a-star-Lindelöf); (3) An open F σ -subset of a selectively a-star-Lindelöf space is selectively a-star-Lindelöf; (4) For any cardinal κ , there exists a Tychonoff selectively a-star-Lindelöf, pseudocompact space X such that e ( X ) ≥ κ . [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
48. On deformations of the dispersionless Hirota equation.
- Author
-
Kryński, Wojciech
- Subjects
- *
GEOMETRY , *SET theory , *TWISTOR theory , *WEYL space , *MATHEMATICAL analysis - Abstract
The class of hyper-CR Einstein–Weyl structures on R 3 can be described in terms of the solutions to the dispersionless Hirota equation. In the present paper we show that simple geometric constructions on the associated twistor space lead to deformations of the Hirota equation that have been introduced recently by B. Kruglikov and A. Panasyuk. Our method produces also the hyper-CR equation and can be applied to other geometric structures related to different twistor constructions. [ABSTRACT FROM AUTHOR]
- Published
- 2018
- Full Text
- View/download PDF
49. Toughness, binding number and restricted matching extension in a graph.
- Author
-
Plummer, Michael D. and Saito, Akira
- Subjects
- *
GRAPH connectivity , *GRAPH theory , *GEOMETRIC vertices , *MATHEMATICAL analysis , *SET theory - Abstract
A connected graph G with at least 2 m + 2 n + 2 vertices is said to satisfy the property E ( m , n ) if G contains a perfect matching and for any two sets of independent edges M and N with | M | = m and | N | = n with M ∩ N = ∅ , there is a perfect matching F in G such that M ⊂ F and N ∩ F = ∅ . In particular, if G is E ( m , 0 ) , we say that G is m -extendable. One of the authors has proved that every m -tough graph of even order at least 2 m + 2 is m -extendable (Plummer, 1988). Chen (1995) and Robertshaw and Woodall (2002) gave sufficient conditions on binding number for m -extendability. In this paper, we extend these results and give lower bounds on toughness and binding number which guarantee E ( m , n ) . [ABSTRACT FROM AUTHOR]
- Published
- 2017
- Full Text
- View/download PDF
50. On fuzzy implications determined by aggregation operators
- Author
-
Ouyang, Yao
- Subjects
- *
AGGREGATION operators , *FUZZY sets , *MATHEMATICAL analysis , *SET theory , *OPERATOR theory , *ALGEBRA , *MATHEMATICS , *NUMERICAL analysis - Abstract
Abstract: Fuzzy implication operators play important roles in both theoretical and applied aspects of fuzzy sets theory. Many papers investigated various properties of different types of implications and the interrelationships among these properties. In this paper, we exploit the minimal conditions which must be satisfied for a binary operation A to generate a residual implication with additional properties. It includes several examples to clarify the situation. [Copyright &y& Elsevier]
- Published
- 2012
- Full Text
- View/download PDF
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