Intuitionistic supra fuzzy topological spaces
International Nuclear Information System (INIS)
Abbas, S.E.
2004-01-01
In this paper, We introduce an intuitionistic supra fuzzy closure space and investigate the relationship between intuitionistic supra fuzzy topological spaces and intuitionistic supra fuzzy closure spaces. Moreover, we can obtain intuitionistic supra fuzzy topological space induced by an intuitionistic fuzzy bitopological space. We study the relationship between intuitionistic supra fuzzy closure space and the intuitionistic supra fuzzy topological space induced by an intuitionistic fuzzy bitopological space
Countable Fuzzy Topological Space and Countable Fuzzy Topological Vector Space
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Apu Kumar Saha
2015-06-01
Full Text Available This paper deals with countable fuzzy topological spaces, a generalization of the notion of fuzzy topological spaces. A collection of fuzzy sets F on a universe X forms a countable fuzzy topology if in the definition of a fuzzy topology, the condition of arbitrary supremum is relaxed to countable supremum. In this generalized fuzzy structure, the continuity of fuzzy functions and some other related properties are studied. Also the class of countable fuzzy topological vector spaces as a generalization of the class of fuzzy topological vector spaces has been introduced and investigated.
Some Results on Fuzzy Soft Topological Spaces
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Cigdem Gunduz (Aras
2013-01-01
Full Text Available We introduce some important properties of fuzzy soft topological spaces. Furthermore, fuzzy soft continuous mapping, fuzzy soft open and fuzzy soft closed mappings, and fuzzy soft homeomorphism for fuzzy soft topological spaces are given and structural characteristics are discussed and studied.
Some weakly mappings on intuitionistic fuzzy topological spaces
Zhen-Guo Xu; Fu-Gui Shi
2008-01-01
In this paper, we shall introduce concepts of fuzzy semiopen set, fuzzy semiclosed set, fuzzy semiinterior, fuzzy semiclosure on intuitionistic fuzzy topological space and fuzzy open (fuzzy closed) mapping, fuzzy irresolute mapping, fuzzy irresolute open (closed) mapping, fuzzy semicontinuous mapping and fuzzy semiopen (semiclosed) mapping between two intuitionistic fuzzy topological spaces. Moreover, we shall discuss their some properties.
Fuzzy soft connected sets in fuzzy soft topological spaces II
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A. Kandil
2017-04-01
Full Text Available In this paper, we introduce some different types of fuzzy soft connected components related to the different types of fuzzy soft connectedness and based on an equivalence relation defined on the set of fuzzy soft points of X. We have investigated some very interesting properties for fuzzy soft connected components. We show that the fuzzy soft C5-connected component may be not exists and if it exists, it may not be fuzzy soft closed set. Also, we introduced some very interesting properties for fuzzy soft connected components in discrete fuzzy soft topological spaces which is a departure from the general topology.
Theta-Generalized closed sets in fuzzy topological spaces
International Nuclear Information System (INIS)
El-Shafei, M.E.; Zakari, A.
2006-01-01
In this paper we introduce the concepts of theta-generalized closed fuzzy sets and generalized fuzzy sets in topological spaces. Furthermore, generalized fuzzy sets are extended to theta-generalized fuzzy sets. Also, we introduce the concepts of fuzzy theta-generalized continuous and fuzzy theta-generalized irresolute mappings. (author)
Soft ideal topological space and mixed fuzzy soft ideal topological space
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Manash Borah
2019-01-01
Full Text Available In this paper we introduce fuzzy soft ideal and mixed fuzzy soft ideal topological spaces and some properties of this space. Also we introduce fuzzy soft $I$-open set, fuzzy soft $\\alpha$-$I$-open set, fuzzy soft pre-$I$-open set, fuzzy soft semi-$I$-open set and fuzzy soft $\\beta$-$I$-open set and discuss some of their properties.
Characterization of convergence in fuzzy topological spaces
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E. Lowen
1985-01-01
Full Text Available In a fuzzy topology on a set X, the limit of a prefilter (i.e. a filter in the lattice [0,1]X is calculated from the fuzzy closure. In this way convergence is derived from a fuzzy topology. In our paper we start with any rule lim which to any prefilter on X assigns, a function lim∈[0,1]X. We give necessary and sufficient conditions for the function →lim in order that it can be derived from a fuzzy topology.
Fuzzy Perfect Mappings and Q-Compactness in Smooth Fuzzy Topological Spaces
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C. Kalaivani
2014-03-01
Full Text Available We point out that the product of two fuzzy closed sets of smooth fuzzy topological spaces need not be fuzzy closed with respect to the the existing notion of product smooth fuzzy topology. To get this property, we introduce a new suitable product smooth fuzzy topology. We investigate whether F1×F2 and (F,H are weakly smooth fuzzy continuity whenever F1, F2, F and H are weakly smooth fuzzy continuous. Using this new product smooth fuzzy topology, we define smooth fuzzy perfect mapping and prove that composition of two smooth fuzzy perfect mappings is smooth fuzzy perfect under some additional conditions. We also introduce two new notions of compactness called Q-compactness and Q-α-compactness; and discuss the compactness of the image of a Q-compact set (Q-α-compact set under a weakly smooth fuzzy continuous function ((α,β-weakly smooth fuzzy continuous function.
Fuzzy Generalized Variational Like Inequality problems in Topological Vector Spaces
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M. K. Ahmad
2013-01-01
Full Text Available This paper is devoted to the existence of solutions for generalized variational like inequalities with fuzzy mappings in topological vector spaces by using a particular form of the generalized KKM-Theorem.
Fuzzy spaces topology change and BH thermodynamics
International Nuclear Information System (INIS)
Silva, C A S; Landim, R R
2014-01-01
What is the ultimate fate of something that falls into a black hole? From this question arises one of the most intricate problems of modern theoretical physics: the black hole information loss paradox. Bekenstein and Hawking have been shown that the entropy in a black hole is proportional to the surface area of its event horizon, which should be quantized in a multiple of the Planck area. This led G.'t Hooft and L. Susskind to propose the holographic principle which states that all the information inside the black hole can be stored on its event horizon. From this results, one may think if the solution to the information paradox could lies in the quantum properties of the black hole horizon. One way to quantize the event horizon is to see it as a fuzzy sphere, which posses a closed relation with Hopf algebras. This relation makes possible a topology change process where a fuzzy sphere splits in two others. In this work it will be shown that, if one quantize the black hole event horizon as a fuzzy sphere taking into account its quantum symmetry properties, a topology change process to black holes can be defined without break unitarity or locality, and we can obtain a possible solution to the information paradox. Moreover, we show that this model can explain the origin of the black hole entropy, and why black holes obey a generalized second law of thermodynamics
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S. Nazmul
2014-03-01
Full Text Available Notions of Lowen type fuzzy soft topological space are introduced and some of their properties are established in the present paper. Besides this, a combined structure of a fuzzy soft topological space and a fuzzy soft group, which is termed here as fuzzy soft topological group is introduced. Homomorphic images and preimages are also examined. Finally, some definitions and results on fuzzy soft set are studied.
Weak forms of continuity in I-double gradation fuzzy topological spaces.
Ghareeb, A
2012-12-01
In this paper, we introduce and characterize double fuzzy weakly preopen and double fuzzy weakly preclosed functions between I-double gradation fuzzy topological spaces and also study these functions in relation to some other types of already known functions.
On generalized fuzzy strongly semiclosed sets in fuzzy topological spaces
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Oya Bedre Ozbakir
2002-01-01
semiclosed, generalized fuzzy almost-strongly semiclosed, generalized fuzzy strongly closed, and generalized fuzzy almost-strongly closed sets. In the light of these definitions, we also define some generalizations of fuzzy continuous functions and discuss the relations between these new classes of functions and other fuzzy continuous functions.
Shah, Mazlina Muzafar; Wahab, Abdul Fatah
2017-08-01
Epilepsy disease occurs because of there is a temporary electrical disturbance in a group of brain cells (nurons). The recording of electrical signals come from the human brain which can be collected from the scalp of the head is called Electroencephalography (EEG). EEG then considered in digital format and in fuzzy form makes it a fuzzy digital space data form. The purpose of research is to identify the area (curve and surface) in fuzzy digital space affected by inside epilepsy seizure in epileptic patient's brain. The main focus for this research is to generalize fuzzy topological digital space, definition and basic operation also the properties by using digital fuzzy set and the operations. By using fuzzy digital space, the theory of digital fuzzy spline can be introduced to replace grid data that has been use previously to get better result. As a result, the flat of EEG can be fuzzy topological digital space and this type of data can be use to interpolate the digital fuzzy spline.
Weakly semi-preopen “semi-preclosed” functions in L-double fuzzy topological spaces
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A. Ghareeb
2016-07-01
Full Text Available In this paper, we introduce a new class of functions called L-double fuzzy weakly semi-preopen (semi-preclosed functions in L-double fuzzy topological spaces. Some characterizations of this class and its properties and the relationship with other classes in L-double fuzzy topological spaces are also discussed.
COMPACTNESS IN INTUITIONISTIC FUZZY MULTISET TOPOLOGY
Kunnambath, Shinoj Thekke; John, Sunil Jacob
2017-01-01
– In this paper, we discussVarious properties of Compact and Homeomorphic Intuitionistic Fuzzy Multiset Topological spacesarious properties of Compact and Homeomorphic Intuitionistic Fuzzy Multiset Topological spaces
$r$-fuzzy regular semi open sets in smooth topological spaces
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Appachi Vadivel
2017-04-01
Full Text Available In this paper, we introduce and study the concept of $r$-fuzzy regular semi open (closed sets in smooth topological spaces. By using $r$-fuzzy regular semi open (closed sets, we define a new fuzzy closure operator namely $r$-fuzzy regular semi interior (closure operator. Also, we introduce fuzzy regular semi continuous and fuzzy regular semi irresolute mappings. Moreover, we investigate the relationship among fuzzy regular semi continuous and fuzzy regular semi irresolute mappings. Finally, we have given some counter examples to show that these types of mappings are not equivalent.
Muzafar Shah, Mazlina; Fatah Wahab, Abdul
2017-09-01
There are an abnormal electric activities or irregular interference in brain of epilepsy patient. Then a sensor will be put in patient’s scalp to measure and records all electric activities in brain. The result of the records known as Electroencephalography (EEG). The EEG has been transfer to flat EEG because it’s easier to analyze. In this study, the uncertainty in flat EEG data will be considered as fuzzy digital space. The purpose of this research is to show that the flat EEG is fuzzy topological digital space. Therefore, the main focus for this research is to introduce fuzzy topological digital space concepts with their properties such as neighbourhood, interior and closure by using fuzzy set digital concept and Chang’s fuzzy topology approach. The product fuzzy topology digital also will be shown. By introduce this concept, the data in flat EEG can considering having fuzzy topology digital properties and can identify the area in fuzzy digital space that has been affected by epilepsy seizure in epileptic patient’s brain.
More on generalized b-closed sets in double fuzzy topological spaces
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Fatimah M. Mohammed
2016-02-01
Full Text Available The purpose of this paper is to introduce and study a new class of sets called (r, s-generalized fuzzy b-regular weakly closed sets which is lies between the new class of (r,s-fuzzy regular weakly closed sets and (r,s-generalized fuzzy b-closed sets in double fuzzy topological spaces. Several fundamental properties are introduced and discussed. Furthermore, the relationships between the new concepts are introduced and established with some interesting counter examples.
On rarely generalized regular fuzzy continuous functions in fuzzy topological spaces
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Appachi Vadivel
2016-11-01
Full Text Available In this paper, we introduce the concept of rarely generalized regular fuzzy continuous functions in the sense of A.P. Sostak's and Ramadan is introduced. Some interesting properties and characterizations of them are investigated. Also, some applications to fuzzy compact spaces are established.
Spatial object modeling in fuzzy topological spaces: with applications to land cover change
Tang, Xinming; Tang, Xinming
2004-01-01
The central topic of this thesis focuses on the accommodation of fuzzy spatial objects in a GIS. Several issues are discussed theoretically and practically, including the definition of fuzzy spatial objects, the topological relations between them, the modeling of fuzzy spatial objects, the
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Anahid Kamali
2015-12-01
Full Text Available In this paper, a new class of fuzzy sets called fuzzy strongly ${{g}^{*}}$-closed sets is introduced and its properties are investigated. Moreover, we study some more properties of this type of closed spaces.
Anahid Kamali; Hamid Moradi; Balwinder Singh
2015-01-01
In this paper, a new class of fuzzy sets called fuzzy strongly ${{g}^{*}}$-closed sets is introduced and its properties are investigated. Moreover, we study some more properties of this type of closed spaces.
Some Properties of Fuzzy Soft Proximity Spaces
Demir, İzzettin; Özbakır, Oya Bedre
2015-01-01
We study the fuzzy soft proximity spaces in Katsaras's sense. First, we show how a fuzzy soft topology is derived from a fuzzy soft proximity. Also, we define the notion of fuzzy soft δ-neighborhood in the fuzzy soft proximity space which offers an alternative approach to the study of fuzzy soft proximity spaces. Later, we obtain the initial fuzzy soft proximity determined by a family of fuzzy soft proximities. Finally, we investigate relationship between fuzzy soft proximities and proximities. PMID:25793224
A study of frontier and semifrontier in intuitionistic fuzzy topological spaces.
Kharal, Athar
2014-01-01
Notions of frontier and semifrontier in intuitionistic fuzzy topology have been studied and several of their properties, characterizations, and examples established. Many counter-examples have been presented to point divergences between the IF topology and its classical form. The paper also presents an open problem and one of its weaker forms.
Intuitionistic fuzzy proximity spaces
Eun Pyo Lee; Seok Jong Lee
2004-01-01
We introduce the concept of the intuitionistic fuzzy proximity as a generalization of fuzzy proximity, and investigate its properties. Also we investigate the relationship among intuitionistic fuzzy proximity and fuzzy proximity, and intuitionistic fuzzy topology.
On topological structures of fuzzy parametrized soft sets.
Atmaca, Serkan; Zorlutuna, Idris
2014-01-01
We introduce the topological structure of fuzzy parametrized soft sets and fuzzy parametrized soft mappings. We define the notion of quasi-coincidence for fuzzy parametrized soft sets and investigated its basic properties. We study the closure, interior, base, continuity, and compactness and properties of these concepts in fuzzy parametrized soft topological spaces.
On fuzzy almost continuous convergence in fuzzy function spaces
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A.I. Aggour
2013-10-01
Full Text Available In this paper, we study the fuzzy almost continuous convergence of fuzzy nets on the set FAC(X, Y of all fuzzy almost continuous functions of a fuzzy topological space X into another Y. Also, we introduce the notions of fuzzy splitting and fuzzy jointly continuous topologies on the set FAC(X, Y and study some of its basic properties.
Compactness in fuzzy function spaces
African Journals Online (AJOL)
In [3] we defined a notion of compactness in FCS, the category of fuzzy convergence spaces as defined by Lowen/Lowen/Wuyts [8]. In their paper the latter also introduced a fuzzy convergence structure c-lim for fuzzy function spaces thus proving that FCS is a topological quasitopos. In this paper we start the investigation of ...
Combinational reasoning of quantitative fuzzy topological relations for simple fuzzy regions.
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Bo Liu
Full Text Available In recent years, formalization and reasoning of topological relations have become a hot topic as a means to generate knowledge about the relations between spatial objects at the conceptual and geometrical levels. These mechanisms have been widely used in spatial data query, spatial data mining, evaluation of equivalence and similarity in a spatial scene, as well as for consistency assessment of the topological relations of multi-resolution spatial databases. The concept of computational fuzzy topological space is applied to simple fuzzy regions to efficiently and more accurately solve fuzzy topological relations. Thus, extending the existing research and improving upon the previous work, this paper presents a new method to describe fuzzy topological relations between simple spatial regions in Geographic Information Sciences (GIS and Artificial Intelligence (AI. Firstly, we propose a new definition for simple fuzzy line segments and simple fuzzy regions based on the computational fuzzy topology. And then, based on the new definitions, we also propose a new combinational reasoning method to compute the topological relations between simple fuzzy regions, moreover, this study has discovered that there are (1 23 different topological relations between a simple crisp region and a simple fuzzy region; (2 152 different topological relations between two simple fuzzy regions. In the end, we have discussed some examples to demonstrate the validity of the new method, through comparisons with existing fuzzy models, we showed that the proposed method can compute more than the existing models, as it is more expressive than the existing fuzzy models.
Combinational Reasoning of Quantitative Fuzzy Topological Relations for Simple Fuzzy Regions
Liu, Bo; Li, Dajun; Xia, Yuanping; Ruan, Jian; Xu, Lili; Wu, Huanyi
2015-01-01
In recent years, formalization and reasoning of topological relations have become a hot topic as a means to generate knowledge about the relations between spatial objects at the conceptual and geometrical levels. These mechanisms have been widely used in spatial data query, spatial data mining, evaluation of equivalence and similarity in a spatial scene, as well as for consistency assessment of the topological relations of multi-resolution spatial databases. The concept of computational fuzzy topological space is applied to simple fuzzy regions to efficiently and more accurately solve fuzzy topological relations. Thus, extending the existing research and improving upon the previous work, this paper presents a new method to describe fuzzy topological relations between simple spatial regions in Geographic Information Sciences (GIS) and Artificial Intelligence (AI). Firstly, we propose a new definition for simple fuzzy line segments and simple fuzzy regions based on the computational fuzzy topology. And then, based on the new definitions, we also propose a new combinational reasoning method to compute the topological relations between simple fuzzy regions, moreover, this study has discovered that there are (1) 23 different topological relations between a simple crisp region and a simple fuzzy region; (2) 152 different topological relations between two simple fuzzy regions. In the end, we have discussed some examples to demonstrate the validity of the new method, through comparisons with existing fuzzy models, we showed that the proposed method can compute more than the existing models, as it is more expressive than the existing fuzzy models. PMID:25775452
The Countabilities of Soft Topological Spaces
Weijian Rong
2012-01-01
Soft topological spaces are considered as mathematical tools for dealing with uncertainties, and a fuzzy topological space is a special case of the soft topological space. The purpose of this paper is to study soft topological spaces. We introduce some new concepts in soft topological spaces such as soft first-countable spaces, soft second-countable spaces and soft separable spaces, and some basic properties of these concepts are explored.
Intuitionistic fuzzy metric spaces
International Nuclear Information System (INIS)
Park, Jin Han
2004-01-01
Using the idea of intuitionistic fuzzy set due to Atanassov [Intuitionistic fuzzy sets. in: V. Sgurev (Ed.), VII ITKR's Session, Sofia June, 1983; Fuzzy Sets Syst. 20 (1986) 87], we define the notion of intuitionistic fuzzy metric spaces as a natural generalization of fuzzy metric spaces due to George and Veeramani [Fuzzy Sets Syst. 64 (1994) 395] and prove some known results of metric spaces including Baire's theorem and the Uniform limit theorem for intuitionistic fuzzy metric spaces
Fuzzy Λ gX r -sets and generalization of closed sets in generalized fuzzy topological spaces
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Jayasree Chakraborty
2017-06-01
Full Text Available The aim of this paper is to introduce fuzzy ΛgXr-set and to study some of its generalized forms. The structure constituted by fuzzy Λ g X r -set is also included in the treatise. Moreover we define generalized fuzzy gX -closed set and fuzzy Λ g X r -closed set, which are the weaker forms of fuzzy gX -closed set. The above two weaker forms are independent to each other but jointly they imply fuzzy gX -closed set. Finally, in addition, as the application of fuzzy Λ g X r -closed set, we study fuzzy (Λ , g X r Y g - continuity and fuzzy (Λ , gf g X r X Y g g -continuity and a few of their properties. In general, fuzzy contra ( , X Y g g -continuity does not imply fuzzy ( , X Y g g -continuity, but this paper provides one condition under which the fact is true.
(r,s)-Fuzzy F-open sets and (r,s)-fuzzy F-closed spaces
International Nuclear Information System (INIS)
Azab Abd-Allah, M.; El-Saady, Kamal; Ghareeb, A.
2009-01-01
In this paper, we introduce the concepts of (r,s)-fuzzy F-open and (r,s)-fuzzy F-closed sets in double fuzzy topological spaces. We used them to explain the notions of (r,s)-fuzzy F-closed spaces. Also, we give some characterization of (r,s)-fuzzy F-closeness in terms of fuzzy filterbasis.
Some fixed point theorems in fuzzy reflexive Banach spaces
International Nuclear Information System (INIS)
Sadeqi, I.; Solaty kia, F.
2009-01-01
In this paper, we first show that there are some gaps in the fixed point theorems for fuzzy non-expansive mappings which are proved by Bag and Samanta, in [Bag T, Samanta SK. Fixed point theorems on fuzzy normed linear spaces. Inf Sci 2006;176:2910-31; Bag T, Samanta SK. Some fixed point theorems in fuzzy normed linear spaces. Inform Sci 2007;177(3):3271-89]. By introducing the notion of fuzzy and α- fuzzy reflexive Banach spaces, we obtain some results which help us to establish the correct version of fuzzy fixed point theorems. Second, by applying Theorem 3.3 of Sadeqi and Solati kia [Sadeqi I, Solati kia F. Fuzzy normed linear space and it's topological structure. Chaos, Solitons and Fractals, in press] which says that any fuzzy normed linear space is also a topological vector space, we show that all topological version of fixed point theorems do hold in fuzzy normed linear spaces.
Fact or Fuzzy? On the Topology of Space Perception in Digital Architeture
DEFF Research Database (Denmark)
Markussen, Thomas
2008-01-01
The advent of new digital design techniques and thereby the possibility to work more intensively with topology is believed to have shaken the conceptual grounds in architecture. In other words, that we are facing a paradigm shift. In one of his highly influential contributions to architectural th...... shall shed light on how neuroscience may and may not inform architectural theory....
Some Additions to the Fuzzy Convergent and Fuzzy Bounded Sequence Spaces of Fuzzy Numbers
Şengönül, M.; Zararsız, Z.
2011-01-01
Some properties of the fuzzy convergence and fuzzy boundedness of a sequence of fuzzy numbers were studied in Choi (1996). In this paper, we have consider, some important problems on these spaces and shown that these spaces are fuzzy complete module spaces. Also, the fuzzy α-, fuzzy β-, and fuzzy γ-duals of the fuzzy module spaces of fuzzy numbers have been computeded, and some matrix transformations are given.
Observational modeling of topological spaces
International Nuclear Information System (INIS)
Molaei, M.R.
2009-01-01
In this paper a model for a multi-dimensional observer by using of the fuzzy theory is presented. Relative form of Tychonoff theorem is proved. The notion of topological entropy is extended. The persistence of relative topological entropy under relative conjugate relation is proved.
(r, s-(τ12,τ12*-θ-Generalized double fuzzy closed sets in bitopological spaces
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E. El-Sanousy
2016-10-01
Full Text Available In this paper, we introduce the notion of (r, s-(i, j-θ-generalized double fuzzy closed sets in double fuzzy bitopological spaces. A new θ-double fuzzy closure C12θ on double fuzzy bitopological spaces by using double supra fuzzy topological spaces are defined. Furthermore, generalized double fuzzy θ-continuous (resp. irresolute and double fuzzy strongly θ-continuous mappings are introduced and some of their properties studied.
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Halis Aygün
2008-01-01
Full Text Available We introduce definitions of fuzzy inverse compactness, fuzzy inverse countable compactness, and fuzzy inverse Lindelöfness on arbitrary -fuzzy sets in -fuzzy topological spaces. We prove that the proposed definitions are good extensions of the corresponding concepts in ordinary topology and obtain different characterizations of fuzzy inverse compactness.
Introduction to generalized topological spaces
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Irina Zvina
2011-04-01
Full Text Available We introduce the notion of generalized topological space (gt-space. Generalized topology of gt-space has the structure of frame and is closed under arbitrary unions and finite intersections modulo small subsets. The family of small subsets of a gt-space forms an ideal that is compatible with the generalized topology. To support the definition of gt-space we prove the frame embedding modulo compatible ideal theorem. Weprovide some examples of gt-spaces and study key topological notions (continuity, separation axioms, cardinal invariants in terms of generalized spaces.
Wθg-Closed and Wδg-Closed in [0,1]-Topological Spaces
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M. E. El-Shafei
2011-01-01
Full Text Available We investigate various classes of generalized closed fuzzy sets in [0,1]-topological spaces, namely, Wθg-closed fuzzy sets and Wδg-closed fuzzy sets. Also, we introduce a new separation axiom FT3/4∗ of the [0,1]-topological spaces, and we prove that every FT3/4∗-space is a FT3/4-space. Furthermore, we using the new generalized closed fuzzy sets to construct new types of fuzzy mappings.
Fuzzy Geometry of Commutative Spaces and Quantum Dynamics
International Nuclear Information System (INIS)
Mayburov, S.N.
2016-01-01
Fuzzy topology and geometry considered as the possible mathematical framework for novel quantum-mechanical formalism. In such formalism the states of massive particle m correspond to the elements of fuzzy manifold called fuzzy points. Due to the manifold weak topology, m space coordinate x acquires principal uncertainty σ x and described by the positive, normalized density w(r-vector , t) in 3-dimensional case. It’s shown that the evolution of m state on such 3-dimensional manifold corresponds to Shroedinger dynamics of massive quantum particle
On Neutrosophic Soft Topological Space
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Tuhin Bera
2018-03-01
Full Text Available In this paper, the concept of connectedness and compactness on neutrosophic soft topological space have been introduced along with the investigation of their several characteristics. Some related theorems have been established also. Then, the notion of neutrosophic soft continuous mapping on a neutrosophic soft topological space and it’s properties are developed here.
On the intuitionistic fuzzy inner product spaces
International Nuclear Information System (INIS)
Goudarzi, M.; Vaezpour, S.M.; Saadati, R.
2009-01-01
In this paper, the definition of intuitionistic fuzzy inner product is given. By virtue of this definition, some convergence theorems, Schwarts inequality and the orthogonal concept for intuitionistic fuzzy inner product spaces are established and introduced. Moreover the relationship between this kind of spaces and intuitionistic fuzzy normed spaces is considered.
Time-Space Topology Optimization
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard
2008-01-01
A method for space-time topology optimization is outlined. The space-time optimization strategy produces structures with optimized material distributions that vary in space and in time. The method is demonstrated for one-dimensional wave propagation in an elastic bar that has a time-dependent Young...
Fuzzy polynucleotide spaces and metrics.
Nieto, Juan J; Torres, A; Georgiou, D N; Karakasidis, T E
2006-04-01
The study of genetic sequences is of great importance in biology and medicine. Mathematics is playing an important role in the study of genetic sequences and, generally, in bioinformatics. In this paper, we extend the work concerning the Fuzzy Polynucleotide Space (FPS) introduced in Torres, A., Nieto, J.J., 2003. The fuzzy polynucleotide Space: Basic properties. Bioinformatics 19(5); 587-592 and Nieto, J.J., Torres, A., Vazquez-Trasande, M.M. 2003. A metric space to study differences between polynucleotides. Appl. Math. Lett. 27:1289-1294: by studying distances between nucleotides and some complete genomes using several metrics. We also present new results concerning the notions of similarity, difference and equality between polynucleotides. The results are encouraging since they demonstrate how the notions of distance and similarity between polynucleotides in the FPS can be employed in the analysis of genetic material.
Topological vector spaces and distributions
Horvath, John
2012-01-01
""The most readable introduction to the theory of vector spaces available in English and possibly any other language.""-J. L. B. Cooper, MathSciNet ReviewMathematically rigorous but user-friendly, this classic treatise discusses major modern contributions to the field of topological vector spaces. The self-contained treatment includes complete proofs for all necessary results from algebra and topology. Suitable for undergraduate mathematics majors with a background in advanced calculus, this volume will also assist professional mathematicians, physicists, and engineers.The precise exposition o
Time-Space Topology Optimization
DEFF Research Database (Denmark)
Jensen, Jakob Søndergaard
2008-01-01
A method for space-time topology optimization is outlined. The space-time optimization strategy produces structures with optimized material distributions that vary in space and in time. The method is demonstrated for one-dimensional wave propagation in an elastic bar that has a time-dependent Young......’s modulus and is subjected to a transient load. In the example an optimized dynamic structure is demonstrated that compresses a propagating Gauss pulse....
Constructive topology of bishop spaces
Petrakis, Iosif
2015-01-01
The theory of Bishop spaces (TBS) is so far the least developed approach to constructive topology with points. Bishop introduced function spaces, here called Bishop spaces, in 1967, without really exploring them, and in 2012 Bridges revived the subject. In this Thesis we develop TBS. Instead of having a common space-structure on a set X and R, where R denotes the set of constructive reals, that determines a posteriori which functions of type X -> R are continuous with respect to it, wi...
International Nuclear Information System (INIS)
Abbas, S.E.
2004-01-01
In this paper, fuzzy SP-irresolute, fuzzy SP-irresolute open and fuzzy SP-irresolute closed functions between fuzzy topological spaces in Sostak sense are defined. Their properties and the relationships between these functions and other functions introduced previously are investigated. Next fuzzy SP-connectedness is introduced and studied with the help of r-fuzzy strongly preopen sets
Neutrosophic Crisp Sets & Neutrosophic Crisp Topological Spaces
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A. A. Salama
2014-03-01
Full Text Available In this paper, we generalize the crisp topological spaces to the notion of neutrosophic crisp topological space, and we construct the basic concepts of the neutrosophic crisp topology. In addition to these, we introduce the definitions of neutrosophic crisp continuous function and neutrosophic crisp compact spaces. Finally, some characterizations concerning neutrosophic crisp compact spaces are presented and one obtains several properties. Possible application to GIS topology rules are touched upon.
Topology with applications topological spaces via near and far
Naimpally, Somashekhar A
2013-01-01
The principal aim of this book is to introduce topology and its many applications viewed within a framework that includes a consideration of compactness, completeness, continuity, filters, function spaces, grills, clusters and bunches, hyperspace topologies, initial and final structures, metric spaces, metrization, nets, proximal continuity, proximity spaces, separation axioms, and uniform spaces. This book provides a complete framework for the study of topology with a variety of applications in science and engineering that include camouflage filters, classification, digital image processing, forgery detection, Hausdorff raster spaces, image analysis, microscopy, paleontology, pattern recognition, population dynamics, stem cell biology, topological psychology, and visual merchandising. It is the first complete presentation on topology with applications considered in the context of proximity spaces, and the nearness and remoteness of sets of objects. A novel feature throughout this book is the use of near and...
Implicit Functions from Topological Vector Spaces to Banach Spaces
Glockner, Helge
2003-01-01
We prove implicit function theorems for mappings on topological vector spaces over valued fields. In the real and complex cases, we obtain implicit function theorems for mappings from arbitrary (not necessarily locally convex) topological vector spaces to Banach spaces.
Invertibility in L-Topological Spaces
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Anjaly Jose
2014-03-01
Full Text Available In this paper, we extend the concept of invertibility to L-topological spaces and delineate its properties. Then, we study further completely invertible L-topological spaces and introduce two types of invertible L-topologies based on the inverting maps, studying their sums, subspaces and simple extensions.
Dimensional Reduction over Fuzzy Coset Spaces
Aschieri, P; Manousselis, P; Madore, J
2004-01-01
We examine gauge theories on Minkowski space-time times fuzzy coset spaces. This means that the extra space dimensions instead of being a continuous coset space S/R are a corresponding finite matrix approximation. The gauge theory defined on this non-commutative setup is reduced to four dimensions and the rules of the corresponding dimensional reduction are established. We investigate in particular the case of the fuzzy sphere including the dimensional reduction of fermion fields.
Dimensional Reduction over Fuzzy Coset Spaces
Aschieri, P.; Madore, J.; Manousselis, P.; Zoupanos, G.
2004-04-01
We examine gauge theories on Minkowski space-time times fuzzy coset spaces. This means that the extra space dimensions instead of being a continuous coset space S/R are a corresponding finite matrix approximation. The gauge theory defined on this non-commutative setup is reduced to four dimensions and the rules of the corresponding dimensional reduction are established. We investigate in particular the case of the fuzzy sphere including the dimensional reduction of fermion fields.
Algebraic topology of finite topological spaces and applications
Barmak, Jonathan A
2011-01-01
This volume deals with the theory of finite topological spaces and its relationship with the homotopy and simple homotopy theory of polyhedra. The interaction between their intrinsic combinatorial and topological structures makes finite spaces a useful tool for studying problems in Topology, Algebra and Geometry from a new perspective. In particular, the methods developed in this manuscript are used to study Quillen’s conjecture on the poset of p-subgroups of a finite group and the Andrews-Curtis conjecture on the 3-deformability of contractible two-dimensional complexes. This self-contained work constitutes the first detailed exposition on the algebraic topology of finite spaces. It is intended for topologists and combinatorialists, but it is also recommended for advanced undergraduate students and graduate students with a modest knowledge of Algebraic Topology.
Contraction theorems in fuzzy metric space
International Nuclear Information System (INIS)
Farnoosh, R.; Aghajani, A.; Azhdari, P.
2009-01-01
In this paper, the results on fuzzy contractive mapping proposed by Dorel Mihet will be proved for B-contraction and C-contraction in the case of George and Veeramani fuzzy metric space. The existence of fixed point with weaker conditions will be proved; that is, instead of the convergence of subsequence, p-convergence of subsequence is used.
Topological Schemas of Memory Spaces
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Andrey Babichev
2018-04-01
Full Text Available Hippocampal cognitive map—a neuronal representation of the spatial environment—is widely discussed in the computational neuroscience literature for decades. However, more recent studies point out that hippocampus plays a major role in producing yet another cognitive framework—the memory space—that incorporates not only spatial, but also non-spatial memories. Unlike the cognitive maps, the memory spaces, broadly understood as “networks of interconnections among the representations of events,” have not yet been studied from a theoretical perspective. Here we propose a mathematical approach that allows modeling memory spaces constructively, as epiphenomena of neuronal spiking activity and thus to interlink several important notions of cognitive neurophysiology. First, we suggest that memory spaces have a topological nature—a hypothesis that allows treating both spatial and non-spatial aspects of hippocampal function on equal footing. We then model the hippocampal memory spaces in different environments and demonstrate that the resulting constructions naturally incorporate the corresponding cognitive maps and provide a wider context for interpreting spatial information. Lastly, we propose a formal description of the memory consolidation process that connects memory spaces to the Morris' cognitive schemas-heuristic representations of the acquired memories, used to explain the dynamics of learning and memory consolidation in a given environment. The proposed approach allows evaluating these constructs as the most compact representations of the memory space's structure.
On Fuzzy -Contractive Mappings in Fuzzy Metric Spaces
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Miheţ Dorel
2007-01-01
Full Text Available We answer into affirmative an open question raised by A. Razani in 2005. An essential role in our proofs is played by the separation axiom in the definition of a fuzzy metric space in the sense of George and Veeramani.
Finite Topological Spaces as a Pedagogical Tool
Helmstutler, Randall D.; Higginbottom, Ryan S.
2012-01-01
We propose the use of finite topological spaces as examples in a point-set topology class especially suited to help students transition into abstract mathematics. We describe how carefully chosen examples involving finite spaces may be used to reinforce concepts, highlight pathologies, and develop students' non-Euclidean intuition. We end with a…
On type-2 m-topological spaces
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Sk. Nazmul
2017-12-01
Full Text Available In the present paper, we define a notion of an m2-topological space by introducing a count of openness of a multiset (mset in short and study the properties of m2-subspaces, mgp-maps etc. Decomposition theorems involving m-topologies and m2-topologies are established. The behaviour of the functional image and functional preimage of an m2-topologies, the continuity of the identity mapping and a constant mapping in m2-topologies are also examined.
A Category of L-Fuzzy Convergence Spaces | Jäger | Quaestiones ...
African Journals Online (AJOL)
In this paper we take convergence of stratified L-filters as a primitive notion and construct in this way a Cartesian closed category, which contains the category of stratified L-topological spaces as reflexive subcategory. The class of spaces with non-idempotent stratified fuzzy interior operator is characterized as subclass of ...
On two examples in linear topological spaces
International Nuclear Information System (INIS)
Iyahen, S.O.
1985-11-01
This note first gives examples of B-complete linear topological spaces, and shows that neither the closed graph theorem nor the open mapping theorem holds for linear mappings from such a space to itself. It then looks at Hausdorff linear topological spaces for which coarser Hausdorff linear topologies can be extended from hyperplanes. For B-complete spaces, those which are barrelled necessarily have countable dimension, and conversely. The paper had been motivated by two questions arising in earlier studies related to the closed graph and open mapping theorems; answers to these questions are contained therein. (author)
Redundancy of multiset topological spaces
Ghareeb, A.
2016-01-01
In this paper, we prove the redundancies of multiset topologies. It is shown that there is a complement preserving isomorphism between $(P^\\star(U),\\sqsubseteq)$ and $(\\mathcal{P}(X\\times\\mathbb{N}),\\subseteq)$. It therefore follows that multiset topologies are superfluous and unnecessary in the theoretical view point.
Modified intuitionistic fuzzy metric spaces and some fixed point theorems
International Nuclear Information System (INIS)
Saadati, R.; Sedghi, S.; Shobe, N.
2008-01-01
Since the intuitionistic fuzzy metric space has extra conditions (see [Gregori V, Romaguera S, Veereamani P. A note on intuitionistic fuzzy metric spaces. Chaos, Solitons and Fractals 2006;28:902-5]). In this paper, we consider modified intuitionistic fuzzy metric spaces and prove some fixed point theorems in these spaces. All the results presented in this paper are new
The Teaching of Mathematics: Universal Topological Spaces.
Magill, K. D., Jr.
1988-01-01
The problem of finding all topological spaces is considered. Two characterizations are presented whose proofs involve only elementary notions and techniques. The problem is appropriate for students in a beginning topology course after they have been presented with the Embedding Lemma. (DC)
Modern methods in topological vector spaces
Wilansky, Albert
2013-01-01
Designed for a one-year course in topological vector spaces, this text is geared toward advanced undergraduates and beginning graduate students of mathematics. The subjects involve properties employed by researchers in classical analysis, differential and integral equations, distributions, summability, and classical Banach and Frechét spaces. Optional problems with hints and references introduce non-locally convex spaces, Köthe-Toeplitz spaces, Banach algebra, sequentially barrelled spaces, and norming subspaces.Extensive introductory chapters cover metric ideas, Banach space, topological vect
On Convergence of Fixed Points in Fuzzy Metric Spaces
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Yonghong Shen
2013-01-01
Full Text Available We mainly focus on the convergence of the sequence of fixed points for some different sequences of contraction mappings or fuzzy metrics in fuzzy metric spaces. Our results provide a novel research direction for fixed point theory in fuzzy metric spaces as well as a substantial extension of several important results from classical metric spaces.
Intuitionistic fuzzy 2-metric space and its completion
International Nuclear Information System (INIS)
Mursaleen, M.; Lohani, Q.M. Danish; Mohiuddine, S.A.
2009-01-01
Recently, Mursaleen and Lohani [Mursaleen M, Lohani Danish. Intuitionistic fuzzy 2-normed space and some related concepts. Chaos, Solitons and Fractals (2008), doi:10.1016/j.chaos.2008.11.006] have introduced the concept of intuitionistic fuzzy 2-normed space. In this paper, we introduce the concept of intuitionistic fuzzy 2-metric space and study its completion.
Topological entropy of continuous functions on topological spaces
International Nuclear Information System (INIS)
Liu Lei; Wang Yangeng; Wei Guo
2009-01-01
Adler, Konheim and McAndrew introduced the concept of topological entropy of a continuous mapping for compact dynamical systems. Bowen generalized the concept to non-compact metric spaces, but Walters indicated that Bowen's entropy is metric-dependent. We propose a new definition of topological entropy for continuous mappings on arbitrary topological spaces (compactness, metrizability, even axioms of separation not necessarily required), investigate fundamental properties of the new entropy, and compare the new entropy with the existing ones. The defined entropy generates that of Adler, Konheim and McAndrew and is metric-independent for metrizable spaces. Yet, it holds various basic properties of Adler, Konheim and McAndrew's entropy, e.g., the entropy of a subsystem is bounded by that of the original system, topologically conjugated systems have a same entropy, the entropy of the induced hyperspace system is larger than or equal to that of the original system, and in particular this new entropy coincides with Adler, Konheim and McAndrew's entropy for compact systems
Functional Equations in Fuzzy Banach Spaces
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M. Eshaghi Gordji
2012-01-01
generalized Hyers-Ulam stability of the following additive-quadratic functional equation f(x+ky+f(x−ky=f(x+y+f(x−y+(2(k+1/kf(ky−2(k+1f(y for fixed integers k with k≠0,±1 in fuzzy Banach spaces.
Decomposition of fuzzy continuity and fuzzy ideal continuity via fuzzy idealization
International Nuclear Information System (INIS)
Zahran, A.M.; Abbas, S.E.; Abd El-baki, S.A.; Saber, Y.M.
2009-01-01
Recently, El-Naschie has shown that the notion of fuzzy topology may be relevant to quantum paretical physics in connection with string theory and E-infinity space time theory. In this paper, we study the concepts of r-fuzzy semi-I-open, r-fuzzy pre-I-open, r-fuzzy α-I-open and r-fuzzy β-I-open sets, which is properly placed between r-fuzzy openness and r-fuzzy α-I-openness (r-fuzzy pre-I-openness) sets regardless the fuzzy ideal topological space in Sostak sense. Moreover, we give a decomposition of fuzzy continuity, fuzzy ideal continuity and fuzzy ideal α-continuity, and obtain several characterization and some properties of these functions. Also, we investigate their relationship with other types of function.
State space Newton's method for topology optimization
DEFF Research Database (Denmark)
Evgrafov, Anton
2014-01-01
We introduce a new algorithm for solving certain classes of topology optimization problems, which enjoys fast local convergence normally achieved by the full space methods while working in a smaller reduced space. The computational complexity of Newton’s direction finding subproblem in the algori......We introduce a new algorithm for solving certain classes of topology optimization problems, which enjoys fast local convergence normally achieved by the full space methods while working in a smaller reduced space. The computational complexity of Newton’s direction finding subproblem...
Topological methods in Euclidean spaces
Naber, Gregory L
2000-01-01
Extensive development of a number of topics central to topology, including elementary combinatorial techniques, Sperner's Lemma, the Brouwer Fixed Point Theorem, homotopy theory and the fundamental group, simplicial homology theory, the Hopf Trace Theorem, the Lefschetz Fixed Point Theorem, the Stone-Weierstrass Theorem, and Morse functions. Includes new section of solutions to selected problems.
Some observations on a fuzzy metric space
Energy Technology Data Exchange (ETDEWEB)
Gregori, V.
2017-07-01
Let $(X,d)$ be a metric space. In this paper we provide some observations about the fuzzy metric space in the sense of Kramosil and Michalek $(Y,N,/wedge)$, where $Y$ is the set of non-negative real numbers $[0,/infty[$ and $N(x,y,t)=1$ if $d(x,y)/leq t$ and $N(x,y,t)=0$ if $d(x,y)/geq t$. (Author)
Fuzzy Dodecahedron topology and E-infinity spacetime as a model for quantum physics
International Nuclear Information System (INIS)
El Naschie, M.S.
2006-01-01
The geometry of classical platonic solids and their generalization to four-dimensional fuzzy polytopes are considered. Subsequently it is shown how the so obtained relationships and the associated symmetry groups are related to high energy particle physics. In particular the topology of a fuzzy Dodecahedron and four-dimensional polytopes are used to give information about the elementary particles content of the standard model of high energy physics
Elements of mathematics topological vector spaces
Bourbaki, Nicolas
2003-01-01
This is a softcover reprint of the English translation of 1987 of the second edition of Bourbaki's Espaces Vectoriels Topologiques (1981). This second edition is a brand new book and completely supersedes the original version of nearly 30 years ago. But a lot of the material has been rearranged, rewritten, or replaced by a more up-to-date exposition, and a good deal of new material has been incorporated in this book, all reflecting the progress made in the field during the last three decades. Table of Contents. Chapter I: Topological vector spaces over a valued field. Chapter II: Convex sets and locally convex spaces. Chapter III: Spaces of continuous linear mappings. Chapter IV: Duality in topological vector spaces. Chapter V: Hilbert spaces (elementary theory). Finally, there are the usual "historical note", bibliography, index of notation, index of terminology, and a list of some important properties of Banach spaces. (Based on Math Reviews, 1983).
Mean value theorem in topological vector spaces
International Nuclear Information System (INIS)
Khan, L.A.
1994-08-01
The aim of this note is to give shorter proofs of the mean value theorem, the mean value inequality, and the mean value inclusion for the class of Gateaux differentiable functions having values in a topological vector space. (author). 6 refs
Common fixed point theorems for fuzzy mappings in metric space under {phi}-contraction condition
Energy Technology Data Exchange (ETDEWEB)
Abu-Donia, H.M. [Department of Mathematics, Faculty of Science, Zagazig University, Zagazig (Egypt)
2007-10-15
Some common fixed point theorems for multi-valued mappings under {phi}-contraction condition have been studied by Rashwan [Rashwan RA, Ahmed MA. Fixed points for {phi}-contraction type multivalued mappings. J Indian Acad Math 1995;17(2):194-204]. Butnariu [Butnariu D. Fixed point for fuzzy mapping. Fuzzy Sets Syst 1982;7:191-207] and Helipern [Hilpern S. Fuzzy mapping and fixed point theorem. J Math Anal Appl 1981;83:566-9] also, discussed some fixed point theorems for fuzzy mappings in the category of metric spaces. In this paper, we discussed some common fixed point theorems for fuzzy mappings in metric space under {phi}-contraction condition. Our investigation are related to the fuzzy form of Hausdorff metric which is a basic tool for computing Hausdorff dimensions. These dimensions help in understanding {epsilon} {sup {infinity}}-space [El-Naschie MS. On the unification of the fundamental forces and complex time in the {epsilon} {sup {infinity}}-space. Chaos, Solitons and Fractals 2000;11:1149-62] and are used in high energy physics [El-Naschie MS. Wild topology hyperbolic geometry and fusion algebra of high energy particle physics. Chaos, Solitons and Fractals 2002;13:1935-45].
Common fixed point theorems for fuzzy mappings in metric space under φ-contraction condition
International Nuclear Information System (INIS)
Abu-Donia, H.M.
2007-01-01
Some common fixed point theorems for multi-valued mappings under φ-contraction condition have been studied by Rashwan [Rashwan RA, Ahmed MA. Fixed points for φ-contraction type multivalued mappings. J Indian Acad Math 1995;17(2):194-204]. Butnariu [Butnariu D. Fixed point for fuzzy mapping. Fuzzy Sets Syst 1982;7:191-207] and Helipern [Hilpern S. Fuzzy mapping and fixed point theorem. J Math Anal Appl 1981;83:566-9] also, discussed some fixed point theorems for fuzzy mappings in the category of metric spaces. In this paper, we discussed some common fixed point theorems for fuzzy mappings in metric space under φ-contraction condition. Our investigation are related to the fuzzy form of Hausdorff metric which is a basic tool for computing Hausdorff dimensions. These dimensions help in understanding ε ∞ -space [El-Naschie MS. On the unification of the fundamental forces and complex time in the ε ∞ -space. Chaos, Solitons and Fractals 2000;11:1149-62] and are used in high energy physics [El-Naschie MS. Wild topology hyperbolic geometry and fusion algebra of high energy particle physics. Chaos, Solitons and Fractals 2002;13:1935-45
Derived length for arbitrary topological spaces
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A. J. Jayanthan
1992-01-01
Full Text Available The notion of derived length is as old as that of ordinal numbers itself. It is also known as the Cantor-Bendixon length. It is defined only for dispersed (that is scattered spaces. In this paper this notion has been extended in a natural way for all topological spaces such that all its pleasing properties are retained. In this process we solve a problem posed by V. Kannan. ([1] Page 158.
On topological spaces whose topology is induced by a binary relation
African Journals Online (AJOL)
We study the problem of characterizing which topologies on a nonemptybset are generated by a binary relation by means of its lower and upper contour sets. In this direction we consider different classical categories of topological spaces whose topology is defined by at least one binary relation. Given a topology defined by ...
C- sets and decomposition of continuity in generalized topological spaces
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R. Jamunarani
2013-12-01
some decomposition of continuity between generalized topological spaces. Moreover, we prove that some of the results established in [3] are already established results in topological spaces. Generalization of this results are also given.
Alabiso, Carlo
2015-01-01
This book is an introduction to the theory of Hilbert space, a fundamental tool for non-relativistic quantum mechanics. Linear, topological, metric, and normed spaces are all addressed in detail, in a rigorous but reader-friendly fashion. The rationale for an introduction to the theory of Hilbert space, rather than a detailed study of Hilbert space theory itself, resides in the very high mathematical difficulty of even the simplest physical case. Within an ordinary graduate course in physics there is insufficient time to cover the theory of Hilbert spaces and operators, as well as distribution theory, with sufficient mathematical rigor. Compromises must be found between full rigor and practical use of the instruments. The book is based on the author's lessons on functional analysis for graduate students in physics. It will equip the reader to approach Hilbert space and, subsequently, rigged Hilbert space, with a more practical attitude. With respect to the original lectures, the mathematical flavor in all sub...
Topology of actions and homogeneous spaces
International Nuclear Information System (INIS)
Kozlov, Konstantin L
2013-01-01
Topologization of a group of homeomorphisms and its action provide additional possibilities for studying the topological space, the group of homeomorphisms, and their interconnections. The subject of the paper is the use of the property of d-openness of an action (introduced by Ancel under the name of weak micro-transitivity) in the study of spaces with various forms of homogeneity. It is proved that a d-open action of a Čech-complete group is open. A characterization of Polish SLH spaces using d-openness is given, and it is established that any separable metrizable SLH space has an SLH completion that is a Polish space. Furthermore, the completion is realized in coordination with the completion of the acting group with respect to the two-sided uniformity. A sufficient condition is given for extension of a d-open action to the completion of the space with respect to the maximal equiuniformity with preservation of d-openness. A result of van Mill is generalized, namely, it is proved that any homogeneous CDH metrizable compactum is the only G-compactification of the space of rational numbers for the action of some Polish group. Bibliography: 39 titles.
Additive subgroups of topological vector spaces
Banaszczyk, Wojciech
1991-01-01
The Pontryagin-van Kampen duality theorem and the Bochner theorem on positive-definite functions are known to be true for certain abelian topological groups that are not locally compact. The book sets out to present in a systematic way the existing material. It is based on the original notion of a nuclear group, which includes LCA groups and nuclear locally convex spaces together with their additive subgroups, quotient groups and products. For (metrizable, complete) nuclear groups one obtains analogues of the Pontryagin duality theorem, of the Bochner theorem and of the Lévy-Steinitz theorem on rearrangement of series (an answer to an old question of S. Ulam). The book is written in the language of functional analysis. The methods used are taken mainly from geometry of numbers, geometry of Banach spaces and topological algebra. The reader is expected only to know the basics of functional analysis and abstract harmonic analysis.
Configuration spaces geometry, topology and representation theory
Cohen, Frederick; Concini, Corrado; Feichtner, Eva; Gaiffi, Giovanni; Salvetti, Mario
2016-01-01
This book collects the scientific contributions of a group of leading experts who took part in the INdAM Meeting held in Cortona in September 2014. With combinatorial techniques as the central theme, it focuses on recent developments in configuration spaces from various perspectives. It also discusses their applications in areas ranging from representation theory, toric geometry and geometric group theory to applied algebraic topology.
Doubravsky, Karel; Dohnal, Mirko
2015-01-01
Complex decision making tasks of different natures, e.g. economics, safety engineering, ecology and biology, are based on vague, sparse, partially inconsistent and subjective knowledge. Moreover, decision making economists / engineers are usually not willing to invest too much time into study of complex formal theories. They require such decisions which can be (re)checked by human like common sense reasoning. One important problem related to realistic decision making tasks are incomplete data sets required by the chosen decision making algorithm. This paper presents a relatively simple algorithm how some missing III (input information items) can be generated using mainly decision tree topologies and integrated into incomplete data sets. The algorithm is based on an easy to understand heuristics, e.g. a longer decision tree sub-path is less probable. This heuristic can solve decision problems under total ignorance, i.e. the decision tree topology is the only information available. But in a practice, isolated information items e.g. some vaguely known probabilities (e.g. fuzzy probabilities) are usually available. It means that a realistic problem is analysed under partial ignorance. The proposed algorithm reconciles topology related heuristics and additional fuzzy sets using fuzzy linear programming. The case study, represented by a tree with six lotteries and one fuzzy probability, is presented in details.
Configuration Spaces and the Topology of Curves in Projective Space
Kallel, Sadok
2000-01-01
We survey and expand on the work of Segal, Milgram and the author on the topology of spaces of maps of positive genus curves into $n$-th complex projective space, $n\\geq 1$ (in both the holomorphic and continuous categories). Both based and unbased maps are studied and in particular we compute the fundamental groups of the spaces in question. The relevant case when $n=1$ is given by a non-trivial extension which we fully determine.
Soft Connected Spaces and Soft Paracompact Spaces
Fucai Lin
2013-01-01
Soft topological spaces are considered as mathematical tools for dealing with uncertainties, and a fuzzy topological space is a special case of the soft topological space. The purpose of this paper is to study soft topological spaces. We introduce some new concepts in soft topological spaces such as soft closed mapping, soft open mappings, soft connected spaces and soft paracompact spaces. We also redefine the concept of soft points such that it is reasonable in soft topological spaces. Mo...
Fuzzy Boundary and Fuzzy Semiboundary
M. Athar; B. Ahmad
2008-01-01
We present several properties of fuzzy boundary and fuzzy semiboundary which have been supported by examples. Properties of fuzzy semi-interior, fuzzy semiclosure, fuzzy boundary, and fuzzy semiboundary have been obtained in product-related spaces. We give necessary conditions for fuzzy continuous (resp., fuzzy semicontinuous, fuzzy irresolute) functions. Moreover, fuzzy continuous (resp., fuzzy semicontinuous, fuzzy irresolute) functions have been characterized via fuzzy-derived (resp., fuzz...
Kuratowski, Kazimierz
1968-01-01
Topology, Volume II deals with topology and covers topics ranging from compact spaces and connected spaces to locally connected spaces, retracts, and neighborhood retracts. Group theory and some cutting problems are also discussed, along with the topology of the plane. Comprised of seven chapters, this volume begins with a discussion on the compactness of a topological space, paying particular attention to Borel, Lebesgue, Riesz, Cantor, and Bolzano-Weierstrass conditions. Semi-continuity and topics in dimension theory are also considered. The reader is then introduced to the connecte
Hocking, John G
1988-01-01
""As textbook and reference work, this is a valuable addition to the topological literature."" - Mathematical ReviewsDesigned as a text for a one-year first course in topology, this authoritative volume offers an excellent general treatment of the main ideas of topology. It includes a large number and variety of topics from classical topology as well as newer areas of research activity.There are four set-theoretic chapters, followed by four primarily algebraic chapters. Chapter I covers the fundamentals of topological and metrical spaces, mappings, compactness, product spaces, the Tychonoff t
C*-algebras over topological spaces
DEFF Research Database (Denmark)
Meyer, Ralf; Nest, Ryszard
2012-01-01
We define the filtrated K-theory of a C*-algebra over a finite topological space X and explain how to construct a spectral sequence that computes the bivariant Kasparov theory over X in terms of filtrated K-theory. For finite spaces with a totally ordered lattice of open subsets, this spectral...... sequence becomes an exact sequence as in the Universal Coefficient Theorem, with the same consequences for classification. We also exhibit an example where filtrated K-theory is not yet a complete invariant. We describe two C*-algebras over a space X with four points that have isomorphic filtrated K......-theory without being KK(X)-equivalent. For this space X, we enrich filtrated K-theory by another K-theory functor to a complete invariant up to KK(X)-equivalence that satisfies a Universal Coefficient Theorem....
Stabilities of Cubic Mappings in Fuzzy Normed Spaces
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Ghaffari Ali
2010-01-01
Full Text Available Rassias(2001 introduced the pioneering cubic functional equation in the history of mathematical analysis: and solved the pertinent famous Ulam stability problem for this inspiring equation. This Rassias cubic functional equation was the historic transition from the following famous Euler-Lagrange-Rassias quadratic functional equation: to the cubic functional equations. In this paper, we prove the Ulam-Hyers stability of the cubic functional equation: in fuzzy normed linear spaces. We use the definition of fuzzy normed linear spaces to establish a fuzzy version of a generalized Hyers-Ulam-Rassias stability for above equation in the fuzzy normed linear space setting. The fuzzy sequentially continuity of the cubic mappings is discussed.
Fuzzy Logic: Toward Measuring Gottfredson's Concept of Occupational Social Space.
Hesketh, Beryl; And Others
1989-01-01
Investigated the application of fuzzy graphic rating scale to measurement of preferences for occupational sex type, prestige, and interests using Gottfredson's concept of occupational social space. Reported reliability and validity data with illustrative examples of respondents' interpretations of their own fuzzy ratings. Outlined counseling and…
On Intuitionistic Fuzzy β-Almost Compactness and β-Nearly Compactness.
Renuka, R; Seenivasan, V
2015-01-01
The concept of intuitionistic fuzzy β-almost compactness and intuitionistic fuzzy β-nearly compactness in intuitionistic fuzzy topological spaces is introduced and studied. Besides giving characterizations of these spaces, we study some of their properties. Also, we investigate the behavior of intuitionistic fuzzy β-compactness, intuitionistic fuzzy β-almost compactness, and intuitionistic fuzzy β-nearly compactness under several types of intuitionistic fuzzy continuous mappings.
Decomposition of Fuzzy Soft Sets with Finite Value Spaces
Jun, Young Bae
2014-01-01
The notion of fuzzy soft sets is a hybrid soft computing model that integrates both gradualness and parameterization methods in harmony to deal with uncertainty. The decomposition of fuzzy soft sets is of great importance in both theory and practical applications with regard to decision making under uncertainty. This study aims to explore decomposition of fuzzy soft sets with finite value spaces. Scalar uni-product and int-product operations of fuzzy soft sets are introduced and some related properties are investigated. Using t-level soft sets, we define level equivalent relations and show that the quotient structure of the unit interval induced by level equivalent relations is isomorphic to the lattice consisting of all t-level soft sets of a given fuzzy soft set. We also introduce the concepts of crucial threshold values and complete threshold sets. Finally, some decomposition theorems for fuzzy soft sets with finite value spaces are established, illustrated by an example concerning the classification and rating of multimedia cell phones. The obtained results extend some classical decomposition theorems of fuzzy sets, since every fuzzy set can be viewed as a fuzzy soft set with a single parameter. PMID:24558342
Topology, isomorphic smoothness and polyhedrality in Banach spaces
Smith, Richard J.
2018-01-01
In recent decades, topology has come to play an increasing role in some geometric aspects of Banach space theory. The class of so-called $w^*$-locally relatively compact sets was introduced recently by Fonf, Pallares, Troyanski and the author, and were found to be a useful topological tool in the theory of isomorphic smoothness and polyhedrality in Banach spaces. We develop the topological theory of these sets and present some Banach space applications.
Approximate Euler-Lagrange Quadratic Mappings in Fuzzy Banach Spaces
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Hark-Mahn Kim
2013-01-01
Full Text Available We consider general solution and the generalized Hyers-Ulam stability of an Euler-Lagrange quadratic functional equation in fuzzy Banach spaces, where , are nonzero rational numbers with , .
Directory of Open Access Journals (Sweden)
Yuanjiang Huang
2014-01-01
Full Text Available The sensor nodes in the Wireless Sensor Networks (WSNs are prone to failures due to many reasons, for example, running out of battery or harsh environment deployment; therefore, the WSNs are expected to be able to maintain network connectivity and tolerate certain amount of node failures. By applying fuzzy-logic approach to control the network topology, this paper aims at improving the network connectivity and fault-tolerant capability in response to node failures, while taking into account that the control approach has to be localized and energy efficient. Two fuzzy controllers are proposed in this paper: one is Learning-based Fuzzy-logic Topology Control (LFTC, of which the fuzzy controller is learnt from a training data set; another one is Rules-based Fuzzy-logic Topology Control (RFTC, of which the fuzzy controller is obtained through designing if-then rules and membership functions. Both LFTC and RFTC do not rely on location information, and they are localized. Comparing them with other three representative algorithms (LTRT, List-based, and NONE through extensive simulations, our two proposed fuzzy controllers have been proved to be very energy efficient to achieve desired node degree and improve the network connectivity when sensor nodes run out of battery or are subject to random attacks.
Nω –CLOSED SETS IN NEUTROSOPHIC TOPOLOGICAL SPACES
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Santhi R.
2016-08-01
Full Text Available Neutrosophic set and Neutrosophic Topological spaces has been introduced by Salama. Neutrosophic Closed set and Neutrosophic Continuous Functions were introduced by Salama et. al.. In this paper, we introduce the concept of Nω- closed sets and their properties in Neutrosophic topological spaces.
Rigged Hilbert spaces and topologies on operator algebras
International Nuclear Information System (INIS)
Freidrich, M.; Lassner, G.
1979-01-01
To any Oπ-algebra of unbounded operators there corresponds a rigged Hilbert space so that all operators are continuous with respect to the topologies. This leads to different topologies of uniformly bounded convergence on the operator algebra, which are investigated in this paper. Particularly consistent results are obtained if the rigged Hilbert space is a reflexive one
Topological vector spaces admissible in economic equilibrium theory
DEFF Research Database (Denmark)
Keiding, Hans
2009-01-01
In models of economic equilibrium in markets with infinitely many commodities, the commodity space is an ordered topological vector space endowed with additional structure. In the present paper, we consider ordered topological vector spaces which are admissible (for equilibrium analysis) in the s......) in the sense that every economy which is reasonably well behaved posesses an equilibrium. It turns out that this condition may be characterized in terms of topology and order. This characterization implies that the commodity space has the structure of a Kakutani space....
Topology of Document Retrieval Systems.
Everett, Daniel M.; Cater, Steven C.
1992-01-01
Explains the use of a topological structure to examine the closeness between documents in retrieval systems and analyzes the topological structure of a vector-space model, a fuzzy-set model, an extended Boolean model, a probabilistic model, and a TIRS (Topological Information Retrieval System) model. Proofs for the results are appended. (17…
Somewhat Slightly Generalized Double Fuzzy Semicontinuous Functions
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Fatimah M. Mohammed
2014-01-01
Full Text Available The aim of this paper is to introduce the concepts of somewhat slightly generalized double fuzzy semicontinuous functions and somewhat slightly generalized double fuzzy semiopen functions in double fuzzy topological spaces. Some interesting properties and characterizations of these functions are introduced and discussed. Furthermore, the relationships among the new concepts are discussed with some necessary examples.
Function spaces with uniform, fine and graph topologies
McCoy, Robert A; Jindal, Varun
2018-01-01
This book presents a comprehensive account of the theory of spaces of continuous functions under uniform, fine and graph topologies. Besides giving full details of known results, an attempt is made to give generalizations wherever possible, enriching the existing literature. The goal of this monograph is to provide an extensive study of the uniform, fine and graph topologies on the space C(X,Y) of all continuous functions from a Tychonoff space X to a metric space (Y,d); and the uniform and fine topologies on the space H(X) of all self-homeomorphisms on a metric space (X,d). The subject matter of this monograph is significant from the theoretical viewpoint, but also has applications in areas such as analysis, approximation theory and differential topology. Written in an accessible style, this book will be of interest to researchers as well as graduate students in this vibrant research area.
Extracting Topological Relations Between Indoor Spaces from Point Clouds
Tran, H.; Khoshelham, K.; Kealy, A.; Díaz-Vilariño, L.
2017-09-01
3D models of indoor environments are essential for many application domains such as navigation guidance, emergency management and a range of indoor location-based services. The principal components defined in different BIM standards contain not only building elements, such as floors, walls and doors, but also navigable spaces and their topological relations, which are essential for path planning and navigation. We present an approach to automatically reconstruct topological relations between navigable spaces from point clouds. Three types of topological relations, namely containment, adjacency and connectivity of the spaces are modelled. The results of initial experiments demonstrate the potential of the method in supporting indoor navigation.
On Fuzzy Ã‰Â›-Contractive Mappings in Fuzzy Metric Spaces
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Dorel Miheţ
2007-04-01
Full Text Available We answer into affirmative an open question raised by A. Razani in 2005. An essential role in our proofs is played by the separation axiom in the definition of a fuzzy metric space in the sense of George and Veeramani.
Bonachéra, Fanny; Horvath, Dragos
2008-02-01
Topological fuzzy pharmacophore triplets (2D-FPT), using the number of interposed bonds to measure separation between the atoms representing pharmacophore types, were employed to establish and validate quantitative structure-activity relationships (QSAR). Thirteen data sets for which state-of-the-art QSAR models were reported in literature were revisited in order to benchmark 2D-FPT biological activity-explaining propensities. Linear and nonlinear QSAR models were constructed for each compound series (following the original author's splitting into training/validation subsets) with three different 2D-FPT versions, using the genetic algorithm-driven Stochastic QSAR sampler (SQS) to pick relevant triplets and fit their coefficients. 2D-FPT QSARs are computationally cheap, interpretable, and perform well in benchmarking. In a majority of cases (10/13), default 2D-FPT models validated better than or as well as the best among those reported, including 3D overlay-dependent approaches. Most of the analogues series, either unaffected by protonation equilibria or unambiguously adopting expected protonation states, were equally well described by rule- or pKa-based pharmacophore flagging. Thermolysin inhibitors represent a notable exception: pKa-based flagging boosts model quality, although--surprisingly--not due to proteolytic equilibrium effects. The optimal degree of 2D-FPT fuzziness is compound set dependent. This work further confirmed the higher robustness of nonlinear over linear SQS models. In spite of the wealth of studied sets, benchmarking is nevertheless flawed by low intraset diversity: a whole series of thereby caused artifacts were evidenced, implicitly raising questions about the way QSAR studies are conducted nowadays. An in-depth investigation of thrombin inhibition models revealed that some of the selected triplets make sense (one of these stands for a topological pharmacophore covering the P1 and P2 binding pockets). Nevertheless, equations were either
Moduli spaces of curves and enumerative geometry via topological recursion
Lewański, D.
2017-01-01
The thesis considers several enumerative geometric problems concerning the topology of the moduli space of curves and their combinatorics. These enumerative geometric problems are analysed from different intertwined points of view and using different mathematical tools, including Hurwitz theory,
Nonseparable closed vector subspaces of separable topological vector spaces
Czech Academy of Sciences Publication Activity Database
Kąkol, Jerzy; Leiderman, A. G.; Morris, S. A.
2017-01-01
Roč. 182, č. 1 (2017), s. 39-47 ISSN 0026-9255 R&D Projects: GA ČR GF16-34860L Institutional support: RVO:67985840 Keywords : locally convex topological vector space * separable topological space Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.716, year: 2016 https://link.springer.com/article/10.1007%2Fs00605-016-0876-2
International Nuclear Information System (INIS)
Jesic, Sinisa N.; Babacev, Natasa A.
2008-01-01
The purpose of this paper is to prove some common fixed point theorems for a pair of R-weakly commuting mappings defined on intuitionistic fuzzy metric spaces [Park JH. Intuitionistic fuzzy metric spaces. Chaos, Solitons and Fractals 2004;22:1039-46] and L-fuzzy metric spaces [Saadati R, Razani A, Adibi H. A common fixed point theorem in L-fuzzy metric spaces. Chaos, Solitons and Fractals, doi:10.1016/j.chaos.2006.01.023], with nonlinear contractive condition, defined with function, first observed by Boyd and Wong [Boyd DW, Wong JSW. On nonlinear contractions. Proc Am Math Soc 1969;20:458-64]. Following Pant [Pant RP. Common fixed points of noncommuting mappings. J Math Anal Appl 1994;188:436-40] we define R-weak commutativity for a pair of mappings and then prove the main results. These results generalize some known results due to Saadati et al., and Jungck [Jungck G. Commuting maps and fixed points. Am Math Mon 1976;83:261-3]. Some examples and comments according to the preceding results are given
Topology as fluid geometry two-dimensional spaces, volume 2
Cannon, James W
2017-01-01
This is the second of a three volume collection devoted to the geometry, topology, and curvature of 2-dimensional spaces. The collection provides a guided tour through a wide range of topics by one of the twentieth century's masters of geometric topology. The books are accessible to college and graduate students and provide perspective and insight to mathematicians at all levels who are interested in geometry and topology. The second volume deals with the topology of 2-dimensional spaces. The attempts encountered in Volume 1 to understand length and area in the plane lead to examples most easily described by the methods of topology (fluid geometry): finite curves of infinite length, 1-dimensional curves of positive area, space-filling curves (Peano curves), 0-dimensional subsets of the plane through which no straight path can pass (Cantor sets), etc. Volume 2 describes such sets. All of the standard topological results about 2-dimensional spaces are then proved, such as the Fundamental Theorem of Algebra (two...
International Nuclear Information System (INIS)
Hawking, S.W.; King, A.R.; McCarthy, P.J.
1976-01-01
A new topology is proposed for strongly causal space--times. Unlike the standard manifold topology (which merely characterizes continuity properties), the new topology determines the causal, differential, and conformal structures of space--time. The topology is more appealing, physical, and manageable than the topology previously proposed by Zeeman for Minkowski space. It thus seems that many calculations involving the above structures may be made purely topological
Grill Nano topological spaces with grill Nano generalized closed sets
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A.A. Azzam
2017-04-01
Full Text Available The grill Nano generalized closed sets is an expansion of Nano generalized closed sets in grill Nano topological spaces, which is the frame of reference measurement, inference and reasoning in many applications such as computer science and information systems. So, this paper aims to study and analyze this expansion through the topological structure via the concept of grill. Some important characteristics and main properties which are related with these sets are obtained.
An embedding in inductive limits of linear topological spaces
International Nuclear Information System (INIS)
Iyahen, S.O.
1984-11-01
Let (E,u) be the inductive limit of a sequence (Esub(n),usub(n)) of linear topological spaces such that E is the union of linear subspaces Esub(n). The two related questions which receive attention here are as follows. When is a continuous linear map from a linear topological space F into (E,u) essentially a continuous linear map from F into some (Esub(n),usub(n)), and when is a bounded subset of (E,u) necessarily a bounded subset of some (Esub(n),usub(n)). The motivation is the result of A. Grothendieck, that both answers are in the affirmative if F and all of (Esub(n),usub(n)) are Frechet spaces. In this paper, more general conditions are given. For the situation in which the linear topological spaces are not locally convex, difficulties arise from inadequacy of convex bounded sets; to these, solutions are sought. (author)
Generalized topological spaces in evolutionary theory and combinatorial chemistry.
Stadler, Bärbel M R; Stadler, Peter F
2002-01-01
The search spaces in combinatorial chemistry as well as the sequence spaces underlying (molecular) evolution are conventionally thought of as graphs. Recombination, however, implies a nongraphical structure of the combinatorial search spaces. These structures, and their implications for search process itself, are heretofore not well understood in general. In this contribution we review a very general formalism from point set topology and discuss its application to combinatorial search spaces, fitness landscapes, evolutionary trajectories, and artificial chemistries.
Fuzzy spaces, the M(atrix) model and the quantum Hall effect
International Nuclear Information System (INIS)
Karabali, Dimitra; Nair, V.P.; Randjbar-Daem, S.
2004-06-01
This is a short review of recent work on fuzzy spaces in their relation to the M(atrix) theory and the quantum Hall effect. We give an introduction to fuzzy spaces and how the limit of large matrices is obtained. The complex projective spaces CP k , and to a lesser extent spheres, are considered. Quantum Hall effect and the behavior of edge excitations of a droplet of fermions on these spaces and their relation to fuzzy spaces are also discussed. (author)
DW complexes and their underlying topological spaces | Ntumba ...
African Journals Online (AJOL)
The naïve concept of a DW complex is that of a differential space that can be built up from cells and whose differential structure is defined in terms of differential structures on Euclidean unit closed balls. This concept stems from an analogue in the category of topological spaces: the so-called CW complex. The paper goes as ...
Directory of Open Access Journals (Sweden)
Nanxiang Yu
2017-01-01
Full Text Available We propose the solution concepts for the fuzzy optimization problems in the quotient space of fuzzy numbers. The Karush-Kuhn-Tucker (KKT optimality conditions are elicited naturally by introducing the Lagrange function multipliers. The effectiveness is illustrated by examples.
The Volatility of Data Space: Topology Oriented Sensitivity Analysis
Du, Jing; Ligmann-Zielinska, Arika
2015-01-01
Despite the difference among specific methods, existing Sensitivity Analysis (SA) technologies are all value-based, that is, the uncertainties in the model input and output are quantified as changes of values. This paradigm provides only limited insight into the nature of models and the modeled systems. In addition to the value of data, a potentially richer information about the model lies in the topological difference between pre-model data space and post-model data space. This paper introduces an innovative SA method called Topology Oriented Sensitivity Analysis, which defines sensitivity as the volatility of data space. It extends SA into a deeper level that lies in the topology of data. PMID:26368929
On πgp-continuous functions in topological spaces
International Nuclear Information System (INIS)
Park, Jin Han; Park, Jin Keun
2004-01-01
The concept of πgp-closed sets was introduced by Park [On πgp-closed sets in topological spaces, Indian J. Pure Appl. Math., in press]. The aim of this paper is to consider and characterize πgp-irresolute and πgp-continuous functions via the concept of πgp-closed sets and to relate these concepts to the classes of πGPO-compact spaces and πGP-connected spaces
Gateaux and Frechet Derivative in Intuitionistic Fuzzy Normed Linear spaces
Dinda, B.; Samanta, T. K.; Bera, U. K.
2010-01-01
Intuitionistic Fuzzy derivative, Intuitionistic Fuzzy Gateaux derivative, Intuitionistic Fuzzy Fr\\'{e}chet derivative are defined and a few of their properties are studied. The relation between Intuitionistic Fuzzy Gateaux derivative and Intuitionistic Fuzzy Fr\\'{e}chet derivative are emphasized.
Pβ-connectedness in topological spaces
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Tyagi Brij K.
2017-12-01
Full Text Available A new property called Pβ-connectedness is introduced which is stronger than connectedness and equivalent to pre-connectedness. The properties of this notion are explored and its relationship with other forms of connectedness, for example hyperconnectedness etc. are discussed. Locally pre-indiscrete spaces are defined as the spaces in which pre-open sets are closed. In such spaces connectedness becomes equivalent to pre-connectedness and hence to Pβ-connectedness, and semi-connectedness becomes equivalent to Pβ- connectedness. The notion of locally Pβ-connected space is introduced. The behavior of Pβ-connectedness under several types of mappings is investigated. An intermediate value theorem is obtained.
Fuzzy Riesz subspaces, fuzzy ideals, fuzzy bands and fuzzy band projections
Hong, Liang
2015-01-01
Fuzzy ordered linear spaces, Riesz spaces, fuzzy Archimedean spaces and $\\sigma$-complete fuzzy Riesz spaces were defined and studied in several works. Following the efforts along this line, we define fuzzy Riesz subspaces, fuzzy ideals, fuzzy bands and fuzzy band projections and establish their fundamental properties.
Generalized Star ωα-Closed Sets in Topological Spaces
Patil, P.G.; Benchalli, SS; Mirajakar, Pallavi
2016-01-01
The aim of this paper is to introduce a new class ofclosed sets called generalized star ωα-closed sets using ωα-closedsets in topological spaces. This new class of sets lies between theclass of closed sets and the class of generalized ωα-closed sets.Further some of their properties are investigated.
Note on generalized topological spaces with hereditary classes
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V. Renukadevi
2014-01-01
Full Text Available In this paper, we extend the study of $\\Psi_\\mathcal{H}$ operator introduced and studied in [5] and rectify the errors in the paper. Moreover, characterizations of $\\mu-$codense and strongly $\\mu-$codense hereditary classes in generalized topological spaces are also given.
Relation of the runaway avalanche threshold to momentum space topology
McDevitt, Christopher J.; Guo, Zehua; Tang, Xian-Zhu
2018-02-01
The underlying physics responsible for the formation of an avalanche instability due to the generation of secondary electrons is studied. A careful examination of the momentum space topology of the runaway electron population is carried out with an eye toward identifying how qualitative changes in the momentum space of the runaway electrons is correlated with the avalanche threshold. It is found that the avalanche threshold is tied to the merger of an O and X point in the momentum space of the primary runaway electron population. Such a change of the momentum space topology is shown to be accurately described by a simple analytic model, thus providing a powerful means of determining the avalanche threshold for a range of model assumptions.
Transport equations in weak topologies of dual Banach spaces
International Nuclear Information System (INIS)
Greenberg, W.; Polewczak, J.
1989-01-01
Nonlinear transport equations are studied, in which the nonlinearity, arising from the collision operator, is well behaved in the weak topology of a weakly compactly generated Banach space. The Cauchy problem is posed for general semilinear evolution equations, which can model a variety of diffusion and kinetic equations. Local existence theorems are obtained for such spaces. In particular, the results are applicable to transport equations in L ∞ with appropriate weak (i.e., L 1 ) continuity properties
Generalizations of γ-open set in topological spaces
Energy Technology Data Exchange (ETDEWEB)
Bhattacharya, Baby, E-mail: babybhatt75@gmail.com; Paul, Arnab, E-mail: mrarnabpaul87@gmail.com [Department of Mathematics, NIT Agartala, Jirania, Tripura (India)
2016-06-21
The main aim of this work is to study three generalized forms of γ-open set due to D. Andrijevic (D. Andrijevic, On the Topology Generated by pre-open sets, Presented at the Sixth Prague Topological Symposium, 39 (1987), 367-376)in a topological space. Out of which the dual appearance of one is the stronger form of b-locally closed set in the sense of Arafa A. Nasef (A. A Nasef,On b-locally closed sets and related topics, CHAOS SOLITONS & FRACTALS 12(2001) 1909-1915). Also, we introduce the concept of different types of continuity and study their basic properties by using these newly defined sets. Finally, we establish the interrelationships among themselves together with some already existing generalized forms of continuity.
Generalizations of γ-open set in topological spaces
International Nuclear Information System (INIS)
Bhattacharya, Baby; Paul, Arnab
2016-01-01
The main aim of this work is to study three generalized forms of γ-open set due to D. Andrijevic (D. Andrijevic, On the Topology Generated by pre-open sets, Presented at the Sixth Prague Topological Symposium, 39 (1987), 367-376)in a topological space. Out of which the dual appearance of one is the stronger form of b-locally closed set in the sense of Arafa A. Nasef (A. A Nasef,On b-locally closed sets and related topics, CHAOS SOLITONS & FRACTALS 12(2001) 1909-1915). Also, we introduce the concept of different types of continuity and study their basic properties by using these newly defined sets. Finally, we establish the interrelationships among themselves together with some already existing generalized forms of continuity.
Fuzzy Euclidean wormholes in de Sitter space
Energy Technology Data Exchange (ETDEWEB)
Chen, Pisin; Hu, Yao-Chieh; Yeom, Dong-han, E-mail: pisinchen@phys.ntu.edu.tw, E-mail: r04244003@ntu.edu.tw, E-mail: innocent.yeom@gmail.com [Leung Center for Cosmology and Particle Astrophysics, National Taiwan University, Taipei 10617, Taiwan (China)
2017-07-01
We investigate Euclidean wormholes in Einstein gravity with a massless scalar field in de Sitter space. Euclidean wormholes are possible due to the analytic continuation of the time as well as complexification of fields, where we need to impose the classicality after the Wick-rotation to the Lorentzian signatures. For some parameters, wormholes are preferred than Hawking-Moss instantons, and hence wormholes can be more fundamental than Hawking-Moss type instantons. Euclidean wormholes can be interpreted in three ways: (1) classical big bounce, (2) either tunneling from a small to a large universe or a creation of a collapsing and an expanding universe from nothing, and (3) either a transition from a contracting to a bouncing phase or a creation of two expanding universes from nothing. These various interpretations shed some light on challenges of singularities. In addition, these will help to understand tensions between various kinds of quantum gravity theories.
Distributed control topologies for deep space formation flying spacecraft
Hadaegh, F. Y.; Smith, R. S.
2002-01-01
A formation of satellites flying in deep space can be specified in terms of the relative satellite positions and absolute satellite orientations. The redundancy in the relative position specification generates a family of control topologies with equivalent stability and reference tracking performance, one of which can be implemented without requiring communication between the spacecraft. A relative position design formulation is inherently unobservable, and a methodology for circumventing this problem is presented. Additional redundancy in the control actuation space can be exploited for feed-forward control of the formation centroid's location in space, or for minimization of total fuel consumption.
g* λµ- closed sets ingeneralized topological spaces
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P. Jeyanthi
2016-04-01
Full Text Available In this paper we introduce some new classes of generalized closed sets called *λµ -g-closed, *λµ -g µ -closed and g* λµ -closed sets in generalized topological spaces, which are related to the classes of gµ -closed sets, g-λµ -closed sets and λµ -g-closed sets. We investigate the properties of the newly introduced classes, as well as the connections among the above mentioned classes of generalized closed sets. Also, we give a unified framework for the study of several types of generalized closed sets in a space endowed with two generalized topologies.
On Some Maps in Supra Topological Ordered Spaces
Al-shami, Tareq Mohammed
2018-01-01
In [6] the notion of supra semi open sets was presented and some of its properties were discussed. In this study, we introduce and investigate four main concepts namely supra continuous (supra open, supra closed, supra homeomorphism) maps via supra topological ordered spaces. Our findings in this work generalize some previous results in ([1], [13]). Many examples are considered to show the concepts introduced and main results obtained herein.
Generalized fixed point theorems for compatible mappings with some types in fuzzy metric spaces
International Nuclear Information System (INIS)
Cho, Yeol Je; Sedghi, Shaban; Shobe, Nabi
2009-01-01
In this paper, we give some new definitions of compatible mappings of types (I) and (II) in fuzzy metric spaces and prove some common fixed point theorems for four mappings under the condition of compatible mappings of types (I) and (II) in complete fuzzy metric spaces. Our results extend, generalize and improve the corresponding results given by many authors.
Generalized fixed point theorems for compatible mappings with some types in fuzzy metric spaces
Energy Technology Data Exchange (ETDEWEB)
Cho, Yeol Je [Department of Mathematics Education and the RINS, College of Education, Gyeongsang National University, Chinju 660-701 (Korea, Republic of)], E-mail: yjcho@gsnu.ac.kr; Sedghi, Shaban [Department of Mathematics, Islamic Azad University, Ghaemshahr Branch Ghaemshahr P.O. Box 163 (Iran, Islamic Republic of)], E-mail: sedghi_gh@yahoo.com; Shobe, Nabi [Department of Mathematics, Islamic Azad University, Babol Branch (Iran, Islamic Republic of)], E-mail: nabi_shobe@yahoo.com
2009-03-15
In this paper, we give some new definitions of compatible mappings of types (I) and (II) in fuzzy metric spaces and prove some common fixed point theorems for four mappings under the condition of compatible mappings of types (I) and (II) in complete fuzzy metric spaces. Our results extend, generalize and improve the corresponding results given by many authors.
Localifecation of variable-basis topological systems | Solovyov ...
African Journals Online (AJOL)
The paper provides another approach to the notion of variable-basis topological system generalizing the fixed-basis concept of S. Vickers, considers functorial relationships between the categories of modified variable-basis topological systems and variable-basis fuzzy topological spaces in the sense of S.E. Rodabaugh ...
The separating topology for the space-times of general relativity
International Nuclear Information System (INIS)
Lindstroem, U.
1977-08-01
The separating topology, first suggested by Zeeman, is defined for the space-times of general relativity. It is defined by a basis. A number of properties are derived. The topology induces the ordinary Euclidean topology on space-like hypersurfaces as well as on timelike curves and the discrete topology on null-cones. The group of auto-homeomorphisms is found to be the group of smooth conformal diffeomorphisms if the space-time is strongly causal. (author)
Directory of Open Access Journals (Sweden)
Wei Huang
2013-01-01
Full Text Available We introduce a new category of fuzzy inference systems with the aid of a multiobjective opposition-based space search algorithm (MOSSA. The proposed MOSSA is essentially a multiobjective space search algorithm improved by using an opposition-based learning that employs a so-called opposite numbers mechanism to speed up the convergence of the optimization algorithm. In the identification of fuzzy inference system, the MOSSA is exploited to carry out the parametric identification of the fuzzy model as well as to realize its structural identification. Experimental results demonstrate the effectiveness of the proposed fuzzy models.
On fuzzy quasi continuity and an application of fuzzy set theory
International Nuclear Information System (INIS)
Mahmoud, R.A.
2003-01-01
Where as classical topology has been developed closely connected with classical analysis describing topological phenomena in analysis, fuzzy topology with its important application in quantum gravity indicated by Witten and Elnaschie, has only been introduced as an analogue of the classical topology. The development of fuzzy topology without close relations to analytical problems did not give the possibility of testing successfully the applicability of the new notions and results. Till now this situation did not change, essentially. Although, many types of fuzzy sets and fuzzy functions having the quasi-property in both of weak and strong than openness and continuity, respectively, have been studied in detail. Many properties on fuzzy topological spaces such as compactness are discussed via fuzzy notion. While others are far from being completely devoted in its foundation. So, this paper is devoted to present a new class of fuzzy quasi-continuous functions via fuzzy compactness has been defined. Some characterizations and several properties of this new concept were discussed. Possible application to high energy physics and quantum gravity are indicated
Momentum-space cigar geometry in topological phases
Palumbo, Giandomenico
2018-01-01
In this paper, we stress the importance of momentum-space geometry in the understanding of two-dimensional topological phases of matter. We focus, for simplicity, on the gapped boundary of three-dimensional topological insulators in class AII, which are described by a massive Dirac Hamiltonian and characterized by an half-integer Chern number. The gap is induced by introducing a magnetic perturbation, such as an external Zeeman field or a ferromagnet on the surface. The quantum Bures metric acquires a central role in our discussion and identifies a cigar geometry. We first derive the Chern number from the cigar geometry and we then show that the quantum metric can be seen as a solution of two-dimensional non-Abelian BF theory in momentum space. The gauge connection for this model is associated to the Maxwell algebra, which takes into account the Lorentz symmetries related to the Dirac theory and the momentum-space magnetic translations connected to the magnetic perturbation. The Witten black-hole metric is a solution of this gauge theory and coincides with the Bures metric. This allows us to calculate the corresponding momentum-space entanglement entropy that surprisingly carries information about the real-space conformal field theory describing the defect lines that can be created on the gapped boundary.
A-Soft Separation Axioms in Soft Topological Space
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Luay Abd –Al-Hani Al-Sweedi
2018-01-01
Full Text Available The important science tools in a different kinds and specialties , that considered the basic mainstay of ( the set theory and because of huge development in all life fields. This causes great problems , that need solution and parallel tools for those developments , so the scientis become responsible to work on the development of number theory and open new horizons , that a new science had appeared which is ( soft figures theory which is considered the important tool to solve most difficult problems or overcome them ,in these sciences and their specific life specialization, economy, medicine , geometry and others. Also the theory of soft numbers had entered in general topology in power full and active way. The last years a new science has appeared is (soft topological space. The main idea of this research is to define the separation axioms in (soft topological space and practically in certain point , and to study the most important properties and results of it .
Exploration of the topology of chemical spaces with network measures.
Krein, Michael P; Sukumar, N
2011-11-17
Discontinuous changes in molecular structure (resulting from continuous transformations of molecular coordinates) lead to changes in chemical properties and biological activities that chemists attempt to describe through structure-activity or structure-property relationships (QSAR/QSPR). Such relationships are commonly envisioned in a continuous high-dimensional space of numerical descriptors, referred to as chemistry space. The choice of descriptors defining coordinates within chemistry space and the choice of similarity metrics thus influence the partitioning of this space into regions corresponding to local structural similarity. These are the regions (known as domains of applicability) most likely to be successfully modeled by a structure-activity relationship. In this work the network topology and scaling relationships of chemistry spaces are first investigated independent of a specific biological activity. Chemistry spaces studied include the ZINC data set, a qHTS PubChem bioassay, as well as the space of protein binding sites from the PDB. The characteristics of these networks are compared and contrasted with those of the bioassay SALI subnetwork, which maps discontinuities or cliffs in the structure-activity landscape. Mapping the locations of activity cliffs and comparing the global characteristics of SALI subnetworks with those of the underlying chemistry space networks generated using different representations, can guide the choice of a better representation. A higher local density of SALI edges with a particular representation indicates a more challenging structure-activity relationship using that fingerprint in that region of chemistry space.
Topological properties of function spaces over ordinal spaces
Czech Academy of Sciences Publication Activity Database
Gabriyelyan, S.; Grebík, Jan; Kąkol, Jerzy; Zdomskyy, L.
2017-01-01
Roč. 111, č. 4 (2017), s. 1157-1161 ISSN 1578-7303 R&D Projects: GA ČR GF16-34860L Institutional support: RVO:67985840 Keywords : Ascoli * rK-space * ordinal space Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.690, year: 2016 https://link. springer .com/article/10.1007%2Fs13398-016-0354-7
Topological properties of function spaces over ordinal spaces
Czech Academy of Sciences Publication Activity Database
Gabriyelyan, S.; Grebík, Jan; Kąkol, Jerzy; Zdomskyy, L.
2017-01-01
Roč. 111, č. 4 (2017), s. 1157-1161 ISSN 1578-7303 R&D Projects: GA ČR GF16-34860L Institutional support: RVO:67985840 Keywords : Ascoli * rK-space * ordinal space Subject RIV: BA - General Mathematics OBOR OECD: Pure mathematics Impact factor: 0.690, year: 2016 https://link.springer.com/article/10.1007%2Fs13398-016-0354-7
Topological Vector Space-Valued Cone Metric Spaces and Fixed Point Theorems
Directory of Open Access Journals (Sweden)
Radenović Stojan
2010-01-01
Full Text Available We develop the theory of topological vector space valued cone metric spaces with nonnormal cones. We prove three general fixed point results in these spaces and deduce as corollaries several extensions of theorems about fixed points and common fixed points, known from the theory of (normed-valued cone metric spaces. Examples are given to distinguish our results from the known ones.
Geometric and Topological Invariants of the Hypothesis Space
Rodríguez, Carlos C.
2011-03-01
The form and shape of a hypothesis space imposes natural objective constraints to any inferential process. This contribution summarizes what is currently known and the mathematics that are thought to be needed for new developments in this area. For example, it is well known that the quality of best possible estimators deteriorates with increasing volume, dimension and curvature of the hypothesis space. It is also known that regular statistical parametric models are finite dimensional Riemannian manifolds admitting a family of dual affine connections. Fisher information is the metric induced on the hypothesis space by the Hellinger distance. Nonparametric models are infinite dimensional manifolds. Global negative curvature implies asymptotic inadmissibility of uniform priors. When there is uncertainty about the model and the prior, entropic methods are more robust than standard Bayesian inference. The presence of some types of singularities allow the existence of faster than normal estimators …, etc. The large number of fundamental statistical concepts with geometric and topological content suggest to try to look at Riemannian Geometry, Algebraic Geometry, K-theory, Algebraic Topology, Knot-theory and other branches of current mathematics, not as empty esoteric abstractions but as allies for statistical inference.
g* λµ- closed sets ingeneralized topological spaces
P. Jeyanthi; P. Nalayini; Marcelina Mocana
2016-01-01
In this paper we introduce some new classes of generalized closed sets called *λµ -g-closed, *λµ -g µ -closed and g* λµ -closed sets in generalized topological spaces, which are related to the classes of gµ -closed sets, g-λµ -closed sets and λµ -g-closed sets. We investigate the properties of the newly introduced classes, as well as the connections among the above mentioned classes of generalized closed sets. Also, we give a unified framework for the study of several types of generalized cl...
Stringy Fuzziness as the Custodial of Time-Space Noncommutativity
Barbón, José L F
2000-01-01
We study aspects of obtaining field theories with noncommuting time-space coordinates as limits of open-string theories in constant electric-field backgrounds. We find that, within the standard closed-string backgrounds, there is an obstruction to decoupling the time-space noncommutativity scale from that of the string fuzziness scale. We speculate that this censorship may be string-theory's way of protecting the causality and unitarity structure. We study the moduli space of the obstruction in terms of the open- and closed-string backgrounds. Cases of both zero and infinite brane tensions as well as zero string couplings are obtained. A decoupling can be achieved formally by considering complex values of the dilaton and inverting the role of space and time of the light cone. This is reminiscent of a black-hole horizon. We study the corresponding supergravity solution in the large-N limit and find that the geometry has a naked singularity at the physical scale of noncommutativity.
Stringy fuzziness as the custodian of time-space noncommutativity
Barbón, José L F
2000-01-01
We study aspects of obtaining field theories with noncommuting time- space coordinates as limits of open-string theories in constant electric-field backgrounds. We find that, within the standard closed- string backgrounds, there is an obstruction to decoupling the time- space noncommutativity scale from that of the string fuzziness scale. We speculate that this censorship may be string-theory's way of protecting the causality and unitarity structure. We study the moduli space of the obstruction in terms of the open- and closed-string backgrounds. Cases of both zero and infinite brane tensions as well as zero string couplings are obtained. A decoupling can be achieved formally by considering complex values of the dilaton and inverting the role of space and time in the light cone. This is reminiscent of a black-hole horizon. We study the corresponding supergravity solution in the large-N limit and find that the geometry has a naked singularity at the physical scale of noncommutativity. (23 refs).
Using Fuzzy Clustering for Real-time Space Flight Safety
Lee, Charles; Haskell, Richard E.; Hanna, Darrin; Alena, Richard L.
2004-01-01
To ensure space flight safety, it is necessary to monitor myriad sensor readings on the ground and in flight. Since a space shuttle has many sensors, monitoring data and drawing conclusions from information contained within the data in real time is challenging. The nature of the information can be critical to the success of the mission and safety of the crew and therefore, must be processed with minimal data-processing time. Data analysis algorithms could be used to synthesize sensor readings and compare data associated with normal operation with the data obtained that contain fault patterns to draw conclusions. Detecting abnormal operation during early stages in the transition from safe to unsafe operation requires a large amount of historical data that can be categorized into different classes (non-risk, risk). Even though the 40 years of shuttle flight program has accumulated volumes of historical data, these data don t comprehensively represent all possible fault patterns since fault patterns are usually unknown before the fault occurs. This paper presents a method that uses a similarity measure between fuzzy clusters to detect possible faults in real time. A clustering technique based on a fuzzy equivalence relation is used to characterize temporal data. Data collected during an initial time period are separated into clusters. These clusters are characterized by their centroids. Clusters formed during subsequent time periods are either merged with an existing cluster or added to the cluster list. The resulting list of cluster centroids, called a cluster group, characterizes the behavior of a particular set of temporal data. The degree to which new clusters formed in a subsequent time period are similar to the cluster group is characterized by a similarity measure, q. This method is applied to downlink data from Columbia flights. The results show that this technique can detect an unexpected fault that has not been present in the training data set.
National Research Council Canada - National Science Library
Udupa, Jayaram
2001-01-01
.... During this project period, the following have been accomplished: The development and validation of a new method of lesion and density detection based on fuzzy connectedness that utilizes the relative strength of connectedness among objects...
Remarks on soft omega-closed sets in soft topological spaces
Directory of Open Access Journals (Sweden)
Nirmala Rebecca Paul
2015-05-01
Full Text Available The paper introduces soft omega-closed sets in soft topological spaces and establishes the relationship between other existing generlised closed sets in soft topological spaces. It derives the basic properties of soft omega-closed sets. As an application it proves that a soft omega-closed set in a soft compact space is soft compact.
Some analogies of the Banach contraction principle in fuzzy modular spaces.
Wongkum, Kittipong; Chaipunya, Parin; Kumam, Poom
2013-01-01
We established some theorems under the aim of deriving variants of the Banach contraction principle, using the classes of inner contractions and outer contractions, on the structure of fuzzy modular spaces.
Intuitionistic Fuzzy Hyperhomomorphism and Intuitionistic Fuzzy Normal Subhypergroups
Abdulmula, Karema S; Salleh, Abdul Razak
2012-01-01
The purpose of this paper is to introduce some basic concepts of intuitionistic fuzzy hyperalgebra. We continue our study of intuitionistic fuzzy hypergroups, by generalising the concept of fuzzy homomorphism and fuzzy normal subgroup based on fuzzy spaces to intuitionistic fuzzy hyperhomomorphism based on intuitionstic fuzzy spaces. We will introduce the notion of an intuitionistic fuzzy quotient hypergroup induced by an intuitionistic fuzzy normal subhypergroup under intuitionistic fuzzy hy...
Intuitionistic H-fuzzy relations
Directory of Open Access Journals (Sweden)
Kul Hur
2005-10-01
Full Text Available We introduce the category IRel(H consisting of intuitionistic fuzzy relational spaces on sets and we study structures of the category IRel(H in the viewpoint of the topological universe introduced by Nel. Thus we show that IRel(H satisfies all the conditions of a topological universe over Set except the terminal separator property and IRel(H is cartesian closed over Set.
On some classes of nearly open sets in nano topological spaces
Directory of Open Access Journals (Sweden)
A. A. Nasef
2016-10-01
Full Text Available One of the aims of this paper is to study some near nano open sets in nano topological spaces. Secondly, some properties for near nano open (closed sets. Also, we introduce the notion of nano β-continuity and we study the relationships between some types of nano continuous functions between nano topological spaces. Finally, we introduce two application examples in nano topology.
Fuzzy mobile-robot positioning in intelligent spaces using wireless sensor networks.
Herrero, David; Martínez, Humberto
2011-01-01
This work presents the development and experimental evaluation of a method based on fuzzy logic to locate mobile robots in an Intelligent Space using wireless sensor networks (WSNs). The problem consists of locating a mobile node using only inter-node range measurements, which are estimated by radio frequency signal strength attenuation. The sensor model of these measurements is very noisy and unreliable. The proposed method makes use of fuzzy logic for modeling and dealing with such uncertain information. Besides, the proposed approach is compared with a probabilistic technique showing that the fuzzy approach is able to handle highly uncertain situations that are difficult to manage by well-known localization methods.
Navigating features: a topologically informed chart of electromyographic features space.
Phinyomark, Angkoon; Khushaba, Rami N; Ibáñez-Marcelo, Esther; Patania, Alice; Scheme, Erik; Petri, Giovanni
2017-12-01
The success of biological signal pattern recognition depends crucially on the selection of relevant features. Across signal and imaging modalities, a large number of features have been proposed, leading to feature redundancy and the need for optimal feature set identification. A further complication is that, due to the inherent biological variability, even the same classification problem on different datasets can display variations in the respective optimal sets, casting doubts on the generalizability of relevant features. Here, we approach this problem by leveraging topological tools to create charts of features spaces. These charts highlight feature sub-groups that encode similar information (and their respective similarities) allowing for a principled and interpretable choice of features for classification and analysis. Using multiple electromyographic (EMG) datasets as a case study, we use this feature chart to identify functional groups among 58 state-of-the-art EMG features, and to show that they generalize across three different forearm EMG datasets obtained from able-bodied subjects during hand and finger contractions. We find that these groups describe meaningful non-redundant information, succinctly recapitulating information about different regions of feature space. We then recommend representative features from each group based on maximum class separability, robustness and minimum complexity. © 2017 The Authors.
Topological Methods for Visualization
Energy Technology Data Exchange (ETDEWEB)
Berres, Anne Sabine [Los Alamos National Lab. (LANL), Los Alamos, NM (United Stat
2016-04-07
This slide presentation describes basic topological concepts, including topological spaces, homeomorphisms, homotopy, betti numbers. Scalar field topology explores finding topological features and scalar field visualization, and vector field topology explores finding topological features and vector field visualization.
Topology and mental distress: self-care in the life spaces of home.
Tucker, Ian; Smith, Lesley-Ann
2014-01-01
This article develops a topological approach derived from Kurt Lewin to analyse the psychological life space/s produced in a mental health service user's home. Drawing on arguments that space plays an important part in the organisation and management of mental distress, photographs of a service user's home are analysed as topological spaces. The article argues that topological theory can contribute to community health psychology through framing psychological distress as spatially distributed, meaning individual bodies, environments and action are conceptualised as equally contributing to the organisation and management of health-related experience and activity.
The Chern-Simons one-form and gravity on a fuzzy space
International Nuclear Information System (INIS)
Nair, V.P.
2006-01-01
The one-dimensional NxN-matrix Chern-Simons action is given, for large N and for slowly varying fields, by the (2k+1)-dimensional Chern-Simons action S CS , where the gauge fields in S CS parametrize the different ways in which the large N limit can be taken. Since some of these gauge fields correspond to the isometries of the space, we argue that gravity on fuzzy spaces can be described by the one-dimensional matrix Chern-Simons action at finite N and by the higher dimensional Chern-Simons action when the fuzzy space is approximated by a continuous manifold
Topology on grill-filter space and continuity
Directory of Open Access Journals (Sweden)
Shyamapada Modak
2013-12-01
Full Text Available This paper will discuss about a new topology, obtained from a grill and a filter on the same set. The Characterizations and open base of the new topology are also aim of this paper. The generalized continuity is also a part of this paper.
Topology of digital images visual pattern discovery in proximity spaces
Peters, James F
2014-01-01
This book carries forward recent work on visual patterns and structures in digital images and introduces a near set-based a topology of digital images. Visual patterns arise naturally in digital images viewed as sets of non-abstract points endowed with some form of proximity (nearness) relation. Proximity relations make it possible to construct uniform topolo- gies on the sets of points that constitute a digital image. In keeping with an interest in gaining an understanding of digital images themselves as a rich source of patterns, this book introduces the basics of digital images from a computer vision perspective. In parallel with a computer vision perspective on digital images, this book also introduces the basics of prox- imity spaces. Not only the traditional view of spatial proximity relations but also the more recent descriptive proximity relations are considered. The beauty of the descriptive proximity approach is that it is possible to discover visual set patterns among sets that are non-overlapping ...
Artificial Hydrocarbon Networks Fuzzy Inference System
Ponce, Hiram; Ponce, Pedro; Molina, Arturo
2013-01-01
This paper presents a novel fuzzy inference model based on artificial hydrocarbon networks, a computational algorithm for modeling problems based on chemical hydrocarbon compounds. In particular, the proposed fuzzy-molecular inference model (FIM-model) uses molecular units of information to partition the output space in the defuzzification step. Moreover, these molecules are linguistic units that can be partially understandable due to the organized structure of the topology and metadata param...
Energy-spectrum against topological charge in a nonlinear model in three space-dimensions
International Nuclear Information System (INIS)
Kundu, A.
1981-08-01
A nonlinear field model in three space-dimensions with nontrivial Hopf invariant is studied in an intermediate S 3 -manifold. Energy-spectrum of the system for different values of topological charge is calculated numerically, which with fair accuracy coincides with E 1 n(n+1)/2 where n=topological charge. (author)
International Nuclear Information System (INIS)
Xu Tianzhou; Rassias, John Michael; Xu Wanxin
2010-01-01
We establish some stability results concerning the general mixed additive-cubic functional equation in non-Archimedean fuzzy normed spaces. In addition, we establish some results of approximately general mixed additive-cubic mappings in non-Archimedean fuzzy normed spaces. The results improve and extend some recent results.
International Nuclear Information System (INIS)
Sharma, Sushil; Deshpande, Bhavana
2009-01-01
The purpose of this paper is to prove some common fixed point theorems for finite number of discontinuous, noncompatible mappings on noncomplete intuitionistic fuzzy metric spaces. Our results extend, generalize and intuitionistic fuzzify several known results in fuzzy metric spaces. We give an example and also give formulas for total number of commutativity conditions for finite number of mappings.
Fuzzy Adaptive Control for Intelligent Autonomous Space Exploration Problems
Esogbue, Augustine O.
1998-01-01
The principal objective of the research reported here is the re-design, analysis and optimization of our newly developed neural network fuzzy adaptive controller model for complex processes capable of learning fuzzy control rules using process data and improving its control through on-line adaption. The learned improvement is according to a performance objective function that provides evaluative feedback; this performance objective is broadly defined to meet long-range goals over time. Although fuzzy control had proven effective for complex, nonlinear, imprecisely-defined processes for which standard models and controls are either inefficient, impractical or cannot be derived, the state of the art prior to our work showed that procedures for deriving fuzzy control, however, were mostly ad hoc heuristics. The learning ability of neural networks was exploited to systematically derive fuzzy control and permit on-line adaption and in the process optimize control. The operation of neural networks integrates very naturally with fuzzy logic. The neural networks which were designed and tested using simulation software and simulated data, followed by realistic industrial data were reconfigured for application on several platforms as well as for the employment of improved algorithms. The statistical procedures of the learning process were investigated and evaluated with standard statistical procedures (such as ANOVA, graphical analysis of residuals, etc.). The computational advantage of dynamic programming-like methods of optimal control was used to permit on-line fuzzy adaptive control. Tests for the consistency, completeness and interaction of the control rules were applied. Comparisons to other methods and controllers were made so as to identify the major advantages of the resulting controller model. Several specific modifications and extensions were made to the original controller. Additional modifications and explorations have been proposed for further study. Some of
A study of entropy/clarity of genetic sequences using metric spaces and fuzzy sets.
Georgiou, D N; Karakasidis, T E; Nieto, Juan J; Torres, A
2010-11-07
The study of genetic sequences is of great importance in biology and medicine. Sequence analysis and taxonomy are two major fields of application of bioinformatics. In the present paper we extend the notion of entropy and clarity to the use of different metrics and apply them in the case of the Fuzzy Polynuclotide Space (FPS). Applications of these notions on selected polynucleotides and complete genomes both in the I(12×k) space, but also using their representation in FPS are presented. Our results show that the values of fuzzy entropy/clarity are indicative of the degree of complexity necessary for the description of the polynucleotides in the FPS, although in the latter case the interpretation is slightly different than in the case of the I(12×k) hypercube. Fuzzy entropy/clarity along with the use of appropriate metrics can contribute to sequence analysis and taxonomy. Copyright © 2010 Elsevier Ltd. All rights reserved.
Topological Structures of Derivative Weighted Composition Operators on the Bergman Space
Directory of Open Access Journals (Sweden)
Ce-Zhong Tong
2015-01-01
Full Text Available We characterize the difference of derivative weighted composition operators on the Bergman space in the unit disk and determine when linear-fractional derivative weighted composition operators belong to the same component of the space of derivative weighted composition operators on the Bergman space under the operator norm topology.
Some fixed point results in fuzzy metric spaces using a control function
Directory of Open Access Journals (Sweden)
C. T. Aage
2017-02-01
Full Text Available In this paper, we establish the results on existence and uniqueness of fixed point for φ-contractive and generalized C-contractive mapping in the fuzzy metric space in the sense of George and Veeramani. We use the notion of altering distance for proving the results.
Prediction of Secondary Dendrite Arm Spacing in Squeeze Casting Using Fuzzy Logic Based Approaches
Directory of Open Access Journals (Sweden)
Patel M.G.C.
2015-03-01
Full Text Available The quality of the squeeze castings is significantly affected by secondary dendrite arm spacing, which is influenced by squeeze cast input parameters. The relationships of secondary dendrite arm spacing with the input parameters, namely time delay, pressure duration, squeeze pressure, pouring and die temperatures are complex in nature. The present research work focuses on the development of input-output relationships using fuzzy logic approach. In fuzzy logic approach, squeeze cast process variables are expressed as a function of input parameters and secondary dendrite arm spacing is expressed as an output parameter. It is important to note that two fuzzy logic based approaches have been developed for the said problem. The first approach deals with the manually constructed mamdani based fuzzy system and the second approach deals with automatic evolution of the Takagi and Sugeno’s fuzzy system. It is important to note that the performance of the developed models is tested for both linear and non-linear type membership functions. In addition the developed models were compared with the ten test cases which are different from those of training data. The developed fuzzy systems eliminates the need of a number of trials in selection of most influential squeeze cast process parameters. This will reduce time and cost of trial experimentations. The results showed that, all the developed models can be effectively used for making prediction. Further, the present research work will help foundrymen to select parameters in squeeze casting to obtain the desired quality casting without much of time and resource consuming.
International Nuclear Information System (INIS)
Doebner, H.; Mann, H.
1997-01-01
We consider configuration spaces of nonidentical pointlike particles. The physically motivated assumption that any two particles cannot be located at the same point in space endash time leads to nontrivial topological structure of the configuration space. For a quantum mechanical description of such a system, we classify complex vector bundles over the configuration space and obtain potentials of topological origin, similar to those that occur in the fiber bundle approach to Dirac close-quote s magnetic monopole or in Yang endash Mills theory. copyright 1997 American Institute of Physics
Chai, Runqi; Savvaris, Al; Tsourdos, Antonios
2016-06-01
In this paper, a fuzzy physical programming (FPP) method has been introduced for solving multi-objective Space Manoeuvre Vehicles (SMV) skip trajectory optimization problem based on hp-adaptive pseudospectral methods. The dynamic model of SMV is elaborated and then, by employing hp-adaptive pseudospectral methods, the problem has been transformed to nonlinear programming (NLP) problem. According to the mission requirements, the solutions were calculated for each single-objective scenario. To get a compromised solution for each target, the fuzzy physical programming (FPP) model is proposed. The preference function is established with considering the fuzzy factor of the system such that a proper compromised trajectory can be acquired. In addition, the NSGA-II is tested to obtain the Pareto-optimal solution set and verify the Pareto optimality of the FPP solution. Simulation results indicate that the proposed method is effective and feasible in terms of dealing with the multi-objective skip trajectory optimization for the SMV.
Fuzzy Mobile-Robot Positioning in Intelligent Spaces Using Wireless Sensor Networks
Directory of Open Access Journals (Sweden)
David Herrero
2011-11-01
Full Text Available This work presents the development and experimental evaluation of a method based on fuzzy logic to locate mobile robots in an Intelligent Space using Wireless Sensor Networks (WSNs. The problem consists of locating a mobile node using only inter-node range measurements, which are estimated by radio frequency signal strength attenuation. The sensor model of these measurements is very noisy and unreliable. The proposed method makes use of fuzzy logic for modeling and dealing with such uncertain information. Besides, the proposed approach is compared with a probabilistic technique showing that the fuzzy approach is able to handle highly uncertain situations that are difficult to manage by well-known localization methods.
Artificial Hydrocarbon Networks Fuzzy Inference System
Directory of Open Access Journals (Sweden)
Hiram Ponce
2013-01-01
Full Text Available This paper presents a novel fuzzy inference model based on artificial hydrocarbon networks, a computational algorithm for modeling problems based on chemical hydrocarbon compounds. In particular, the proposed fuzzy-molecular inference model (FIM-model uses molecular units of information to partition the output space in the defuzzification step. Moreover, these molecules are linguistic units that can be partially understandable due to the organized structure of the topology and metadata parameters involved in artificial hydrocarbon networks. In addition, a position controller for a direct current (DC motor was implemented using the proposed FIM-model in type-1 and type-2 fuzzy inference systems. Experimental results demonstrate that the fuzzy-molecular inference model can be applied as an alternative of type-2 Mamdani’s fuzzy control systems because the set of molecular units can deal with dynamic uncertainties mostly present in real-world control applications.
Abelian gauge theory in topologically non-trivial space
International Nuclear Information System (INIS)
Hosoya, Akio; Soda, Jiro.
1989-05-01
We quantize the (1+1)-dimensional Abelian gauge theory on cylinder to illustrate our idea how to extract global modes of topological orign. A new analysis is made for the (2+1)-dimensional Maxwell theory on T 2 (torus) x R(time). The dynamics is explicitly given for the Wilson loops around cycles of the torus with arbitrary moduli parameters. We also discuss an extension to antisymmetric tensor fields in higher dimensions. (author)
Topological sectors and measures on moduli space in quantum Yang-Mills on a Riemann surface
Fine, Dana Stanley
1996-03-01
Previous path integral treatments of Yang-Mills on a Riemann surface automatically sum over principal fiber bundles of all possible topological types in computing quantum expectations. This paper extends the path integral formulation to treat separately each topological sector. The formulation is sufficiently explicit to calculate Wilson line expectations exactly. Further, it suggests two new measures on the moduli space of flat connections, one of which proves to agree with the small-volume limit of the Yang-Mills measure.
Topological Field Theory of the Initial Singularity of Space-Time
Bogdanoff, I
2000-01-01
Here we suggest a possible resolution of the initial space-time singularity. In this novel approach, the initial singularity of space-time corresponds to a 0 size singular gravitational instanton, characterised by a Riemannian metric configuration (++++) in dimension D = 4. Associated with the 0 scale of space-time, the initial singularity is thus not considered in terms of divergences of physical fields but can be resolved in terms of topological field symmetries and associated invariants (in particular the first Donaldson invariant ). In this perspective, we here introduce a new topological invariant, associated with 0 scale, of the form Z = Tr (-1)s which we call "singularity invariant".
Scale-space measures for graph topology link protein network architecture to function.
Hulsman, Marc; Dimitrakopoulos, Christos; de Ridder, Jeroen
2014-06-15
The network architecture of physical protein interactions is an important determinant for the molecular functions that are carried out within each cell. To study this relation, the network architecture can be characterized by graph topological characteristics such as shortest paths and network hubs. These characteristics have an important shortcoming: they do not take into account that interactions occur across different scales. This is important because some cellular functions may involve a single direct protein interaction (small scale), whereas others require more and/or indirect interactions, such as protein complexes (medium scale) and interactions between large modules of proteins (large scale). In this work, we derive generalized scale-aware versions of known graph topological measures based on diffusion kernels. We apply these to characterize the topology of networks across all scales simultaneously, generating a so-called graph topological scale-space. The comprehensive physical interaction network in yeast is used to show that scale-space based measures consistently give superior performance when distinguishing protein functional categories and three major types of functional interactions-genetic interaction, co-expression and perturbation interactions. Moreover, we demonstrate that graph topological scale spaces capture biologically meaningful features that provide new insights into the link between function and protein network architecture. Matlab(TM) code to calculate the scale-aware topological measures (STMs) is available at http://bioinformatics.tudelft.nl/TSSA © The Author 2014. Published by Oxford University Press.
On the approximative normal values of multivalued operators in topological vector space
International Nuclear Information System (INIS)
Nguyen Minh Chuong; Khuat van Ninh
1989-09-01
In this paper the problem of approximation of normal values of multivalued linear closed operators from topological vector Mackey space into E-space is considered. Existence of normal value and convergence of approximative values to normal value are proved. (author). 4 refs
Energy Technology Data Exchange (ETDEWEB)
Na, Man Gyun [Department of Nuclear Engineering, Chosun University, 375 Seosuk-dong, Dong-gu, Gwangju 501-759 (Korea, Republic of)]. E-mail: magyna@chosun.ac.kr; Upadhyaya, Belle R. [Department of Nuclear Engineering, University of Tennessee, Knoxville, TN 37996-2300 (United States)
2006-11-15
In this work, a model predictive control method combined with fuzzy identification, is applied to the design of the thermoelectric (TE) power control in the SP-100 space reactor. The future TE power is predicted by using the fuzzy model identified by a subtractive clustering method of a fast and robust algorithm. The objectives of the proposed fuzzy model predictive controller are to minimize both the difference between the predicted TE power and the desired power, and the variation of control drum angle that adjusts the control reactivity. Also, the objectives are subject to maximum and minimum control drum angle and maximum drum angle variation speed. The genetic algorithm that is effective in accomplishing multiple objectives is used to optimize the fuzzy model predictive controller. A lumped parameter simulation model of the SP-100 nuclear space reactor is used to verify the proposed controller. The results of numerical simulations to check the performance of the proposed controller show that the TE generator power level controlled by the proposed controller could track the target power level effectively, satisfying all control constraints.
The Ascoli property for function spaces and the weak topology of Banach and Fréchet spaces
Czech Academy of Sciences Publication Activity Database
Gabriyelyan, S.; Kąkol, Jerzy; Plebanek, G.
2016-01-01
Roč. 233, č. 2 (2016), s. 119-139 ISSN 0039-3223 R&D Projects: GA ČR GF16-34860L Institutional support: RVO:67985840 Keywords : locally convex-space Subject RIV: BA - General Mathematics Impact factor: 0.535, year: 2016 https://www.impan.pl/pl/wydawnictwa/czasopisma-i-serie-wydawnicze/studia- mathematica /all/233/2/91577/the-ascoli-property-for-function-spaces-and-the-weak-topology-of-banach-and-frechet-spaces
Topological properties of some sequences defined over 2-normed spaces.
Dutta, Hemen; Kilicman, Adem; Altun, Omer
2016-01-01
The paper investigates some classes of real number sequences over 2-normed spaces defined by means of Orlicz functions, a bounded sequence of strictly positive real numbers, a multiplier and a normal paranormed sequence space. Relevant properties of such classes have been investigated. Moreover, relationships among different such classes of sequences have also been studied under various parameters and conditions. Finally, the spaces are investigated for some other useful properties. The conclusion section provides many interesting facts for further research.
Bratsas, Charalampos; Koutkias, Vassilis; Kaimakamis, Evangelos; Bamidis, Panagiotis; Maglaveras, Nicos
2007-01-01
Medical Computational Problem (MCP) solving is related to medical problems and their computerized algorithmic solutions. In this paper, an extension of an ontology-based model to fuzzy logic is presented, as a means to enhance the information retrieval (IR) procedure in semantic management of MCPs. We present herein the methodology followed for the fuzzy expansion of the ontology model, the fuzzy query expansion procedure, as well as an appropriate ontology-based Vector Space Model (VSM) that was constructed for efficient mapping of user-defined MCP search criteria and MCP acquired knowledge. The relevant fuzzy thesaurus is constructed by calculating the simultaneous occurrences of terms and the term-to-term similarities derived from the ontology that utilizes UMLS (Unified Medical Language System) concepts by using Concept Unique Identifiers (CUI), synonyms, semantic types, and broader-narrower relationships for fuzzy query expansion. The current approach constitutes a sophisticated advance for effective, semantics-based MCP-related IR.
Wang, Huiya; Feng, Jun; Wang, Hongyu
2017-07-20
Detection of clustered microcalcification (MC) from mammograms plays essential roles in computer-aided diagnosis for early stage breast cancer. To tackle problems associated with the diversity of data structures of MC lesions and the variability of normal breast tissues, multi-pattern sample space learning is required. In this paper, a novel grouped fuzzy Support Vector Machine (SVM) algorithm with sample space partition based on Expectation-Maximization (EM) (called G-FSVM) is proposed for clustered MC detection. The diversified pattern of training data is partitioned into several groups based on EM algorithm. Then a series of fuzzy SVM are integrated for classification with each group of samples from the MC lesions and normal breast tissues. From DDSM database, a total of 1,064 suspicious regions are selected from 239 mammography, and the measurement of Accuracy, True Positive Rate (TPR), False Positive Rate (FPR) and EVL = TPR* 1-FPR are 0.82, 0.78, 0.14 and 0.72, respectively. The proposed method incorporates the merits of fuzzy SVM and multi-pattern sample space learning, decomposing the MC detection problem into serial simple two-class classification. Experimental results from synthetic data and DDSM database demonstrate that our integrated classification framework reduces the false positive rate significantly while maintaining the true positive rate.
On generalized δ-semiclosed sets in topological spaces
International Nuclear Information System (INIS)
Park, Jin Han; Song, Dae Seob; Saadati, Reza
2007-01-01
The aim of this paper is to introduce the class of gδs-closed sets and obtain the characterizations of T 3/4 space due to Dontchev and Ganster [Dontchev J, Ganster M. On δ-generalized closed set and T 3/4 -spaces. Mem Fac Sci Kochi Univ Ser A (Math) 1996;17:15-31]. We also introduce the notion of gδs-continuity and investigate the relationships between it and other types of continuity
A Class of Fan-Browder Type Fixed-Point Theorem and Its Applications in Topological Space
Directory of Open Access Journals (Sweden)
Yi-An Chen
2010-01-01
Full Text Available A fixed-point theorem is proved under noncompact setting of general topological spaces. By applying the fixed-point theorem, several new existence theorems of solutions for equilibrium problems are proved under noncompact setting of topological spaces. These theorems improve and generalize the corresponding results in related literature.
Martin, J. Larry
A test was designed to measure whether or not the child's conceptualization of space would demand that two topological properties of figures (connectedness, and openness and closedness) remain invariant when the figures were subjected to transformations. Ninety children, 30 from each of ages four, six, and eight, were tested. Six items were given…
The duality in the topological vector spaces and the linear physical system theory
International Nuclear Information System (INIS)
Oliveira Castro, F.M. de.
1980-01-01
The excitation-response relation in a linear, passive, and causal physical system who has the property of this relation be invariant for a time translation is univocally determined by the general form of the linear and continuous functionals defined on the linear topological space chosen for the representation of the excitations. (L.C.) [pt
Brown, Robert B.
1994-01-01
A software pilot model for Space Shuttle proximity operations is developed, utilizing fuzzy logic. The model is designed to emulate a human pilot during the terminal phase of a Space Shuttle approach to the Space Station. The model uses the same sensory information available to a human pilot and is based upon existing piloting rules and techniques determined from analysis of human pilot performance. Such a model is needed to generate numerous rendezvous simulations to various Space Station assembly stages for analysis of current NASA procedures and plume impingement loads on the Space Station. The advantages of a fuzzy logic pilot model are demonstrated by comparing its performance with NASA's man-in-the-loop simulations and with a similar model based upon traditional Boolean logic. The fuzzy model is shown to respond well from a number of initial conditions, with results typical of an average human. In addition, the ability to model different individual piloting techniques and new piloting rules is demonstrated.
The topology of the possible: formal spaces underlying patterns of evolutionary change.
Stadler, B M; Stadler, P F; Wagner, G P; Fontana, W
2001-11-21
The current implementation of the Neo-Darwinian model of evolution typically assumes that the set of possible phenotypes is organized into a highly symmetric and regular space equipped with a notion of distance, for example, a Euclidean vector space. Recent computational work on a biophysical genotype-phenotype model based on the folding of RNA sequences into secondary structures suggests a rather different picture. If phenotypes are organized according to genetic accessibility, the resulting space lacks a metric and is formalized by an unfamiliar structure, known as a pre-topology. Patterns of phenotypic evolution-such as punctuation, irreversibility, modularity--result naturally from the properties of this space. The classical framework, however, addresses these patterns by exclusively invoking natural selection on suitably imposed fitness landscapes. We propose to extend the explanatory level for phenotypic evolution from fitness considerations alone to include the topological structure of phenotype space as induced by the genotype-phenotype map. We introduce the mathematical concepts and tools necessary to formalize the notion of accessibility pre-topology relative to which we can speak of continuity in the genotype-phenotype map and in evolutionary trajectories. We connect the factorization of a pre-topology into a product space with the notion of phenotypic character and derive a condition for factorization. Based on anecdotal evidence from the RNA model, we conjecture that this condition is not globally fulfilled, but rather confined to regions where the genotype-phenotype map is continuous. Equivalently, local regions of genotype space on which the map is discontinuous are associated with the loss of character autonomy. This is consistent with the importance of these regions for phenotypic innovation. The intention of the present paper is to offer a perspective, a framework to implement this perspective, and a few results illustrating how this framework can
Space station common module network topology and hardware development
Anderson, P.; Braunagel, L.; Chwirka, S.; Fishman, M.; Freeman, K.; Eason, D.; Landis, D.; Lech, L.; Martin, J.; Mccorkle, J.
1990-01-01
Conceptual space station common module power management and distribution (SSM/PMAD) network layouts and detailed network evaluations were developed. Individual pieces of hardware to be developed for the SSM/PMAD test bed were identified. A technology assessment was developed to identify pieces of equipment requiring development effort. Equipment lists were developed from the previously selected network schematics. Additionally, functional requirements for the network equipment as well as other requirements which affected the suitability of specific items for use on the Space Station Program were identified. Assembly requirements were derived based on the SSM/PMAD developed requirements and on the selected SSM/PMAD network concepts. Basic requirements and simplified design block diagrams are included. DC remote power controllers were successfully integrated into the DC Marshall Space Flight Center breadboard. Two DC remote power controller (RPC) boards experienced mechanical failure of UES 706 stud-mounted diodes during mechanical installation of the boards into the system. These broken diodes caused input to output shorting of the RPC's. The UES 706 diodes were replaced on these RPC's which eliminated the problem. The DC RPC's as existing in the present breadboard configuration do not provide ground fault protection because the RPC was designed to only switch the hot side current. If ground fault protection were to be implemented, it would be necessary to design the system so the RPC switched both the hot and the return sides of power.
Field theory amplitudes in a space with SU(2) fuzziness
Komaie-Moghaddam, H.; Fatollahi, A. H.; Khorrami, M.
2008-02-01
The structure of transition amplitudes in field theory in a three-dimensional space whose spatial coordinates are noncommutative and satisfy the SU(2) Lie algebra commutation relations is examined. In particular, the basic notions for constructing the observables of the theory as well as subtleties related to the proper treatment of δ distributions (corresponding to conservation laws) are introduced. Explicit examples are given for scalar field theory amplitudes in the lowest order of perturbation.
Ahn, Junyeong; Yang, Bohm-Jung
2017-04-01
We study a topological phase transition between a normal insulator and a quantum spin Hall insulator in two-dimensional (2D) systems with time-reversal and twofold rotation symmetries. Contrary to the case of ordinary time-reversal invariant systems, where a direct transition between two insulators is generally predicted, we find that the topological phase transition in systems with an additional twofold rotation symmetry is mediated by an emergent stable 2D Weyl semimetal phase between two insulators. Here the central role is played by the so-called space-time inversion symmetry, the combination of time-reversal and twofold rotation symmetries, which guarantees the quantization of the Berry phase around a 2D Weyl point even in the presence of strong spin-orbit coupling. Pair creation and pair annihilation of Weyl points accompanying partner exchange between different pairs induces a jump of a 2D Z2 topological invariant leading to a topological phase transition. According to our theory, the topological phase transition in HgTe /CdTe quantum well structure is mediated by a stable 2D Weyl semimetal phase because the quantum well, lacking inversion symmetry intrinsically, has twofold rotation about the growth direction. Namely, the HgTe /CdTe quantum well can show 2D Weyl semimetallic behavior within a small but finite interval in the thickness of HgTe layers between a normal insulator and a quantum spin Hall insulator. We also propose that few-layer black phosphorus under perpendicular electric field is another candidate system to observe the unconventional topological phase transition mechanism accompanied by the emerging 2D Weyl semimetal phase protected by space-time inversion symmetry.
Ahn, Junyeong; Yang, Bohm-Jung
2017-04-14
We study a topological phase transition between a normal insulator and a quantum spin Hall insulator in two-dimensional (2D) systems with time-reversal and twofold rotation symmetries. Contrary to the case of ordinary time-reversal invariant systems, where a direct transition between two insulators is generally predicted, we find that the topological phase transition in systems with an additional twofold rotation symmetry is mediated by an emergent stable 2D Weyl semimetal phase between two insulators. Here the central role is played by the so-called space-time inversion symmetry, the combination of time-reversal and twofold rotation symmetries, which guarantees the quantization of the Berry phase around a 2D Weyl point even in the presence of strong spin-orbit coupling. Pair creation and pair annihilation of Weyl points accompanying partner exchange between different pairs induces a jump of a 2D Z_{2} topological invariant leading to a topological phase transition. According to our theory, the topological phase transition in HgTe/CdTe quantum well structure is mediated by a stable 2D Weyl semimetal phase because the quantum well, lacking inversion symmetry intrinsically, has twofold rotation about the growth direction. Namely, the HgTe/CdTe quantum well can show 2D Weyl semimetallic behavior within a small but finite interval in the thickness of HgTe layers between a normal insulator and a quantum spin Hall insulator. We also propose that few-layer black phosphorus under perpendicular electric field is another candidate system to observe the unconventional topological phase transition mechanism accompanied by the emerging 2D Weyl semimetal phase protected by space-time inversion symmetry.
On Intuitionistic Fuzzy Filters of Intuitionistic Fuzzy Coframes
Directory of Open Access Journals (Sweden)
Rajesh K. Thumbakara
2013-01-01
Full Text Available Frame theory is the study of topology based on its open set lattice, and it was studied extensively by various authors. In this paper, we study quotients of intuitionistic fuzzy filters of an intuitionistic fuzzy coframe. The quotients of intuitionistic fuzzy filters are shown to be filters of the given intuitionistic fuzzy coframe. It is shown that the collection of all intuitionistic fuzzy filters of a coframe and the collection of all intutionistic fuzzy quotient filters of an intuitionistic fuzzy filter are coframes.
On some problems of descriptive set theory in topological spaces
International Nuclear Information System (INIS)
Choban, M M
2005-01-01
Problems concerning the structure of Borel sets, their classification, and invariance of certain properties of sets under maps of given types arose in the first half of the previous century in the works of A. Lebesgue, R. Baire, N. N. Luzin, P. S. Alexandroff, P. S. Urysohn, P. S. Novikov, L. V. Keldysh, and A. A. Lyapunov and gave rise to many investigations. In this paper some results related to questions of F. Hausdorff, Luzin, Alexandroff, Urysohn, M. Katetov, and A. H. Stone are obtained. In 1934 Hausdorff posed the problem of invariance of the property of being an absolute B-set (that is, a Borel set in some complete separable metric space) under open continuous maps. By a theorem of Keldysh, the answer to this question is negative in general. The present paper gives additional conditions under which the answer to Hausdorff's question is positive. Some general problems of the theory of operations on sets are also treated
On some problems of descriptive set theory in topological spaces
Energy Technology Data Exchange (ETDEWEB)
Choban, M M [Tiraspol State University, Chisinau (Moldova, Republic of)
2005-08-31
Problems concerning the structure of Borel sets, their classification, and invariance of certain properties of sets under maps of given types arose in the first half of the previous century in the works of A. Lebesgue, R. Baire, N. N. Luzin, P. S. Alexandroff, P. S. Urysohn, P. S. Novikov, L. V. Keldysh, and A. A. Lyapunov and gave rise to many investigations. In this paper some results related to questions of F. Hausdorff, Luzin, Alexandroff, Urysohn, M. Katetov, and A. H. Stone are obtained. In 1934 Hausdorff posed the problem of invariance of the property of being an absolute B-set (that is, a Borel set in some complete separable metric space) under open continuous maps. By a theorem of Keldysh, the answer to this question is negative in general. The present paper gives additional conditions under which the answer to Hausdorff's question is positive. Some general problems of the theory of operations on sets are also treated.
Quantum influence of topological defects in Goedel-type space-times
Energy Technology Data Exchange (ETDEWEB)
Carvalho, Josevi [Universidade Federal de Campina Grande, Unidade Academica de Tecnologia de Alimentos, Centro de Ciencias e Tecnologia Agroalimentar, Pombal, PB (Brazil); Carvalho, M.; Alexandre, M. de [Universidade Federal de Alagoas, Instituto de Fisica, Maceio, AL (Brazil); Furtado, Claudio [Universidade Federal da Paraiba, Cidade Universitaria, Departamento de Fisica, CCEN, Joao Pessoa, PB (Brazil)
2014-06-15
In this contribution, some solutions of the Klein-Gordon equation in Goedel-type metrics with an embedded cosmic string are considered. The quantum dynamics of a scalar particle in three spaces whose metrics are described by different classes of Goedel solutions, with a cosmic string passing through the spaces, is found. The energy levels and eigenfunctions of the Klein-Gordon operator are obtained. We show that these eigenvalues and eigenfunctions depend on the parameter characterizing the presence of a cosmic string in the space-time. We note that the presence of topological defects breaks the degeneracy of energy levels. (orig.)
Kraaij, R.C.
2016-01-01
Let X be a separable metric space and let β be the strict topology on the space of bounded continuous functions on X, which has the space of τ-additive Borel measures as a continuous dual space. We prove a Banach-Dieudonné type result for the space of bounded continuous functions equipped with β:
Floquet many-body engineering: topology and many-body physics in phase space lattices
Liang, Pengfei; Marthaler, Michael; Guo, Lingzhen
2018-02-01
Hamiltonians which are inaccessible in static systems can be engineered in periodically driven many-body systems, i.e., Floquet many-body systems. We propose to use interacting particles in a one-dimensional (1D) harmonic potential with periodic kicking to investigate two-dimensional topological and many-body physics. Depending on the driving parameters, the Floquet Hamiltonian of single kicked harmonic oscillator has various lattice structures in phase space. The noncommutative geometry of phase space gives rise to the topology of the system. We investigate the effective interactions of particles in phase space and find that the point-like contact interaction in quasi-1D real space becomes a long-rang Coulomb-like interaction in phase space, while the hardcore interaction in pure-1D real space becomes a confinement quark-like potential in phase space. We also find that the Floquet exchange interaction does not disappear even in the classical limit, and can be viewed as an effective long-range spin–spin interaction induced by collision. Our proposal may provide platforms to explore new physics and exotic phases by Floquet many-body engineering.
Semi-precontinuous functions and properties of generalized semi-preclosed sets in topological spaces
Navalagi, G. B.
2002-01-01
Andrijević (1986) introduced the class of semi-preopen sets in topological spaces. Since then many authors including Andrijević have studied this class of sets by defining their neighborhoods, separation axioms and functions. The purpose of this paper is to provide the new characterizations of semi-preopen and semi-preclosed sets by defining the concepts of semi-precontinuous mappings, semi-preopen mappings, semi-preclosed mappings, semi-preirresolute mappings, pre-sem...
A Robust Algorithm to Determine the Topology of Space from the Cosmic Microwave Background Radiation
Weeks, Jeffrey R.
2001-01-01
Satellite measurements of the cosmic microwave back-ground radiation will soon provide an opportunity to test whether the universe is multiply connected. This paper presents a new algorithm for deducing the topology of the universe from the microwave background data. Unlike an older algorithm, the new algorithm gives the curvature of space and the radius of the last scattering surface as outputs, rather than requiring them as inputs. The new algorithm is also more tolerant of erro...
On α- τ-disconnectedness and α- τ-connectedness in topological spaces
Directory of Open Access Journals (Sweden)
Sanjay Mishra
2015-07-01
Full Text Available The aims of this paper is to introduce new approach of separate sets, disconnected sets and connected sets called α- τ-separate sets, α- τ-disconnected sets and α- τ-connected sets of topological spaces with the help of α-open and α-closed sets. On the basis of new introduce approach, some relationship of α- τ-disconnected and α- τ-connected set with α- τ-separate sets have been investigated thoroughly.
Ho, Shinn-Ying; Chen, Hung-Ming; Ho, Shinn-Jang; Chen, Tai-Kang
2004-04-01
An evolutionary approach to designing accurate classifiers with a compact fuzzy-rule base using a scatter partition of feature space is proposed, in which all the elements of the fuzzy classifier design problem have been moved in parameters of a complex optimization problem. An intelligent genetic algorithm (IGA) is used to effectively solve the design problem of fuzzy classifiers with many tuning parameters. The merits of the proposed method are threefold: 1) the proposed method has high search ability to efficiently find fuzzy rule-based systems with high fitness values, 2) obtained fuzzy rules have high interpretability, and 3) obtained compact classifiers have high classification accuracy on unseen test patterns. The sensitivity of control parameters of the proposed method is empirically analyzed to show the robustness of the IGA-based method. The performance comparison and statistical analysis of experimental results using ten-fold cross validation show that the IGA-based method without heuristics is efficient in designing accurate and compact fuzzy classifiers using 11 well-known data sets with numerical attribute values.
Fuzzy adaptive robust control for space robot considering the effect of the gravity
Directory of Open Access Journals (Sweden)
Qin Li
2014-12-01
Full Text Available Space robot is assembled and tested in gravity environment, and completes on-orbit service (OOS in microgravity environment. The kinematic and dynamic characteristic of the robot will change with the variations of gravity in different working condition. Fully considering the change of kinematic and dynamic models caused by the change of gravity environment, a fuzzy adaptive robust control (FARC strategy which is adaptive to these model variations is put forward for trajectory tracking control of space robot. A fuzzy algorithm is employed to approximate the nonlinear uncertainties in the model, adaptive laws of the parameters are constructed, and the approximation error is compensated by using a robust control algorithm. The stability of the control system is guaranteed based on the Lyapunov theory and the trajectory tracking control simulation is performed. The simulation results are compared with the proportional plus derivative (PD controller, and the effectiveness to achieve better trajectory tracking performance under different gravity environment without changing the control parameters and the advantage of the proposed controller are verified.
Topological structure of the space of phenotypes: the case of RNA neutral networks.
Directory of Open Access Journals (Sweden)
Jacobo Aguirre
Full Text Available The evolution and adaptation of molecular populations is constrained by the diversity accessible through mutational processes. RNA is a paradigmatic example of biopolymer where genotype (sequence and phenotype (approximated by the secondary structure fold are identified in a single molecule. The extreme redundancy of the genotype-phenotype map leads to large ensembles of RNA sequences that fold into the same secondary structure and can be connected through single-point mutations. These ensembles define neutral networks of phenotypes in sequence space. Here we analyze the topological properties of neutral networks formed by 12-nucleotides RNA sequences, obtained through the exhaustive folding of sequence space. A total of 4(12 sequences fragments into 645 subnetworks that correspond to 57 different secondary structures. The topological analysis reveals that each subnetwork is far from being random: it has a degree distribution with a well-defined average and a small dispersion, a high clustering coefficient, and an average shortest path between nodes close to its minimum possible value, i.e. the Hamming distance between sequences. RNA neutral networks are assortative due to the correlation in the composition of neighboring sequences, a feature that together with the symmetries inherent to the folding process explains the existence of communities. Several topological relationships can be analytically derived attending to structural restrictions and generic properties of the folding process. The average degree of these phenotypic networks grows logarithmically with their size, such that abundant phenotypes have the additional advantage of being more robust to mutations. This property prevents fragmentation of neutral networks and thus enhances the navigability of sequence space. In summary, RNA neutral networks show unique topological properties, unknown to other networks previously described.
Probabilistic uniformities of uniform spaces
International Nuclear Information System (INIS)
Rodriguez Lopez, J.; Romaguera, S.; Sanchis, M.
2017-01-01
The theory of metric spaces in the fuzzy context has shown to be an interesting area of study not only from a theoretical point of view but also for its applications. Nevertheless, it is usual to consider these spaces as classical topological or uniform spaces and there are not too many results about constructing fuzzy topological structures starting from a fuzzy metric. Maybe, H/ o hle was the first to show how to construct a probabilistic uniformity and a Lowen uniformity from a probabilistic pseudometric /cite{Hohle78,Hohle82a}. His method can be directly translated to the context of fuzzy metrics and allows to characterize the categories of probabilistic uniform spaces or Lowen uniform spaces by means of certain families of fuzzy pseudometrics /cite{RL}. On the other hand, other different fuzzy uniformities can be constructed in a fuzzy metric space: a Hutton $[0,1]$-quasi-uniformity /cite{GGPV06}; a fuzzifiying uniformity /cite{YueShi10}, etc. The paper /cite{GGRLRo} gives a study of several methods of endowing a fuzzy pseudometric space with a probabilistic uniformity and a Hutton $[0,1]$-quasi-uniformity. In 2010, J. Guti/'errez Garc/'{/i}a, S. Romaguera and M. Sanchis /cite{GGRoSanchis10} proved that the category of uniform spaces is isomorphic to a category formed by sets endowed with a fuzzy uniform structure, i. e. a family of fuzzy pseudometrics satisfying certain conditions. We will show here that, by means of this isomorphism, we can obtain several methods to endow a uniform space with a probabilistic uniformity. Furthermore, these constructions allow to obtain a factorization of some functors introduced in /cite{GGRoSanchis10}. (Author)
Probabilistic uniformities of uniform spaces
Energy Technology Data Exchange (ETDEWEB)
Rodriguez Lopez, J.; Romaguera, S.; Sanchis, M.
2017-07-01
The theory of metric spaces in the fuzzy context has shown to be an interesting area of study not only from a theoretical point of view but also for its applications. Nevertheless, it is usual to consider these spaces as classical topological or uniform spaces and there are not too many results about constructing fuzzy topological structures starting from a fuzzy metric. Maybe, H/{sup o}hle was the first to show how to construct a probabilistic uniformity and a Lowen uniformity from a probabilistic pseudometric /cite{Hohle78,Hohle82a}. His method can be directly translated to the context of fuzzy metrics and allows to characterize the categories of probabilistic uniform spaces or Lowen uniform spaces by means of certain families of fuzzy pseudometrics /cite{RL}. On the other hand, other different fuzzy uniformities can be constructed in a fuzzy metric space: a Hutton $[0,1]$-quasi-uniformity /cite{GGPV06}; a fuzzifiying uniformity /cite{YueShi10}, etc. The paper /cite{GGRLRo} gives a study of several methods of endowing a fuzzy pseudometric space with a probabilistic uniformity and a Hutton $[0,1]$-quasi-uniformity. In 2010, J. Guti/'errez Garc/'{/i}a, S. Romaguera and M. Sanchis /cite{GGRoSanchis10} proved that the category of uniform spaces is isomorphic to a category formed by sets endowed with a fuzzy uniform structure, i. e. a family of fuzzy pseudometrics satisfying certain conditions. We will show here that, by means of this isomorphism, we can obtain several methods to endow a uniform space with a probabilistic uniformity. Furthermore, these constructions allow to obtain a factorization of some functors introduced in /cite{GGRoSanchis10}. (Author)
De la Sen, M.
2015-01-01
In the framework of complete probabilistic metric spaces and, in particular, in probabilistic Menger spaces, this paper investigates some relevant properties of convergence of sequences to probabilistic α-fuzzy fixed points under some types of probabilistic contractive conditions.
Topological entropy and renormalization group flow in 3-dimensional spherical spaces
International Nuclear Information System (INIS)
Asorey, M.; Beneventano, C.G.; Cavero-Peláez, I.; D’Ascanio, D.; Santangelo, E.M.
2015-01-01
We analyze the renormalization group (RG) flow of the temperature independent term of the entropy in the high temperature limit β/a≪1 of a massive field theory in 3-dimensional spherical spaces, M 3 , with constant curvature 6/a 2 . For masses lower than ((2π)/β), this term can be identified with the free energy of the same theory on M 3 considered as a 3-dimensional Euclidean space-time. The non-extensive part of this free energy, S hol , is generated by the holonomy of the spatial metric connection. We show that for homogeneous spherical spaces the holonomy entropy S hol decreases monotonically when the RG scale flows to the infrared. At the conformal fixed points the values of the holonomy entropy do coincide with the genuine topological entropies recently introduced. The monotonic behavior of the RG flow leads to an inequality between the topological entropies of the conformal field theories connected by such flow, i.e. S top UV >S top IR . From a 3-dimensional viewpoint the same term arises in the 3-dimensional Euclidean effective action and has the same monotonic behavior under the RG group flow. We conjecture that such monotonic behavior is generic, which would give rise to a 3-dimensional generalization of the c-theorem, along the lines of the 2-dimensional c-theorem and the 4-dimensional a-theorem. The conjecture is related to recent formulations of the F-theorem. In particular, the holonomy entropy on lens spaces is directly related to the topological Rényi entanglement entropy on disks of 2-dimensional flat spaces.
Topological recursion for chord diagrams, RNA complexes, and cells in moduli spaces
DEFF Research Database (Denmark)
Andersen, Jørgen Goul; chekhov, Leonid; Penner, Robert
2013-01-01
We introduce and study the Hermitian matrix model with potential V(x)=x^2/2-stx/(1-tx), which enumerates the number of linear chord diagrams of fixed genus with specified numbers of backbones generated by s and chords generated by t. For the one-cut solution, the partition function, correlators a...... topology as well as the number of cells in Riemann's moduli spaces for bordered surfaces. The free energies are computed here in principle for all genera and explicitly for genera less than four....... and free energies are convergent for small t and all s as a perturbation of the Gaussian potential, which arises for st=0. This perturbation is computed using the formalism of the topological recursion. The corresponding enumeration of chord diagrams gives at once the number of RNA complexes of a given...
Energy Technology Data Exchange (ETDEWEB)
Mackey, Lester [Department of Statistics, Stanford University,Stanford, CA 94305 (United States); Nachman, Benjamin [Department of Physics, Stanford University,Stanford, CA 94305 (United States); SLAC National Accelerator Laboratory, Stanford University,2575 Sand Hill Rd, Menlo Park, CA 94025 (United States); Schwartzman, Ariel [SLAC National Accelerator Laboratory, Stanford University,2575 Sand Hill Rd, Menlo Park, CA 94025 (United States); Stansbury, Conrad [Department of Physics, Stanford University,Stanford, CA 94305 (United States)
2016-06-01
Collimated streams of particles produced in high energy physics experiments are organized using clustering algorithms to form jets. To construct jets, the experimental collaborations based at the Large Hadron Collider (LHC) primarily use agglomerative hierarchical clustering schemes known as sequential recombination. We propose a new class of algorithms for clustering jets that use infrared and collinear safe mixture models. These new algorithms, known as fuzzy jets, are clustered using maximum likelihood techniques and can dynamically determine various properties of jets like their size. We show that the fuzzy jet size adds additional information to conventional jet tagging variables in boosted topologies. Furthermore, we study the impact of pileup and show that with some slight modifications to the algorithm, fuzzy jets can be stable up to high pileup interaction multiplicities.
De la Sen, Manuel; Abbas, Mujahid; Saleem, Naeem
2016-01-01
This paper discusses some convergence properties in fuzzy ordered proximal approaches defined by [Formula: see text]-sequences of pairs, where [Formula: see text] is a surjective self-mapping and [Formula: see text] where Aand Bare nonempty subsets of and abstract nonempty set X and [Formula: see text] is a partially ordered non-Archimedean fuzzy metric space which is endowed with a fuzzy metric M, a triangular norm * and an ordering [Formula: see text] The fuzzy set M takes values in a sequence or set [Formula: see text] where the elements of the so-called switching rule [Formula: see text] are defined from [Formula: see text] to a subset of [Formula: see text] Such a switching rule selects a particular realization of M at the nth iteration and it is parameterized by a growth evolution sequence [Formula: see text] and a sequence or set [Formula: see text] which belongs to the so-called [Formula: see text]-lower-bounding mappings which are defined from [0, 1] to [0, 1]. Some application examples concerning discrete systems under switching rules and best approximation solvability of algebraic equations are discussed.
N=2 topological gauge theory, the Euler characteristic of moduli spaces, and the Casson invariant
International Nuclear Information System (INIS)
Blau, M.; Thompson, G.
1991-11-01
Gauge theory with a topological N=2 symmetry is discussed. This theory captures the de Rahm complex and Riemannian geometry of some underlying moduli space M and the partition function equals the Euler number χ (M) of M. Moduli spaces of instantons and of flat connections in 2 and 3 dimensions are explicitly dealt with. To motivate the constructions the relation between the Mathai-Quillen formalism and supersymmetric quantum mechanics are explained and a new kind of supersymmetric quantum mechanics is introduced, based on the Gauss-Codazzi equations. The gauge theory actions are interpreted from the Atiyah-Jeffrey point of view and related to super-symmetric quantum mechanics on spaces of connections. As a consequence of these considerations the Euler number χ (M) of the moduli space of flat connections as a generalization to arbitrary three-manifolds of the Casson invariant. The possibility of constructing a topological version of the Penner matrix model is also commented. (author). 63 refs
Introduction to Fuzzy Set Theory
Kosko, Bart
1990-01-01
An introduction to fuzzy set theory is described. Topics covered include: neural networks and fuzzy systems; the dynamical systems approach to machine intelligence; intelligent behavior as adaptive model-free estimation; fuzziness versus probability; fuzzy sets; the entropy-subsethood theorem; adaptive fuzzy systems for backing up a truck-and-trailer; product-space clustering with differential competitive learning; and adaptive fuzzy system for target tracking.
The topology of perceptive functions as a corollary of the theorem of existence in closed spaces.
Bounias, M; Bonaly, A
1997-01-01
The capability for a system of perceiving both outer objects and an inner self are two fundamental features of abstract mathematical objects endowed with the properties of topologically closed sets. Such structures exist upon intersection of topological spaces owning different dimensions. Then, the theorem of Jordan-Veblen provides their capability of being observable, while the theorems of Brouwer and of Banach-Caccioppoli provide two kinds of fixed points which account for the properties of so-called right and left brain functions. Fixed points account for the biological 'self', and the system provides theoretical justification for the existence of brain structure/function relationships, including memory, emotion, and respective characteristics of right and left hemispheres. Hence, an abstract topological reasoning based on set properties, provides evidence that the observer's function directly infers from the phenomenon of existence and that it belongs to the same mathematical system as the property of being observable. Order relations are raised from equivalence relations by Poincaré groups, upon mappings on the sets of functions and related homotopic transformations in sequences of intersections. Therefore, time is a construction of abstract brain functions, and a living organism just fills the system with appropriate molecular structures.
Topology of Innovation Spaces in the Knowledge Networks Emerging through Questions-And-Answers.
Andjelković, Miroslav; Tadić, Bosiljka; Mitrović Dankulov, Marija; Rajković, Milan; Melnik, Roderick
2016-01-01
The communication processes of knowledge creation represent a particular class of human dynamics where the expertise of individuals plays a substantial role, thus offering a unique possibility to study the structure of knowledge networks from online data. Here, we use the empirical evidence from questions-and-answers in mathematics to analyse the emergence of the network of knowledge contents (or tags) as the individual experts use them in the process. After removing extra edges from the network-associated graph, we apply the methods of algebraic topology of graphs to examine the structure of higher-order combinatorial spaces in networks for four consecutive time intervals. We find that the ranking distributions of the suitably scaled topological dimensions of nodes fall into a unique curve for all time intervals and filtering levels, suggesting a robust architecture of knowledge networks. Moreover, these networks preserve the logical structure of knowledge within emergent communities of nodes, labeled according to a standard mathematical classification scheme. Further, we investigate the appearance of new contents over time and their innovative combinations, which expand the knowledge network. In each network, we identify an innovation channel as a subgraph of triangles and larger simplices to which new tags attach. Our results show that the increasing topological complexity of the innovation channels contributes to network's architecture over different time periods, and is consistent with temporal correlations of the occurrence of new tags. The methodology applies to a wide class of data with the suitable temporal resolution and clearly identified knowledge-content units.
Characterizing real-space topology in Rice-Mele model by thermodynamics
You, Jia-Bin; Yang, Wanli
2018-01-01
The thermodynamic quantities which are related to energy-level statistics are used to characterize the real-space topology of the Rice-Mele model. Through studying the energy spectrum of the model under different boundary conditions, we found that the non-normalizable wave function for the infinite domain is reduced to the edge state adhered to the boundary. For the finite domain with symmetric boundary condition, the critical point for the topological phase transition is equal to the inverse of the domain length. In contrast, the critical point is zero for the semi-infinite domain. Additionally, the symmetry of the energy spectrum is found to be sensitive to the boundary conditions of the Rice-Mele model, and the emergence of the edge states as well as the topological phase transition can be reflected in the thermodynamic properties. A potentially practical scheme is proposed for simulating the Rice-Mele model and detecting the relevant thermodynamic quantities in the context of Bose-Einstein condensate.
Research into topology optimization and the FDM method for a space cracked membrane
Hu, Qingxi; Li, Wanyuan; Zhang, Haiguang; Liu, Dali; Peng, Fujun; Duan, Yongchao
2017-07-01
The problem that the space membranes are easily torn open is the main focus in this paper, and a bionic strengthening-ribs structure is proposed for a space membrane based on interdisciplinary strengths, such as topology optimization, composite materials, and rapid prototyping. The optimization method and modeling method of membranes with bionic strengthening-ribs was studied. The PEEK and SCF/PEEK composite material which are applied to the space environment are chosen, and FDM technology is used. Through topology optimization, bionic strengthening-ribs with good tensile and tear capacities were obtained. Cracked membranes, cracked membranes with PEEK strengthening-ribs and SCF/PEEK strengthening-ribs were tested and test data were obtained. An extension situation and tension fracture were compared for three cases. The experimental results showed that membranes with the bionic strengthening-ribs structure have better mechanical properties, and the strength of the membranes with PEEK and SCF/PEEK strengthening-ribs were raised, respectively, up to 266.9% and 185.9%. The strengthening-ribs structure greatly improves the capacity to halt membrane crack-growth, which has an important significance to avoid membrane tear, and to ensure the spacecraft orbital lifetime.
Weakly Compatible Mappings along with $CLR_{S}$ property in Fuzzy Metric Spaces
Directory of Open Access Journals (Sweden)
Saurabh Manro
2013-11-01
Full Text Available The aim of this work is to use newly introduced property, which is so called common limit in the range $(CLR_{S}$ for four self-mappings, and prove some theorems which satisfy this property. Moreover, we establish some new existence of a common fixed point theorem for generalized contractive mappings in fuzzy metric spaces by using this new property and give some examples to support our results. Ours results does not require condition of closeness of range and so our theorems generalize, unify, and extend many results in literature. Our results improve and extend the results of Cho et al. [4], Pathak et al. [20] and Imdad et. al. [10] besides several known results.
Roiban, Radu; Volovich, Anastasia
2004-09-24
It has recently been proposed that the D-instanton expansion of the open topological B model on P(3|4) is equivalent to the perturbative expansion of the maximally supersymmetric Yang-Mills theory in four dimensions. In this letter we show how to construct the gauge theory results for all n-point conjugate-maximal-helicity-violating amplitudes by computing the integral over the moduli space of curves of degree n-3 in P(3|4), providing strong support to the string theory construction.
Space station common module power system network topology and hardware development
Landis, D. M.
1985-01-01
Candidate power system newtork topologies for the space station common module are defined and developed and the necessary hardware for test and evaluation is provided. Martin Marietta's approach to performing the proposed program is presented. Performance of the tasks described will assure systematic development and evaluation of program results, and will provide the necessary management tools, visibility, and control techniques for performance assessment. The plan is submitted in accordance with the data requirements given and includes a comprehensive task logic flow diagram, time phased manpower requirements, a program milestone schedule, and detailed descriptions of each program task.
Surface states of topological insulators: the Dirac fermion in curved two-dimensional spaces.
Lee, Dung-Hai
2009-11-06
The surface of a topological insulator is a closed two-dimensional manifold. The surface states are described by the Dirac Hamiltonian in curved two-dimensional spaces. For a slablike sample with a magnetic field perpendicular to its top and bottom surfaces, there are chiral states delocalized on the four side faces. These "chiral sheets" carry both charge and spin currents. In strong magnetic fields, the quantized charge Hall effect [sigma(xy) = (2n + 1)e2/h] will coexist with spin Hall effect.
Measuring space-time fuzziness with high energy γ-ray detectors
Directory of Open Access Journals (Sweden)
Cattaneo Paolo Walter
2017-01-01
Full Text Available There are several suggestions to probe space-time fuzziness (also known as space-time foam due to the quantum mechanics nature of space-time. These effects are predicted to be very small, being related to the Planck length, so that the only hope to experimentally detect them is to look at particles propagating along cosmological distances. Some phenomenological approaches suggest that photons originating from pointlike sources at cosmological distance experience path length fluctuation that could be detected. Also the direction of flight of such photons may be subject to a dispersion such that the image of a point-like source is blurred and detected as a disk. An experimentally accessible signature may be images of point-like sources larger that the size due to the Point Spread Function of the instrument. This additional broadening should increase with distance and photon energy. Some concrete examples that can be studied with the AGILE and FERMI-LAT γ -ray satellite experiments are discussed.
An adaptive fuzzy neural network for MIMO system model approximation in high-dimensional spaces.
Chak, C K; Feng, G; Ma, J
1998-01-01
An adaptive fuzzy system implemented within the framework of neural network is proposed. The integration of the fuzzy system into a neural network enables the new fuzzy system to have learning and adaptive capabilities. The proposed fuzzy neural network can locate its rules and optimize its membership functions by competitive learning, Kalman filter algorithm and extended Kalman filter algorithms. A key feature of the new architecture is that a high dimensional fuzzy system can be implemented with fewer number of rules than the Takagi-Sugeno fuzzy systems. A number of simulations are presented to demonstrate the performance of the proposed system including modeling nonlinear function, operator's control of chemical plant, stock prices and bioreactor (multioutput dynamical system).
International Nuclear Information System (INIS)
Chaichian, M.; Tureanu, A.; Demichev, A.; Presnajder, P.; Sheikh-Jabbari, M.M.
2001-02-01
After discussing the peculiarities of quantum systems on noncommutative (NC) spaces with nontrivial topology and the operator representation of the *-product on them, we consider the Aharonov-Bohm and Casimir effects for such spaces. For the case of the Aharonov-Bohm effect, we have obtained an explicit expression for the shift of the phase, which is gauge invariant in the NC sense. The Casimir energy of a field theory on a NC cylinder is divergent, while it becomes finite on a torus, when the dimensionless parameter of noncommutativity is a rational number. The latter corresponds to a well-defined physical picture. Certain distinctions from other treatments based on a different way of taking the noncommutativity into account are also discussed. (author)
Carrico, T.; Langster, T.; Carrico, J.; Alfano, S.; Loucks, M.; Vallado, D.
The authors present several spacecraft rendezvous and close proximity maneuvering techniques modeled with a high-precision numerical integrator using full force models and closed loop control with a Fuzzy Logic intelligent controller to command the engines. The authors document and compare the maneuvers, fuel use, and other parameters. This paper presents an innovative application of an existing capability to design, simulate and analyze proximity maneuvers; already in use for operational satellites performing other maneuvers. The system has been extended to demonstrate the capability to develop closed loop control laws to maneuver spacecraft in close proximity to another, including stand-off, docking, lunar landing and other operations applicable to space situational awareness, space based surveillance, and operational satellite modeling. The fully integrated end-to-end trajectory ephemerides are available from the authors in electronic ASCII text by request. The benefits of this system include: A realistic physics-based simulation for the development and validation of control laws A collaborative engineering environment for the design, development and tuning of spacecraft law parameters, sizing actuators (i.e., rocket engines), and sensor suite selection. An accurate simulation and visualization to communicate the complexity, criticality, and risk of spacecraft operations. A precise mathematical environment for research and development of future spacecraft maneuvering engineering tasks, operational planning and forensic analysis. A closed loop, knowledge-based control example for proximity operations. This proximity operations modeling and simulation environment will provide a valuable adjunct to programs in military space control, space situational awareness and civil space exploration engineering and decision making processes.
Some exact solutions for maximally symmetric topological defects in Anti de Sitter space
Alvarez, Orlando; Haddad, Matthew
2018-03-01
We obtain exact analytical solutions for a class of SO( l) Higgs field theories in a non-dynamic background n-dimensional anti de Sitter space. These finite transverse energy solutions are maximally symmetric p-dimensional topological defects where n = ( p + 1) + l. The radius of curvature of anti de Sitter space provides an extra length scale that allows us to study the equations of motion in a limit where the masses of the Higgs field and the massive vector bosons are both vanishing. We call this the double BPS limit. In anti de Sitter space, the equations of motion depend on both p and l. The exact analytical solutions are expressed in terms of standard special functions. The known exact analytical solutions are for kink-like defects ( p = 0 , 1 , 2 , . . . ; l = 1), vortex-like defects ( p = 1 , 2 , 3; l = 2), and the 't Hooft-Polyakov monopole ( p = 0; l = 3). A bonus is that the double BPS limit automatically gives a maximally symmetric classical glueball type solution. In certain cases where we did not find an analytic solution, we present numerical solutions to the equations of motion. The asymptotically exponentially increasing volume with distance of anti de Sitter space imposes different constraints than those found in the study of defects in Minkowski space.
Fixed Point in Topological Vector Space-Valued Cone Metric Spaces
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Muhammad Arshad
2010-01-01
Full Text Available We obtain common fixed points of a pair of mappings satisfying a generalized contractive type condition in TVS-valued cone metric spaces. Our results generalize some well-known recent results in the literature.
Some new results for Banach contractions and Edelstein contractive mappings on fuzzy metric spaces
International Nuclear Information System (INIS)
Ciric, Ljubomir
2009-01-01
The main purpose of this paper is to introduce a new class of Banach type fuzzy contractions and to present some fixed and common fixed point theorems for these mappings, as well as for the Edelstein fuzzy locally contractive mappings. Two examples are presented to show that our results are genuine generalizations of many known results.
Directory of Open Access Journals (Sweden)
M. Pattnaik
2013-08-01
Full Text Available In this paper the concept of fuzzy Non-Linear Programming Technique is applied to solve an economic order quantity (EOQ model under restricted space. Since various types of uncertainties and imprecision are inherent in real inventory problems they are classically modeled using the approaches from the probability theory. However, there are uncertainties that cannot be appropriately treated by usual probabilistic models. The questions how to define inventory optimization tasks in such environment how to interpret optimal solutions arise. This paper allows the modification of the Single item EOQ model in presence of fuzzy decision making process where demand is related to the unit price and the setup cost varies with the quantity produced/Purchased. This paper considers the modification of objective function and storage area in the presence of imprecisely estimated parameters. The model is developed for the problem by employing different modeling approaches over an infinite planning horizon. It incorporates all concepts of a fuzzy arithmetic approach, the quantity ordered and the demand per unit compares both fuzzy non linear and other models. Investigation of the properties of an optimal solution allows developing an algorithm whose validity is illustrated through an example problem and ugh MATLAB (R2009a version software, the two and three dimensional diagrams are represented to the application. Sensitivity analysis of the optimal solution is also studied with respect to changes in different parameter values and to draw managerial insights of the decision problem.
Age at Onset of Blindness and Development of Space Concepts: From Topological to Projective Space.
Birns, Shayne L.
1986-01-01
A study involving 23 blind students (6-12 years old) revealed that age at onset of blindness did not appear to be critical in mastery of space concepts. One-third of the Ss exhibited atypical spatial development, g mastering relative positions of left and right before mirror-image orientation. (Author/CL)
A new topology on the space of Lorentzian metrics on a fixed manifold
Noldus, Johan
2002-12-01
We give a covariant definition of closeness between (time-oriented) Lorentzian metrics on a manifold M, using a family of functions which measure the difference in volume form on one hand and, on the other, the difference in causal structure relative to a volume scale. These functions will distinguish two geometric properties of the Alexandrov sets A(p, q), tilde A(p, q) relative to two spacetime points q and p and metrics g and tilde g. It will be shown that this family generates uniformities and consequently a topology on the space of Lorentzian metrics which is Hausdorff when restricted to strongly causal metrics. This family of functions will depend on parameters for a volume scale, length scale (relative to the volume scale) and an index which labels a submanifold with compact closure of the given manifold M.
Topological string in harmonic space and correlation functions in S3 stringy cosmology
International Nuclear Information System (INIS)
Saidi, El Hassan; Sedra, Moulay Brahim
2006-01-01
We develop the harmonic space method for conifold and use it to study local complex deformations of T*S 3 preserving manifestly SL(2,C) isometry. We derive the perturbative manifestly SL(2,C) invariant partition function Z top of topological string B model on locally deformed conifold. Generic n momentum and winding modes of 2D c=1 noncritical theory are described by highest υ (n,0) and lowest components υ (0,n) of SL(2,C) spin s=n2 multiplets (υ (n-k,k) ), 0= α + and V α - . We also derive a dictionary giving the passage from Laurent (Fourier) analysis on T*S 1 (S 1 ) to the harmonic method on T*S 3 (S 3 ). The manifestly SU(2,C) covariant correlation functions of the S 3 quantum cosmology model of Gukov-Saraikin-Vafa are also studied
Non-topological gravitating defects in five-dimensional anti-de Sitter space
Giovannini, Massimo
2006-01-01
A class of five-dimensional warped solutions is presented. The geometry is everywhere regular and tends to five-dimensional anti-de Sitter space for large absolute values of the bulk coordinate. The physical features of the solutions change depending on the value of an integer parameter. In particular, a set of solutions describes generalized gravitating kinks where the scalar field interpolates between two different minima of the potential. The other category of solutions describes instead gravitating defects where the scalar profile is always finite and reaches the same constant asymptote both for positive and negative values of the bulk coordinate. In this sense the profiles are non-topological. The physical features of the zero modes are discussed.
Spaans, M.
2013-01-01
General Relativity is extended into the quantum domain. A thought experiment is ex- plored to derive a specific topological build-up for Planckian space-time. The presented arguments are inspired by Feynman’s path integral for superposition andWheeler’s quan- tum foam of Planck mass mini black
Gamelin, Theodore W
1999-01-01
A fresh approach to introductory topology, this volume explains nontrivial applications of metric space topology to analysis, clearly establishing their relationship. Also, topics from elementary algebraic topology focus on concrete results with minimal algebraic formalism. The first two chapters consider metric space and point-set topology; the second two, algebraic topological material. 1983 edition. Solutions to Selected Exercises. List of Notations. Index. 51 illustrations.
Directory of Open Access Journals (Sweden)
Rafael de Carvalho Miranda
2014-01-01
Full Text Available The development of discrete-event simulation software was one of the most successful interfaces in operational research with computation. As a result, research has been focused on the development of new methods and algorithms with the purpose of increasing simulation optimization efficiency and reliability. This study aims to define optimum variation intervals for each decision variable through a proposed approach which combines the data envelopment analysis with the Fuzzy logic (Fuzzy-DEA-BCC, seeking to improve the decision-making units’ distinction in the face of uncertainty. In this study, Taguchi’s orthogonal arrays were used to generate the necessary quantity of DMUs, and the output variables were generated by the simulation. Two study objects were utilized as examples of mono- and multiobjective problems. Results confirmed the reliability and applicability of the proposed method, as it enabled a significant reduction in search space and computational demand when compared to conventional simulation optimization techniques.
Hybrid neural network and fuzzy logic approaches for rendezvous and capture in space
Berenji, Hamid R.; Castellano, Timothy
1991-01-01
The nonlinear behavior of many practical systems and unavailability of quantitative data regarding the input-output relations makes the analytical modeling of these systems very difficult. On the other hand, approximate reasoning-based controllers which do not require analytical models have demonstrated a number of successful applications such as the subway system in the city of Sendai. These applications have mainly concentrated on emulating the performance of a skilled human operator in the form of linguistic rules. However, the process of learning and tuning the control rules to achieve the desired performance remains a difficult task. Fuzzy Logic Control is based on fuzzy set theory. A fuzzy set is an extension of a crisp set. Crisp sets only allow full membership or no membership at all, whereas fuzzy sets allow partial membership. In other words, an element may partially belong to a set.
Metric and topology on a non-standard real line and non-standard space-time
International Nuclear Information System (INIS)
Tahir Shah, K.
1981-04-01
We study metric and topological properties of extended real line R* and compare it with the non-standard model of real line *R. We show that some properties, like triangular inequality, cannot be carried over R* from R. This confirms F. Wattenberg's result for measure theory on Dedekind completion of *R. Based on conclusions from these results we propose a non-standard model of space-time. This space-time is without undefined objects like singularities. (author)
Further considerations on the separating topology for the space-times of general relativity
International Nuclear Information System (INIS)
Lindstroem, U.
1977-11-01
The separating topology S studied in an earlier report is reexamined. Using methods and ideas in papers by Goebel, Hawking, King and McCarthy a new class of topologies (Ssub(nm)) is introduced. The topology Ssub(nm) is the finest which induces Euclidean topology on timelike Csup(n)- and spacelike Csup(m)-curves. It is shown that S 00 =S 10 =S 01 =S 11 =S. A relation between (Ssub(nm)) and some topologies studied by Goebel is derived. For an arbitrary spacetime the group of S-homeomorphisms is shown to be the smooth conformal diffeomorphism group. The restriction to strongly causal spacetimes employed in the former report is no longer necessary. The question of whether S is the coarsest of comparable topologies having this homeomorphism group, is finally considered
A Study on Neutrosophic Frontier and Neutrosophic Semi-frontier in Neutrosophic Topological Spaces
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P. Iswarya
2017-02-01
Full Text Available In this paper neutrosophic frontier and neutrosophic semi-frontier in neutrosophic topology are introduced and several of their properties, characterizations and examples are established.
Milewski, Emil G
2013-01-01
REA's Essentials provide quick and easy access to critical information in a variety of different fields, ranging from the most basic to the most advanced. As its name implies, these concise, comprehensive study guides summarize the essentials of the field covered. Essentials are helpful when preparing for exams, doing homework and will remain a lasting reference source for students, teachers, and professionals. Topology includes an overview of elementary set theory, relations and functions, ordinals and cardinals, topological spaces, continuous functions, metric spaces and normed spaces, co
Lu, Thomas; Pham, Timothy; Liao, Jason
2011-01-01
This paper presents the development of a fuzzy logic function trained by an artificial neural network to classify the system noise temperature (SNT) of antennas in the NASA Deep Space Network (DSN). The SNT data were classified into normal, marginal, and abnormal classes. The irregular SNT pattern was further correlated with link margin and weather data. A reasonably good correlation is detected among high SNT, low link margin and the effect of bad weather; however we also saw some unexpected non-correlations which merit further study in the future.
Essentials of topology with applications
Krantz, Steven G
2009-01-01
Fundamentals What Is Topology? First Definitions Mappings The Separation Axioms Compactness Homeomorphisms Connectedness Path-Connectedness Continua Totally Disconnected Spaces The Cantor Set Metric Spaces Metrizability Baire's Theorem Lebesgue's Lemma and Lebesgue NumbersAdvanced Properties of Topological Spaces Basis and Sub-Basis Product Spaces Relative Topology First Countable, Second Countable, and So ForthCompactifications Quotient Topologies Uniformities Morse Theory Proper Mappings Paracompactness An Application to Digital ImagingBasic Algebraic Topology Homotopy Theory Homology Theory
On Lacunary p-Absolutely Summable Fuzzy Real-Valued Double Sequence Space
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Dutta Amar Jyoti
2014-07-01
Full Text Available In this article, we introduce the class of p-absolutely summable fuzzy real valued double sequence (2lpFθ We have studied some algebraic properties like solid, symmetric, convergence free, sequence algebra. Further, we establish some relation with the class of p-Cesàro summable double sequences and some other important inclusion results.
Large N topologically twisted index: necklace quivers, dualities, and Sasaki-Einstein spaces
Hosseini, Seyed Morteza; Mekareeya, Noppadol
2016-08-01
In this paper, we calculate the topological free energy for a number of {N} ≥ 2 Yang-Mills-Chern-Simons-matter theories at large N and fixed Chern-Simons levels. The topological free energy is defined as the logarithm of the partition function of the theory on S 2 × S 1 with a topological A-twist along S 2 and can be reduced to a matrix integral by exploiting the localization technique. The theories of our interest are dual to a variety of Calabi-Yau four-fold singularities, including a product of two asymptotically locally Euclidean singularities and the cone over various well-known homogeneous Sasaki-Einstein seven-manifolds, N 0,1,0, V 5,2, and Q 1,1,1. We check that the large N topological free energy can be matched for theories which are related by dualities, including mirror symmetry and SL(2,{Z}) duality.
Energy Technology Data Exchange (ETDEWEB)
Jassar, S.; Zhao, L. [Department of Electrical and Computer Engineering, Ryerson University, 350 Victoria Street, Toronto, ON (Canada); Liao, Z. [Department of Architectural Science, Ryerson University (Canada)
2009-08-15
The heating systems are conventionally controlled by open-loop control systems because of the absence of practical methods for estimating average air temperature in the built environment. An inferential sensor model, based on adaptive neuro-fuzzy inference system modeling, for estimating the average air temperature in multi-zone space heating systems is developed. This modeling technique has the advantage of expert knowledge of fuzzy inference systems (FISs) and learning capability of artificial neural networks (ANNs). A hybrid learning algorithm, which combines the least-square method and the back-propagation algorithm, is used to identify the parameters of the network. This paper describes an adaptive network based inferential sensor that can be used to design closed-loop control for space heating systems. The research aims to improve the overall performance of heating systems, in terms of energy efficiency and thermal comfort. The average air temperature results estimated by using the developed model are strongly in agreement with the experimental results. (author)
Warner, S
1993-01-01
This text brings the reader to the frontiers of current research in topological rings. The exercises illustrate many results and theorems while a comprehensive bibliography is also included. The book is aimed at those readers acquainted with some very basic point-set topology and algebra, as normally presented in semester courses at the beginning graduate level or even at the advanced undergraduate level. Familiarity with Hausdorff, metric, compact and locally compact spaces and basic properties of continuous functions, also with groups, rings, fields, vector spaces and modules, and with Zorn''s Lemma, is also expected.
Predictability in space launch vehicle anomaly detection using intelligent neuro-fuzzy systems
Gulati, Sandeep; Toomarian, Nikzad; Barhen, Jacob; Maccalla, Ayanna; Tawel, Raoul; Thakoor, Anil; Daud, Taher
1994-01-01
Included in this viewgraph presentation on intelligent neuroprocessors for launch vehicle health management systems (HMS) are the following: where the flight failures have been in launch vehicles; cumulative delay time; breakdown of operations hours; failure of Mars Probe; vehicle health management (VHM) cost optimizing curve; target HMS-STS auxiliary power unit location; APU monitoring and diagnosis; and integration of neural networks and fuzzy logic.
Directory of Open Access Journals (Sweden)
Yue Ma
2011-12-01
Full Text Available In this paper, stabilizing control of tracked unmanned ground vehicle in 3-D space was presented. Firstly, models of major modules of tracked UGV were established. Next, to reveal the mechanism of disturbances applied on the UGV, two kinds of representative disturbances (slope and general disturbances in yaw motion were discussed in depth. Consequently, an attempting PID method was employed to compensate the impacts of disturbances andsimulation results proved the validity for disturbance incited by slope force, but revealed the lack for general disturbance on yaw motion. Finally, a hierarchical fuzzy controller combined with PID controller was proposed. In lower level, there were two PID controllers to compensate the disturbance of slope force, and on top level, the fuzzy logic controller was employed to correct the yaw motion error based on the differences between the model and the real UGV, which was able to guide the UGV maintain on the stable state. Simulation results demonstrated the excellent effectiveness of the newly designed controller.
Fractal analysis of polyferric chloride-humic acid (PFC-HA) flocs in different topological spaces.
Wang, Yili; Lu, Jia; Baiyu, Du; Shi, Baoyou; Wang, Dongsheng
2009-01-01
The fractal dimensions in different topological spaces of polyferric chloride-humic acid (PFC-HA) flocs, formed in flocculating different kinds of humic acids (HA) water at different initial pH (9.0, 7.0, 5.0) and PFC dosages, were calculated by effective density-maximum diameter, image analysis, and N2 absorption-desorption methods, respectively. The mass fractal dimensions (Df) of PFC-HA flocs were calculated by bi-logarithm relation of effective density with maximum diameter and Logan empirical equation. The Df value was more than 2.0 at initial pH of 7.0, which was 11% and 13% higher than those at pH 9.0 and 5.0, respectively, indicating the most compact flocs formed in flocculated HA water at initial pH of 7.0. The image analysis for those flocs indicates that after flocculating the HA water at initial pH greater than 7.0 with PFC flocculant, the fractal dimensions of D2 (logA vs. logdL) and D3 (logVsphere VS. logdL) of PFC-HA flocs decreased with the increase of PFC dosages, and PFC-HA flocs showed a gradually looser structure. At the optimum dosage of PFC, the D2 (logA vs. logdL) values of the flocs show 14%-43% difference with their corresponding Df, and they even had different tendency with the change of initial pH values. However, the D2 values of the flocs formed at three different initial pH in HA solution had a same tendency with the corresponding Dr. Based on fractal Frenkel-Halsey-Hill (FHH) adsorption and desorption equations, the pore surface fractal dimensions (Ds) for dried powders of PFC-HA flocs formed in HA water with initial pH 9.0 and 7.0 were all close to 2.9421, and the Ds values of flocs formed at initial pH 5.0 were less than 2.3746. It indicated that the pore surface fractal dimensions of PFC-HA flocs dried powder mainly show the irregularity from the mesopore-size distribution and marcopore-size distribution.
Directory of Open Access Journals (Sweden)
Sanping Rao
2013-01-01
Full Text Available This paper is an attempt to develop quantitative domain theory over frames. Firstly, we propose the notion of a fuzzy basis, and several equivalent characterizations of fuzzy bases are obtained. Furthermore, the concept of a fuzzy algebraic domain is introduced, and a relationship between fuzzy algebraic domains and fuzzy domains is discussed from the viewpoint of fuzzy basis. We finally give an application of fuzzy bases, where the image of a fuzzy domain can be preserved under some special kinds of fuzzy Galois connections.
Scale-space measures for graph topology link protein network architecture to function
Hulsman, M.; Dimitrakopoulos, C.; De Ridder, J.
2014-01-01
MOTIVATION: The network architecture of physical protein interactions is an important determinant for the molecular functions that are carried out within each cell. To study this relation, the network architecture can be characterized by graph topological characteristics such as shortest paths and
Large $N$ topologically twisted index: necklace quivers, dualities, and Sasaki-Einstein spaces
Hosseini, Seyed Morteza
2016-01-01
In this paper, we calculate the topological free energy for a number of ${\\mathcal N} \\geq 2$ Yang-Mills-Chern-Simons-matter theories at large $N$ and fixed Chern-Simons levels. The topological free energy is defined as the logarithm of the partition function of the theory on $S^2 \\times S^1$ with a topological A-twist along $S^2$ and can be reduced to a matrix integral by exploiting the localization technique. The theories of our interest are dual to a variety of Calabi-Yau four-fold singularities, including a product of two asymptotically locally Euclidean singularities and the cone over various well-known homogeneous Sasaki-Einstein seven-manifolds, $N^{0,1,0}$, $V^{5,2}$, and $Q^{1,1,1}$. We check that the large $N$ topological free energy can be matched for theories which are related by dualities, including mirror symmetry and $\\mathrm{SL}(2,\\mathbb{Z})$ duality.
The Topological Panorama Camera: A New Tool for Teaching Concepts Related to Space and Time.
Gelphman, Janet L.; And Others
1992-01-01
Included are the description, operating characteristics, uses, and future plans for the Topological Panorama Camera, which is an experimental, robotic photographic device capable of producing visual renderings of the mathematical characteristics of an equation in terms of position changes of an object or in terms of the shape of the space…
Differential topology an introduction
Gauld, David B
2006-01-01
Offering classroom-proven results, Differential Topology presents an introduction to point set topology via a naive version of nearness space. Its treatment encompasses a general study of surgery, laying a solid foundation for further study and greatly simplifying the classification of surfaces.This self-contained treatment features 88 helpful illustrations. Its subjects include topological spaces and properties, some advanced calculus, differentiable manifolds, orientability, submanifolds and an embedding theorem, and tangent spaces. Additional topics comprise vector fields and integral curv
Directory of Open Access Journals (Sweden)
Nga Le Thi Thuy
2017-12-01
Full Text Available A swarm robot is a collection of large numbers of simple robots used to perform complex tasks that a single robot cannot perform or only perform ineffectively. The swarm robot works successfully only when the cooperation mechanism among individual robots is satisfied. The cooperation mechanism studied in this article ensures the formation and the distance between each pair of individual robots while moving to their destination while avoiding obstacles. The solved problems in this article include; controlling the suction/thrust force between each pair of individual robots in the swarm based on the fuzzy logic structure of the Singer-Input-Singer-Output under Mamdani law; demonstrating the stability of the system based on the Lyapunov theory; and applying control to the multitasking system of the swarm robot based on Null-Space-Behavioral control. Finally, the simulation results make certain that all the individual robots assemble after moving and avoid obstacles.
Topology Optimization and Robotic Fabrication of Advanced Timber Space-frame Structures
DEFF Research Database (Denmark)
Søndergaard, Asbjørn; Amir, Oded; Eversmann, Phillip
2016-01-01
-based topology optimization with digital procedures for rationalization and robotic assembly of bespoke timber members, through a procedural, cross-application workflow. Through this, a direct chaining of optimization and robotic fabrication is established, in which optimization data is driving subsequent...... processes solving timber joint intersections, robotically controlling member prefabrication, and spatial robotic assembly of the optimized timber structures. The implication of this concept is studied through pilot fabrication and load-testing of a full scale prototype structure....
Wormholes in chemical space connecting torus knot and torus link pi-electron density topologies.
Rzepa, Henry S
2009-03-07
Möbius aromaticities can be considered as deriving from cyclic delocalized pi-electron densities rho(r)(pi) which have the topological form of either a two-component torus link or a single-component torus knot. These two topological forms are distinguished by their (non-zero) linking number L(k), which describes how many times the two components of a torus link cross each other or the single component of a torus knot crosses with itself. The special case of Hückel or benzenoid aromaticity is associated with a pi-electron density that takes the form of a two-component torus link for which the linking number is zero. A class of molecule has been identified which here is termed a Janus aromatic, and which bears the characteristics of both a two-component torus link and a single-component torus knot in the topology of the pi-electron density. This is achieved by the formation of one (or more) wormholes or throats in the pi-electron density connecting the two torus forms, which can impart a Janus-like dual personality to the aromaticity of the system. The impact of such wormholes on the overall pi-delocalized aromaticity of such molecules is approximately estimated using a NICS(rcp) index, and subdivides into two types; those where the forms of aromaticity associated with a torus link and a torus knot cooperate and those where they oppose.
Fuzzy Stability of Quadratic Functional Equations
Directory of Open Access Journals (Sweden)
Jang Sun-Young
2010-01-01
Full Text Available The fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated by Moslehian et al. In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations and in fuzzy Banach spaces.
Fuzzy Stability of Quadratic Functional Equations
Dong Yun Shin; Choonkil Park; Sun-Young Jang; Jung Rye Lee
2010-01-01
The fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated by Moslehian et al. In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations and in fuzzy Banach spaces.
Games for topological fixpoint logic
Bezhanishvili, N.; Kupke, C.
2016-01-01
Topological fixpoint logics are a family of logics that admits topological models and where the fixpoint operators are defined with respect to the topological interpretations. Here we consider a topological fixpoint logic for relational structures based on Stone spaces, where the fixpoint operators
Boost-Based MPPT Converter Topology Trade-Off for Space Applications
Garcia, O.; Alou, P.; Oliver, J. A.; Diaz, D.; Meneses, D.; Cobos, J. A.; Soto, A.; Lapena, E.; Rancano, J.
2008-09-01
High power and high voltage - 100V - power buses are often required not only in the frame of the telecommunication spacecrafts, but also for those scientific and interplanetary mission cases where a high user power load demand is driving the design of the power subsystem. On many cases, the use of Maximum Power Point Tracking (MPPT) is essential for an optimum power subsystem sizing.The adaptation to 100V of the existing MPPT concepts for 28V buses - like GOCE, ROSETTA, etc. - is not immediate, as happens in general terms with the upgrading of Power Conditioning Units from 28V to 50V and 100V. Moreover, for those cases where the solar array voltage is under the bus voltage, a step-up boost power cell is mandatory for the MPPT implementation.This paper will focus on the definition of the main performance characteristics that must have a converter power cell to fit the above mentioned application range. Starting with the establishment of the relevant trade-off parameters, in terms of power handling capability, input and output operational voltage ranges (both in nominal and emergency conditions), conducted emissions, bus capacitor and solar array output impedance considerations, several candidate topologies are analysed: conventional boost, interleaved DCM and CCM boost, two inductor boost, boost with ripple cancellation and boost with switch near ground. Some critical aspects like mass, efficiency and number of reactive and power switching elements are also covered.Special attention is paid to the feasibility of the design for the control loop that will govern the converter operation when forming part of a PCU, taking into account the effects of the RHPZ inherent to most of the boost converter topologies. Some of the candidate topologies where prototyped to demonstrate in the laboratory the performances identified during the analysis phase.
Fuzzy Set Field and Fuzzy Metric
Gebray, Gebru; Reddy, B. Krishna
2014-01-01
The notation of fuzzy set field is introduced. A fuzzy metric is redefined on fuzzy set field and on arbitrary fuzzy set in a field. The metric redefined is between fuzzy points and constitutes both fuzziness and crisp property of vector. In addition, a fuzzy magnitude of a fuzzy point in a field is defined.
Fomenko, Anatoly
2016-01-01
This classic text of the renowned Moscow mathematical school equips the aspiring mathematician with a solid grounding in the core of topology, from a homotopical perspective. Its comprehensiveness and depth of treatment are unmatched among topology textbooks: in addition to covering the basics—the fundamental notions and constructions of homotopy theory, covering spaces and the fundamental group, CW complexes, homology and cohomology, homological algebra—the book treats essential advanced topics, such as obstruction theory, characteristic classes, Steenrod squares, K-theory and cobordism theory, and, with distinctive thoroughness and lucidity, spectral sequences. The organization of the material around the major achievements of the golden era of topology—the Adams conjecture, Bott periodicity, the Hirzebruch–Riemann–Roch theorem, the Atiyah–Singer index theorem, to name a few—paints a clear picture of the canon of the subject. Grassmannians, loop spaces, and classical groups play a central role ...
Basic topological and geometric properties of Ces`aro–Orlicz spaces
Indian Academy of Sciences (India)
Abstract. Necessary and sufficient conditions under which the Ces`aro–Orlicz sequence space cesφ is nontrivial are presented. It is proved that for the Luxemburg norm, Ces`aro–. Orlicz spaces cesφ have the Fatou property. Consequently, the spaces are complete. It is also proved that the subspace of order continuous ...
Topological antiferromagnetic spintronics
Šmejkal, Libor; Mokrousov, Yuriy; Yan, Binghai; MacDonald, Allan H.
2018-03-01
The recent demonstrations of electrical manipulation and detection of antiferromagnetic spins have opened up a new chapter in the story of spintronics. Here, we review the emerging research field that is exploring the links between antiferromagnetic spintronics and topological structures in real and momentum space. Active topics include proposals to realize Majorana fermions in antiferromagnetic topological superconductors, to control topological protection and Dirac points by manipulating antiferromagnetic order parameters, and to exploit the anomalous and topological Hall effects of zero-net-moment antiferromagnets. We explain the basic concepts behind these proposals, and discuss potential applications of topological antiferromagnetic spintronics.
Hu, Rui; Liu, Shutian; Li, Quhao
2017-05-20
For the development of a large-aperture space telescope, one of the key techniques is the method for designing the flexures for mounting the primary mirror, as the flexures are the key components. In this paper, a topology-optimization-based method for designing flexures is presented. The structural performances of the mirror system under multiple load conditions, including static gravity and thermal loads, as well as the dynamic vibration, are considered. The mirror surface shape error caused by gravity and the thermal effect is treated as the objective function, and the first-order natural frequency of the mirror structural system is taken as the constraint. The pattern repetition constraint is added, which can ensure symmetrical material distribution. The topology optimization model for flexure design is established. The substructuring method is also used to condense the degrees of freedom (DOF) of all the nodes of the mirror system, except for the nodes that are linked to the mounting flexures, to reduce the computation effort during the optimization iteration process. A potential optimized configuration is achieved by solving the optimization model and post-processing. A detailed shape optimization is subsequently conducted to optimize its dimension parameters. Our optimization method deduces new mounting structures that significantly enhance the optical performance of the mirror system compared to the traditional methods, which only focus on the parameters of existing structures. Design results demonstrate the effectiveness of the proposed optimization method.
ProtNN: fast and accurate protein 3D-structure classification in structural and topological space.
Dhifli, Wajdi; Diallo, Abdoulaye Baniré
2016-01-01
Studying the functions and structures of proteins is important for understanding the molecular mechanisms of life. The number of publicly available protein structures has increasingly become extremely large. Still, the classification of a protein structure remains a difficult, costly, and time consuming task. The difficulties are often due to the essential role of spatial and topological structures in the classification of protein structures. We propose ProtNN, a novel classification approach for protein 3D-structures. Given an unannotated query protein structure and a set of annotated proteins, ProtNN assigns to the query protein the class with the highest number of votes across the k nearest neighbor reference proteins, where k is a user-defined parameter. The search of the nearest neighbor annotated structures is based on a protein-graph representation model and pairwise similarities between vector embedding of the query and the reference protein structures in structural and topological spaces. We demonstrate through an extensive experimental evaluation that ProtNN is able to accurately classify several datasets in an extremely fast runtime compared to state-of-the-art approaches. We further show that ProtNN is able to scale up to a whole PDB dataset in a single-process mode with no parallelization, with a gain of thousands order of magnitude in runtime compared to state-of-the-art approaches.
Networks for the weak topology of Banach and Fréchet spaces
Czech Academy of Sciences Publication Activity Database
Gabriyelyan, S.; Kąkol, Jerzy; Kubiś, Wieslaw; Marciszewski, W.
2015-01-01
Roč. 432, č. 2 (2015), s. 1183-1199 ISSN 0022-247X R&D Projects: GA ČR(CZ) GA14-07880S Institutional support: RVO:67985840 Keywords : Fréchet space * space of continuous functions * locally convex space Subject RIV: BA - General Mathematics Impact factor: 1.014, year: 2015 http://www.sciencedirect.com/science/article/pii/S0022247X15006836
Change of the topology of a physical space in the closed Universe
International Nuclear Information System (INIS)
Guts, A.K.
1982-01-01
The conditions under which a physical space (three-dimensional connective variety) changes the number of connected components are determined. Connectivity breaking means separation of a certain closed field from of the three-dimensional space. It is shown that the small fields separation is prevented by power potential barrier. It follows from the data of the study that neutron stars are close to the possibility of separation from the surrounding space
p-topological Cauchy completions
Directory of Open Access Journals (Sweden)
J. Wig
1999-01-01
Full Text Available The duality between “regular” and “topological” as convergence space properties extends in a natural way to the more general properties “p-regular” and “p-topological.” Since earlier papers have investigated regular, p-regular, and topological Cauchy completions, we hereby initiate a study of p-topological Cauchy completions. A p-topological Cauchy space has a p-topological completion if and only if it is “cushioned,” meaning that each equivalence class of nonconvergent Cauchy filters contains a smallest filter. For a Cauchy space allowing a p-topological completion, it is shown that a certain class of Reed completions preserve the p-topological property, including the Wyler and Kowalsky completions, which are, respectively, the finest and the coarsest p-topological completions. However, not all p-topological completions are Reed completions. Several extension theorems for p-topological completions are obtained. The most interesting of these states that any Cauchy-continuous map between Cauchy spaces allowing p-topological and p′-topological completions, respectively, can always be extended to a θ-continuous map between any p-topological completion of the first space and any p′-topological completion of the second.
Weak Darboux property and transitivity of linear mappings on topological vector spaces
Directory of Open Access Journals (Sweden)
V. K. Maslyuchenko
2013-06-01
Full Text Available It is shown that every linear mapping ontopological vector spaces always has weak Darboux property, therefore, it is continuous ifand only if it is transitive. For finite-dimensional mapping $f$ with values in Hausdorfftopological vector space the following conditions are equivalent: (i $f$ iscontinuous; (ii graph of $f$ is closed; (iii kernel of $f$ is closed; (iv $f$ istransition map.
International Nuclear Information System (INIS)
Groote, S.; Koerner, J.G.; Pivovarov, A.A.
2007-01-01
We review recently developed new powerful techniques to compute a class of Feynman diagrams at any loop order, known as sunrise-type diagrams. These sunrise-type topologies have many important applications in many different fields of physics and we believe it to be timely to discuss their evaluation from a unified point of view. The method is based on the analysis of the diagrams directly in configuration space which, in the case of the sunrise-type diagrams and diagrams related to them, leads to enormous simplifications as compared to the traditional evaluation of loops in momentum space. We present explicit formulae for their analytical evaluation for arbitrary mass configurations and arbitrary dimensions at any loop order. We discuss several limiting cases in their kinematical regimes which are e.g. relevant for applications in HQET and NRQCD. We completely solve the problem of renormalization using simple formulae for the counterterms within dimensional regularization. An important application is the computation of the multi-particle phase space in D-dimensional space-time which we discuss. We present some examples of their numerical evaluation in the general case of D-dimensional space-time as well as in integer dimensions D = D 0 for different values of dimensions including the most important practical cases D 0 = 2, 3, 4. Substantial simplifications occur for odd integer space-time dimensions where the final results can be expressed in closed form through elementary functions. We discuss the use of recurrence relations naturally emerging in configuration space for the calculation of special series of integrals of the sunrise topology. We finally report on results for the computation of an extension of the basic sunrise topology, namely the spectacle topology and the topology where an irreducible loop is added
International Nuclear Information System (INIS)
Ashtekar, A.; Sen, A.
1980-01-01
Schwarzschild--Kruskal space--time admits a two-parameter family of everywhere regular, static, source-free Maxwell fields. It is shown that there exists a corresponding two-parameter family of unitarily inequivalent representations of the canonical commutation relations. Elements of the underlying Hilbert space may be interpreted as ''quantum fluctuations of the Maxwell field off nontrivial classical vacua.'' The representation corresponding to the ''trivial'' sector: i.e., the zero classical solution: is the usual Fock representation. All others are ''non-Fock.'' In particular, in all other sectors, the Maxwell field develops a nonzero vacuum expectation value. The parameters labelling the family can be interpreted as electric and magnetic charges. Therefore, unitary inequivalence naturally leads to superselection rules for these charges. These features arise in spite of the linearity of field equations only because the space--time topology is ''nontrivial.'' Also, because of linearity, an exact analysis is possible at the quantum level; recourse to perturbation theory is unnecessary
Measure and category a survey of the analogies between topological and measure spaces
Oxtoby, John C
1980-01-01
In this edition, a set of Supplementary Notes and Remarks has been added at the end, grouped according to chapter. Some of these call attention to subsequent developments, others add further explanation or additional remarks. Most of the remarks are accompanied by a briefly indicated proof, which is sometimes different from the one given in the reference cited. The list of references has been expanded to include many recent contributions, but it is still not intended to be exhaustive. John C. Oxtoby Bryn Mawr, April 1980 Preface to the First Edition This book has two main themes: the Baire category theorem as a method for proving existence, and the "duality" between measure and category. The category method is illustrated by a variety of typical applications, and the analogy between measure and category is explored in all of its ramifications. To this end, the elements of metric topology are reviewed and the principal properties of Lebesgue measure are derived. It turns out that Lebesgue integration is not es...
Design, implementation and performance comparison of multiplier topologies in power-delay space
Directory of Open Access Journals (Sweden)
Mansi Jhamb
2016-03-01
Full Text Available With the advancements in the semiconductor industry, designing a high performance processor is a prime concern. Multiplier is one of the most crucial parts in almost every digital signal processing applications. This paper addresses the implementation of an 8-bit multiplier design employing CMOS full adder, full adder using Double Pass Transistor (DPL and multioutput carry Lookahead logic (CLA. DPL adder avoids the noise margin problem and speed degradation at low value of supply voltages associated with complementary pass transistor (CPL logic circuits. Multioutput carry lookahead adder leads to significant improvement in the speed of the overall circuitry. The investigation is carried out with simulation runs on HSPICE environment using 90 nm process technology at 25 °C. Finally, the design guidelines are derived to select the most suitable topology for the desired applications. Investigation reveals that multiplier design using multioutput carry lookahead adder proves to be more speed efficient in comparison with the other two considered design strategies.
Topology optimization and digital assembly of advanced space-frame structures
DEFF Research Database (Denmark)
Søndergaard, Asbjørn; Amir, Oded; Michael, Knauss
2014-01-01
this paper presents a novel method for integrated design, optimization and fabrication of optimized space-frame structures in an autonomous, digital process. Comparative numerical studies are presented, demonstrating achievable mass reduction by application of the method by comparison to equivalent...... to normative space truss designs and dimensions. As such, a principal digital fabrication and assembly scheme is developed, where an architectural design methodology relative to the described process is established, and the proposed process demonstrated through scaled digital fabrication experiments....
Ozturk, Taha Yasin; Bayramov, Sadi
2014-01-01
Various soft topologies are being introduced on a given function space soft topological spaces. In this paper, soft compact-open topology is defined in functional spaces of soft topological spaces. Further, these functional spaces are studied and interrelations between various functional spaces with soft compact-open topology are established.
Smets, P
1995-01-01
We start by describing the nature of imperfect data, and giving an overview of the various models that have been proposed. Fuzzy sets theory is shown to be an extension of classical set theory, and as such has a proeminent role or modelling imperfect data. The mathematic of fuzzy sets theory is detailled, in particular the role of the triangular norms. The use of fuzzy sets theory in fuzzy logic and possibility theory,the nature of the generalized modus ponens and of the implication operator for approximate reasoning are analysed. The use of fuzzy logic is detailled for application oriented towards process control and database problems.
Rahonis, George
The theory of fuzzy recognizable languages over bounded distributive lattices is presented as a paradigm of recognizable formal power series. Due to the idempotency properties of bounded distributive lattices, the equality of fuzzy recognizable languages is decidable, the determinization of multi-valued automata is effective, and a pumping lemma exists. Fuzzy recognizable languages over finite and infinite words are expressively equivalent to sentences of the multi-valued monadic second-order logic. Fuzzy recognizability over bounded ℓ-monoids and residuated lattices is briefly reported. The chapter concludes with two applications of fuzzy recognizable languages to real world problems in medicine.
Fuzzy Cores and Fuzzy Balancedness
van Gulick, G.; Norde, H.W.
2011-01-01
We study the relation between the fuzzy core and balancedness for fuzzy games. For regular games, this relation has been studied by Bondareva (1963) and Shapley (1967). First, we gain insight in this relation when we analyse situations where the fuzzy game is continuous. Our main result shows that
Graph topologies on closed multifunctions
Directory of Open Access Journals (Sweden)
Giuseppe Di Maio
2003-10-01
Full Text Available In this paper we study function space topologies on closed multifunctions, i.e. closed relations on X x Y using various hypertopologies. The hypertopologies are in essence, graph topologies i.e topologies on functions considered as graphs which are subsets of X x Y . We also study several topologies, including one that is derived from the Attouch-Wets filter on the range. We state embedding theorems which enable us to generalize and prove some recent results in the literature with the use of known results in the hyperspace of the range space and in the function space topologies of ordinary functions.
Chatterjee, D
2007-01-01
About the Book: This book provides exposition of the subject both in its general and algebraic aspects. It deals with the notions of topological spaces, compactness, connectedness, completeness including metrizability and compactification, algebraic aspects of topological spaces through homotopy groups and homology groups. It begins with the basic notions of topological spaces but soon going beyond them reaches the domain of algebra through the notions of homotopy, homology and cohomology. How these approaches work in harmony is the subject matter of this book. The book finally arrives at the
Mendelson, Bert
1990-01-01
Highly regarded for its exceptional clarity, imaginative and instructive exercises, and fine writing style, this concise book offers an ideal introduction to the fundamentals of topology. It provides a simple, thorough survey of elementary topics, starting with set theory and advancing to metric and topological spaces, connectedness, and compactness. 1975 edition.
Topological properties of the continuous function spaces on some ordered compacta
Czech Academy of Sciences Publication Activity Database
Kubiś, Wieslaw; Moltó, A.; Troyanski, S.
2013-01-01
Roč. 21, č. 4 (2013), s. 649-659 ISSN 1877-0533 R&D Projects: GA ČR(CZ) GAP201/12/0290 Institutional support: RVO:67985840 Keywords : compact semilattice * pointwise SLD * space of continuous functions Subject RIV: BA - General Mathematics Impact factor: 0.918, year: 2013 http://link.springer.com/article/10.1007%2Fs11228-013-0258-z
A note on the L-fuzzy Banach's contraction principle
International Nuclear Information System (INIS)
Martinez-Moreno, J.; Roldan, A.; Roldan, C.
2009-01-01
Recently, Alaca et al. [Alaca C, Turkoglu D, Yildiz C. Fixed points in intuitionistic fuzzy metric spaces. Chaos, Solitons and Fractals 2006;29:10738] proved fuzzy Banach fixed point theorem in intuitionistic fuzzy metric spaces and Saadati [Saadati R. Notes to the paper 'fixed points in intuitionistic fuzzy metric spaces' and its generalization to L-fuzzy metric spaces. Chaos, Solitions and Fractals 2008;35:80-176] extended it in generalized fuzzy metric spaces. The purpose of this paper is to give a correct proof of the main result in Saadati [Saadati R. Notes to the paper 'fixed points in intuitionistic fuzzy metric spaces' and its generalization to L-fuzzy metric spaces. Chaos, Solitions and Fractals 2008;35:80-176].
Directory of Open Access Journals (Sweden)
Messaoud Bounkhel
2013-01-01
Full Text Available For a set-valued mapping M defined between two Hausdorff topological vector spaces E and F and with closed convex graph and for a given point (x,y∈E×F, we study the minimal time function associated with the images of M and a bounded set Ω⊂F defined by M,Ω(x,y:=inf{t≥0:M(x∩(y+tΩ≠∅}. We prove and extend various properties on directional derivatives and subdifferentials of M,Ω at those points of (x,y∈E×F (both cases: points in the graph gph M and points outside the graph. These results are used to prove, in terms of the minimal time function, various new characterizations of the convex tangent cone and the convex normal cone to the graph of M at points inside gph M and to the graph of the enlargement set-valued mapping at points outside gph M. Our results extend many existing results, from Banach spaces and normed vector spaces to Hausdorff topological vector spaces (Bounkhel, 2012; Bounkhel and Thibault, 2002; Burke et al., 1992; He and Ng, 2006; and Jiang and He 2009. An application of the minimal time function M,Ω to the calmness property of perturbed optimization problems in Hausdorff topological vector spaces is given in the last section of the paper.
Buscema, Massimo; Massini, Giulia; Sacco, Pier Luigi
2018-02-01
This paper offers the first systematic presentation of the topological approach to the analysis of epidemic and pseudo-epidemic spatial processes. We introduce the basic concepts and proofs, at test the approach on a diverse collection of case studies of historically documented epidemic and pseudo-epidemic processes. The approach is found to consistently provide reliable estimates of the structural features of epidemic processes, and to provide useful analytical insights and interpretations of fragmentary pseudo-epidemic processes. Although this analysis has to be regarded as preliminary, we find that the approach's basic tenets are strongly corroborated by this first test and warrant future research in this vein.
Noncommuting Momenta of Topological Solitons
Watanabe, Haruki; Murayama, Hitoshi
2014-05-01
We show that momentum operators of a topological soliton may not commute among themselves when the soliton is associated with the second cohomology H2 of the target space. The commutation relation is proportional to the winding number, taking a constant value within each topological sector. The noncommutativity makes it impossible to specify the momentum of a topological soliton, and induces a Magnus force.
On power idealization filter topologies of lattice implication algebras.
Bai, Shi-Zhong; Wu, Xiu-Yun
2014-01-01
The aim of this paper is to introduce power idealization filter topologies with respect to filter topologies and power ideals of lattice implication algebras, and to investigate some properties of power idealization filter topological spaces and their quotient spaces.
Energy Technology Data Exchange (ETDEWEB)
Lefrancois, M
2005-12-15
In particle physics, the Standard Model describes the interactions between fundamental particles. However, it was not able till now to unify quantum field theory and general relativity. This thesis focuses on two different unification approaches, though they might show some compatibility: topological field theories and quantum mechanics on non-commutative space. Topological field theories have been introduced some twenty years ago and have a very strong link to mathematics: their observables are topological invariants of the manifold they are defined on. In this thesis, we first give interest to topological Yang-Mills. We develop a superspace formalism and give a systematic method for the determination of the observables. This approach allows, once projected on a particular super gauge (of Wess-Zumino type), to recover the existing results but it also gives a generalisation to the case of an unspecified super-gauge. We have then be able to show that the up-to-now known observables correspond to the most general form of the solutions. This superspace formalism can be applied to more complex models; the case of topological gravity is given here in example. Quantum mechanics on noncommutative space provides an extension of the Heisenberg algebra of ordinary quantum mechanics. What differs here is that the components of the position or momentum operators do not commute with each other anymore. This implies to introduce a fundamental length. The second part of this thesis focuses on the description of the commutation algebra. Applications are made to low-dimensional quantum systems (Landau system, harmonic oscillator...) and to supersymmetric systems. (author)
Directory of Open Access Journals (Sweden)
Chen Yu-Fan
2006-01-01
Full Text Available An adaptive minimum mean-square error (MMSE array receiver based on the fuzzy-logic recursive least-squares (RLS algorithm is developed for asynchronous DS-CDMA interference suppression in the presence of frequency-selective multipath fading. This receiver employs a fuzzy-logic control mechanism to perform the nonlinear mapping of the squared error and squared error variation, denoted by ( , , into a forgetting factor . For the real-time applicability, a computationally efficient version of the proposed receiver is derived based on the least-mean-square (LMS algorithm using the fuzzy-inference-controlled step-size . This receiver is capable of providing both fast convergence/tracking capability as well as small steady-state misadjustment as compared with conventional LMS- and RLS-based MMSE DS-CDMA receivers. Simulations show that the fuzzy-logic LMS and RLS algorithms outperform, respectively, other variable step-size LMS (VSS-LMS and variable forgetting factor RLS (VFF-RLS algorithms at least 3 dB and 1.5 dB in bit-error-rate (BER for multipath fading channels.
Relational Demonic Fuzzy Refinement
Directory of Open Access Journals (Sweden)
Fairouz Tchier
2014-01-01
Full Text Available We use relational algebra to define a refinement fuzzy order called demonic fuzzy refinement and also the associated fuzzy operators which are fuzzy demonic join (⊔fuz, fuzzy demonic meet (⊓fuz, and fuzzy demonic composition (□fuz. Our definitions and properties are illustrated by some examples using mathematica software (fuzzy logic.
Directory of Open Access Journals (Sweden)
Jingwei Shen
2017-02-01
Full Text Available Determining the spatial relations between objects is a primary function of a geographic information system (GIS. One important aspect of spatial relations is topological relations, which remain constant under topological transformations. Describing the geometry of a spatial object using the OpenGIS Simple Features Specification requires only simple features: the interior, boundary and exterior of a spatial object are defined. This paper proposes a comprehensive model, the 27-intersection model (27IM, which considers both the dimensions and the number of intersections. Some propositions are presented to exclude relations that the 27IM cannot implement. The 27IM describes six groups of topological relations: point/point, point/line, point/region, line/line, line/region and region/region. The formalism of the 27IM and the corresponding geometric interpretations between spatial objects are illustrated and then compared to the topological relations represented by the existing models, the nine-intersection model (9IM, the dimensionally-extended nine-intersection matrix (DE-9IM and the separation number extended nine-intersection matrix (SNE-9IM. The results show that (1 the 27IM can represent the topological relations between two-dimensional spatial objects, (2 the 27IM can distinguish more topological relations than can the 9IM, DE-9IM or the SNE-9IM and that (3 the interoperability of the 27IM with the 9IM, DE-9IM and SNE-9IM is good.
DEFF Research Database (Denmark)
Anker, Thomas Boysen; Kappel, Klemens; Eadie, Douglas
2012-01-01
This article clarifies the commonplace assumption that brands make promises by developing definitions of brand promise delivery. Distinguishing between clear and fuzzy brand promises, we develop definitions of what it is for a brand to deliver on fuzzy functional, symbolic, and experiential...
DEFF Research Database (Denmark)
Berks, G.; Keyserlingk, Diedrich Graf von; Jantzen, Jan
2000-01-01
and clustering are the basic concerns in medicine. Classification depends on definitions of the classes and their required degree of participant of the elements in the cases' symptoms. In medicine imprecise conditions are the rule and therefore fuzzy methods are much more suitable than crisp ones. Fuzzy c...
The coarsest Hausdorff Lebesgue topology | Conradie ...
African Journals Online (AJOL)
If a Riesz space E contains an order dense Riesz subspace which admits a Hausdorff Lebesgue (i.e. order continuous) topology, then there is a coarsest Hausdorff Lebesgue topology on E. This topology extends uniquely to a Hausdorff Lebesgue topology on the universal completion of E, and is always minimal amongst ...
Amorphous Gyroscopic Topological Metamaterials
Mitchell, Noah P.; Nash, Lisa M.; Hexner, Daniel; Turner, Ari M.; Irvine, William T. M.
Mechanical topological metamaterials display striking mechanical responses, such as unidirectional surface modes that are impervious to disorder. This behavior arises from the topology of their vibrational spectra. All examples of topological metamaterials to date are finely-tuned structures such as crystalline lattices or jammed packings. Here, we present robust recipes for building amorphous topological metamaterials with arbitrary underlying structure and no long-range order. Using interacting gyroscopes as a model system, we demonstrate through experiment, simulation, and theoretical methods that the local geometry and interactions are sufficient to generate topological mobility gaps, allowing for spatially-resolved, real-space calculations of the Chern number. The robustness of our approach enables the design and self-assembly of non-crystalline materials with protected, unidirectional waveguides on the micro and macro scale.
Bonissone CIDU Presentation: Design of Local Fuzzy Models
National Aeronautics and Space Administration — After reviewing key background concepts in fuzzy systems and evolutionary computing, we will focus on the use of local fuzzy models, which are related to both kernel...
Neural Representation of Spatial Topology in the Rodent Hippocampus
Chen, Zhe; Gomperts, Stephen N.; Yamamoto, Jun; Wilson, Matthew A.
2014-01-01
Pyramidal cells in the rodent hippocampus often exhibit clear spatial tuning in navigation. Although it has been long suggested that pyramidal cell activity may underlie a topological code rather than a topographic code, it remains unclear whether an abstract spatial topology can be encoded in the ensemble spiking activity of hippocampal place cells. Using a statistical approach developed previously, we investigate this question and related issues in greater details. We recorded ensembles of hippocampal neurons as rodents freely foraged in one and two-dimensional spatial environments, and we used a “decode-to-uncover” strategy to examine the temporally structured patterns embedded in the ensemble spiking activity in the absence of observed spatial correlates during periods of rodent navigation or awake immobility. Specifically, the spatial environment was represented by a finite discrete state space. Trajectories across spatial locations (“states”) were associated with consistent hippocampal ensemble spiking patterns, which were characterized by a state transition matrix. From this state transition matrix, we inferred a topology graph that defined the connectivity in the state space. In both one and two-dimensional environments, the extracted behavior patterns from the rodent hippocampal population codes were compared against randomly shuffled spike data. In contrast to a topographic code, our results support the efficiency of topological coding in the presence of sparse sample size and fuzzy space mapping. This computational approach allows us to quantify the variability of ensemble spiking activity, to examine hippocampal population codes during off-line states, and to quantify the topological complexity of the environment. PMID:24102128
Games for Topological Fixpoint Logic
Directory of Open Access Journals (Sweden)
Nick Bezhanishvili
2016-09-01
Full Text Available Topological fixpoint logics are a family of logics that admits topological models and where the fixpoint operators are defined with respect to the topological interpretations. Here we consider a topological fixpoint logic for relational structures based on Stone spaces, where the fixpoint operators are interpreted via clopen sets. We develop a game-theoretic semantics for this logic. First we introduce games characterising clopen fixpoints of monotone operators on Stone spaces. These fixpoint games allow us to characterise the semantics for our topological fixpoint logic using a two-player graph game. Adequacy of this game is the main result of our paper. Finally, we define bisimulations for the topological structures under consideration and use our game semantics to prove that the truth of a formula of our topological fixpoint logic is bisimulation-invariant.
Fuzzy cores and fuzzy balancedness
van Gulick, G.; Norde, H.W.
2013-01-01
We study the relation between the fuzzy core and balancedness for fuzzy games. For regular games, this relation has been studied by Bondareva (Problemy Kibernet 10:119–139, 1963) and Shapley (Naval Res Logist Q 14: 453–460, 1967). First, we gain insight in this relation when we analyse situations
Algebraic topology and concurrency
DEFF Research Database (Denmark)
Fajstrup, Lisbeth; Raussen, Martin; Goubault, Eric
2006-01-01
We show in this article that some concepts from homotopy theory, in algebraic topology,are relevant for studying concurrent programs. We exhibit a natural semantics of semaphore programs, based on partially ordered topological spaces, which are studied up to “elastic deformation” or homotopy...... differences between ordinary and directed homotopy through examples. We also relate the topological view to a combinatorial view of concurrent programs closer to transition systems, through the notion of a cubical set. Finally we apply some of these concepts to the proof of the safeness of a two...
Flegg, H Graham
2001-01-01
This excellent introduction to topology eases first-year math students and general readers into the subject by surveying its concepts in a descriptive and intuitive way, attempting to build a bridge from the familiar concepts of geometry to the formalized study of topology. The first three chapters focus on congruence classes defined by transformations in real Euclidean space. As the number of permitted transformations increases, these classes become larger, and their common topological properties become intuitively clear. Chapters 4-12 give a largely intuitive presentation of selected topics.
Elementary topology problem textbook
Viro, O Ya; Netsvetaev, N Yu; Kharlamov, V M
2008-01-01
This textbook on elementary topology contains a detailed introduction to general topology and an introduction to algebraic topology via its most classical and elementary segment centered at the notions of fundamental group and covering space. The book is tailored for the reader who is determined to work actively. The proofs of theorems are separated from their formulations and are gathered at the end of each chapter. This makes the book look like a pure problem book and encourages the reader to think through each formulation. A reader who prefers a more traditional style can either find the pr
Topological properties of instantons
International Nuclear Information System (INIS)
Mello, E.R.B. de.
1978-07-01
The pure Yang-Mills theory defined in R 4 space is considered and some relevant properties of gauge field like Instanton are shown. The vacuum structure of the theory is discussed, as well as the problem of topological numbers associated with the Instantons and anti-Instantons solutions. A procedure is presented showing how we can alter this topological number by of any variation in the field parameters. (Author) [pt
AL-Hawary, Talal Ali
2012-01-01
The aim of this paper is to discuss properties of fuzzy regular-flats, fuzzy C- flats, fuzzy alternative-sets and fuzzy i-flats. Moreover, we characterize some peculiar fuzzy matroids via these notions. Finally, we provide a decomposition of fuzzy strong maps.
Topological insulators and topological superconductors
Bernevig, Andrei B
2013-01-01
This graduate-level textbook is the first pedagogical synthesis of the field of topological insulators and superconductors, one of the most exciting areas of research in condensed matter physics. Presenting the latest developments, while providing all the calculations necessary for a self-contained and complete description of the discipline, it is ideal for graduate students and researchers preparing to work in this area, and it will be an essential reference both within and outside the classroom. The book begins with simple concepts such as Berry phases, Dirac fermions, Hall conductance and its link to topology, and the Hofstadter problem of lattice electrons in a magnetic field. It moves on to explain topological phases of matter such as Chern insulators, two- and three-dimensional topological insulators, and Majorana p-wave wires. Additionally, the book covers zero modes on vortices in topological superconductors, time-reversal topological superconductors, and topological responses/field theory and topolo...
Directory of Open Access Journals (Sweden)
Manikandan Ramasamy
2017-07-01
Full Text Available Automation has been growing in recent years for the manufacturing industries to increase productivity. Multiple robotic arms are used to handle materials for lifting in flexible directions. The vertical rotation of a 360 degree single arm is considered in this research on a position servo drive with brushless DC motor. The load torque of an arm varies depending upon the angular displacement due to gravity, so it requires four-quadrant operation of the drive with a robust feedback controller. This paper deals with the design and performance comparison of a conventional PID feedback controller with a fuzzy-based PID controller and suggests the most suitable controller. The design was implemented in real time through the dSPACE DS1104 controller environment to verify the dynamic behaviors of the arm.
Heitzig, Jobst; Kittel, Tim; Donges, Jonathan; Molkenthin, Nora
2016-04-01
To keep the Earth System in a desirable region of its state space, such as defined by the recently suggested "tolerable environment and development window", "guardrails", "planetary boundaries", or "safe (and just) operating space for humanity", one not only needs to understand the quantitative internal dynamics of the system and the available options for influencing it (management), but also the structure of the system's state space with regard to certain qualitative differences. Important questions are: Which state space regions can be reached from which others with or without leaving the desirable region? Which regions are in a variety of senses "safe" to stay in when management options might break away, and which qualitative decision problems may occur as a consequence of this topological structure? In this work, we develop a mathematical theory of the qualitative topology of the state space of a dynamical system with management options and desirable states, as a complement to the existing literature on optimal control which is more focussed on quantitative optimization and is much applied in both the engineering and the integrated assessment literature. We suggest a certain terminology for the various resulting regions of the state space and perform a detailed formal classification of the possible states with respect to the possibility of avoiding or leaving the undesired region. Our results indicate that before performing some form of quantitative optimization such as of indicators of human well-being for achieving certain sustainable development goals, a sustainable and resilient management of the Earth System may require decisions of a more discrete type that come in the form of several dilemmas, e.g., choosing between eventual safety and uninterrupted desirability, or between uninterrupted safety and larger flexibility. We illustrate the concepts and dilemmas drawing on conceptual models from climate science, ecology, coevolutionary Earth System modeling
Goodman, Sue E
2009-01-01
Beginning Topology is designed to give undergraduate students a broad notion of the scope of topology in areas of point-set, geometric, combinatorial, differential, and algebraic topology, including an introduction to knot theory. A primary goal is to expose students to some recent research and to get them actively involved in learning. Exercises and open-ended projects are placed throughout the text, making it adaptable to seminar-style classes. The book starts with a chapter introducing the basic concepts of point-set topology, with examples chosen to captivate students' imaginations while i
Topological susceptibility from slabs
Energy Technology Data Exchange (ETDEWEB)
Bietenholz, Wolfgang [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A.P. 70-543, Distrito Federal, C.P. 04510 (Mexico); Forcrand, Philippe de [Institute for Theoretical Physics, ETH Zürich,CH-8093 Zürich (Switzerland); CERN, Physics Department, TH Unit, CH-1211 Geneva 23 (Switzerland); Gerber, Urs [Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, A.P. 70-543, Distrito Federal, C.P. 04510 (Mexico); Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo,Edificio C-3, Apdo. Postal 2-82, Morelia, Michoacán, C.P. 58040 (Mexico)
2015-12-14
In quantum field theories with topological sectors, a non-perturbative quantity of interest is the topological susceptibility χ{sub t}. In principle it seems straightforward to measure χ{sub t} by means of Monte Carlo simulations. However, for local update algorithms and fine lattice spacings, this tends to be difficult, since the Monte Carlo history rarely changes the topological sector. Here we test a method to measure χ{sub t} even if data from only one sector are available. It is based on the topological charges in sub-volumes, which we denote as slabs. Assuming a Gaussian distribution of these charges, this method enables the evaluation of χ{sub t}, as we demonstrate with numerical results for non-linear σ-models.
Topological Susceptibility from Slabs
Bietenholz, Wolfgang; Gerber, Urs
2015-01-01
In quantum field theories with topological sectors, a non-perturbative quantity of interest is the topological susceptibility chi_t. In principle it seems straightforward to measure chi_t by means of Monte Carlo simulations. However, for local update algorithms and fine lattice spacings, this tends to be difficult, since the Monte Carlo history rarely changes the topological sector. Here we test a method to measure chi_t even if data from only one sector are available. It is based on the topological charges in sub-volumes, which we denote as slabs. Assuming a Gaussian distribution of these charges, this method enables the evaluation of chi_t, as we demonstrate with numerical results for non-linear sigma-models.
Vivodtzev, Fabien; Pascucci, Valerio
2015-01-01
This book contains papers presented at the Workshop on the Analysis of Large-scale, High-Dimensional, and Multi-Variate Data Using Topology and Statistics, held in Le Barp, France, June 2013. It features the work of some of the most prominent and recognized leaders in the field who examine challenges as well as detail solutions to the analysis of extreme scale data. The book presents new methods that leverage the mutual strengths of both topological and statistical techniques to support the management, analysis, and visualization of complex data. It covers both theory and application and provides readers with an overview of important key concepts and the latest research trends. Coverage in the book includes multi-variate and/or high-dimensional analysis techniques, feature-based statistical methods, combinatorial algorithms, scalable statistics algorithms, scalar and vector field topology, and multi-scale representations. In addition, the book details algorithms that are broadly applicable and can be us...
Nguyen, Hung T
2005-01-01
THE CONCEPT OF FUZZINESS Examples Mathematical modeling Some operations on fuzzy sets Fuzziness as uncertainty Exercises SOME ALGEBRA OF FUZZY SETS Boolean algebras and lattices Equivalence relations and partitions Composing mappings Isomorphisms and homomorphisms Alpha-cuts Images of alpha-level sets Exercises FUZZY QUANTITIES Fuzzy quantities Fuzzy numbers Fuzzy intervals Exercises LOGICAL ASPECTS OF FUZZY SETS Classical two-valued logic A three-valued logic Fuzzy logic Fuzzy and Lukasiewi
Platz, M.; Rapp, J.; Groessler, M.; Niehaus, E.; Babu, A.; Soman, B.
2014-11-01
A Spatial Decision Support System (SDSS) provides support for decision makers and should not be viewed as replacing human intelligence with machines. Therefore it is reasonable that decision makers are able to use a feature to analyze the provided spatial decision support in detail to crosscheck the digital support of the SDSS with their own expertise. Spatial decision support is based on risk and resource maps in a Geographic Information System (GIS) with relevant layers e.g. environmental, health and socio-economic data. Spatial fuzzy logic allows the representation of spatial properties with a value of truth in the range between 0 and 1. Decision makers can refer to the visualization of the spatial truth of single risk variables of a disease. Spatial fuzzy logic rules that support the allocation of limited resources according to risk can be evaluated with measure theory on topological spaces, which allows to visualize the applicability of this rules as well in a map. Our paper is based on the concept of a spatial fuzzy logic on topological spaces that contributes to the development of an adaptive Early Warning And Response System (EWARS) providing decision support for the current or future spatial distribution of a disease. It supports the decision maker in testing interventions based on available resources and apply risk mitigation strategies and provide guidance tailored to the geo-location of the user via mobile devices. The software component of the system would be based on open source software and the software developed during this project will also be in the open source domain, so that an open community can build on the results and tailor further work to regional or international requirements and constraints. A freely available EWARS Spatial Fuzzy Logic Demo was developed wich enables a user to visualize risk and resource maps based on individual data in several data formats.
Multiple Instance Fuzzy Inference
2015-12-02
and learn the fuzzy inference system’s parameters [24, 25]. In this later technique, supervised and unsupervised learning algorithms are devised to...algorithm ( unsupervised learning ) can be used to identify local contexts of the input space, and a linear classifier (supervised learning ) can be used...instance level (patch-level) labels and would require the image to be correctly segmented and labeled prior to learning . Figure 1.1: Example of an image
8th International Conference on Fuzzy Information and Engineering
Wang, Pei-Zhuang; Liu, Zeng-Liang; Zhong, Yu-Bin
2016-01-01
This proceedings book presents edited results of the eighth International Conference on Fuzzy Information and Engineering (ICFIE'2015) and on Oriental Thinking and Fuzzy Logic, in August 17-20, 2015, in Dalian, China. The book contains 65 high-quality papers and is divided into six main parts: "Fuzzy Information Processing", "Fuzzy Engineering", "Internet and Big Data Applications", "Factor Space and Factorial Neural Networks", "Information Granulation and Granular Computing" as well as "Extenics and Innovation Methods".
Bounded Rationality of Generalized Abstract Fuzzy Economies
Directory of Open Access Journals (Sweden)
Lei Wang
2014-01-01
Full Text Available By using a nonlinear scalarization technique, the bounded rationality model M for generalized abstract fuzzy economies in finite continuous spaces is established. Furthermore, by using the model M, some new theorems for structural stability and robustness to (λ,ϵ-equilibria of generalized abstract fuzzy economies are proved.
Indian Academy of Sciences (India)
Topology is usually taught in India in the second year of a master's degree programme. Much of the time is spent on developing such basic notions as connectedness, compactness, product topology, and the course ends with. Tychonov's theorem or Urysohn's lemma. At best, the student learns a bit about the fundamental ...
A note on 'Some results on the IF-normed spaces'
International Nuclear Information System (INIS)
Saadati, Reza
2009-01-01
Recently, Lael and Nourouzi [Some results on the IF-normed spaces. Chaos, Solitons and Fractals 2006; doi:10.1016/j.chaos.2006.10.019] introduced and studied a new notation of IF-normed spaces by using the idea of intuitionistic fuzzy normed spaces due to Saadati and Park [On the intuitionistic fuzzy topological spaces. Chaos, Solitons and Fractals 2006;27:331-44], a special continuous t-norm i.e. min and a special continuous s-norm i.e. max. In this note, we consider the modified definition of IF-normed space i.e. LF-normed spaces and prove the open mapping and closed graph theorems for this space using arbitrary continuous t-norm.
Fuzzy Object Skeletonization: Theory, Algorithms, and Applications.
K Saha, Punam; Jin, Dakai; Liu, Yinxiao; E Christensen, Gary; Chen, Cheng
2017-08-10
Skeletonization offers a compact representation of an object while preserving important topological and geometrical features. Literature on skeletonization of binary objects is quite mature. However, challenges involved with skeletonization of fuzzy objects are mostly unanswered. This paper presents a new theory and algorithm of skeletonization for fuzzy objects, evaluates its performance, and demonstrates its applications. A formulation of fuzzy grassfire propagation is introduced; its relationships with fuzzy distance functions, level sets, and geodesics are discussed; and new results are presented. A notion of collision-impact of fire-fronts at skeletal points is introduced, and its role in filtering noisy skeletal points is demonstrated. A fuzzy object skeletonization algorithm is developed using new ideas of surface- and curve-skeletal voxels, digital collision-impact, and continuity of skeletal surfaces. A skeletal noise pruning algorithm is presented using branch-level significance. Accuracy and robustness of the new algorithm are examined on computer-generated phantoms and micro- and conventional CT imaging of trabecular bone specimens. An application of fuzzy object skeletonization to compute structure-width at a low image resolution is demonstrated, and its ability to predict bone strength is examined. Finally, the performance of the new fuzzy object skeletonization algorithm is compared with two binary object skeletonization methods.
Topological Rankings in Communication Networks
DEFF Research Database (Denmark)
Aabrandt, Andreas; Hansen, Vagn Lundsgaard; Træholt, Chresten
2015-01-01
In the theory of communication the central problem is to study how agents exchange information. This problem may be studied using the theory of connected spaces in topology, since a communication network can be modelled as a topological space such that agents can communicate if and only...... if they belong to the same path connected component of that space. In order to study combinatorial properties of such a communication network, notions from algebraic topology are applied. This makes it possible to determine the shape of a network by concrete invariants, e.g. the number of connected components...
Coverings, Networks and Weak Topologies
Czech Academy of Sciences Publication Activity Database
Dow, A.; Junnila, H.; Pelant, Jan
2006-01-01
Roč. 53, č. 2 (2006), s. 287-320 ISSN 0025-5793 R&D Projects: GA ČR GA201/97/0216 Institutional research plan: CEZ:AV0Z10190503 Keywords : Banach spaces * weak topologies * networks topologies Subject RIV: BA - General Mathematics
Deo, Satya
2018-01-01
This book presents the first concepts of the topics in algebraic topology such as the general simplicial complexes, simplicial homology theory, fundamental groups, covering spaces and singular homology theory in greater detail. Originally published in 2003, this book has become one of the seminal books. Now, in the completely revised and enlarged edition, the book discusses the rapidly developing field of algebraic topology. Targeted to undergraduate and graduate students of mathematics, the prerequisite for this book is minimal knowledge of linear algebra, group theory and topological spaces. The book discusses about the relevant concepts and ideas in a very lucid manner, providing suitable motivations and illustrations. All relevant topics are covered, including the classical theorems like the Brouwer’s fixed point theorem, Lefschetz fixed point theorem, Borsuk-Ulam theorem, Brouwer’s separation theorem and the theorem on invariance of the domain. Most of the exercises are elementary, but sometimes chal...
Topology, calculus and approximation
Komornik, Vilmos
2017-01-01
Presenting basic results of topology, calculus of several variables, and approximation theory which are rarely treated in a single volume, this textbook includes several beautiful, but almost forgotten, classical theorems of Descartes, Erdős, Fejér, Stieltjes, and Turán. The exposition style of Topology, Calculus and Approximation follows the Hungarian mathematical tradition of Paul Erdős and others. In the first part, the classical results of Alexandroff, Cantor, Hausdorff, Helly, Peano, Radon, Tietze and Urysohn illustrate the theories of metric, topological and normed spaces. Following this, the general framework of normed spaces and Carathéodory's definition of the derivative are shown to simplify the statement and proof of various theorems in calculus and ordinary differential equations. The third and final part is devoted to interpolation, orthogonal polynomials, numerical integration, asymptotic expansions and the numerical solution of algebraic and differential equations. Students of both pure an...
Directory of Open Access Journals (Sweden)
St Laurent Georges
2010-03-01
Full Text Available Abstract Background Signal transduction networks represent the information processing systems that dictate which dynamical regimes of biochemical activity can be accessible to a cell under certain circumstances. One of the major concerns in molecular systems biology is centered on the elucidation of the robustness properties and information processing capabilities of signal transduction networks. Achieving this goal requires the establishment of causal relations between the design principle of biochemical reaction systems and their emergent dynamical behaviors. Methods In this study, efforts were focused in the construction of a relatively well informed, deterministic, non-linear dynamic model, accounting for reaction mechanisms grounded on standard mass action and Hill saturation kinetics, of the canonical reaction topology underlying Toll-like receptor 4 (TLR4-mediated signaling events. This signaling mechanism has been shown to be deployed in macrophages during a relatively short time window in response to lypopolysaccharyde (LPS stimulation, which leads to a rapidly mounted innate immune response. An extensive computational exploration of the biochemical reaction space inhabited by this signal transduction network was performed via local and global perturbation strategies. Importantly, a broad spectrum of biologically plausible dynamical regimes accessible to the network in widely scattered regions of parameter space was reconstructed computationally. Additionally, experimentally reported transcriptional readouts of target pro-inflammatory genes, which are actively modulated by the network in response to LPS stimulation, were also simulated. This was done with the main goal of carrying out an unbiased statistical assessment of the intrinsic robustness properties of this canonical reaction topology. Results Our simulation results provide convincing numerical evidence supporting the idea that a canonical reaction mechanism of the TLR4
Illustrated introduction to topology and homotopy
Kalajdzievski, Sasho
2015-01-01
TOPOLOGYSets, Numbers, Cardinals, and Ordinals Sets and Numbers Sets and Cardinal Numbers Axiom of Choice and Equivalent Statements Metric Spaces: Definition, Examples, and BasicsMetric Spaces: Definition and Examples Metric Spaces: Basics Topological Spaces: Definition and ExamplesThe Definition and Some Simple Examples Some Basic Notions Bases Dense and Nowhere Dense Sets Continuous Mappings Subspaces, Quotient Spaces, Manifolds, and CW-Complexes Subspaces Quotient Spaces The Gluing Lemma, Topological Sums, and Some Special Quotient Spaces Manifolds and CW-ComplexesProducts of SpacesFinite Products of Spaces Infinite Products of Spaces Box Topology Connected Spaces and Path Connected Spaces Connected Spaces: Definition and Basic Facts Properties of Connected Spaces Path Connected Spaces Path Connected Spaces: More Properties and Related Matters Locally Connected and Locally Path Connected Spaces Compactness and Related Matters Compact Spaces: Definition Properties of Compact Spaces Compact, Lindelöf, and C...
Fuzziness and fuzzy modelling in Bulgaria's energy policy decision-making dilemma
International Nuclear Information System (INIS)
Wang Xingquan
2006-01-01
The decision complexity resulting from imprecision in decision variables and parameters, a major difficulty for conventional decision analysis methods, can be relevantly analysed and modelled by fuzzy logic. Bulgaria's nuclear policy decision-making process implicates such complexity of imprecise nature: stakeholders, criteria, measurement, etc. Given the suitable applicability of fuzzy logic in this case, this article tries to offer a concrete fuzzy paradigm including delimitation of decision space, quantification of imprecise variables, and, of course, parameterisation. (author)
Fuzziness and fuzzy modelling in Bulgaria's energy policy decision-making dilemma
Energy Technology Data Exchange (ETDEWEB)
Wang Xingquan [GREGOR, University Paris I, Pantheon-Sorbonne, Paris (France)]. E-mail: wangxingquan@gmail.com
2006-07-01
The decision complexity resulting from imprecision in decision variables and parameters, a major difficulty for conventional decision analysis methods, can be relevantly analysed and modelled by fuzzy logic. Bulgaria's nuclear policy decision-making process implicates such complexity of imprecise nature: stakeholders, criteria, measurement, etc. Given the suitable applicability of fuzzy logic in this case, this article tries to offer a concrete fuzzy paradigm including delimitation of decision space, quantification of imprecise variables, and, of course, parameterisation. (author)
Buchstaber, Victor M
2015-01-01
This book is about toric topology, a new area of mathematics that emerged at the end of the 1990s on the border of equivariant topology, algebraic and symplectic geometry, combinatorics, and commutative algebra. It has quickly grown into a very active area with many links to other areas of mathematics, and continues to attract experts from different fields. The key players in toric topology are moment-angle manifolds, a class of manifolds with torus actions defined in combinatorial terms. Construction of moment-angle manifolds relates to combinatorial geometry and algebraic geometry of toric v
Franz, Marcel
2013-01-01
Topological Insulators, volume six in the Contemporary Concepts of Condensed Matter Series, describes the recent revolution in condensed matter physics that occurred in our understanding of crystalline solids. The book chronicles the work done worldwide that led to these discoveries and provides the reader with a comprehensive overview of the field. Starting in 2004, theorists began to explore the effect of topology on the physics of band insulators, a field previously considered well understood. However, the inclusion of topology brings key new elements into this old field. Whereas it was
Location Discovery Based on Fuzzy Geometry in Passive Sensor Networks
Directory of Open Access Journals (Sweden)
Rui Wang
2011-01-01
Full Text Available Location discovery with uncertainty using passive sensor networks in the nation's power grid is known to be challenging, due to the massive scale and inherent complexity. For bearings-only target localization in passive sensor networks, the approach of fuzzy geometry is introduced to investigate the fuzzy measurability for a moving target in R2 space. The fuzzy analytical bias expressions and the geometrical constraints are derived for bearings-only target localization. The interplay between fuzzy geometry of target localization and the fuzzy estimation bias for the case of fuzzy linear observer trajectory is analyzed in detail in sensor networks, which can realize the 3-dimensional localization including fuzzy estimate position and velocity of the target by measuring the fuzzy azimuth angles at intervals of fixed time. Simulation results show that the resulting estimate position outperforms the traditional least squares approach for localization with uncertainty.
International Nuclear Information System (INIS)
Watanabe, K.
1990-01-01
Studies have been made on fuzzy diagnosis using inverse problem solutions of the fuzzy relational equation of ao R=b, where a is the failure vector, R the fuzzy relation matrix and b the sympton vector. Four phases of analyses were carried out in this study. First, fault tree analysis was undertaken to investigate what kind of causes produce fall of water level in a steam drum of ATR (Advanced Thermal Reactor), which is heavy-water-moderated boiling-water-cooled pressure-tube-type reactor. Next, simulation for 100 seconds was executed to determine how plant parameters respond to an occurrence of a transient induced by the cause. Third, the simulation data was analysed utilizing an autoregressive model. From this analysis, a total of 36 coherency functions up to 0.5 Hz in each transient were computed among nine important and detectable plant parameters, that is neutron flux, flow rate of coolant, steam and feed water, water level in the steam drum, pressure and opening area of control valve in a steam pipe, feed water temperature and electrical power. Last, the inverse problem of the fuzzy relational equation was solved. Relation matrices were adjusted from 0.00 to 1.00, after nine membership functions following the Gussian distribution for the symptom vector were estimated from correlation values of the coherency functions
PS-Regular Sets in Topology and Generalized Topology
Directory of Open Access Journals (Sweden)
Ankit Gupta
2014-01-01
Full Text Available We define and study a new class of regular sets called PS-regular sets. Properties of these sets are investigated for topological spaces and generalized topological spaces. Decompositions of regular open sets and regular closed sets are provided using PS-regular sets. Semiconnectedness is characterized by using PS-regular sets. PS-continuity and almost PS-continuity are introduced and investigated.
Directory of Open Access Journals (Sweden)
Serkan Karatas
2016-12-01
Full Text Available In this paper, we redefine the neutrosophic set operations and, by using them, we introduce neutrosophic topology and investigate some related properties such as neutrosophic closure, neutrosophic closure, neutrosophic interior, neutrosophic exterior, neutrosophic boundary and neutrosophic subspace.
Relational Demonic Fuzzy Refinement
Tchier, Fairouz
2014-01-01
We use relational algebra to define a refinement fuzzy order called demonic fuzzy refinement and also the associated fuzzy operators which are fuzzy demonic join $({\\bigsqcup }_{\\mathrm{\\text{f}}\\mathrm{\\text{u}}\\mathrm{\\text{z}}})$ , fuzzy demonic meet $({\\sqcap }_{\\mathrm{\\text{f}}\\mathrm{\\text{u}}\\mathrm{\\text{z}}})$ , and fuzzy demonic composition $({\\square }_{\\mathrm{\\text{f}}\\mathrm{\\text{u}}\\mathrm{\\text{z}}})$ . Our definitions and properties are illustrated by some examples using ma...
Topological approximations of multisets
Directory of Open Access Journals (Sweden)
El-Sayed A. Abo-Tabl
2013-07-01
Full Text Available Rough set theory is a powerful mathematical tool for dealing with inexact, uncertain or vague information. The core concept of rough set theory are information systems and approximation operators of approximation spaces. In this paper, we define and investigate three types of lower and upper multiset approximations of any multiset. These types based on the multiset base of multiset topology induced by a multiset relation. Moreover, the relationships between generalized rough msets and mset topologies are given. In addition, an illustrative example is given to illustrate the relationships between different types of generalized definitions of rough multiset approximations.
Intuitionistic Fuzzy Cycles and Intuitionistic Fuzzy Trees
Alshehri, N. O.
2014-01-01
Connectivity has an important role in neural networks, computer network, and clustering. In the design of a network, it is important to analyze connections by the levels. The structural properties of intuitionistic fuzzy graphs provide a tool that allows for the solution of operations research problems. In this paper, we introduce various types of intuitionistic fuzzy bridges, intuitionistic fuzzy cut vertices, intuitionistic fuzzy cycles, and intuitionistic fuzzy trees in intuitionistic fuzzy graphs and investigate some of their interesting properties. Most of these various types are defined in terms of levels. We also describe comparison of these types. PMID:24701155
Topological Structure of Vague Soft Sets
Directory of Open Access Journals (Sweden)
Chang Wang
2014-01-01
Full Text Available We introduce vague soft topological spaces which are defined over an initial universe with a fixed set of parameters. The notions of vague soft open sets, vague soft closed sets, vague soft interior, vague soft closure, and vague soft boundary are introduced and their basic properties and relations are investigated. Furthermore, with the help of examples they established that some properties of topological spaces and soft topological spaces do not hold in vague soft topological spaces. Vague soft connectedness and vague soft compactness are also studied.
Topologies on the algebra of test functions
International Nuclear Information System (INIS)
Hofmann, G.
1977-01-01
The algebraical structure of deltasub(THETA) (tensor algebra over the Schwartz space) defines two topologies, tausub(P)tausub(THETA). Some properties are studied of the locally convex topologies situated between tausub(P) and tausub(THETA). A lot of topologies is constructed in which the cone of positive elements is a normal one and regards the continuity of the Wightman functionals of free fields and of the Wick squares in free fields and their derivatives in such topologies
Directory of Open Access Journals (Sweden)
Selma Ozcag
2003-04-01
Full Text Available Textures were introduced by the second author as a point-based setting for the study of fuzzy sets, and have since proved to be an appropriate framework for the development of complement-free mathematical concepts. In this paper the authors lay the foundation for a theory of uniformities in a textural context. Analogues are given for both the diagonal and covering approaches to the classical theory of uniform structures, the notion of uniform topology is generalized and an analogue given for the well known result that a topological space is uniformizable if and only if it is completely regular. Finally a textural analogue of the classical interplay between uniformities and families of pseudo-metrics is presented.
Riemann, topology, and physics
Monastyrsky, Michael I
2008-01-01
This significantly expanded second edition of Riemann, Topology, and Physics combines a fascinating account of the life and work of Bernhard Riemann with a lucid discussion of current interaction between topology and physics. The author, a distinguished mathematical physicist, takes into account his own research at the Riemann archives of Göttingen University and developments over the last decade that connect Riemann with numerous significant ideas and methods reflected throughout contemporary mathematics and physics. Special attention is paid in part one to results on the Riemann–Hilbert problem and, in part two, to discoveries in field theory and condensed matter such as the quantum Hall effect, quasicrystals, membranes with nontrivial topology, "fake" differential structures on 4-dimensional Euclidean space, new invariants of knots and more. In his relatively short lifetime, this great mathematician made outstanding contributions to nearly all branches of mathematics; today Riemann’s name appears prom...
Characterizations of N-Ary Fuzzy Set Operations Which Induce Homomorphic Random Set Operations
1982-01-01
ordinary set operation * being continuous iff \\, is independent. Then the characterization for 0 in Theorem 5 continuous willi respect to topologies (V. 9...946-9!, 1. 113J Manes. E.G.. Review of *Fuzzy Switching and Auto- mata: Theory and Applications’. SIAM Review. 23. 12) Dubois, D. and 11. Prade . Fuzzy
Advances in type-2 fuzzy sets and systems theory and applications
Mendel, Jerry; Tahayori, Hooman
2013-01-01
This book explores recent developments in the theoretical foundations and novel applications of general and interval type-2 fuzzy sets and systems, including: algebraic properties of type-2 fuzzy sets, geometric-based definition of type-2 fuzzy set operators, generalizations of the continuous KM algorithm, adaptiveness and novelty of interval type-2 fuzzy logic controllers, relations between conceptual spaces and type-2 fuzzy sets, type-2 fuzzy logic systems versus perceptual computers; modeling human perception of real world concepts with type-2 fuzzy sets, different methods for generating membership functions of interval and general type-2 fuzzy sets, and applications of interval type-2 fuzzy sets to control, machine tooling, image processing and diet. The applications demonstrate the appropriateness of using type-2 fuzzy sets and systems in real world problems that are characterized by different degrees of uncertainty.
Towards topological quantum computer
Melnikov, D.; Mironov, A.; Mironov, S.; Morozov, A.; Morozov, An.
2018-01-01
Quantum R-matrices, the entangling deformations of non-entangling (classical) permutations, provide a distinguished basis in the space of unitary evolutions and, consequently, a natural choice for a minimal set of basic operations (universal gates) for quantum computation. Yet they play a special role in group theory, integrable systems and modern theory of non-perturbative calculations in quantum field and string theory. Despite recent developments in those fields the idea of topological quantum computing and use of R-matrices, in particular, practically reduce to reinterpretation of standard sets of quantum gates, and subsequently algorithms, in terms of available topological ones. In this paper we summarize a modern view on quantum R-matrix calculus and propose to look at the R-matrices acting in the space of irreducible representations, which are unitary for the real-valued couplings in Chern-Simons theory, as the fundamental set of universal gates for topological quantum computer. Such an approach calls for a more thorough investigation of the relation between topological invariants of knots and quantum algorithms.
Towards topological quantum computer
Directory of Open Access Journals (Sweden)
D. Melnikov
2018-01-01
Full Text Available Quantum R-matrices, the entangling deformations of non-entangling (classical permutations, provide a distinguished basis in the space of unitary evolutions and, consequently, a natural choice for a minimal set of basic operations (universal gates for quantum computation. Yet they play a special role in group theory, integrable systems and modern theory of non-perturbative calculations in quantum field and string theory. Despite recent developments in those fields the idea of topological quantum computing and use of R-matrices, in particular, practically reduce to reinterpretation of standard sets of quantum gates, and subsequently algorithms, in terms of available topological ones. In this paper we summarize a modern view on quantum R-matrix calculus and propose to look at the R-matrices acting in the space of irreducible representations, which are unitary for the real-valued couplings in Chern–Simons theory, as the fundamental set of universal gates for topological quantum computer. Such an approach calls for a more thorough investigation of the relation between topological invariants of knots and quantum algorithms.
Alkouri, Abd Ulazeez M.; Salleh, Abdul Razak
2014-09-01
In this paper we combine two definitions, namely fuzzy soft multiset and complex fuzzy set to construct the definition of a complex fuzzy soft multiset and study its properties. In other words, we study the extension of a fuzzy soft multiset from real numbers to complex numbers. We also introduce its basic operations, namely complement, union and intersection. Some examples are given.
Arnold, Vladimir; Zorich, Anton
1999-01-01
This volume offers an account of the present state of the art in pseudoperiodic topology-a young branch of mathematics, born at the boundary between the ergodic theory of dynamical systems, topology, and number theory. Related topics include the theory of algorithms, convex integer polyhedra, Morse inequalities, real algebraic geometry, statistical physics, and algebraic number theory. The book contains many new results. Most of the articles contain brief surveys on the topics, making the volume accessible to a broad audience. From the Preface by V.I. Arnold: "The authors … have done much to s
Basic algebraic topology and its applications
Adhikari, Mahima Ranjan
2016-01-01
This book provides an accessible introduction to algebraic topology, a ﬁeld at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book oﬀers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike. Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. T...
Chen, Guanrong
2005-01-01
Introduction to Fuzzy Systems provides students with a self-contained introduction that requires no preliminary knowledge of fuzzy mathematics and fuzzy control systems theory. Simplified and readily accessible, it encourages both classroom and self-directed learners to build a solid foundation in fuzzy systems. After introducing the subject, the authors move directly into presenting real-world applications of fuzzy logic, revealing its practical flavor. This practicality is then followed by basic fuzzy systems theory. The book also offers a tutorial on fuzzy control theory, based mainly on th
Concept Model on Topological Learning
Ae, Tadashi; Kioi, Kazumasa
2010-11-01
We discuss a new model for concept based on topological learning, where the learning process on the neural network is represented by mathematical topology. The topological learning of neural networks is summarized by a quotient of input space and the hierarchical step induces a tree where each node corresponds to a quotient. In general, the concept acquisition is a difficult problem, but the emotion for a subject is represented by providing the questions to a person. Therefore, a kind of concept is captured by such data and the answer sheet can be mapped into a topology consisting of trees. In this paper, we will discuss a way of mapping the emotional concept to a topological learning model.
Topological susceptibility from the overlap
DEFF Research Database (Denmark)
Del Debbio, Luigi; Pica, Claudio
2003-01-01
The chiral symmetry at finite lattice spacing of Ginsparg-Wilson fermionic actions constrains the renormalization of the lattice operators; in particular, the topological susceptibility does not require any renormalization, when using a fermionic estimator to define the topological charge....... Therefore, the overlap formalism appears as an appealing candidate to study the continuum limit of the topological susceptibility while keeping the systematic errors under theoretical control. We present results for the SU(3) pure gauge theory using the index of the overlap Dirac operator to study...... the topology of the gauge configurations. The topological charge is obtained from the zero modes of the overlap and using a new algorithm for the spectral flow analysis. A detailed comparison with cooling techniques is presented. Particular care is taken in assessing the systematic errors. Relatively high...
Fuzzy Logic for Incidence Geometry
2016-01-01
The paper presents a mathematical framework for approximate geometric reasoning with extended objects in the context of Geography, in which all entities and their relationships are described by human language. These entities could be labelled by commonly used names of landmarks, water areas, and so forth. Unlike single points that are given in Cartesian coordinates, these geographic entities are extended in space and often loosely defined, but people easily perform spatial reasoning with extended geographic objects “as if they were points.” Unfortunately, up to date, geographic information systems (GIS) miss the capability of geometric reasoning with extended objects. The aim of the paper is to present a mathematical apparatus for approximate geometric reasoning with extended objects that is usable in GIS. In the paper we discuss the fuzzy logic (Aliev and Tserkovny, 2011) as a reasoning system for geometry of extended objects, as well as a basis for fuzzification of the axioms of incidence geometry. The same fuzzy logic was used for fuzzification of Euclid's first postulate. Fuzzy equivalence relation “extended lines sameness” is introduced. For its approximation we also utilize a fuzzy conditional inference, which is based on proposed fuzzy “degree of indiscernibility” and “discernibility measure” of extended points. PMID:27689133
Coupland, Simon
2006-01-01
There has recently been a significant increase in academic interest in the field oftype-2 fuzzy sets and systems. Type-2 fuzzy systems offer the ability to model and reason with uncertain concepts. When faced with uncertainties type-2 fuzzy systems should, theoretically, give an increase in performance over type-l fuzzy systems. However, the computational complexity of generalised type-2 fuzzy systems is significantly higher than type-l systems. A direct consequence of this is that, prior to ...
Unified Theories from Fuzzy Extra Dimensions
Aschieri, P.; Manousselis, P.; Zoupanos, G.
2004-01-01
We combine and exploit ideas from Coset Space Dimensional Reduction (CSDR) methods and Non-commutative Geometry. We consider the dimensional reduction of gauge theories defined in high dimensions where the compact directions are a fuzzy space (matrix manifold). In the CSDR one assumes that the form of space-time is M^D=M^4 x S/R with S/R a homogeneous space. Then a gauge theory with gauge group G defined on M^D can be dimensionally reduced to M^4 in an elegant way using the symmetries of S/R, in particular the resulting four dimensional gauge is a subgroup of G. In the present work we show that one can apply the CSDR ideas in the case where the compact part of the space-time is a finite approximation of the homogeneous space S/R, i.e. a fuzzy coset. In particular we study the fuzzy sphere case.
Oliver, Bob; Pawałowski, Krzystof
1991-01-01
As part of the scientific activity in connection with the 70th birthday of the Adam Mickiewicz University in Poznan, an international conference on algebraic topology was held. In the resulting proceedings volume, the emphasis is on substantial survey papers, some presented at the conference, some written subsequently.
DEFF Research Database (Denmark)
Bendsøe, Martin P.; Sigmund, Ole
2007-01-01
Taking as a starting point a design case for a compliant mechanism (a force inverter), the fundamental elements of topology optimization are described. The basis for the developments is a FEM format for this design problem and emphasis is given to the parameterization of design as a raster image...
Indian Academy of Sciences (India)
TOPOLOGY. Allen Hatcher. October 2004 Volume 9 Number 10. GENERAL ARTICLES. 10 Taylor the Sailor. V Radhakrishnan. 19 Twisted Winged Endoparasitoids. An Enigma for Entomologists. Alpana Mazumdar. 25 Xanthan - A Versatile Gum. Anil Lachke. 34 From Natural Numbers to Numbers and. Curves in Nature - II.
Frank-Kamenetskii, Maxim D.
2013-01-01
A new variety on non-coding RNA has been discovered by several groups: circular RNA (circRNA). This discovery raises intriguing questions about the possibility of the existence of knotted RNA molecules and the existence of a new class of enzymes changing RNA topology, RNA topoisomerases.
Indian Academy of Sciences (India)
tion - 6. How Architectural Features Affect. Building During Earthquakes? C VRMurty. 48 Turbulence and Dispersion. K 5 Gandhi. BOOK REVIEWS. 86 Algebraic Topology. Siddhartha Gadgil. Front Cover. - .. ..-.......... -. Back Cover. Two-dimensional vertical section through a turbulent plume. (Courtesy: G S Shat, CAOS, IISc.).
Hierarchization process by possibilistic fuzzy clustering of fuzzy rules
Salgado, Paulo; Cunha, Manuela; Pavão, João; Igrejas, Getúlio
2010-01-01
This paper presents a possibilistic fuzzy clustering algorithm that is applied to a multidimensional fuzzy set or fuzzy rules. This method can be used to decompose the fuzzy system into an hierarchical structure. The methodology presented leads to a fuzzy partition of the fuzzy rules, one for each cluster, which corresponds to a new set of fuzzy sub-systems. This technique is tested to organize the fuzzy model into a new and more comprehensive structure.
Huang, Huaqing; Jin, Kyung-Hwan; Zhang, Shunhong; Liu, Feng
2018-02-22
Two-dimensional (2D) electrides are layered ionic crystals in which anionic electrons are confined in the interlayer space. Here, we report a discovery of nontrivial [Formula: see text] topology in the electronic structures of 2D electride Y 2 C. Based on first-principles calculations, we found a topological [Formula: see text] invariant of (1; 111) for the bulk band and topologically protected surface states in the surfaces of Y 2 C, signifying its nontrivial electronic topology. We suggest a spin-resolved angle-resolved photoemission spectroscopy (ARPES) measurement to detect the unique helical spin texture of the spin-polarized topological surface state, which will provide characteristic evidence for the nontrivial electronic topology of Y 2 C. Furthermore, the coexistence of 2D surface electride states and topological surface state enables us to explain the outstanding discrepancy between the recent ARPES experiments and theoretical calculations. Our findings establish a preliminary link between the electride in chemistry and the band topology in condensed-matter physics, which are expected to inspire further interdisciplinary research between these fields.
A version of Stone-Weierstrass theorem in Fuzzy Analysis
Energy Technology Data Exchange (ETDEWEB)
Font, J.J.; Sanchis, D.; Sanchis, M.
2017-07-01
Fuzzy numbers provide formalized tools to deal with non-precise quantities. They are indeed fuzzy sets in the real line and were introduced in 1978 by Dubois and Prade , who also defined their basic operations. Since then, Fuzzy Analysis has developed based on the notion of fuzzy number just as much as classical Real Analysis did based on the concept of real number. Such development was eased by a characterization of fuzzy numbers provided in 1986 by Goetschel and Voxman leaning on their level sets. As in the classical setting, continuous fuzzy-valued functions (fuzzy functions) are the central core of the theory. The principal difference with regard to real-valued continuous functions is the fact that the fuzzy numbers do not form a vectorial space, which determines all the results, and, especially, the proofs. The study of fuzzy functions has developed, principally, about two lines of investigation: - Differential fuzzy equations, which have turned out to be the natural way of modelling physical and engineering problems in contexts where the parameters are vague or incomplete. - The problem of approximation of fuzzy functions, basically using the approximation capability of fuzzy neural networks. We will focus on this second line of investigation, though our approach will be more general and based on an adaptation of the famous Stone-Weierstrass Theorem to the fuzzy context. This way so, we introduce the concept of “multiplier” of a set of fuzzy functions and use it to give a constructive proof of a Stone-Weiestrass type theorem for fuzzy functions. (Author)
Adaptive Fuzzy Systems in Computational Intelligence
Berenji, Hamid R.
1996-01-01
In recent years, the interest in computational intelligence techniques, which currently includes neural networks, fuzzy systems, and evolutionary programming, has grown significantly and a number of their applications have been developed in the government and industry. In future, an essential element in these systems will be fuzzy systems that can learn from experience by using neural network in refining their performances. The GARIC architecture, introduced earlier, is an example of a fuzzy reinforcement learning system which has been applied in several control domains such as cart-pole balancing, simulation of to Space Shuttle orbital operations, and tether control. A number of examples from GARIC's applications in these domains will be demonstrated.
Topological transformation groups and Dugundji compacta
International Nuclear Information System (INIS)
Kozlov, Konstantin L; Chatyrko, Vitalii A
2010-01-01
The presence of an algebraic structure on a space, which is compatible with its topology, in many cases imposes very strong restrictions on the properties of the space itself. Conditions are found which must be satisfied by the actions in order for the phase space to be a d-space (Dugundji compactum). This investigation allows the range of G-spaces that are d-spaces (Dugundji compacta) to be substantially widened. It is shown that all the cases known to the authors where a G-space (a topological group, one of its quotient spaces) is a d-space can be realized using equivariant maps. Bibliography: 39 titles.
Elements of mathematics general topology
Bourbaki, Nicolas
1995-01-01
This is the softcover reprint of the English translation of 1971 (available from Springer since 1989) of the first 4 chapters of Bourbaki's Topologie générale. It gives all the basics of the subject, starting from definitions. Important classes of topological spaces are studied, uniform structures are introduced and applied to topological groups. Real numbers are constructed and their properties established. Part II, comprising the later chapters, Ch. 5-10, is also available in English in softcover.
International Conference on Algebraic Topology
Cohen, Ralph; Miller, Haynes; Ravenel, Douglas
1989-01-01
These are proceedings of an International Conference on Algebraic Topology, held 28 July through 1 August, 1986, at Arcata, California. The conference served in part to mark the 25th anniversary of the journal Topology and 60th birthday of Edgar H. Brown. It preceded ICM 86 in Berkeley, and was conceived as a successor to the Aarhus conferences of 1978 and 1982. Some thirty papers are included in this volume, mostly at a research level. Subjects include cyclic homology, H-spaces, transformation groups, real and rational homotopy theory, acyclic manifolds, the homotopy theory of classifying spaces, instantons and loop spaces, and complex bordism.
Defuzzification Strategies for Fuzzy Classifications of Remote Sensing Data
Directory of Open Access Journals (Sweden)
Peter Hofmann
2016-06-01
Full Text Available The classes in fuzzy classification schemes are defined as fuzzy sets, partitioning the feature space through fuzzy rules, defined by fuzzy membership functions. Applying fuzzy classification schemes in remote sensing allows each pixel or segment to be an incomplete member of more than one class simultaneously, i.e., one that does not fully meet all of the classification criteria for any one of the classes and is member of more than one class simultaneously. This can lead to fuzzy, ambiguous and uncertain class assignation, which is unacceptable for many applications, indicating the need for a reliable defuzzification method. Defuzzification in remote sensing has to date, been performed by “crisp-assigning” each fuzzy-classified pixel or segment to the class for which it best fulfills the fuzzy classification rules, regardless of its classification fuzziness, uncertainty or ambiguity (maximum method. The defuzzification of an uncertain or ambiguous fuzzy classification leads to a more or less reliable crisp classification. In this paper the most common parameters for expressing classification uncertainty, fuzziness and ambiguity are analysed and discussed in terms of their ability to express the reliability of a crisp classification. This is done by means of a typical practical example from Object Based Image Analysis (OBIA.
Xu, Zeshui
2014-01-01
This book provides the readers with a thorough and systematic introduction to hesitant fuzzy theory. It presents the most recent research results and advanced methods in the field. These includes: hesitant fuzzy aggregation techniques, hesitant fuzzy preference relations, hesitant fuzzy measures, hesitant fuzzy clustering algorithms and hesitant fuzzy multi-attribute decision making methods. Since its introduction by Torra and Narukawa in 2009, hesitant fuzzy sets have become more and more popular and have been used for a wide range of applications, from decision-making problems to cluster analysis, from medical diagnosis to personnel appraisal and information retrieval. This book offers a comprehensive report on the state-of-the-art in hesitant fuzzy sets theory and applications, aiming at becoming a reference guide for both researchers and practitioners in the area of fuzzy mathematics and other applied research fields (e.g. operations research, information science, management science and engineering) chara...
Carlsson, Christer; Fullér, Robert
2004-01-01
Fuzzy Logic in Management demonstrates that difficult problems and changes in the management environment can be more easily handled by bringing fuzzy logic into the practice of management. This explicit theme is developed through the book as follows: Chapter 1, "Management and Intelligent Support Technologies", is a short survey of management leadership and what can be gained from support technologies. Chapter 2, "Fuzzy Sets and Fuzzy Logic", provides a short introduction to fuzzy sets, fuzzy relations, the extension principle, fuzzy implications and linguistic variables. Chapter 3, "Group Decision Support Systems", deals with group decision making, and discusses methods for supporting the consensus reaching processes. Chapter 4, "Fuzzy Real Options for Strategic Planning", summarizes research where the fuzzy real options theory was implemented as a series of models. These models were thoroughly tested on a number of real life investments, and validated in 2001. Chapter 5, "Soft Computing Methods for Reducing...
Fault Diagnosis in Deaerator Using Fuzzy Logic
Directory of Open Access Journals (Sweden)
S Srinivasan
2007-01-01
Full Text Available In this paper a fuzzy logic based fault diagnosis system for a deaerator in a power plant unit is presented. The system parameters are obtained using the linearised state space deaerator model. The fuzzy inference system is created and rule base are evaluated relating the parameters to the type and severity of the faults. These rules are fired for specific changes in system parameters and the faults are diagnosed.
Czech Academy of Sciences Publication Activity Database
Běhounek, Libor; Cintula, Petr
2005-01-01
Roč. 154, - (2005), s. 34-55 ISSN 0165-0114 R&D Projects: GA AV ČR IAA1030004; GA MŠk OC 274.001 Grant - others:COST(EU) Action 274 TARSKI Institutional research plan: CEZ:AV0Z10300504 Keywords : formal fuzzy logic * fuzzy set * foundations of fuzzy mathematics * LPi logic * higher-order fuzzy logic * fuzzy type theory * multi-sorted fuzzy logic Subject RIV: BA - General Mathematics Impact factor: 1.039, year: 2005
Why fuzzy controllers should be fuzzy
International Nuclear Information System (INIS)
Nowe, A.
1996-01-01
Fuzzy controllers are usually looked at as crisp valued mappings especially when artificial intelligence learning techniques are used to build up the controller. By doing so the semantics of a fuzzy conclusion being a fuzzy restriction on the viable control actions is non-existing. In this paper the authors criticise from an approximation point of view using a fuzzy controller to express a crisp mapping does not seem the right way to go. Secondly it is illustrated that interesting information is contained in a fuzzy conclusion when indeed this conclusion is considered as a fuzzy restriction. This information turns out to be very valuable when viability problems are concerned, i.e. problems where the objective is to keep a system within predefined boundaries
Smooth Optimal Control for a Class of Switched Systems Based on Fuzzy Theory and PSO
Atashpaz-Gargari, Esmaeil
2017-10-01
This paper proposes an approach to smooth optimal control design of two-point boundary value problem of switched systems with fuzzy operating regions. The switched system is modeled via a T-S fuzzy system, and then the fuzzy inference method of T-S fuzzy system is used to transform the switched system to a nonlinear system. For this nonlinear system, an optimal controller is designed. The control signal is a fuzzy control with weighted average defuzzifier. The fuzzy sets are used to partition the time space and a Particle Swarm Optimization (PSO) algorithm is proposed to optimize the weights. Simulations results demonstrate the applicability and effectiveness of the proposed method.
Similarity Measures of Sequence of Fuzzy Numbers and Fuzzy Risk Analysis
Directory of Open Access Journals (Sweden)
Zarife Zararsız
2015-01-01
Full Text Available We present the methods to evaluate the similarity measures between sequence of triangular fuzzy numbers for making contributions to fuzzy risk analysis. Firstly, we calculate the COG (center of gravity points of sequence of triangular fuzzy numbers. After, we present the methods to measure the degree of similarity between sequence of triangular fuzzy numbers. In addition, we give an example to compare the methods mentioned in the text. Furthermore, in this paper, we deal with the (t1,t2 type fuzzy number. By defining the algebraic operations on the (t1,t2 type fuzzy numbers we can solve the equations in the form x+u(t1,t2=v(t1,t2, where u(t1,t2 and v(t1,t2 are fuzzy number. By this way, we can build an algebraic structure on fuzzy numbers. Additionally, the generalized difference sequence spaces of triangular fuzzy numbers [l∞(Ft]B(r^,s^, [c(Ft]B(r^,s^, and [c0(Ft]B(r^,s^, consisting of all sequences u∗=(u(t1,t2k such that Br^,s^u∗ is in the spaces l∞(Ft, c(Ft, and c0(Ft, have been constructed, respectively. Furthermore, some classes of matrix transformations from the space cFtB(r^,s^ and μ(Ft to μ(Ft and cFtB(r^,s^ are characterized, respectively, where μ(Ft is any sequence space.
Construction of Fuzzy Ontologies from Fuzzy UML Models
Directory of Open Access Journals (Sweden)
Fu Zhang
2013-05-01
Full Text Available The success and proliferation of the Semantic Web depends heavily on construction of Web ontologies. However, classical ontology construction approaches are not sufficient for handling imprecise and uncertain information that is commonly found in many application domains. Therefore, great efforts on construction of fuzzy ontologies have been made in recent years. In this paper, we propose a formal approach and develop an automated tool for constructing fuzzy ontologies from fuzzy UML models. , we propose formalization methods of fuzzy UML models and fuzzy ontologies, where fuzzy UML models and fuzzy ontologies can be represented and interpreted by their respective formal definitions and semantic interpretation methods. , we propose an approach for constructing fuzzy ontologies from fuzzy UML models, i.e., transforming fuzzy UML models (including the structure and instance information of fuzzy UML models into fuzzy ontologies. , following the proposed approach, we implement a prototype transformation tool called that can construct fuzzy ontologies from fuzzy UML models. Constructing fuzzy ontologies from fuzzy UML models will facilitate the development of Web ontologies. , in order to show that the constructed fuzzy ontologies may be useful for reasoning on fuzzy UML models, we investigate how to reason on fuzzy UML models based on the constructed fuzzy ontologies, and it turns out that the reasoning tasks of fuzzy UML models can be checked by means of the reasoning mechanism of fuzzy ontologies.
Fuzzy Neuroidal Nets and Recurrent Fuzzy Computations
Czech Academy of Sciences Publication Activity Database
Wiedermann, Jiří
2001-01-01
Roč. 11, č. 6 (2001), s. 675-686 ISSN 1210-0552. [SOFSEM 2001 Workshop on Soft Computing. Piešťany, 29.11.2001-30.11.2001] R&D Projects: GA ČR GA201/00/1489; GA AV ČR KSK1019101 Institutional research plan: AV0Z1030915 Keywords : fuzzy computing * fuzzy neural nets * fuzzy Turing machines * non-uniform computational complexity Subject RIV: BA - General Mathematics
Robinson, Michael
2014-01-01
Signal processing is the discipline of extracting information from collections of measurements. To be effective, the measurements must be organized and then filtered, detected, or transformed to expose the desired information. Distortions caused by uncertainty, noise, and clutter degrade the performance of practical signal processing systems. In aggressively uncertain situations, the full truth about an underlying signal cannot be known. This book develops the theory and practice of signal processing systems for these situations that extract useful, qualitative information using the mathematics of topology -- the study of spaces under continuous transformations. Since the collection of continuous transformations is large and varied, tools which are topologically-motivated are automatically insensitive to substantial distortion. The target audience comprises practitioners as well as researchers, but the book may also be beneficial for graduate students.
DEFF Research Database (Denmark)
Blok, Anders
2010-01-01
Climate change is quickly becoming a ubiquitous socionatural reality, mediating extremes of sociospatial scale from the bodily to the planetary. Although environmentalism invites us to ‘think globally and act locally', the meaning of these scalar designations remains ambiguous. This paper explores...... the topological presuppositions of social theory in the context of global climate change, asking how carbon emissions ‘translate' into various sociomaterial forms. Staging a meeting between Tim Ingold's phenomenology of globes and spheres and the social topologies of actor-network theory (ANT), the paper advances...... a ‘relational-scalar' analytics of spatial practices, technoscience, and power. As technoscience gradually constructs a networked global climate, this ‘grey box' comes to circulate within fluid social spaces, taking on new shades as it hybridizes knowledges, symbols, and practices. Global climates thus come...
Arockiarani; J. Martina Jency
2017-01-01
The focus of this paper is to present the concept of fuzzy neutrosophic relations. Further we study the composition of fuzzy neutrosophic relations with the choice of t-norms and tconorms and characterize their properties.
Fuzzy logic controller optimization
Sepe, Jr., Raymond B; Miller, John Michael
2004-03-23
A method is provided for optimizing a rotating induction machine system fuzzy logic controller. The fuzzy logic controller has at least one input and at least one output. Each input accepts a machine system operating parameter. Each output produces at least one machine system control parameter. The fuzzy logic controller generates each output based on at least one input and on fuzzy logic decision parameters. Optimization begins by obtaining a set of data relating each control parameter to at least one operating parameter for each machine operating region. A model is constructed for each machine operating region based on the machine operating region data obtained. The fuzzy logic controller is simulated with at least one created model in a feedback loop from a fuzzy logic output to a fuzzy logic input. Fuzzy logic decision parameters are optimized based on the simulation.
Relativity of topology and dynamics
International Nuclear Information System (INIS)
Finkelstein, D.; Rodriguez, E.
1984-01-01
Recent developments in quantum set theory are used to formulate a program for quantum topological physics. The world is represented in Hilbert space whose psi vectors represent abstract complexes generated from the null set by one bracket operator and the usual Grassmann (or Clifford) product. Such a theory may be more basic than field theory, in that it may generate its own natural topology, time, kinematics and dynamics, without benefit of an absolute time-space dimension, topology, or Hamiltonian. For example there is a natural expression for the quantum gravitational field in terms of quantum topological operators. In such a theory the usual spectrum of possible dimensions describes only one of an indefinite hierarchy of levels, each with a similar spectrum, describing nonspatial infrastructure. While c simplices have no continuous symmetry, the q simplex has an orthogonal group (O(m,n). Because quantum theory cannot take the universe as physical system, a ''third relativity'' is proposed. The division between observer and observed is arbitrary. Then it is wrong to ask for ''the'' topology and dynamics of a system, in the same sense that it is wrong to ask for the ''the'' psi vectors of a system; topology and dynamics, like psi vectors, are not absolute but relative to the observer. (author)
International Nuclear Information System (INIS)
Gregoire, Thomas; Wacker, Jay G.
2002-01-01
New theories of electroweak symmetry breaking have recently been constructed that stabilize the weak scale and do not rely upon supersymmetry. In these theories the Higgs boson is a weakly coupled pseudo-Goldstone boson. In this note we study the class of theories that can be described by theory spaces and show that the fundamental group of theory space describes all the relevant classical physics in the low energy theory. The relationship between the low energy physics and the topological properties of theory space allow a systematic method for constructing theory spaces that give any desired low energy particle content and potential. This provides us with tools for analyzing and constructing new theories of electroweak symmetry breaking. (author)
Guillemin, Victor
2010-01-01
Differential Topology provides an elementary and intuitive introduction to the study of smooth manifolds. In the years since its first publication, Guillemin and Pollack's book has become a standard text on the subject. It is a jewel of mathematical exposition, judiciously picking exactly the right mixture of detail and generality to display the richness within. The text is mostly self-contained, requiring only undergraduate analysis and linear algebra. By relying on a unifying idea-transversality-the authors are able to avoid the use of big machinery or ad hoc techniques to establish the main
Proceedings of the Second Joint Technology Workshop on Neural Networks and Fuzzy Logic, volume 2
Lea, Robert N. (Editor); Villarreal, James A. (Editor)
1991-01-01
Documented here are papers presented at the Neural Networks and Fuzzy Logic Workshop sponsored by NASA and the University of Texas, Houston. Topics addressed included adaptive systems, learning algorithms, network architectures, vision, robotics, neurobiological connections, speech recognition and synthesis, fuzzy set theory and application, control and dynamics processing, space applications, fuzzy logic and neural network computers, approximate reasoning, and multiobject decision making.
Preimage entropy dimension of topological dynamical systems
Liu, Lei; Zhou, Xiaomin; Zhou, Xiaoyao
2014-01-01
We propose a new definition of preimage entropy dimension for continuous maps on compact metric spaces, investigate fundamental properties of the preimage entropy dimension, and compare the preimage entropy dimension with the topological entropy dimension. The defined preimage entropy dimension holds various basic properties of topological entropy dimension, for example, the preimage entropy dimension of a subsystem is bounded by that of the original system and topologically conjugated system...
Charges and Electromagnetic Radiation as Topological Excitations
Directory of Open Access Journals (Sweden)
Manfried Faber
2017-01-01
Full Text Available We discuss a model with stable topological solitons in Minkowski space with only three degrees of freedom, the rotational angles of a spatial Dreibein. This model has four types of solitons differing in two topological quantum numbers which we identify with electric charge and spin. The vacuum has a two-dimensional degeneracy leading to two types of massless excitations, characterised by a topological quantum number which could have a physical equivalent in the photon number.
An Intrinsic Topology for Orthomodular Lattices
Brunet, Olivier
2007-11-01
We present a general way to define a topology on orthomodular lattices. We show that in the case of a Hilbert lattice, this topology is equivalent to that induced by the metrics of the corresponding Hilbert space. Moreover, we show that in the case of a boolean algebra, the obtained topology is the discrete one. Thus, our construction provides a general tool for studying orthomodular lattices but also a way to distinguish classical and quantum logics.
Czech Academy of Sciences Publication Activity Database
Mesiar, Radko
2005-01-01
Roč. 28, č. 156 (2005), s. 365-370 ISSN 0165-0114 R&D Projects: GA ČR(CZ) GA402/04/1026 Institutional research plan: CEZ:AV0Z10750506 Keywords : fuzzy measures * fuzzy integral * regular fuzzy integral Subject RIV: BA - General Mathematics Impact factor: 1.039, year: 2005
DEFF Research Database (Denmark)
Rodríguez, J. Tinguaro; Franco de los Ríos, Camilo; Gómez, Daniel
2015-01-01
In this paper we want to stress the relevance of paired fuzzy sets, as already proposed in previous works of the authors, as a family of fuzzy sets that offers a unifying view for different models based upon the opposition of two fuzzy sets, simply allowing the existence of different types...
Howard, Ayanna
2005-01-01
The Fuzzy Logic Engine is a software package that enables users to embed fuzzy-logic modules into their application programs. Fuzzy logic is useful as a means of formulating human expert knowledge and translating it into software to solve problems. Fuzzy logic provides flexibility for modeling relationships between input and output information and is distinguished by its robustness with respect to noise and variations in system parameters. In addition, linguistic fuzzy sets and conditional statements allow systems to make decisions based on imprecise and incomplete information. The user of the Fuzzy Logic Engine need not be an expert in fuzzy logic: it suffices to have a basic understanding of how linguistic rules can be applied to the user's problem. The Fuzzy Logic Engine is divided into two modules: (1) a graphical-interface software tool for creating linguistic fuzzy sets and conditional statements and (2) a fuzzy-logic software library for embedding fuzzy processing capability into current application programs. The graphical- interface tool was developed using the Tcl/Tk programming language. The fuzzy-logic software library was written in the C programming language.
Intuitionistic Fuzzy Subbialgebras and Duality
Directory of Open Access Journals (Sweden)
Wenjuan Chen
2014-01-01
Full Text Available We investigate connections between bialgebras and Atanassov’s intuitionistic fuzzy sets. Firstly we define an intuitionistic fuzzy subbialgebra of a bialgebra with an intuitionistic fuzzy subalgebra structure and also with an intuitionistic fuzzy subcoalgebra structure. Secondly we investigate the related properties of intuitionistic fuzzy subbialgebras. Finally we prove that the dual of an intuitionistic fuzzy strong subbialgebra is an intuitionistic fuzzy strong subbialgebra.
Refining Linear Fuzzy Rules by Reinforcement Learning
Berenji, Hamid R.; Khedkar, Pratap S.; Malkani, Anil
1996-01-01
Linear fuzzy rules are increasingly being used in the development of fuzzy logic systems. Radial basis functions have also been used in the antecedents of the rules for clustering in product space which can automatically generate a set of linear fuzzy rules from an input/output data set. Manual methods are usually used in refining these rules. This paper presents a method for refining the parameters of these rules using reinforcement learning which can be applied in domains where supervised input-output data is not available and reinforcements are received only after a long sequence of actions. This is shown for a generalization of radial basis functions. The formation of fuzzy rules from data and their automatic refinement is an important step in closing the gap between the application of reinforcement learning methods in the domains where only some limited input-output data is available.
Adding dynamic rules to self-organizing fuzzy systems
Buhusi, Catalin V.
1992-01-01
This paper develops a Dynamic Self-Organizing Fuzzy System (DSOFS) capable of adding, removing, and/or adapting the fuzzy rules and the fuzzy reference sets. The DSOFS background consists of a self-organizing neural structure with neuron relocation features which will develop a map of the input-output behavior. The relocation algorithm extends the topological ordering concept. Fuzzy rules (neurons) are dynamically added or released while the neural structure learns the pattern. The DSOFS advantages are the automatic synthesis and the possibility of parallel implementation. A high adaptation speed and a reduced number of neurons is needed in order to keep errors under some limits. The computer simulation results are presented in a nonlinear systems modelling application.
Optimality Conditions for Fuzzy Number Quadratic Programming with Fuzzy Coefficients
Directory of Open Access Journals (Sweden)
Xue-Gang Zhou
2014-01-01
Full Text Available The purpose of the present paper is to investigate optimality conditions and duality theory in fuzzy number quadratic programming (FNQP in which the objective function is fuzzy quadratic function with fuzzy number coefficients and the constraint set is fuzzy linear functions with fuzzy number coefficients. Firstly, the equivalent quadratic programming of FNQP is presented by utilizing a linear ranking function and the dual of fuzzy number quadratic programming primal problems is introduced. Secondly, we present optimality conditions for fuzzy number quadratic programming. We then prove several duality results for fuzzy number quadratic programming problems with fuzzy coefficients.
Coherence of Radial Implicative Fuzzy Systems with Nominal Consequents
Czech Academy of Sciences Publication Activity Database
Coufal, David
-, č. 4 (2006), s. 60-66 ISSN 1509-4553 R&D Projects: GA MŠk 1M0545 Institutional research plan: CEZ:AV0Z10300504 Keywords : implicative fuzzy system * radial fuzzy system * nominal output space * coherence Subject RIV: IN - Informatics, Computer Science
Fuzzy Lyapunov Reinforcement Learning for Non Linear Systems.
Kumar, Abhishek; Sharma, Rajneesh
2017-03-01
We propose a fuzzy reinforcement learning (RL) based controller that generates a stable control action by lyapunov constraining fuzzy linguistic rules. In particular, we attempt at lyapunov constraining the consequent part of fuzzy rules in a fuzzy RL setup. Ours is a first attempt at designing a linguistic RL controller with lyapunov constrained fuzzy consequents to progressively learn a stable optimal policy. The proposed controller does not need system model or desired response and can effectively handle disturbances in continuous state-action space problems. Proposed controller has been employed on the benchmark Inverted Pendulum (IP) and Rotational/Translational Proof-Mass Actuator (RTAC) control problems (with and without disturbances). Simulation results and comparison against a) baseline fuzzy Q learning, b) Lyapunov theory based Actor-Critic, and c) Lyapunov theory based Markov game controller, elucidate stability and viability of the proposed control scheme. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.
Mathematics of Fuzzy Sets and Fuzzy Logic
Bede, Barnabas
2013-01-01
This book presents a mathematically-based introduction into the fascinating topic of Fuzzy Sets and Fuzzy Logic and might be used as textbook at both undergraduate and graduate levels and also as reference guide for mathematician, scientists or engineers who would like to get an insight into Fuzzy Logic. Fuzzy Sets have been introduced by Lotfi Zadeh in 1965 and since then, they have been used in many applications. As a consequence, there is a vast literature on the practical applications of fuzzy sets, while theory has a more modest coverage. The main purpose of the present book is to reduce this gap by providing a theoretical introduction into Fuzzy Sets based on Mathematical Analysis and Approximation Theory. Well-known applications, as for example fuzzy control, are also discussed in this book and placed on new ground, a theoretical foundation. Moreover, a few advanced chapters and several new results are included. These comprise, among others, a new systematic and constructive approach for fuzzy infer...
How we pass from fuzzy $po$-semigroups to fuzzy $po$-$\\Gamma$-semigroups
Kehayopulu, Niovi
2014-01-01
The results on fuzzy ordered semigroups (or on fuzzy semigroups) can be transferred to fuzzy ordered gamma (or to fuzzy gamma) semigroups. We show the way we pass from fuzzy ordered semigroups to fuzzy ordered gamma semigroups.
Recurrent fuzzy ranking methods
Hajjari, Tayebeh
2012-11-01
With the increasing development of fuzzy set theory in various scientific fields and the need to compare fuzzy numbers in different areas. Therefore, Ranking of fuzzy numbers plays a very important role in linguistic decision-making, engineering, business and some other fuzzy application systems. Several strategies have been proposed for ranking of fuzzy numbers. Each of these techniques has been shown to produce non-intuitive results in certain case. In this paper, we reviewed some recent ranking methods, which will be useful for the researchers who are interested in this area.
Myravyova, E. A.; Sharipov, M. I.; Radakina, D. S.
2017-10-01
During writing this work, the fuzzy controller with a double base of rules was studied, which was applied for the synthesis of the automated control system. A method for fuzzy controller adaptation has been developed. The adaptation allows the fuzzy controller to automatically compensate for parametric interferences that occur at the control object. Specifically, the fuzzy controller controlled the outlet steam temperature in the boiler unit BKZ-75-39 GMA. The software code was written in the programming support environment Unity Pro XL designed for fuzzy controller adaptation.
Fuzzy Dynamic Discrimination Algorithms for Distributed Knowledge Management Systems
Directory of Open Access Journals (Sweden)
Vasile MAZILESCU
2010-12-01
Full Text Available A reduction of the algorithmic complexity of the fuzzy inference engine has the following property: the inputs (the fuzzy rules and the fuzzy facts can be divided in two parts, one being relatively constant for a long a time (the fuzzy rule or the knowledge model when it is compared to the second part (the fuzzy facts for every inference cycle. The occurrence of certain transformations over the constant part makes sense, in order to decrease the solution procurement time, in the case that the second part varies, but it is known at certain moments in time. The transformations attained in advance are called pre-processing or knowledge compilation. The use of variables in a Business Rule Management System knowledge representation allows factorising knowledge, like in classical knowledge based systems. The language of the first-degree predicates facilitates the formulation of complex knowledge in a rigorous way, imposing appropriate reasoning techniques. It is, thus, necessary to define the description method of fuzzy knowledge, to justify the knowledge exploiting efficiency when the compiling technique is used, to present the inference engine and highlight the functional features of the pattern matching and the state space processes. This paper presents the main results of our project PR356 for designing a compiler for fuzzy knowledge, like Rete compiler, that comprises two main components: a static fuzzy discrimination structure (Fuzzy Unification Tree and the Fuzzy Variables Linking Network. There are also presented the features of the elementary pattern matching process that is based on the compiled structure of fuzzy knowledge. We developed fuzzy discrimination algorithms for Distributed Knowledge Management Systems (DKMSs. The implementations have been elaborated in a prototype system FRCOM (Fuzzy Rule COMpiler.
Introduction to set theory and topology
Kuratowski, Kazimierz; Stark, M
1972-01-01
Introduction to Set Theory and Topology describes the fundamental concepts of set theory and topology as well as its applicability to analysis, geometry, and other branches of mathematics, including algebra and probability theory. Concepts such as inverse limit, lattice, ideal, filter, commutative diagram, quotient-spaces, completely regular spaces, quasicomponents, and cartesian products of topological spaces are considered. This volume consists of 21 chapters organized into two sections and begins with an introduction to set theory, with emphasis on the propositional calculus and its applica
Margalef-Roig, J
1992-01-01
...there are reasons enough to warrant a coherent treatment of the main body of differential topology in the realm of Banach manifolds, which is at the same time correct and complete. This book fills the gap: whenever possible the manifolds treated are Banach manifolds with corners. Corners add to the complications and the authors have carefully fathomed the validity of all main results at corners. Even in finite dimensions some results at corners are more complete and better thought out here than elsewhere in the literature. The proofs are correct and with all details. I see this book as a reliable monograph of a well-defined subject; the possibility to fall back to it adds to the feeling of security when climbing in the more dangerous realms of infinite dimensional differential geometry. Peter W. Michor
Lattice QCD without topology barriers
Lüscher, Martin
2011-01-01
As the continuum limit is approached, lattice QCD simulations tend to get trapped in the topological charge sectors of field space and may consequently give biased results in practice. We propose to bypass this problem by imposing open (Neumann) boundary conditions on the gauge field in the time direction. The topological charge can then flow in and out of the lattice, while many properties of the theory (the hadron spectrum, for example) are not affected. Extensive simulations of the SU(3) gauge theory, using the HMC and the closely related SMD algorithm, confirm the absence of topology barriers if these boundary conditions are chosen. Moreover, the calculated autocorrelation times are found to scale approximately like the square of the inverse lattice spacing, thus supporting the conjecture that the HMC algorithm is in the universality class of the Langevin equation.
B Gibilisco, Michael; E Albert, Karen; N Mordeson, John; J Wierman, Mark; D Clark, Terry
2014-01-01
This book offers a comprehensive analysis of the social choice literature and shows, by applying fuzzy sets, how the use of fuzzy preferences, rather than that of strict ones, may affect the social choice theorems. To do this, the book explores the presupposition of rationality within the fuzzy framework and shows that the two conditions for rationality, completeness and transitivity, do exist with fuzzy preferences. Specifically, this book examines: the conditions under which a maximal set exists; the Arrow’s theorem; the Gibbard-Satterthwaite theorem; and the median voter theorem. After showing that a non-empty maximal set does exists for fuzzy preference relations, this book goes on to demonstrating the existence of a fuzzy aggregation rule satisfying all five Arrowian conditions, including non-dictatorship. While the Gibbard-Satterthwaite theorem only considers individual fuzzy preferences, this work shows that both individuals and groups can choose alternatives to various degrees, resulting in a so...
Special functions in Fuzzy Analysis
Angel Garrido
2006-01-01
In the treatment of Fuzzy Logic an useful tool appears: the membership function, with the information about the degree of completion of a condition which defines the respective Fuzzy Set or Fuzzy Relation. With their introduction, it is possible to prove some results on the foundations of Fuzzy Logic and open new ways in Fuzzy Analysis.
Special functions in Fuzzy Analysis
Directory of Open Access Journals (Sweden)
Angel Garrido
2006-01-01
Full Text Available In the treatment of Fuzzy Logic an useful tool appears: the membership function, with the information about the degree of completion of a condition which defines the respective Fuzzy Set or Fuzzy Relation. With their introduction, it is possible to prove some results on the foundations of Fuzzy Logic and open new ways in Fuzzy Analysis.
Approximate Reasoning with Fuzzy Booleans
van den Broek, P.M.; Noppen, J.A.R.
This paper introduces, in analogy to the concept of fuzzy numbers, the concept of fuzzy booleans, and examines approximate reasoning with the compositional rule of inference using fuzzy booleans. It is shown that each set of fuzzy rules is equivalent to a set of fuzzy rules with singleton crisp
Topological Photonics for Continuous Media
Silveirinha, Mario
Photonic crystals have revolutionized light-based technologies during the last three decades. Notably, it was recently discovered that the light propagation in photonic crystals may depend on some topological characteristics determined by the manner how the light states are mutually entangled. The usual topological classification of photonic crystals explores the fact that these structures are periodic. The periodicity is essential to ensure that the underlying wave vector space is a closed surface with no boundary. In this talk, we prove that it is possible calculate Chern invariants for a wide class of continuous bianisotropic electromagnetic media with no intrinsic periodicity. The nontrivial topology of the relevant continuous materials is linked with the emergence of edge states. Moreover, we will demonstrate that continuous photonic media with the time-reversal symmetry can be topologically characterized by a Z2 integer. This novel classification extends for the first time the theory of electronic topological insulators to a wide range of photonic platforms, and is expected to have an impact in the design of novel photonic systems that enable a topologically protected transport of optical energy. This work is supported in part by Fundacao para a Ciencia e a Tecnologia Grant Number PTDC/EEI-TEL/4543/2014.
Topological orders in rigid states
International Nuclear Information System (INIS)
Wen, X.G.
1990-01-01
The authors study a new kind of ordering topological order in rigid states (the states with no local gapless excitations). This paper concentrates on characterization of the different topological orders. As an example the authors discuss in detail chiral spin states of 2+1 dimensional spin systems. Chiral spin states are described by the topological Chern-Simons theories in the continuum limit. The authors show that the topological orders can be characterized by a non-Abelian gauge structure over the moduli space which parametrizes a family of the model Hamiltonians supporting topologically ordered ground states. In 2 + 1 dimensions, the non-Abelian gauge structure determines possible fractional statistics of the quasi-particle excitations over the topologically ordered ground states. The dynamics of the low lying global excitations is shown to be independent of random spatial dependent perturbations. The ground state degeneracy and the non-Abelian gauge structures discussed in this paper are very robust, even against those perturbations that break translation symmetry. The authors also discuss the symmetry properties of the degenerate ground states of chiral spin states. The authors find that some degenerate ground states of chiral spin states on torus carry non-trivial quantum numbers of the 90 degrees rotation
Topological Semimetals Studied by Ab Initio Calculations
Hirayama, Motoaki; Okugawa, Ryo; Murakami, Shuichi
2018-04-01
In topological semimetals such as Weyl, Dirac, and nodal-line semimetals, the band gap closes at points or along lines in k space which are not necessarily located at high-symmetry positions in the Brillouin zone. Therefore, it is not straightforward to find these topological semimetals by ab initio calculations because the band structure is usually calculated only along high-symmetry lines. In this paper, we review recent studies on topological semimetals by ab initio calculations. We explain theoretical frameworks which can be used for the search for topological semimetal materials, and some numerical methods used in the ab initio calculations.
Emerging Trends in Topological Insulators and Topological ...
Indian Academy of Sciences (India)
Moreover, proximity induced superconductivity in these systemscan lead to a state that supports zero energy Majoranafermions, and the phase is known as topological superconductors.In this article, the basic idea of topological insulatorsand topological superconductors are presented alongwith their experimental ...
Induced topological pressure for topological dynamical systems
International Nuclear Information System (INIS)
Xing, Zhitao; Chen, Ercai
2015-01-01
In this paper, inspired by the article [J. Jaerisch et al., Stochastics Dyn. 14, 1350016, pp. 1-30 (2014)], we introduce the induced topological pressure for a topological dynamical system. In particular, we prove a variational principle for the induced topological pressure
Directory of Open Access Journals (Sweden)
Dmitri A. Viattchenin
2009-06-01
Full Text Available This paper describes a modification of a possibilistic clustering method based on the concept of allotment among fuzzy clusters. Basic ideas of the method are considered and the concept of a principal allotment among fuzzy clusters is introduced. The paper provides the description of the plan of the algorithm for detection principal allotment. An analysis of experimental results of the proposed algorithm’s application to the Tamura’s portrait data in comparison with the basic version of the algorithm and with the NERFCM-algorithm is carried out. A methodology of the algorithm’s application to the dimensionality reduction problem is outlined and the application of the methodology is illustrated on the example of Anderson’s Iris data in comparison with the result of principal component analysis. Preliminary conclusions are formulated also.
An improved genetic algorithm with dynamic topology
International Nuclear Information System (INIS)
Cai Kai-Quan; Tang Yan-Wu; Zhang Xue-Jun; Guan Xiang-Min
2016-01-01
The genetic algorithm (GA) is a nature-inspired evolutionary algorithm to find optima in search space via the interaction of individuals. Recently, researchers demonstrated that the interaction topology plays an important role in information exchange among individuals of evolutionary algorithm. In this paper, we investigate the effect of different network topologies adopted to represent the interaction structures. It is found that GA with a high-density topology ends up more likely with an unsatisfactory solution, contrarily, a low-density topology can impede convergence. Consequently, we propose an improved GA with dynamic topology, named DT-GA, in which the topology structure varies dynamically along with the fitness evolution. Several experiments executed with 15 well-known test functions have illustrated that DT-GA outperforms other test GAs for making a balance of convergence speed and optimum quality. Our work may have implications in the combination of complex networks and computational intelligence. (paper)
Deformations of topological open strings
Hofman, C.; Ma, Whee Ky
Deformations of topological open string theories are described, with an emphasis on their algebraic structure. They are encoded in the mixed bulk-boundary correlators. They constitute the Hochschild complex of the open string algebra - the complex of multilinear maps on the boundary Hilbert space.
A NOTE ON FUZZY CLOSURE OF A FUZZY SET
Directory of Open Access Journals (Sweden)
Bhimraj Basumatary
2015-10-01
Full Text Available In this article fuzzy closure has been discussed with the help of extended definition of fuzzy set on the assumption that the union of a fuzzy set and its complement is universal set and intersection of a fuzzy set and its complement is empty set. Also we have discussed some proposition of fuzzy closure with the help of numerical example on the basis of extended definition of fuzzy set.
An Efficient Inductive Genetic Learning Algorithm for Fuzzy Relational Rules
Directory of Open Access Journals (Sweden)
Antonio
2012-04-01
Full Text Available Fuzzy modelling research has traditionally focused on certain types of fuzzy rules. However, the use of alternative rule models could improve the ability of fuzzy systems to represent a specific problem. In this proposal, an extended fuzzy rule model, that can include relations between variables in the antecedent of rules is presented. Furthermore, a learning algorithm based on the iterative genetic approach which is able to represent the knowledge using this model is proposed as well. On the other hand, potential relations among initial variables imply an exponential growth in the feasible rule search space. Consequently, two filters for detecting relevant potential relations are added to the learning algorithm. These filters allows to decrease the search space complexity and increase the algorithm efficiency. Finally, we also present an experimental study to demonstrate the benefits of using fuzzy relational rules.
Adaptive fuzzy system for 3-D vision
Mitra, Sunanda
1993-01-01
An adaptive fuzzy system using the concept of the Adaptive Resonance Theory (ART) type neural network architecture and incorporating fuzzy c-means (FCM) system equations for reclassification of cluster centers was developed. The Adaptive Fuzzy Leader Clustering (AFLC) architecture is a hybrid neural-fuzzy system which learns on-line in a stable and efficient manner. The system uses a control structure similar to that found in the Adaptive Resonance Theory (ART-1) network to identify the cluster centers initially. The initial classification of an input takes place in a two stage process; a simple competitive stage and a distance metric comparison stage. The cluster prototypes are then incrementally updated by relocating the centroid positions from Fuzzy c-Means (FCM) system equations for the centroids and the membership values. The operational characteristics of AFLC and the critical parameters involved in its operation are discussed. The performance of the AFLC algorithm is presented through application of the algorithm to the Anderson Iris data, and laser-luminescent fingerprint image data. The AFLC algorithm successfully classifies features extracted from real data, discrete or continuous, indicating the potential strength of this new clustering algorithm in analyzing complex data sets. The hybrid neuro-fuzzy AFLC algorithm will enhance analysis of a number of difficult recognition and control problems involved with Tethered Satellite Systems and on-orbit space shuttle attitude controller.
Probabilistic fuzzy clustering algorithm for fuzzy rules decomposition
Salgado, Paulo; Igrejas, Getúlio
2007-01-01
The Fuzzy C-Means (FCM) clustering algorithm is the best known and the most used method for fuzzy clustering and is generally applied to well defined sets of data. In this work a generalized Probabilistic Fuzzy C-Means (PFCM) algorithm is proposed and applied to fuzzy sets clustering. The methodology presented leads to a fuzzy partition of the fuzzy rules, one for each cluster, which corresponds to a new set of fuzzy sub-systems. When applied to the clustering of a flat fuzzy system the resul...
Axion topological field theory of topological superconductors
Qi, Xiao-Liang; Witten, Edward; Zhang, Shou-Cheng
2013-04-01
Topological superconductors are gapped superconductors with gapless and topologically robust quasiparticles propagating on the boundary. In this paper, we present a topological field theory description of three-dimensional time-reversal invariant topological superconductors. In our theory the topological superconductor is characterized by a topological coupling between the electromagnetic field and the superconducting phase fluctuation, which has the same form as the coupling of “axions” with an Abelian gauge field. As a physical consequence of our theory, we predict the level crossing induced by the crossing of special “chiral” vortex lines, which can be realized by considering s-wave superconductors in proximity with the topological superconductor. Our theory can also be generalized to the coupling with a gravitational field.
DEFF Research Database (Denmark)
Marcussen, Lars
2003-01-01
Rummets topologi, Historiens topologi: betragtninger om menneskets orientering til rum - fra hulen over beherskelse af flere akser til det flydende rum.......Rummets topologi, Historiens topologi: betragtninger om menneskets orientering til rum - fra hulen over beherskelse af flere akser til det flydende rum....
Optical image encryption topology.
Yong-Liang, Xiao; Xin, Zhou; Qiong-Hua, Wang; Sheng, Yuan; Yao-Yao, Chen
2009-10-15
Optical image encryption topology is proposed based on the principle of random-phase encoding. Various encryption topological units, involving peer-to-peer, ring, star, and tree topologies, can be realized by an optical 6f system. These topological units can be interconnected to constitute an optical image encryption network. The encryption and decryption can be performed in both digital and optical methods.
Fuzzy logic in autonomous orbital operations
Lea, Robert N.; Jani, Yashvant
1991-01-01
Fuzzy logic can be used advantageously in autonomous orbital operations that require the capability of handling imprecise measurements from sensors. Several applications are underway to investigate fuzzy logic approaches and develop guidance and control algorithms for autonomous orbital operations. Translational as well as rotational control of a spacecraft have been demonstrated using space shuttle simulations. An approach to a camera tracking system has been developed to support proximity operations and traffic management around the Space Station Freedom. Pattern recognition and object identification algorithms currently under development will become part of this camera system at an appropriate level in the future. A concept to control environment and life support systems for large Lunar based crew quarters is also under development. Investigations in the area of reinforcement learning, utilizing neural networks, combined with a fuzzy logic controller, are planned as a joint project with the Ames Research Center.
Fuzzy spheres from inequivalent coherent states quantizations
International Nuclear Information System (INIS)
Gazeau, Jean Pierre; Huguet, Eric; Lachieze-Rey, Marc; Renaud, Jacques
2007-01-01
The existence of a family of coherent states (CS) solving the identity in a Hilbert space allows, under certain conditions, to quantize functions defined on the measure space of CS parameters. The application of this procedure to the 2-sphere provides a family of inequivalent CS quantizations based on the spin spherical harmonics (the CS quantization from usual spherical harmonics appears to give a trivial issue for the Cartesian coordinates). We compare these CS quantizations to the usual (Madore) construction of the fuzzy sphere. Due to these differences, our procedure yields new types of fuzzy spheres. Moreover, the general applicability of CS quantization suggests similar constructions of fuzzy versions of a large variety of sets
Transportation Network Topologies
Holmes, Bruce J.; Scott, John
2004-01-01
A discomforting reality has materialized on the transportation scene: our existing air and ground infrastructures will not scale to meet our nation's 21st century demands and expectations for mobility, commerce, safety, and security. The consequence of inaction is diminished quality of life and economic opportunity in the 21st century. Clearly, new thinking is required for transportation that can scale to meet to the realities of a networked, knowledge-based economy in which the value of time is a new coin of the realm. This paper proposes a framework, or topology, for thinking about the problem of scalability of the system of networks that comprise the aviation system. This framework highlights the role of integrated communication-navigation-surveillance systems in enabling scalability of future air transportation networks. Scalability, in this vein, is a goal of the recently formed Joint Planning and Development Office for the Next Generation Air Transportation System. New foundations for 21st thinking about air transportation are underpinned by several technological developments in the traditional aircraft disciplines as well as in communication, navigation, surveillance and information systems. Complexity science and modern network theory give rise to one of the technological developments of importance. Scale-free (i.e., scalable) networks represent a promising concept space for modeling airspace system architectures, and for assessing network performance in terms of scalability, efficiency, robustness, resilience, and other metrics. The paper offers an air transportation system topology as framework for transportation system innovation. Successful outcomes of innovation in air transportation could lay the foundations for new paradigms for aircraft and their operating capabilities, air transportation system architectures, and airspace architectures and procedural concepts. The topology proposed considers air transportation as a system of networks, within which
Optimal Network-Topology Design
Li, Victor O. K.; Yuen, Joseph H.; Hou, Ting-Chao; Lam, Yuen Fung
1987-01-01
Candidate network designs tested for acceptability and cost. Optimal Network Topology Design computer program developed as part of study on topology design and analysis of performance of Space Station Information System (SSIS) network. Uses efficient algorithm to generate candidate network designs consisting of subsets of set of all network components, in increasing order of total costs and checks each design to see whether it forms acceptable network. Technique gives true cost-optimal network and particularly useful when network has many constraints and not too many components. Program written in PASCAL.
FUZZY RINGS AND ITS PROPERTIES
Directory of Open Access Journals (Sweden)
Karyati Karyati
2017-01-01
One of algebraic structure that involves a binary operation is a group that is defined an un empty set (classical with an associative binary operation, it has identity elements and each element has an inverse. In the structure of the group known as the term subgroup, normal subgroup, subgroup and factor group homomorphism and its properties. Classical algebraic structure is developed to algebraic structure fuzzy by the researchers as an example semi group fuzzy and fuzzy group after fuzzy sets is introduced by L. A. Zadeh at 1965. It is inspired of writing about semi group fuzzy and group of fuzzy, a research on the algebraic structure of the ring is held with reviewing ring fuzzy, ideal ring fuzzy, homomorphism ring fuzzy and quotient ring fuzzy with its properties. The results of this study are obtained fuzzy properties of the ring, ring ideal properties fuzzy, properties of fuzzy ring homomorphism and properties of fuzzy quotient ring by utilizing a subset of a subset level and strong level as well as image and pre-image homomorphism fuzzy ring. Keywords: fuzzy ring, subset level, homomorphism fuzzy ring, fuzzy quotient ring
Recognition of Handwritten Arabic words using a neuro-fuzzy network
International Nuclear Information System (INIS)
Boukharouba, Abdelhak; Bennia, Abdelhak
2008-01-01
We present a new method for the recognition of handwritten Arabic words based on neuro-fuzzy hybrid network. As a first step, connected components (CCs) of black pixels are detected. Then the system determines which CCs are sub-words and which are stress marks. The stress marks are then isolated and identified separately and the sub-words are segmented into graphemes. Each grapheme is described by topological and statistical features. Fuzzy rules are extracted from training examples by a hybrid learning scheme comprised of two phases: rule generation phase from data using a fuzzy c-means, and rule parameter tuning phase using gradient descent learning. After learning, the network encodes in its topology the essential design parameters of a fuzzy inference system.The contribution of this technique is shown through the significant tests performed on a handwritten Arabic words database
ON SOME DECOMPOSITIONS OF FUZZY SOFT CONTINUITY
Gain, Pradip Kumar; Mukherjee, Prakash; Chakraborty, Ramkrishna Prasad
2015-01-01
– In this article, some open-like fuzzy soft sets such as fuzzy soft semi-open set, fuzzy soft preopen set, fuzzy soft α-open set and corresponding variants of fuzzy soft continuous functions are introduced and discussed. Some other variants of fuzzy soft sets such as fuzzy soft semi-preclosed set, fuzzy soft t-set, fuzzy soft α*-set, fuzzy soft regular open set, fuzzy soft B-set, fuzzy soft C-set and fuzzy soft D(α)-set are defined and some properties of these sets are studied and investigat...
DEFF Research Database (Denmark)
Jantzen, Jan
The objective of this textbook is to acquire an understanding of the behaviour of fuzzy logic controllers. Under certain conditions a fuzzy controller is equivalent to a proportional-integral-derivative (PID) controller. Using that equivalence as a link, the book applies analysis methods from...... linear and nonlinear control theory. In the linear domain, PID tuning methods and stability analyses are transferred to linear fuzzy controllers. The Nyquist plot shows the robustness of different settings of the fuzzy gain parameters. As a result, a fuzzy controller is guaranteed to perform as well...... as any PID controller. In the nonlinear domain, the stability of four standard control surfaces is analysed by means of describing functions and Nyquist plots. The self-organizing controller (SOC) is shown to be a model reference adaptive controller. There is a possibility that a nonlinear fuzzy PID...
Lei, Qian
2017-01-01
This book offers a comprehensive and systematic review of the latest research findings in the area of intuitionistic fuzzy calculus. After introducing the intuitionistic fuzzy numbers’ operational laws and their geometrical and algebraic properties, the book defines the concept of intuitionistic fuzzy functions and presents the research on the derivative, differential, indefinite integral and definite integral of intuitionistic fuzzy functions. It also discusses some of the methods that have been successfully used to deal with continuous intuitionistic fuzzy information or data, which are different from the previous aggregation operators focusing on discrete information or data. Mainly intended for engineers and researchers in the fields of fuzzy mathematics, operations research, information science and management science, this book is also a valuable textbook for postgraduate and advanced undergraduate students alike.
Strongly Correlated Topological Insulators
2016-02-03
Strongly Correlated Topological Insulators In the past year, the grant was used for work in the field of topological phases, with emphasis on finding...surface of topological insulators. In the past 3 years, we have started a new direction, that of fractional topological insulators. These are materials...in which a topologically nontrivial quasi-flat band is fractionally filled and then subject to strong interactions. The views, opinions and/or
Random-walk topological transition revealed via electron counting
Engelhardt, G.; Benito, M.; Platero, G.; Schaller, G.; Brandes, T.
2017-12-01
The appearance of topological effects in systems exhibiting a nontrivial topological band structure strongly relies on the coherent wave nature of the equations of motion. Here, we reveal topological dynamics in a classical stochastic random walk version of the Su-Schrieffer-Heeger model with no relation to coherent wave dynamics. We explain that the commonly used topological invariant in the momentum space translates into an invariant in a counting-field space. This invariant gives rise to clear signatures of the topological phase in an associated escape time distribution.
First Meeting in Topology and Functional Analysis
López-Pellicer, Manuel
2014-01-01
Descriptive topology and functional analysis, with extensive material demonstrating new connections between them, are the subject of the first section of this work. Applications to spaces of continuous functions, topological Abelian groups, linear topological equivalence and to the separable quotient problem are included and are presented as open problems. The second section is devoted to Banach spaces, Banach algebras and operator theory. Each chapter presents a lot of worthwhile and important recent theorems with an abstract discussing the material in the chapter. Each chapter can almost be seen as a survey covering a particular area.
Crystallographic topology and its applications
Energy Technology Data Exchange (ETDEWEB)
Johnson, C.K.; Burnett, M.N. [Oak Ridge National Lab., TN (United States); Dunbar, W.D. [Simon`s Rock Coll., Great Barrington, MA (United States). Div. of Natural Sciences and Mathematics
1996-10-01
Geometric topology and structural crystallography concepts are combined to define a new area we call Structural Crystallographic Topology, which may be of interest to both crystallographers and mathematicians. In this paper, we represent crystallographic symmetry groups by orbifolds and crystal structures by Morse - functions. The Morse function uses mildly overlapping Gaussian thermal-motion probability density functions centered on atomic sites to form a critical net with peak, pass, pale, and pit critical points joined into a graph by density gradient-flow separatrices. Critical net crystal structure drawings can be made with the ORTEP-III graphics pro- An orbifold consists of an underlying topological space with an embedded singular set that represents the Wyckoff sites of the crystallographic group. An orbifold for a point group, plane group, or space group is derived by gluing together equivalent edges or faces of a crystallographic asymmetric unit. The critical-net-on-orbifold model incorporates the classical invariant lattice complexes of crystallography and allows concise quotient-space topological illustrations to be drawn without the repetition that is characteristic of normal crystal structure drawings.
Disjointness of Fuzzy Coalitions
Czech Academy of Sciences Publication Activity Database
Mareš, Milan; Vlach, M.
2008-01-01
Roč. 44, č. 3 (2008), s. 416-429 ISSN 0023-5954 R&D Projects: GA AV ČR IAA1075301; GA ČR GA402/04/1026; GA MŠk 1M0572 Institutional research plan: CEZ:AV0Z10750506 Keywords : Fuzzy coalitionla game * Disjointness of fuzzy sets * Fuzzy coalition Subject RIV: BD - Theory of Information Impact factor: 0.281, year: 2008
Berenji, Hamid R.
1992-01-01
Fuzzy logic and neural networks provide new methods for designing control systems. Fuzzy logic controllers do not require a complete analytical model of a dynamic system and can provide knowledge-based heuristic controllers for ill-defined and complex systems. Neural networks can be used for learning control. In this chapter, we discuss hybrid methods using fuzzy logic and neural networks which can start with an approximate control knowledge base and refine it through reinforcement learning.
Metamathematics of fuzzy logic
Hájek, Petr
1998-01-01
This book presents a systematic treatment of deductive aspects and structures of fuzzy logic understood as many valued logic sui generis. Some important systems of real-valued propositional and predicate calculus are defined and investigated. The aim is to show that fuzzy logic as a logic of imprecise (vague) propositions does have well-developed formal foundations and that most things usually named `fuzzy inference' can be naturally understood as logical deduction.
DEFF Research Database (Denmark)
Dotoli, M.; Jantzen, Jan
1999-01-01
The tutorial concerns automatic control of an inverted pendulum, especially rule based control by means of fuzzy logic. A ball balancer, implemented in a software simulator in Matlab, is used as a practical case study. The objectives of the tutorial are to teach the basics of fuzzy control......, and to show how to apply fuzzy logic in automatic control. The tutorial is distance learning, where students interact one-to-one with the teacher using e-mail....
Descriptive Topology in Selected Topics of Functional Analysis
Kakol, J; Pellicer, Manuel Lopez
2011-01-01
"Descriptive Topology in Selected Topics of Functional Analysis" is a collection of recent developments in the field of descriptive topology, specifically focused on the classes of infinite-dimensional topological vector spaces that appear in functional analysis. Such spaces include Frechet spaces, (LF)-spaces and their duals, and the space of continuous real-valued functions C(X) on a completely regular Hausdorff space X, to name a few. These vector spaces appear in functional analysis in distribution theory, differential equations, complex analysis, and various other analytical set
Fuzzy control and identification
Lilly, John H
2010-01-01
This book gives an introduction to basic fuzzy logic and Mamdani and Takagi-Sugeno fuzzy systems. The text shows how these can be used to control complex nonlinear engineering systems, while also also suggesting several approaches to modeling of complex engineering systems with unknown models. Finally, fuzzy modeling and control methods are combined in the book, to create adaptive fuzzy controllers, ending with an example of an obstacle-avoidance controller for an autonomous vehicle using modus ponendo tollens logic.
T Atanassov, Krassimir
2017-01-01
The book offers a comprehensive survey of intuitionistic fuzzy logics. By reporting on both the author’s research and others’ findings, it provides readers with a complete overview of the field and highlights key issues and open problems, thus suggesting new research directions. Starting with an introduction to the basic elements of intuitionistic fuzzy propositional calculus, it then provides a guide to the use of intuitionistic fuzzy operators and quantifiers, and lastly presents state-of-the-art applications of intuitionistic fuzzy sets. The book is a valuable reference resource for graduate students and researchers alike.
On the Fuzzy Stability of an Affine Functional Equation
Nasiruzzaman, Md.
2015-01-01
In this paper, we obtain the general solution of the following functional equation f(3x + y + z) + f(x + 3y + z) + f(x + y + 3z) + f(x) + f(y) + f(z) = 6f(x + y + z): We establish the Hyers-Ulam-Rassias stability of the above functional equation in the fuzzy normed spaces. Further we show the above functional equation is stable in the sense of Hyers and Ulam in fuzzy normed spaces.
Advances in fuzzy implication functions
Beliakov, Gleb; Sola, Humberto; Pradera, Ana
2013-01-01
Fuzzy implication functions are one of the main operations in fuzzy logic. They generalize the classical implication, which takes values in the set {0,1}, to fuzzy logic, where the truth values belong to the unit interval [0,1]. These functions are not only fundamental for fuzzy logic systems, fuzzy control, approximate reasoning and expert systems, but they also play a significant role in mathematical fuzzy logic, in fuzzy mathematical morphology and image processing, in defining fuzzy subsethood measures and in solving fuzzy relational equations. This volume collects 8 research papers on fuzzy implication functions. Three articles focus on the construction methods, on different ways of generating new classes and on the common properties of implications and their dependencies. Two articles discuss implications defined on lattices, in particular implication functions in interval-valued fuzzy set theories. One paper summarizes the sufficient and necessary conditions of solutions for one distributivity equation...
Oz in pointfree topology | Banaschewski | Quaestiones Mathematicae
African Journals Online (AJOL)
Oz frames are the natural pointfree counterpart of Oz spaces, that is, those topological spaces in which every open set is z-embedded. We give here the point-free analogues of known characterisations of Oz spaces and show that the Lindelöf coreflection of an Oz frame is Oz. The latter result has no spatial version, but has ...
Proceedings of the Second Joint Technology Workshop on Neural Networks and Fuzzy Logic, volume 1
Lea, Robert N. (Editor); Villarreal, James (Editor)
1991-01-01
Documented here are papers presented at the Neural Networks and Fuzzy Logic Workshop sponsored by NASA and the University of Houston, Clear Lake. The workshop was held April 11 to 13 at the Johnson Space Flight Center. Technical topics addressed included adaptive systems, learning algorithms, network architectures, vision, robotics, neurobiological connections, speech recognition and synthesis, fuzzy set theory and application, control and dynamics processing, space applications, fuzzy logic and neural network computers, approximate reasoning, and multiobject decision making.
Fuzzy logic based robotic controller
Attia, F.; Upadhyaya, M.
1994-01-01
Existing Proportional-Integral-Derivative (PID) robotic controllers rely on an inverse kinematic model to convert user-specified cartesian trajectory coordinates to joint variables. These joints experience friction, stiction, and gear backlash effects. Due to lack of proper linearization of these effects, modern control theory based on state space methods cannot provide adequate control for robotic systems. In the presence of loads, the dynamic behavior of robotic systems is complex and nonlinear, especially where mathematical modeling is evaluated for real-time operators. Fuzzy Logic Control is a fast emerging alternative to conventional control systems in situations where it may not be feasible to formulate an analytical model of the complex system. Fuzzy logic techniques track a user-defined trajectory without having the host computer to explicitly solve the nonlinear inverse kinematic equations. The goal is to provide a rule-based approach, which is closer to human reasoning. The approach used expresses end-point error, location of manipulator joints, and proximity to obstacles as fuzzy variables. The resulting decisions are based upon linguistic and non-numerical information. This paper presents a solution to the conventional robot controller which is independent of computationally intensive kinematic equations. Computer simulation results of this approach as obtained from software implementation are also discussed.
Empirical Bayes Approaches to Multivariate Fuzzy Partitions.
Woodbury, Max A.; Manton, Kenneth G.
1991-01-01
An empirical Bayes-maximum likelihood estimation procedure is presented for the application of fuzzy partition models in describing high dimensional discrete response data. The model describes individuals in terms of partial membership in multiple latent categories that represent bounded discrete spaces. (SLD)
OPTIMAL NETWORK TOPOLOGY DESIGN
Yuen, J. H.
1994-01-01
This program was developed as part of a research study on the topology design and performance analysis for the Space Station Information System (SSIS) network. It uses an efficient algorithm to generate candidate network designs (consisting of subsets of the set of all network components) in increasing order of their total costs, and checks each design to see if it forms an acceptable network. This technique gives the true cost-optimal network, and is particularly useful when the network has many constraints and not too many components. It is intended that this new design technique consider all important performance measures explicitly and take into account the constraints due to various technical feasibilities. In the current program, technical constraints are taken care of by the user properly forming the starting set of candidate components (e.g. nonfeasible links are not included). As subsets are generated, they are tested to see if they form an acceptable network by checking that all requirements are satisfied. Thus the first acceptable subset encountered gives the cost-optimal topology satisfying all given constraints. The user must sort the set of "feasible" link elements in increasing order of their costs. The program prompts the user for the following information for each link: 1) cost, 2) connectivity (number of stations connected by the link), and 3) the stations connected by that link. Unless instructed to stop, the program generates all possible acceptable networks in increasing order of their total costs. The program is written only to generate topologies that are simply connected. Tests on reliability, delay, and other performance measures are discussed in the documentation, but have not been incorporated into the program. This program is written in PASCAL for interactive execution and has been implemented on an IBM PC series computer operating under PC DOS. The disk contains source code only. This program was developed in 1985.
A Novel Approach to Implement Takagi-Sugeno Fuzzy Models.
Chang, Chia-Wen; Tao, Chin-Wang
2017-09-01
This paper proposes new algorithms based on the fuzzy c-regressing model algorithm for Takagi-Sugeno (T-S) fuzzy modeling of the complex nonlinear systems. A fuzzy c-regression state model (FCRSM) algorithm is a T-S fuzzy model in which the functional antecedent and the state-space-model-type consequent are considered with the available input-output data. The antecedent and consequent forms of the proposed FCRSM consists mainly of two advantages: one is that the FCRSM has low computation load due to only one input variable is considered in the antecedent part; another is that the unknown system can be modeled to not only the polynomial form but also the state-space form. Moreover, the FCRSM can be extended to FCRSM-ND and FCRSM-Free algorithms. An algorithm FCRSM-ND is presented to find the T-S fuzzy state-space model of the nonlinear system when the input-output data cannot be precollected and an assumed effective controller is available. In the practical applications, the mathematical model of controller may be hard to be obtained. In this case, an online tuning algorithm, FCRSM-FREE, is designed such that the parameters of a T-S fuzzy controller and the T-S fuzzy state model of an unknown system can be online tuned simultaneously. Four numerical simulations are given to demonstrate the effectiveness of the proposed approach.
Coordinated signal control for arterial intersections using fuzzy logic
Kermanian, Davood; Zare, Assef; Balochian, Saeed
2013-09-01
Every day growth of the vehicles has become one of the biggest problems of urbanism especially in major cities. This can waste people's time, increase the fuel consumption, air pollution, and increase the density of cars and vehicles. Fuzzy controllers have been widely used in many consumer products and industrial applications with success over the past two decades. This article proposes a comprehensive model of urban traffic network using state space equations and then using Fuzzy Logic Tool Box and SIMULINK Program MATLAB a fuzzy controller in order to optimize and coordinate signal control at two intersections at an arterial road. The fuzzy controller decides to extend, early cut or terminate a signal phase and phase sequence to ensure smooth flow of traffic with minimal waiting time and length of queue. Results show that the performance of the proposed traffic controller at novel fuzzy model is better that of conventional controllers under normal and abnormal traffic conditions.
Risk analysis with a fuzzy-logic approach of a complex installation
Peikert, Tim; Garbe, Heyno; Potthast, Stefan
2016-09-01
This paper introduces a procedural method based on fuzzy logic to analyze systematic the risk of an electronic system in an intentional electromagnetic environment (IEME). The method analyzes the susceptibility of a complex electronic installation with respect to intentional electromagnetic interference (IEMI). It combines the advantages of well-known techniques as fault tree analysis (FTA), electromagnetic topology (EMT) and Bayesian networks (BN) and extends the techniques with an approach to handle uncertainty. This approach uses fuzzy sets, membership functions and fuzzy logic to handle the uncertainty with probability functions and linguistic terms. The linguistic terms add to the risk analysis the knowledge from experts of the investigated system or environment.
Fuzzy logic applications to expert systems and control
Lea, Robert N.; Jani, Yashvant
1991-01-01
A considerable amount of work on the development of fuzzy logic algorithms and application to space related control problems has been done at the Johnson Space Center (JSC) over the past few years. Particularly, guidance control systems for space vehicles during proximity operations, learning systems utilizing neural networks, control of data processing during rendezvous navigation, collision avoidance algorithms, camera tracking controllers, and tether controllers have been developed utilizing fuzzy logic technology. Several other areas in which fuzzy sets and related concepts are being considered at JSC are diagnostic systems, control of robot arms, pattern recognition, and image processing. It has become evident, based on the commercial applications of fuzzy technology in Japan and China during the last few years, that this technology should be exploited by the government as well as private industry for energy savings.
Deriving photometric redshifts using fuzzy archetypes and self-organizing maps - I. Methodology
Speagle, Joshua S.; Eisenstein, Daniel J.
2017-07-01
We propose a method to substantially increase the flexibility and power of template fitting-based photometric redshifts by transforming a large number of galaxy spectral templates into a corresponding collection of 'fuzzy archetypes' using a suitable set of perturbative priors designed to account for empirical variation in dust attenuation and emission-line strengths. To bypass widely separated degeneracies in parameter space (e.g. the redshift-reddening degeneracy), we train self-organizing maps (SOMs) on large 'model catalogues' generated from Monte Carlo sampling of our fuzzy archetypes to cluster the predicted observables in a topologically smooth fashion. Subsequent sampling over the SOM then allows full reconstruction of the relevant probability distribution functions (PDFs). This combined approach enables the multimodal exploration of known variation among galaxy spectral energy distributions with minimal modelling assumptions. We demonstrate the power of this approach to recover full redshift PDFs using discrete Markov chain Monte Carlo sampling methods combined with SOMs constructed from Large Synoptic Survey Telescope ugrizY and Euclid YJH mock photometry.
Mynard, Frédéric; Seal, Gavin J
2010-02-01
The topological viewpoint on spaces of phenotypes presented in Stadler et al. (J Theor Biol 213:241-274, 2001) is revisited, and a quantified version is proposed. While necessary probabilistic information can be encoded in a topological- like fashion, it turns out that it is not reflected adequately by the concept of continuity. We propose alternative models, but the behavior of maps make these models non-topological in fundamental ways.
Properties of Bipolar Fuzzy Hypergraphs
Akram, M.; Dudek, W. A.; Sarwar, S.
2013-01-01
In this article, we apply the concept of bipolar fuzzy sets to hypergraphs and investigate some properties of bipolar fuzzy hypergraphs. We introduce the notion of $A-$ tempered bipolar fuzzy hypergraphs and present some of their properties. We also present application examples of bipolar fuzzy hypergraphs.
Directory of Open Access Journals (Sweden)
Radko Mesiar
2017-11-01
Full Text Available A revised definition for fuzzy bags is reviewed, developing the concept of bags given by Delgado et al. 2009 from which each bag has two parts, function and summary information. Then, the definitions of fuzzy bag expected value, bag entropy and bag similarity are introduced. By some examples, the new concepts are illustrated.
Extended Fuzzy Clustering Algorithms
U. Kaymak (Uzay); M. Setnes
2000-01-01
textabstractFuzzy clustering is a widely applied method for obtaining fuzzy models from data. It has been applied successfully in various fields including finance and marketing. Despite the successful applications, there are a number of issues that must be dealt with in practical applications of
Clustering by fuzzy neural gas and evaluation of fuzzy clusters.
Geweniger, Tina; Fischer, Lydia; Kaden, Marika; Lange, Mandy; Villmann, Thomas
2013-01-01
We consider some modifications of the neural gas algorithm. First, fuzzy assignments as known from fuzzy c-means and neighborhood cooperativeness as known from self-organizing maps and neural gas are combined to obtain a basic Fuzzy Neural Gas. Further, a kernel variant and a simulated annealing approach are derived. Finally, we introduce a fuzzy extension of the ConnIndex to obtain an evaluation measure for clusterings based on fuzzy vector quantization.
Clustering by Fuzzy Neural Gas and Evaluation of Fuzzy Clusters
Geweniger, Tina; Fischer, Lydia; Kaden, Marika; Lange, Mandy; Villmann, Thomas
2013-01-01
We consider some modifications of the neural gas algorithm. First, fuzzy assignments as known from fuzzy c-means and neighborhood cooperativeness as known from self-organizing maps and neural gas are combined to obtain a basic Fuzzy Neural Gas. Further, a kernel variant and a simulated annealing approach are derived. Finally, we introduce a fuzzy extension of the ConnIndex to obtain an evaluation measure for clusterings based on fuzzy vector quantization.
Topology of polymer chains under nanoscale confinement.
Satarifard, Vahid; Heidari, Maziar; Mashaghi, Samaneh; Tans, Sander J; Ejtehadi, Mohammad Reza; Mashaghi, Alireza
2017-08-24
Spatial confinement limits the conformational space accessible to biomolecules but the implications for bimolecular topology are not yet known. Folded linear biopolymers can be seen as molecular circuits formed by intramolecular contacts. The pairwise arrangement of intra-chain contacts can be categorized as parallel, series or cross, and has been identified as a topological property. Using molecular dynamics simulations, we determine the contact order distributions and topological circuits of short semi-flexible linear and ring polymer chains with a persistence length of l p under a spherical confinement of radius R c . At low values of l p /R c , the entropy of the linear chain leads to the formation of independent contacts along the chain and accordingly, increases the fraction of series topology with respect to other topologies. However, at high l p /R c , the fraction of cross and parallel topologies are enhanced in the chain topological circuits with cross becoming predominant. At an intermediate confining regime, we identify a critical value of l p /R c , at which all topological states have equal probability. Confinement thus equalizes the probability of more complex cross and parallel topologies to the level of the more simple, non-cooperative series topology. Moreover, our topology analysis reveals distinct behaviours for ring- and linear polymers under weak confinement; however, we find no difference between ring- and linear polymers under strong confinement. Under weak confinement, ring polymers adopt parallel and series topologies with equal likelihood, while linear polymers show a higher tendency for series arrangement. The radial distribution analysis of the topology reveals a non-uniform effect of confinement on the topology of polymer chains, thereby imposing more pronounced effects on the core region than on the confinement surface. Additionally, our results reveal that over a wide range of confining radii, loops arranged in parallel and cross
Statistical Methods for Fuzzy Data
Viertl, Reinhard
2011-01-01
Statistical data are not always precise numbers, or vectors, or categories. Real data are frequently what is called fuzzy. Examples where this fuzziness is obvious are quality of life data, environmental, biological, medical, sociological and economics data. Also the results of measurements can be best described by using fuzzy numbers and fuzzy vectors respectively. Statistical analysis methods have to be adapted for the analysis of fuzzy data. In this book, the foundations of the description of fuzzy data are explained, including methods on how to obtain the characterizing function of fuzzy m
Directory of Open Access Journals (Sweden)
Zoltan Erdei
2011-12-01
Full Text Available In this paper the authors present the usefulness of fuzzy logic in controlling engineering processes or applications. Although fuzzy logic does not represent a novelty for the scientific and engineering field, it enjoys a great appreciation from those involved in the two domains. The fact that fuzzy logic uses sentences kindred with the natural language make it easier to comprehend that a complex mathematical model required by the classic control theory. In MatLab software there are dedicated toolboxes to this subject that make the design of a fuzzy controller a facile one. In the paper design methods of a fuzzy controller are being presented both in Simulink and MatLab.
DEFF Research Database (Denmark)
Jantzen, Jan
1998-01-01
Design of a fuzzy controller requires more design decisions than usual, for example regarding rule base, inference engine, defuzzification, and data pre- and post processing. This tutorial paper identifies and describes the design choices related to single-loop fuzzy control, based on an internat...... on an international standard which is underway. The paper contains also a design approach, which uses a PID controller as a starting point. A design engineer can view the paper as an introduction to fuzzy controller design.......Design of a fuzzy controller requires more design decisions than usual, for example regarding rule base, inference engine, defuzzification, and data pre- and post processing. This tutorial paper identifies and describes the design choices related to single-loop fuzzy control, based...
Enhancements Of Fuzzy Q-Learning Algorithm
Directory of Open Access Journals (Sweden)
Grzegorz Głowaty
2005-01-01
Full Text Available Fuzzy Q-Learning algorithm combines reinforcement learning techniques with fuzzy modelling. It provides a ﬂexible solution for automatic discovery of rules for fuzzy systems inthe process of reinforcement learning. In this paper we propose several enhancements tothe original algorithm to make it more performant and more suitable for problems withcontinuous-input continuous-output space. Presented improvements involve generalizationof the set of possible rule conclusions. The aim is not only to automatically discover anappropriate rule-conclusions assignment, but also to automatically deﬁne the actual conclusions set given the all possible rules conclusions. To improve algorithm performance whendealing with environments with inertness, a special rule selection policy is proposed.
Emerging Trends in Topological Insulators and Topological ...
Indian Academy of Sciences (India)
Emerging Trends in Topological Insulators and. Topological Superconductors. Arijit Saha and Arun M Jayannavar. Arijit Saha is a Reader-F at the Institute of Physics,. Bhubaneswar. His research interest lies broadly in the areas of mesoscopic physics and strongly correlated electrons. Arun M Jayannavar is a.
A topological derivative method for topology optimization
DEFF Research Database (Denmark)
Norato, J.; Bendsøe, Martin P.; Haber, RB
2007-01-01
We propose a fictitious domain method for topology optimization in which a level set of the topological derivative field for the cost function identifies the boundary of the optimal design. We describe a fixed-point iteration scheme that implements this optimality criterion subject to a volumetric...
Book Review: Computational Topology
DEFF Research Database (Denmark)
Raussen, Martin
2011-01-01
Computational Topology by Herbert Edelsbrunner and John L. Harer. American Matheamtical Society, 2010 - ISBN 978-0-8218-4925-5......Computational Topology by Herbert Edelsbrunner and John L. Harer. American Matheamtical Society, 2010 - ISBN 978-0-8218-4925-5...
A transductive neuro-fuzzy controller: application to a drilling process.
Gajate, Agustín; Haber, Rodolfo E; Vega, Pastora I; Alique, José R
2010-07-01
Recently, new neuro-fuzzy inference algorithms have been developed to deal with the time-varying behavior and uncertainty of many complex systems. This paper presents the design and application of a novel transductive neuro-fuzzy inference method to control force in a high-performance drilling process. The main goal is to study, analyze, and verify the behavior of a transductive neuro-fuzzy inference system for controlling this complex process, specifically addressing the dynamic modeling, computational efficiency, and viability of the real-time application of this algorithm as well as assessing the topology of the neuro-fuzzy system (e.g., number of clusters, number of rules). A transductive reasoning method is used to create local neuro-fuzzy models for each input/output data set in a case study. The direct and inverse dynamics of a complex process are modeled using this strategy. The synergies among fuzzy, neural, and transductive strategies are then exploited to deal with process complexity and uncertainty through the application of the neuro-fuzzy models within an internal model control (IMC) scheme. A comparative study is made of the adaptive neuro-fuzzy inference system (ANFIS) and the suggested method inspired in a transductive neuro-fuzzy inference strategy. The two neuro-fuzzy strategies are evaluated in a real drilling force control problem. The experimental results demonstrated that the transductive neuro-fuzzy control system provides a good transient response (without overshoot) and better error-based performance indices than the ANFIS-based control system. In particular, the IMC system based on a transductive neuro-fuzzy inference approach reduces the influence of the increase in cutting force that occurs as the drill depth increases, reducing the risk of rapid tool wear and catastrophic tool breakage.
Hesitant intuitionistic fuzzy soft sets
Nazra, Admi; Syafruddin; Lestari, Riri; Catur Wicaksono, Gandung
2017-09-01
This paper aims to extend the hesitant fuzzy soft sets to hesitant intuitionistic fuzzy soft sets by merging the concept of hesitant intuitionistic fuzzy sets and soft sets. The authors define some operations on hesitant intuitionistic fuzzy sets, such as complement, union and intersection, and obtain related properties. The similar operations are defined on hesitant intuitionistic fuzzy soft sets, and also some properties such as assosiative and De Morgan’s laws are obtained.
DEFF Research Database (Denmark)
Raussen, Martin
2007-01-01
Directed spaces are the objects of study within directed algebraic topology. They are characterised by spaces of directed paths associated to a source and a target, both elements of an underlying topological space. The algebraic topology of these path spaces and their connections are studied from...... a categorical perspective. In particular, we study the preorder category associated to a directed space and various "quotient" categories arising from algebraic topological functors. Furthermore, we propose and study a new notion of directed homotopy equivalence between directed spaces....
Tierny, Julien; Favelier, Guillaume; Levine, Joshua A; Gueunet, Charles; Michaux, Michael
2017-08-29
This system paper presents the Topology ToolKit (TTK), a software platform designed for the topological analysis of scalar data in scientific visualization. While topological data analysis has gained in popularity over the last two decades, it has not yet been widely adopted as a standard data analysis tool for end users or developers. TTK aims at addressing this problem by providing a unified, generic, efficient, and robust implementation of key algorithms for the topological analysis of scalar data, including: critical points, integral lines, persistence diagrams, persistence curves, merge trees, contour trees, Morse-Smale complexes, fiber surfaces, continuous scatterplots, Jacobi sets, Reeb spaces, and more. TTK is easily accessible to end users due to a tight integration with ParaView. It is also easily accessible to developers through a variety of bindings (Python, VTK/C++) for fast prototyping or through direct, dependency-free, C++, to ease integration into pre-existing complex systems. While developing TTK, we faced several algorithmic and software engineering challenges, which we document in this paper. In particular, we present an algorithm for the construction of a discrete gradient that complies to the critical points extracted in the piecewise-linear setting. This algorithm guarantees a combinatorial consistency across the topological abstractions supported by TTK, and importantly, a unified implementation of topological data simplification for multi-scale exploration and analysis. We also present a cached triangulation data structure, that supports time efficient and generic traversals, which self-adjusts its memory usage on demand for input simplicial meshes and which implicitly emulates a triangulation for regular grids with no memory overhead. Finally, we describe an original software architecture, which guarantees memory efficient and direct accesses to TTK features, while still allowing for researchers powerful and easy bindings and extensions
Small-world networks of fuzzy chaotic oscillators
Bucolo, M; Fortuna, L
2003-01-01
Small-world topology has been used to build lattices of nonlinear fuzzy systems. Chaotic units, ruled by linguistic description and with specified Lyapunov exponent, have been realized and connected using linear diffusion coefficient. The dynamic features of the networks versus the number of systems connected have been investigated to underline phenomena like spatiotemporal chaos and complete regularization. The synchronization characteristics in case of sparse long-term connections and the performances comparison with regular and random network configurations are shown.
Behavior of impulsive fuzzy cellular neural networks with distributed delays
Directory of Open Access Journals (Sweden)
Kelin Li
2007-04-01
Full Text Available In this paper, we investigate a generalized model of fuzzy cellular neural networks with distributed delays and impulses. By employing the theory of topological degree, M-matrix and Lypunov functional, we find sufficient conditions for the existence, uniqueness and global exponential stability of both the equilibrium point and the periodic solution. Two examples are given to illustrate the results obtained here.
Maps generating the same primal space | Lazaar | Quaestiones ...
African Journals Online (AJOL)
Alexandroff topologies play an enigmatic role in topology. An important family of Alexandroff topologies are the functional Alexandroff spaces introduced by Shirazi and Golestani, and called primal topologies by O. Echi. The primal topology P(ƒ) on χ determined by a function ƒ : χ → χ is the topology whose closed sets are ...
Elementary concepts of topology
Alexandroff, Paul
1961-01-01
Concise work presents topological concepts in clear, elementary fashion without sacrificing their profundity or exactness. Author proceeds from basics of set-theoretic topology, through topological theorems and questions based on concept of the algebraic complex, to the concept of Betti groups.
Free Boolean Topological Groups
Directory of Open Access Journals (Sweden)
Ol’ga Sipacheva
2015-11-01
Full Text Available Known and new results on free Boolean topological groups are collected. An account of the properties that these groups share with free or free Abelian topological groups and properties specific to free Boolean groups is given. Special emphasis is placed on the application of set-theoretic methods to the study of Boolean topological groups.
Construction of fuzzy automata by fuzzy experiments
International Nuclear Information System (INIS)
Mironov, A.
1994-01-01
The solving the problem of canonical realization of partial reaction morphisms (PRM) for automata in toposes and fuzzy automata is addressed. This problem extends the optimal construction problem for finite deterministic automata by experiments. In the present paper the conception of canonical realization of PRM for automata in toposes is introduced and the sufficient conditions for the existence of canonical realizations for PRM in toposes are presented. As a consequence of this result the existence of canonical realizations for PRM in the category of fuzzy sets over arbitrary complete chain is proven
On the epireflective hull of topological nearness groups in the ...
African Journals Online (AJOL)
To find the specific nature of the objects that are in the epireflective hull of the symmetric topological spaces in the category of nearness spaces is a long open problem. See [BCH05]for more information. Here we consider topological nearness groups as a full subcategory of nearness groups and ask the analogous question ...
A new compactness type topological property | Zhao | Quaestiones ...
African Journals Online (AJOL)
By a gauge on a topological space we shall mean a mapping that assigns each element in the space an open neighbourhood. We investigate some topological properties which can be characterized using gauges. The main property we will consider is the gauge compactness. Some problems and possible future work are ...
Topological representation and quantic separation axioms of semi-quantales
Directory of Open Access Journals (Sweden)
Kamal El-Saady
2016-10-01
Full Text Available An adjunction between the category of semi-quantales and the category of lattice-valued quasi-topological spaces is established. Some characterizations of quantic separation axioms, for semi-quantales and lattice-valued quasi-topological spaces, are obtained and some relations among these axioms are established.
Topologies on quantum topoi induced by quantization
Energy Technology Data Exchange (ETDEWEB)
Nakayama, Kunji [Faculty of Law, Ryukoku University, Fushimi-ku, Kyoto 612-8577 (Japan)
2013-07-15
In the present paper, we consider effects of quantization in a topos approach of quantum theory. A quantum system is assumed to be coded in a quantum topos, by which we mean the topos of presheaves on the context category of commutative subalgebras of a von Neumann algebra of bounded operators on a Hilbert space. A classical system is modeled by a Lie algebra of classical observables. It is shown that a quantization map from the classical observables to self-adjoint operators on the Hilbert space naturally induces geometric morphisms from presheaf topoi related to the classical system to the quantum topos. By means of the geometric morphisms, we give Lawvere-Tierney topologies on the quantum topos (and their equivalent Grothendieck topologies on the context category). We show that, among them, there exists a canonical one which we call a quantization topology. We furthermore give an explicit expression of a sheafification functor associated with the quantization topology.
Topologies on quantum topoi induced by quantization
Nakayama, Kunji
2013-07-01
In the present paper, we consider effects of quantization in a topos approach of quantum theory. A quantum system is assumed to be coded in a quantum topos, by which we mean the topos of presheaves on the context category of commutative subalgebras of a von Neumann algebra of bounded operators on a Hilbert space. A classical system is modeled by a Lie algebra of classical observables. It is shown that a quantization map from the classical observables to self-adjoint operators on the Hilbert space naturally induces geometric morphisms from presheaf topoi related to the classical system to the quantum topos. By means of the geometric morphisms, we give Lawvere-Tierney topologies on the quantum topos (and their equivalent Grothendieck topologies on the context category). We show that, among them, there exists a canonical one which we call a quantization topology. We furthermore give an explicit expression of a sheafification functor associated with the quantization topology.
Unified theories from fuzzy extra dimensions
International Nuclear Information System (INIS)
Aschieri, P.; Madore, J.; Manousselis, P.; Zoupanos, G.
2004-01-01
We combine and exploit ideas from Coset Space Dimensional Reduction (CSDR) methods and Non-commutative Geometry. We consider the dimensional reduction of gauge theories defined in high dimensions where the compact directions are a fuzzy space (matrix manifold). In the CSDR one assumes that the form of space-time is M D =M 4 x S/R with S/R a homogeneous space. Then a gauge theory with gauge group G defined on M D can be dimensionally reduced to M 4 in an elegant way using the symmetries of S/R, in particular the resulting four dimensional gauge is a subgroup of G. In the present work we show that one can apply the CSDR ideas in the case where the compact part of the space-time is a finite approximation of the homogeneous space S/R, i.e. a fuzzy coset. In particular we study the fuzzy sphere case. (Abstract Copyright [2004], Wiley Periodicals, Inc.)
Directory of Open Access Journals (Sweden)
D. N. Georgiou
2014-04-01
Full Text Available In this paper we study and discuss the soft set theory giving new definitions, examples, new classes of soft sets, and properties for mappings between different classes of soft sets. Furthermore, we investigate the theory of soft topological spaces and we present new definitions, characterizations, and properties concerning the soft closure, the soft interior, the soft boundary, the soft continuity, the soft open and closed maps, and the soft homeomorphism.
International Nuclear Information System (INIS)
Rome, J.A.; Peng, Y.K.M.
1978-09-01
Guiding center orbits in noncircular axisymmetric tokamak plasmas are studied in the constants of motion (COM) space of (v, zeta, psi/sub m/). Here, v is the particle speed, zeta is the pitch angle with respect to the parallel equilibrium current, J/sub parallels/, and psi/sub m/ is the maximum value of the poloidal flux function (increasing from the magnetic axis) along the guiding center orbit. Two D-shaped equilibria in a flux-conserving tokamak having β's of 1.3% and 7.7% are used as examples. In this space, each confined orbit corresponds to one and only one point and different types of orbits (e.g., circulating, trapped, stagnation and pinch orbits) are represented by separate regions or surfaces in the space. It is also shown that the existence of an absolute minimum B in the higher β (7.7%) equilibrium results in a dramatically different orbit topology from that of the lower β case. The differences indicate the confinement of additional high energy (v → c, within the guiding center approximation) trapped, co- and countercirculating particles whose orbit psi/sub m/ falls within the absolute B well