Compactness of the difference between the porous thermoelastic semigroup and its decoupled semigroup
Directory of Open Access Journals (Sweden)
El Mustapha Ait Benhassi
2015-06-01
Full Text Available Under suitable assumptions, we prove the compactness of the difference between the porous thermoelastic semigroup and its decoupled one. This will be achieved by proving the norm continuity of this difference and the compactness of the difference between the resolvents of their generators. Applications to porous thermoelastic systems are given.
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
Quantitative recurrence for free semigroup actions
Carvalho, Maria; Rodrigues, Fagner B.; Varandas, Paulo
2018-03-01
We consider finitely generated free semigroup actions on a compact metric space and obtain quantitative information on Poincaré recurrence, average first return time and hitting frequency for the random orbits induced by the semigroup action. Besides, we relate the recurrence to balls with the rates of expansion of the semigroup generators and the topological entropy of the semigroup action. Finally, we establish a partial variational principle and prove an ergodic optimization for this kind of dynamical action. MC has been financially supported by CMUP (UID/MAT/00144/2013), which is funded by FCT (Portugal) with national (MEC) and European structural funds (FEDER) under the partnership agreement PT2020. FR and PV were partially supported by BREUDS. PV has also benefited from a fellowship awarded by CNPq-Brazil and is grateful to the Faculty of Sciences of the University of Porto for the excellent research conditions.
Linear topologies and sequential compactness in topological modules
African Journals Online (AJOL)
We prove that an absolute semi-valued ring is rst-countable if the set of invertibles is separable and its closure contains 0. We also show that every linearly topologized topological module over an absolute semi-valued ring whose invertibles approach 0 has the trivial topology. We also show that every sequentially compact ...
Sequential normal compactness versur topological normal compactness in variational analysis
Czech Academy of Sciences Publication Activity Database
Fabian, Marián; Mordukhovich, B. S.
2003-01-01
Roč. 54, č. 6 (2003), s. 1057-1067 ISSN 0362-546X R&D Projects: GA ČR GA201/01/1198 Institutional research plan: CEZ:AV0Z1019905; CEZ:AV0Z1019905 Keywords : variational analysis * sequential and topological normal compactness * Banach spaces Subject RIV: BA - General Mathematics Impact factor: 0.354, year: 2003
Quotient semigroups and extension semigroups
Indian Academy of Sciences (India)
the viewpoint of C∗-algebra and apply them to a survey of extension semigroups. Cer- tain interrelations ... -algebra extension theory and K K-theory, it is crucial to study the theory of quotient semigroups from the ... Similar to the construction of quotient group and quotient linear space, quotient semi- group may be induced ...
Characterizing chain-compact and chain-finite topological semilattices
Banakh, Taras; Bardyla, Serhii
2017-01-01
In the paper we present various characterizations of chain-compact and chain-finite topological semilattices. A topological semilattice $X$ is called chain-compact (resp. chain-finite) if each closed chain in $X$ is compact (finite). In particular, we prove that a (Hausdorff) $T_1$-topological semilattice $X$ is chain-finite (chain-compact) if and only if for any closed subsemilattice $Z\\subset X$ and any continuous homomorphism $h:X\\to Y$ to a (Hausdorff) $T_1$-topological semilattice $Y$ th...
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 ...
Stability of gradient semigroups under perturbations
Aragão-Costa, E. R.; Caraballo, T.; Carvalho, A. N.; Langa, J. A.
2011-07-01
In this paper we prove that gradient-like semigroups (in the sense of Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) are gradient semigroups (possess a Lyapunov function). This is primarily done to provide conditions under which gradient semigroups, in a general metric space, are stable under perturbation exploiting the known fact (see Carvalho and Langa (2009 J. Diff. Eqns 246 2646-68)) that gradient-like semigroups are stable under perturbation. The results presented here were motivated by the work carried out in Conley (1978 Isolated Invariant Sets and the Morse Index (CBMS Regional Conference Series in Mathematics vol 38) (RI: American Mathematical Society Providence)) for groups in compact metric spaces (see also Rybakowski (1987 The Homotopy Index and Partial Differential Equations (Universitext) (Berlin: Springer)) for the Morse decomposition of an invariant set for a semigroup on a compact metric space).
Specification and thermodynamical properties of semigroup actions
Rodrigues, Fagner B.; Varandas, Paulo
2016-05-01
In the present paper, we study the thermodynamical properties of finitely generated continuous subgroup actions. We propose a notion of topological entropy and pressure functions that do not depend on the growth rate of the semigroup and introduce strong and orbital specification properties, under which the semigroup actions have positive topological entropy and all points are entropy points. Moreover, we study the convergence and Lipschitz regularity of the pressure function and obtain relations between topological entropy and exponential growth rate of periodic points in the context of semigroups of expanding maps, obtaining a partial extension of the results obtained by Ruelle for ℤd-actions [D. Ruelle, Trans. Am. Math. Soc., 187, 237-251 (1973)]. The specification properties for semigroup actions and the corresponding one for its generators and the action of push-forward maps are also discussed.
Remarks on numerical semigroups
International Nuclear Information System (INIS)
Torres, F.
1995-12-01
We extend results on Weierstrass semigroups at ramified points of double covering of curves to any numerical semigroup whose genus is large enough. As an application we strengthen the properties concerning Weierstrass weights state in [To]. (author). 25 refs
Numerical semigroups and applications
Assi, Abdallah
2016-01-01
This work presents applications of numerical semigroups in Algebraic Geometry, Number Theory, and Coding Theory. Background on numerical semigroups is presented in the first two chapters, which introduce basic notation and fundamental concepts and irreducible numerical semigroups. The focus is in particular on free semigroups, which are irreducible; semigroups associated with planar curves are of this kind. The authors also introduce semigroups associated with irreducible meromorphic series, and show how these are used in order to present the properties of planar curves. Invariants of non-unique factorizations for numerical semigroups are also studied. These invariants are computationally accessible in this setting, and thus this monograph can be used as an introduction to Factorization Theory. Since factorizations and divisibility are strongly connected, the authors show some applications to AG Codes in the final section. The book will be of value for undergraduate students (especially those at a higher leve...
Higgsless superconductivity from topological defects in compact BF terms
Directory of Open Access Journals (Sweden)
M. Cristina Diamantini
2015-02-01
Full Text Available We present a new Higgsless model of superconductivity, inspired from anyon superconductivity but P- and T-invariant and generalisable to any dimension. While the original anyon superconductivity mechanism was based on incompressible quantum Hall fluids as average field states, our mechanism involves topological insulators as average field states. In D space dimensions it involves a (D−1-form fictitious pseudovector gauge field which originates from the condensation of topological defects in compact low-energy effective BF theories. In the average field approximation, the corresponding uniform emergent charge creates a gap for the (D−2-dimensional branes via the Magnus force, the dual of the Lorentz force. One particular combination of intrinsic and emergent charge fluctuations that leaves the total charge distribution invariant constitutes an isolated gapless mode leading to superfluidity. The remaining massive modes organise themselves into a D-dimensional charged, massive vector. There is no massive Higgs scalar as there is no local order parameter. When electromagnetism is switched on, the photon acquires mass by the topological BF mechanism. Although the charge of the gapless mode (2 and the topological order (4 are the same as those of the standard Higgs model, the two models of superconductivity are clearly different since the origins of the gap, reflected in the high-energy sectors are totally different. In 2D this type of superconductivity is explicitly realised as global superconductivity in Josephson junction arrays. In 3D this model predicts a possible phase transition from topological insulators to Higgsless superconductors.
Higgsless superconductivity from topological defects in compact BF terms
Diamantini, M. Cristina; Trugenberger, Carlo A.
2015-02-01
We present a new Higgsless model of superconductivity, inspired from anyon superconductivity but P- and T-invariant and generalisable to any dimension. While the original anyon superconductivity mechanism was based on incompressible quantum Hall fluids as average field states, our mechanism involves topological insulators as average field states. In D space dimensions it involves a (D - 1)-form fictitious pseudovector gauge field which originates from the condensation of topological defects in compact low-energy effective BF theories. In the average field approximation, the corresponding uniform emergent charge creates a gap for the (D - 2)-dimensional branes via the Magnus force, the dual of the Lorentz force. One particular combination of intrinsic and emergent charge fluctuations that leaves the total charge distribution invariant constitutes an isolated gapless mode leading to superfluidity. The remaining massive modes organise themselves into a D-dimensional charged, massive vector. There is no massive Higgs scalar as there is no local order parameter. When electromagnetism is switched on, the photon acquires mass by the topological BF mechanism. Although the charge of the gapless mode (2) and the topological order (4) are the same as those of the standard Higgs model, the two models of superconductivity are clearly different since the origins of the gap, reflected in the high-energy sectors are totally different. In 2D this type of superconductivity is explicitly realised as global superconductivity in Josephson junction arrays. In 3D this model predicts a possible phase transition from topological insulators to Higgsless superconductors.
On n-weak amenability of Rees semigroup algebras
Indian Academy of Sciences (India)
semigroups. In this work, we shall consider this class of Banach algebras. We examine the n-weak amenability of some semigroup algebras, and give an easier example of a Banach algebra which is n-weakly amenable if n is odd. Let L1(G) be the group algebra of a locally compact group G (§3.3 of [3]). Then Johnson.
The Ellis semigroup of a nonautonomous discrete dynamical system ...
African Journals Online (AJOL)
We introduce the Ellis semigroup of a nonautonomous discrete dynamical system (X, f1,∞) when X is a metric compact space. The underlying set of this semigroup is the pointwise closure of {fn1| n ∈ N) in the space Xx. By using the convergence of a sequence of points with respect to an ultrafilter it is possible to give a ...
Quotient semigroups and extension semigroups
Indian Academy of Sciences (India)
219–275, Contemp. Math. 228, Amer. Math. Soc. (RI: Providence) (1998). [12] Lin H, Classification of simple C∗-algebras of tracial topological rank zero, Duke Math. J. 125(1) (2004) 91–119. [13] Lin H, Classification of simple C. ∗. -algebras and higher dimensional noncommutative tori, Ann. Math. 157(2) (2003) 521–544.
Ergodic theory of amenable semigroup actions
Indian Academy of Sciences (India)
) (1984). [16] Riazi A and Wong J C S, Characterizations of amenable locally compact semigroups,. Pacific J. Math. 108 (1983) 479–496. [17] Rudin W, Functional analysis (New York: McGraw Hill) (1991). [18] Wong J C S, An ergodic property ...
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.
Fuzzy Perfect Mappings and Q-Compactness in Smooth Fuzzy Topological Spaces
Directory of Open Access Journals (Sweden)
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.
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
A note of topological pressure for non-compact sets of a factor map
International Nuclear Information System (INIS)
Li, Qian; Chen, Ercai; Zhou, Xiaoyao
2013-01-01
Using the notion of topological pressure for non-compact sets, we prove a relation for two topological pressures with a factor map. We also provide an application in symbolic dynamics and conformal repellers. These results are generalized to the cases of BS-dimensions
Nineteen papers on algebraic semigroups
Aizenshtat, A Ya; Podran, N E; Ponizovskii, IS; Shain, BM
1988-01-01
This volume contains papers selected by leading specialists in algebraic semigroups in the U.S., the United Kingdom, and Australia. Many of the papers strongly influenced the development of algebraic semigroups, but most were virtually unavailable outside the U.S.S.R. Written by some of the most prominent Soviet researchers in the field, the papers have a particular emphasis on semigroups of transformations. Boris Schein of the University of Arkansas is the translator.
Granular compaction and the topology of pore deformation
Saadatfar, Mohammad; Takeuchi, Hiroshi; Hanifpour, Maryam; Robins, Vanessa; Francois, Nicolas; Hiraoka, Yasuaki
2017-06-01
The mechanism of crystallisation in highly dissipative materials such as foams or granular materials is still widely unknown. In macroscopic granular materials high levels of energy need to be injected to overcome the natural propensity of these dissipative materials to form amorphous structures [1, 2]. The transition from disordered to ordered packings in such systems triggers a wide range of geometrical, topological and mechanical changes at multi length scales [3]. Formation of cavities and patterns by aggregates of grains and their evolution during this transition requires a complete topological description of the system. Here, crystallisation of three-dimensional packings of frictional spheres is studied at the grain scale with x-ray tomography. Using a novel and powerful topological tool, Persistent Homology, we describe the complete formation process of perfect tetrahedral and octahedral patterns: the two building blocks of FCC and HCP crystalline arrangements. Additionally we present possible and allowable deformations of these components that accurately reproduce the main topological features of the system. These results give new insights into the crystallisation of these highly dissipative materials.
Quasi-Hyperbolicity and Delay Semigroups
Directory of Open Access Journals (Sweden)
Shard Rastogi
2016-01-01
Full Text Available We study quasi-hyperbolicity of the delay semigroup associated with the equation u′(t=Bu(t+Φut, where ut is the history function and (B,D(B is the generator of a quasi-hyperbolic semigroup. We give conditions under which the associated solution semigroup of this equation generates a quasi-hyperbolic semigroup.
On the Structure of С*-Algebras Generated by Representations of the Elementary Inverse Semigroup
Directory of Open Access Journals (Sweden)
S.A. Grigoryan
2016-06-01
Full Text Available The class of С*-algebras generated by the elementary inverse semigroup and being deformations of the Toeplitz algebra has been introduced and studied. The properties of these algebras have been investigated. All their irreducible representations and automorphism groups have been described. These algebras have been proved to be Z-graded С*-algebras. For a certain class of algebras in the family under consideration the compact quantum semigroup structure has been constructed.
Gaps in nonsymmetric numerical semigroups
International Nuclear Information System (INIS)
Fel, Leonid G.; Aicardi, Francesca
2006-12-01
There exist two different types of gaps in the nonsymmetric numerical semigroups S(d 1 , . . . , d m ) finitely generated by a minimal set of positive integers {d 1 , . . . , d m }. We give the generating functions for the corresponding sets of gaps. Detailed description of both gap types is given for the 1st nontrivial case m = 3. (author)
The direct product of right zero semigroups and certain groupoids ...
African Journals Online (AJOL)
This paper investigates first the structure of semigroups which are direct products of right zero semigroups and cancellative semigroups with identity. We consider the relationship of these semigroups to right groups (the direct products of groups and right zero semigroups). Finally, we consider groupoids which are direct ...
Conference on Arithmetic and Ideal Theory of Rings and Semigroups
Fontana, Marco; Geroldinger, Alfred; Olberding, Bruce
2016-01-01
This book consists of both expository and research articles solicited from speakers at the conference entitled "Arithmetic and Ideal Theory of Rings and Semigroups," held September 22–26, 2014 at the University of Graz, Graz, Austria. It reflects recent trends in multiplicative ideal theory and factorization theory, and brings together for the first time in one volume both commutative and non-commutative perspectives on these areas, which have their roots in number theory, commutative algebra, and algebraic geometry. Topics discussed include topological aspects in ring theory, Prüfer domains of integer-valued polynomials and their monadic submonoids, and semigroup algebras. It will be of interest to practitioners of mathematics and computer science, and researchers in multiplicative ideal theory, factorization theory, number theory, and algebraic geometry.
Flavor symmetry and topology change in nuclear symmetry energy for compact stars
International Nuclear Information System (INIS)
Lee, Hyun Kyu; Rho, Mannque
2013-01-01
The nuclear symmetry energy figures crucially in the structure of asymmetric nuclei and, more importantly, in the equation of state (EoS) of compact stars. At present it is almost totally unknown, both experimentally and theoretically, in the density regime appropriate for the interior of neutron stars. Basing on a strong-coupled structure of dense baryonic matter encoded in the skyrmion crystal approach with a topology change and resorting to the notion of generalized hidden local symmetry in hadronic interactions, we address a variety of hitherto unexplored issues of nuclear interactions associated with the symmetry energy, i.e., kaon condensation and hyperons, possible topology change in dense matter, nuclear tensor forces, conformal symmetry, chiral symmetry, etc., in the EoS of dense compact-star matter. One of the surprising results coming from HLS structure that is distinct from what is given by standard phenomenological approaches is that at high density, baryonic matter is driven by renormalization group flow to the 'dilaton-limit fixed point' constrained by 'mended symmetries'. We further propose how to formulate kaon condensation and hyperons in compact-star matter in a framework anchored on a single effective Lagrangian by treating hyperons as the Callan–Klebanov kaon-skyrmion bound states simulated on crystal lattice. This formulation suggests that hyperons can figure in the stellar matter — if at all — when or after kaons condense, in contrast to the standard phenomenological approaches where the hyperons appear as the first strangeness degree of freedom in matter, thereby suppressing or delaying kaon condensation. In our simplified description of the stellar structure in terms of symmetry energies, which is compatible with that of the 1.97 solar mass star, kaon condensation plays a role of 'doorway state' to strange quark matter. (author)
On transformation semigroups which are ℬ-semigroups
Directory of Open Access Journals (Sweden)
S. Nenthein
2006-01-01
In 1966, Magill introduced and studied the subsemigroup T¯(X,Y of T(X, where ∅≠Y⊆X and T¯(X,Y={α∈T(X,Y|Yα⊆Y}. If W is a subspace of V, the subsemigroup L¯F(V,W of LF(V will be defined analogously. In this paper, it is shown that T¯(X,Y is a ℬ-semigroup if and only if Y=X, |Y|=1, or |X|≤3, and L¯F(V,W is a ℬ-semigroup if and only if (i W=V, (ii W={0}, or (iii F=ℤ2, dimFV=2, and dimFW=1 .
Theory of semigroups and applications
Sinha, Kalyan B
2017-01-01
The book presents major topics in semigroups, such as operator theory, partial differential equations, harmonic analysis, probability and statistics and classical and quantum mechanics, and applications. Along with a systematic development of the subject, the book emphasises on the explorations of the contact areas and interfaces, supported by the presentations of explicit computations, wherever feasible. Designed into seven chapters and three appendixes, the book targets to the graduate and senior undergraduate students of mathematics, as well as researchers in the respective areas. The book envisages the pre-requisites of a good understanding of real analysis with elements of the theory of measures and integration, and a first course in functional analysis and in the theory of operators. Chapters 4 through 6 contain advanced topics, which have many interesting applications such as the Feynman–Kac formula, the central limit theorem and the construction of Markov semigroups. Many examples have been given in...
Refinement monoids, equidecomposability types, and boolean inverse semigroups
Wehrung, Friedrich
2017-01-01
Adopting a new universal algebraic approach, this book explores and consolidates the link between Tarski's classical theory of equidecomposability types monoids, abstract measure theory (in the spirit of Hans Dobbertin's work on monoid-valued measures on Boolean algebras) and the nonstable K-theory of rings. This is done via the study of a monoid invariant, defined on Boolean inverse semigroups, called the type monoid. The new techniques contrast with the currently available topological approaches. Many positive results, but also many counterexamples, are provided.
Multiplicative perturbations of local C-semigroups
Indian Academy of Sciences (India)
2016-08-26
Aug 26, 2016 ... In this paper, we establish some left and right multiplicative perturbation theorems concerning local -semigroups when the generator of a perturbed local -semigroup S(⋅) may not be densely defined and the perturbation operator is a bounded linear operator from ¯D(A) into () such that = ...
Two-Valued States on Baer *-Semigroups
Freytes, Hector; Domenech, Graciela; de Ronde, Christian
2013-12-01
In this paper we develop an algebraic framework that allows us to extend families of two-valued states on orthomodular lattices to Baer *-semigroups. We apply this general approach to study the full class of two-valued states and the subclass of Jauch-Piron two-valued states on Baer *-semigroups.
Homology and cohomology of Rees semigroup algebras
DEFF Research Database (Denmark)
Grønbæk, Niels; Gourdeau, Frédéric; White, Michael C.
2011-01-01
Let S by a Rees semigroup, and let 1¹(S) be its convolution semigroup algebra. Using Morita equivalence we show that bounded Hochschild homology and cohomology of l¹(S) is isomorphic to those of the underlying discrete group algebra....
Multiplicative perturbations of local C-semigroups
Indian Academy of Sciences (India)
In this paper, we establish some left and right multiplicative perturbation theorems concerning local -semigroups when the generator of a perturbed local -semigroup S ( ⋅ ) may not be densely defined and the perturbation operator is a bounded linear operator from D ( A ) ¯ into () such that = on D ( A ) ¯ ...
Common fixed point theorems for left reversible and near-commutative semigroups and applications
Directory of Open Access Journals (Sweden)
Kang Shin Min
2005-01-01
Full Text Available We prove some common fixed point theorems for left reversible and near-commutative semigroups in compact and complete metric spaces, respectively. As applications, we get the existence and uniqueness of solutions for a class of nonlinear Volterra integral equations.
The theory of finitely generated commutative semigroups
Rédei, L; Stark, M; Gravett, K A H
1966-01-01
The Theory of Finitely Generated Commutative Semigroups describes a theory of finitely generated commutative semigroups which is founded essentially on a single """"fundamental theorem"""" and exhibits resemblance in many respects to the algebraic theory of numbers. The theory primarily involves the investigation of the F-congruences (F is the the free semimodule of the rank n, where n is a given natural number). As applications, several important special cases are given. This volume is comprised of five chapters and begins with preliminaries on finitely generated commutative semigroups before
Semigroups of Herz-Schur multipliers
DEFF Research Database (Denmark)
Knudby, Søren
2014-01-01
function (see Theorem 1.2). It is then shown that a (not necessarily proper) generator of a semigroup of Herz–Schur multipliers splits into a positive definite kernel and a conditionally negative definite kernel. We also show that the generator has a particularly pleasant form if and only if the group...... is amenable. In the second half of the paper we study semigroups of radial Herz–Schur multipliers on free groups. We prove that a generator of such a semigroup is linearly bounded by the word length function (see Theorem 1.6)....
M supergravity and abelian semigroups
International Nuclear Information System (INIS)
Izaurieta, Fernando; RodrIguez, Eduardo; Salgado, Patricio
2008-01-01
A gauge theory for the M algebra in eleven-dimensional spacetime is put forward. The gauge-invariant Lagrangian corresponds to a transgression form. This class of Lagrangians modifies Chern-Simons theory with the addition of a regularizing boundary term.The M algebra-invariant tensor required to define the theory comes from regarding the algebra as an abelian semigroup expansion of the orthsymplectic algebra osp (32|1). The explicit form of the Lagrangian is found by means of a transgression-specific subspace separation method. Dynamical properties are briefly analyzed through an example. The equations of motion are found to place severe constraints on the geometry, which might be partially alleviated by allowing for nonzero torsion.
Construction of a Family of Quantum Ornstein-Uhlenbeck Semigroups
Ki Ko, C
2003-01-01
For a given quasi-free state on the CCR algebra over one dimensional Hilbert space, a family of Markovian semigroups which leave the quasi-free state invariant is constructed by means of noncommutative elliptic operators and Dirichlet forms on von Neumann algebras. The generators (Dirichlet operators) of the semigroups are analyzed and the spectrums together with eigenspaces are found. When restricted to a maximal abelian subalgebra, the semigroups are reduced to a unique Markovian semigroup of classical Ornstein-Uhlenbeck process.
Decision problems for groups and semigroups
International Nuclear Information System (INIS)
Adian, S I; Durnev, V G
2000-01-01
The paper presents a detailed survey of results concerning the main decision problems of group theory and semigroup theory, including the word problem, the isomorphism problem, recognition problems, and other algorithmic questions related to them. The well-known theorems of Markov-Post, P.S. Novikov, Adian-Rabin, Higman, Magnus, and Lyndon are given with complete proofs. As a rule, the proofs presented in this survey are substantially simpler than those given in the original papers. For the sake of completeness, we first prove the insolubility of the halting problem for Turing machines, on which the insolubility of the word problem for semigroups is based. Specific attention is also paid to the simplest examples of semigroups with insoluble word problem. We give a detailed proof of the significant result of Lyndon that, in the class of groups presented by a system of defining relations for which the maximum mutual overlapping of any two relators is strictly less than one fifth of their lengths, the word problem is soluble, while insoluble word problems can occur when non-strict inequality is allowed. A proof of the corresponding result for finitely presented semigroups is also given, when the corresponding fraction is one half
Semigroups of Operators : Theory and Applications
Bobrowski, Adam; Lachowicz, Mirosław
2015-01-01
Many results, both from semigroup theory itself and from the applied sciences, are phrased in discipline-specific languages and hence are hardly known to a broader community. This volume contains a selection of lectures presented at a conference that was organised as a forum for all mathematicians using semigroup theory to learn what is happening outside their own field of research. The collection will help to establish a number of new links between various sub-disciplines of semigroup theory, stochastic processes, differential equations and the applied fields. The theory of semigroups of operators is a well-developed branch of functional analysis. Its foundations were laid at the beginning of the 20th century, while the fundamental generation theorem of Hille and Yosida dates back to the forties. The theory was, from the very beginning, designed as a universal language for partial differential equations and stochastic processes, but at the same time it started to live as an independent branch of operator the...
On Embedding a Semigroup in a Group
Indian Academy of Sciences (India)
ias
algebra textbook, as well as one on number theory, and also had an interest in the history of mathematics”. Mal- cev gave an example to show that there are cancella- tive semigroups which cannot be embedded in a group. Commenting on Sushkevich's persistence with his erro- neous ideas even after being proved wrong ...
Semigroups of transformations with fixed sets | Honyam ...
African Journals Online (AJOL)
Click on the link to view the abstract. Keywords: Transformation semigroup, Green's relations, ideal, rank. Quaestiones Mathematicae 36(2013), 79-92. Full Text: EMAIL FULL TEXT EMAIL FULL TEXT · DOWNLOAD FULL TEXT DOWNLOAD FULL TEXT · http://dx.doi.org/10.2989/16073606.2013.779958 · AJOL African ...
Markov operators, positive semigroups and approximation processes
Altomare, Francesco; Leonessa, Vita; Rasa, Ioan
2015-01-01
In recent years several investigations have been devoted to the study of large classes of (mainly degenerate) initial-boundary value evolution problems in connection with the possibility to obtain a constructive approximation of the associated positive C_0-semigroups. In this research monograph we present the main lines of a theory which finds its root in the above-mentioned research field.
Kumar, Rupesh; Grosbart, Małgorzata; Nurse, Pearl; Bahng, Soon; Wyman, Claire L; Marians, Kenneth J
2017-10-13
MukB is a structural maintenance of chromosome-like protein required for DNA condensation. The complete condensin is a large tripartite complex of MukB, the kleisin, MukF, and an accessory protein, MukE. As found previously, MukB DNA condensation is a stepwise process. We have defined these steps topologically. They proceed first via the formation of negative supercoils that are sequestered by the protein followed by hinge-hinge interactions between MukB dimers that stabilize topologically isolated loops in the DNA. MukB itself is sufficient to mediate both of these topological alterations; neither ATP nor MukEF is required. We show that the MukB hinge region binds DNA and that this region of the protein is involved in sequestration of supercoils. Cells carrying mutations in the MukB hinge that reduce DNA condensation in vitro exhibit nucleoid decondensation in vivo . © 2017 by The American Society for Biochemistry and Molecular Biology, Inc.
International Conference on Semigroups, Algebras and Operator Theory
Meakin, John; Rajan, A
2015-01-01
This book discusses recent developments in semigroup theory and its applications in areas such as operator algebras, operator approximations and category theory. All contributing authors are eminent researchers in their respective fields, from across the world. Their papers, presented at the 2014 International Conference on Semigroups, Algebras and Operator Theory in Cochin, India, focus on recent developments in semigroup theory and operator algebras. They highlight current research activities on the structure theory of semigroups as well as the role of semigroup theoretic approaches to other areas such as rings and algebras. The deliberations and discussions at the conference point to future research directions in these areas. This book presents 16 unpublished, high-quality and peer-reviewed research papers on areas such as structure theory of semigroups, decidability vs. undecidability of word problems, regular von Neumann algebras, operator theory and operator approximations. Interested researchers will f...
Semicrossed products of operator algebras by semigroups
Davidson, Kenneth R; Kakariadis, Evgenios T A
2017-01-01
The authors examine the semicrossed products of a semigroup action by *-endomorphisms on a C*-algebra, or more generally of an action on an arbitrary operator algebra by completely contractive endomorphisms. The choice of allowable representations affects the corresponding universal algebra. The authors seek quite general conditions which will allow them to show that the C*-envelope of the semicrossed product is (a full corner of) a crossed product of an auxiliary C*-algebra by a group action. Their analysis concerns a case-by-case dilation theory on covariant pairs. In the process we determine the C*-envelope for various semicrossed products of (possibly nonselfadjoint) operator algebras by spanning cones and lattice-ordered abelian semigroups.
Maxwell superalgebras and Abelian semigroup expansion
Directory of Open Access Journals (Sweden)
P.K. Concha
2014-09-01
Full Text Available The Abelian semigroup expansion is a powerful and simple method to derive new Lie algebras from a given one. Recently it was shown that the S-expansion of so(3,2 leads us to the Maxwell algebra M. In this paper we extend this result to superalgebras, by proving that different choices of abelian semigroups S lead to interesting D=4 Maxwell Superalgebras. In particular, the minimal Maxwell superalgebra sM and the N-extended Maxwell superalgebra sM(N recently found by the Maurer–Cartan expansion procedure, are derived alternatively as an S-expansion of osp(4|N. Moreover, we show that new minimal Maxwell superalgebras type sMm+2 and their N-extended generalization can be obtained using the S-expansion procedure.
Orbits of operators and operator semigroups
Czech Academy of Sciences Publication Activity Database
Müller, Vladimír
-, č. 1737 (2011), s. 78-90 ISSN 1880-2818. [Noncommutative structure in operator theory and its application. Kyoto, 27.10.2010-29.10.2010] R&D Projects: GA ČR GA201/09/0473; GA AV ČR IAA100190903 Institutional research plan: CEZ:AV0Z10190503 Keywords : orbits of operators * hypercyclicity * semigroups of operators Subject RIV: BA - General Mathematics
Multiplicative perturbations of local C-semigroups
Indian Academy of Sciences (India)
)S(s) = S(t +s)C for all 0 ≤ t,s,t ... locally Lipschitz continuous local C-semigroups (see Theorems 2.6 and 2.10 below) and to extend some Miyadera type additive ..... Applying integration by parts, we get that. ˜S ∗ C−1 ˜Bf(t) = S ∗ C−1 ˜Bf(t) + λ ...
Compact ASD Topologies for Single-Phase Integrated Motor Drives with Sinusoidal Input Current
DEFF Research Database (Denmark)
Klumpner, Christian; Blaabjerg, Frede; Thoegersen, Paul
2005-01-01
A standard configuration of an Adjustable Speed Drive (ASD) consists of two separate units: an AC motor, which runs with fixed speed when it is supplied from a constant frequency grid voltage and a frequency converter, which is used to provide the motor with variable voltage-variable frequency......-density integration of the converter caused by the large size of the passive components (electrolytic capacitors and iron chokes) and vibration of the converter enclosure. This paper analyzes the implementation aspects for obtaining a compact and cost effective single-phase ASD with sinusoidal input current...... for high frequency operation, higher core losses will occur, but outside the converter enclosure. The advantages are: the reduction of the number of active semiconductor devices, the reduction of the ASD size and the better integration potential....
Compact solar UV burst triggered in a magnetic field with a fan-spine topology
Chitta, L. P.; Peter, H.; Young, P. R.; Huang, Y.-M.
2017-09-01
Context. Solar ultraviolet (UV) bursts are small-scale features that exhibit intermittent brightenings that are thought to be due to magnetic reconnection. They are observed abundantly in the chromosphere and transition region, in particular in active regions. Aims: We investigate in detail a UV burst related to a magnetic feature that is advected by the moat flow from a sunspot towards a pore. The moving feature is parasitic in that its magnetic polarity is opposite to that of the spot and the pore. This comparably simple photospheric magnetic field distribution allows for an unambiguous interpretation of the magnetic geometry leading to the onset of the observed UV burst. Methods: We used UV spectroscopic and slit-jaw observations from the Interface Region Imaging Spectrograph (IRIS) to identify and study chromospheric and transition region spectral signatures of said UV burst. To investigate the magnetic topology surrounding the UV burst, we used a two-hour-long time sequence of simultaneous line-of-sight magnetograms from the Helioseismic and Magnetic Imager (HMI) and performed data-driven 3D magnetic field extrapolations by means of a magnetofrictional relaxation technique. We can connect UV burst signatures to the overlying extreme UV (EUV) coronal loops observed by the Atmospheric Imaging Assembly (AIA). Results: The UV burst shows a variety of extremely broad line profiles indicating plasma flows in excess of ±200 km s-1 at times. The whole structure is divided into two spatially distinct zones of predominantly up- and downflows. The magnetic field extrapolations show a persistent fan-spine magnetic topology at the UV burst. The associated 3D magnetic null point exists at a height of about 500 km above the photosphere and evolves co-spatially with the observed UV burst. The EUV emission at the footpoints of coronal loops is correlated with the evolution of the underlying UV burst. Conclusions: The magnetic field around the null point is sheared by
K-theory for group C*-algebras and semigroup C*-algebras
Cuntz, Joachim; Li, Xin; Yu, Guoliang
2017-01-01
This book gives an account of the necessary background for group algebras and crossed products for actions of a group or a semigroup on a space and reports on some very recently developed techniques with applications to particular examples. Much of the material is available here for the first time in book form. The topics discussed are among the most classical and intensely studied C*-algebras. They are important for applications in fields as diverse as the theory of unitary group representations, index theory, the topology of manifolds or ergodic theory of group actions.
Semigroups of transcendental entire functions and their dynamics
Indian Academy of Sciences (India)
DINESH KUMAR
Abstract. We investigate the dynamics of semigroups of transcendental entire func- tions using Fatou–Julia theory. Several results of the dynamics associated with iteration of a transcendental entire function have been extended to transcendental semigroups. We provide some condition for connectivity of the Julia set of the ...
Semigroups of transcendental entire functions and their dynamics
Indian Academy of Sciences (India)
DINESH KUMAR
realm of semigroups of rational and transcendental entire functions. The seminal work in this direction was done by Hinkkanen and Martin [10] related to semigroups of rational functions. In their paper, they extended the classical theory of the dynamics associated to the iteration of a rational function of one complex variable ...
Inverse operator of the generator of a C0-semigroup
Gomilko, A.M.; Zwart, Heiko J.; Tomilov, Y
2007-01-01
Let $A$ be the generator of a uniformly bounded $C_0$-semigroup in a Banach space $X$ such that $A$ has a trivial kernel and a dense range. The question whether $A^{-1}$ is a generator of a $C_0$-semigroup is considered. It is shown that the answer is negative in general for $X = \\ell_p$, $p \\in (1,
Stability of C0 -quasi semigroups in Banach spaces
Sutrima; Rini Indrati, Ch.; Aryati, Lina
2017-12-01
We concern on the non-autonomous abstract Cauchy problems \\dot{x}=A(t)x(t) on Banach spaces X. If A(t) is the infinitesimal generator of a Co-quasi semigroup R(t, s) on X and x 0 ɛ D, domain of A(t), then the solution of the equation has uniquely representation x(t) = R(0,t)x 0. This representation shows that the stability of the quasi semigroup R(t, s) influences the stability of the solution. In this paper, we investigate the stabilities of C 0-quasi semigroups following the existing theory of stabilities of C 0-semigroups T(t) and bounded evolution operators U(t, s). We devote the uniform, exponential, and strong stability of C 0-quasi semigroups in Banach spaces. The results are applicable for a large class of the time-dependent differential equations with unbounded coefficients in Banach spaces.
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 ...
Approximate resonance states in the semigroup decomposition of resonance evolution
Strauss, Y.; Horwitz, L. P.; Volovick, A.
2006-12-01
The semigroup decomposition formalism makes use of the functional model for C•0 class contractive semigroups for the description of the time evolution of resonances. For a given scattering problem the formalism allows for the association of a definite Hilbert space state with a scattering resonance. This state defines a decomposition of matrix elements of the evolution into a term evolving according to a semigroup law and a background term. We discuss the case of multiple resonances and give a bound on the size of the background term. As an example we treat a simple problem of scattering from a square barrier potential on the half-line.
Approximate resonance states in the semigroup decomposition of resonance evolution
International Nuclear Information System (INIS)
Strauss, Y.; Horwitz, L. P.; Volovick, A.
2006-01-01
The semigroup decomposition formalism makes use of the functional model for C ·0 class contractive semigroups for the description of the time evolution of resonances. For a given scattering problem the formalism allows for the association of a definite Hilbert space state with a scattering resonance. This state defines a decomposition of matrix elements of the evolution into a term evolving according to a semigroup law and a background term. We discuss the case of multiple resonances and give a bound on the size of the background term. As an example we treat a simple problem of scattering from a square barrier potential on the half-line
Construction of Lie algebras and invariant tensors through abelian semigroups
International Nuclear Information System (INIS)
Izaurieta, Fernando; RodrIguez, Eduardo; Salgado, Patricio
2008-01-01
The Abelian Semigroup Expansion Method for Lie Algebras is briefly explained. Given a Lie Algebra and a discrete abelian semigroup, the method allows us to directly build new Lie Algebras with their corresponding non-trivial invariant tensors. The Method is especially interesting in the context of M-Theory, because it allows us to construct M-Algebra Invariant Chern-Simons/Transgression Lagrangians in d = 11.
Bounding the number of rational places using Weierstrass semigroups
DEFF Research Database (Denmark)
Geil, Hans Olav; Matsumoto, Ryutaroh
2007-01-01
Let Lambda be a numerical semigroup. Assume there exists an algebraic function field over Fq in one variable which possesses a rational place that has Lambda as its Weierstrass semigroup. We ask the question as to how many rational places such a function field can possibly have and we derive an u...... that Lewittes' bound has important implications to the theory of towers of function fields....
Orthomodular lattices, Foulis Semigroups and Dagger Kernel Categories
Jacobs, Bart
2009-01-01
This paper is a sequel to arXiv:0902.2355 and continues the study of quantum logic via dagger kernel categories. It develops the relation between these categories and both orthomodular lattices and Foulis semigroups. The relation between the latter two notions has been uncovered in the 1960s. The current categorical perspective gives a broader context and reconstructs this relationship between orthomodular lattices and Foulis semigroups as special instance.
Directory of Open Access Journals (Sweden)
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.
DEFF Research Database (Denmark)
Liu, Xiong; Wang, Peng; Loh, Poh Chiang
2011-01-01
Single-phase stand-alone PV system is suitable for household applications in remote area. Hybrid battery/ultra-capacitor energy storage can reduce charge and discharge cycles and avoid deep discharges of battery. This paper proposes a compact seven switches structure for stand-alone PV system......-order harmonic current caused by single-phase inverter. In the proposed compact topology, a small size DC-link capacitor can achieve the same function through charging/discharging control of ultra-capacitor to mitigate second-order ripple current. Simulation results are provided to validate the effectiveness......, which otherwise needs nine switches configuration, inclusive of one switch for boost converter, four switches for single-phase inverter and four switches for two DC/DC converters of battery and ultra-capacitor. It is well-known that a bulky DC-link capacitor is always required to absorb second...
Topological Aspects of Infinitude of Primes in Arithmetic Progressions
Czech Academy of Sciences Publication Activity Database
Marko, F.; Porubský, Štefan
2015-01-01
Roč. 140, č. 2 (2015), s. 221-237 ISSN 0010-1354 R&D Projects: GA ČR(CZ) GAP201/12/2351 Institutional support: RVO:67985807 Keywords : coset topology * topological semigroup * topological density * Dirichlet theorem on primes * arithmetical progression * maximal ideal * ring of finite character * residually finite ring * infinitude of primes * pseudoprime Subject RIV: BA - General Mathematics Impact factor: 0.333, year: 2015
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.
Proceedings – Mathematical Sciences | Indian Academy of Sciences
Indian Academy of Sciences (India)
We investigate involutions and trivolutions in the second dual of algebras related to a locally compact topological semigroup and the Fourier algebra of a locally compact group. We prove, among the other things, that for a large class of topological semigroups namely, compactly cancellative foundation ∗ -semigroup S when ...
Multipliers of weighted semigroups and associated Beurling Banach ...
Indian Academy of Sciences (India)
The class of multipliers on S is denoted by M(S). The set M(S) is a unital, abelian semigroup under the operation composition. For s ∈ S, define Ls : S → S as Ls(t) = st, t ∈ S. Then Ls ∈ M(S), and Ls Lt = Lst, s, t ∈ S. A semigroup S is faithful if for s, t ∈ S, su = tu for all u ∈ S implies s = t. Thus S is identified with an ideal of ...
Spatial Markov Semigroups Admit Hudson-Parthasarathy Dilations
Skeide, Michael
2008-01-01
For many Markov semigroups dilations in the sense of Hudson and Parthasarathy, that is a dilation which is a cocycle perturbation of a noise, have been constructed with the help of quantum stochastic calculi. In these notes we show that every Markov semigroup on the algebra of all bounded operators on a separable Hilbert space that is spatial in the sense of Arveson, admits a Hudson-Parthasarathy dilation. In a sense, the opposite is also true. The proof is based on general results on the the...
On n-weak amenability of Rees semigroup algebras
Indian Academy of Sciences (India)
Then o is a zero for the semigroup S. Suppose that o /∈ S; set So = S∪{o}, and define so = os = o (s ∈ S) and o2 = o. Then So is a semigroup containing S as a .... (λij ) ∈ A(2k+1) = Mn(A(2k+1))withD|Mn = d |Mn.By replacingD byD−d , ... group are those of M(G, P , m, n), together with the element o, identified with the matrix.
International Nuclear Information System (INIS)
Torres, F.
1994-04-01
A curve X is said to be of type (N, γ) if it is an N-sheeted covering of a curve of genus γ with at least one totally ramified point. A numerical subsemigroup H of (N, +) is said to be of type (N, γ) if the first γ positive terms m 1 ,...,m γ are multiplies of N; m γ =2N γ and (2 γ +1) N is an element of H. If the genus of X is large enough and if N and γ satisfy certain arithmetical conditions then X is of type (N,γ) if and only if there is a point P is an element of X such that the Weierstrass semigroup at P is of type (N,γ). (This is a generalization of the γ-hyperelliptic situation). This result implies the existence of symmetric numerical semigroups which cannot be realized as Weierstrass semigroups. (author). 12 refs
Neutronics equations: Positiveness; compactness; spectral theory; time asymptotic behavior
International Nuclear Information System (INIS)
Mokhtar-Kharroubi, M.
1987-12-01
Neutronics equations are studied: the continuous model (with and without delayed neutrons) and the multigroup model. Asymptotic descriptions of these equations (t→+∞) are obtained, either by the Dunford method or by using semigroup perturbation techniques, after deriving the spectral theory for the equations. Compactness problems are reviewed, and a general theory of compact injection in neutronic functional space is derived. The effects of positiveness in neutronics are analyzed: the irreducibility of the transport semigroup, and the properties of the main eigenvalue (existence, nonexistence, frame, strict dominance, strict monotony in relation to all the parameters). A class of transport operators whose real spectrum can be completely described is shown [fr
Strong ergodic theorem for commutative semigroup of non ...
Indian Academy of Sciences (India)
M Azhini
2017-08-14
Aug 14, 2017 ... group of asymptotically nonexpansive in the intermediate sense mappings in a uniformly convex multi-Banach space. Our results enable us to handle simultaneously ergodic theo- rem for asymptotically nonexpansive type mappings and semigroups in the intermediate sense, i.e., we can establish the ...
Strong ergodic theorem for commutative semigroup of non ...
Indian Academy of Sciences (India)
M Azhini
2017-08-14
Aug 14, 2017 ... Chin. Ann. Math. 17 (1996) 726–736. [19] Miyadera I and Kobayasi K, On the asymptotic behavior of almot-orbit of nonlinear contraction semigroups in Banach space, Nonlinear Anal. TMA 6 (1982) 349–356. [20] Moslehian M S, Nikodem K and Popa D, Asymptotic aspect of the quadratic functional equation.
Orstein-Uhlenbeck bridge and applications to Markov semigroups
Czech Academy of Sciences Publication Activity Database
Goldys, B.; Maslowski, Bohdan
2008-01-01
Roč. 118, č. 10 (2008), s. 1738-1767 ISSN 0304-4149 R&D Projects: GA ČR GA201/07/0237 Institutional research plan: CEZ:AV0Z10190503 Keywords : UO Bridge * Markov semigroups * hyperboundedness Subject RIV: BA - General Mathematics Impact factor: 1.068, year: 2008
Spectral analysis of linear relations and degenerate operator semigroups
International Nuclear Information System (INIS)
Baskakov, A G; Chernyshov, K I
2002-01-01
Several problems of the spectral theory of linear relations in Banach spaces are considered. Linear differential inclusions in a Banach space are studied. The construction of the phase space and solutions is carried out with the help of the spectral theory of linear relations, ergodic theorems, and degenerate operator semigroups
Semigroups on Frechet spaces and equations with infinite delays
Indian Academy of Sciences (India)
to cover a large class of functions to be used as initial functions to obtain existence and uniqueness of solutions. Keywords. Functional differential equation; infinite delay; semigroup; Frechet space. 1. Introduction and preliminaries. In this paper we study linear functional differential equations with infinite delay. Consider.
Positive operator semigroups from finite to infinite dimensions
Bátkai, András; Rhandi, Abdelaziz
2017-01-01
This book gives a gentle but up-to-date introduction into the theory of operator semigroups (or linear dynamical systems), which can be used with great success to describe the dynamics of complicated phenomena arising in many applications. Positivity is a property which naturally appears in physical, chemical, biological or economic processes. It adds a beautiful and far reaching mathematical structure to the dynamical systems and operators describing these processes. In the first part, the finite dimensional theory in a coordinate-free way is developed, which is difficult to find in literature. This is a good opportunity to present the main ideas of the Perron-Frobenius theory in a way which can be used in the infinite dimensional situation. Applications to graph matrices, age structured population models and economic models are discussed. The infinite dimensional theory of positive operator semigroups with their spectral and asymptotic theory is developed in the second part. Recent applications illustrate t...
Operator Semigroups meet Complex Analysis, Harmonic Analysis and Mathematical Physics
Chill, Ralph; Tomilov, Yuri
2015-01-01
This proceedings volume originates from a conference held in Herrnhut in June 2013. It provides unique insights into the power of abstract methods and techniques in dealing successfully with numerous applications stemming from classical analysis and mathematical physics. The book features diverse topics in the area of operator semigroups, including partial differential equations, martingale and Hilbert transforms, Banach and von Neumann algebras, Schrödinger operators, maximal regularity and Fourier multipliers, interpolation, operator-theoretical problems (concerning generation, perturbation and dilation, for example), and various qualitative and quantitative Tauberian theorems with a focus on transfinite induction and magics of Cantor. The last fifteen years have seen the dawn of a new era for semigroup theory with the emphasis on applications of abstract results, often unexpected and far removed from traditional ones. The aim of the conference was to bring together prominent experts in the field of modern...
Directory of Open Access Journals (Sweden)
Kim JongKyu
2009-01-01
Full Text Available We study the strong convergence of two kinds of viscosity iteration processes for approximating common fixed points of the pseudocontractive semigroup in uniformly convex Banach spaces with uniformly Gâteaux differential norms. As special cases, we get the strong convergence of the implicit viscosity iteration process for approximating common fixed points of the nonexpansive semigroup in Banach spaces satisfying some conditions. The results presented in this paper extend and generalize some results concerned with the nonexpansive semigroup in (Chen and He, 2007 and the pseudocontractive mapping in (Zegeye et al., 2007 to the pseudocontractive semigroup in Banach spaces under different conditions.
Directory of Open Access Journals (Sweden)
Alkan Özkan
2016-04-01
Full Text Available In this paper, a new class of generalized soft open sets in soft generalized topological spaces as a generalization of compact spaces, called soft b-compact spaces, is introduced and studied. A soft generalized topological space is soft b-compact if every soft b-open soft cover of (F,E contains a finite soft subcover. We characterize soft b-compact space and study some of their basic properties.
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
A noncommutative mean ergodic theorem for partial W*-dynamical semigroups
International Nuclear Information System (INIS)
Ekhaguere, G.O.S.
1992-12-01
A noncommutative mean ergodic theorem for dynamical semigroups of maps on partial W*-algebras of linear operators from a pre-Hilbert space into its completion is proved. This generalizes a similar result of Watanabe for dynamical semigroups of maps on W*-algebras of operators. (author). 14 refs
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.
On the semigroup decomposition of the time evolution of quantum mechanical resonances
Strauss, Y
2005-01-01
A way of utilizing Lax-Phillips type semigroups for the description of the time evolution of resonances for scattering problems involving Hamiltonians with a semibounded spectrum was recently introduced by Y. Strauss. In the proposed framework the evolution is decomposed into a background term and an exponentially decaying resonance term evolving according to a semigroup law given by a Lax-Phillips type semigroup; this is called the semigroup decomposition. However, the proposed framework assumes that the S-matrix in the energy representation is the boundary value on the positive real axis of a bounded analytic function in the upper half-plane. This condition puts strong restrictions on possible applications of this formalism. In this paper it is shown that there is a simple way of weakening the assumptions on the S-matrix analyticity while still obtaining the semigroup decomposition of the evolution of a resonance.
Nearrings some developments linked to semigroups and groups
Ferrero, Celestina Cotti
2002-01-01
This work presents new and old constructions of nearrings. Links between properties of the multiplicative of nearrings (as regularity conditions and identities) and the structure of nearrings are studied. Primality and minimality properties of ideals are collected. Some types of `simpler' nearrings are examined. Some nearrings of maps on a group are reviewed and linked with group-theoretical and geometrical questions. Audience: Researchers working in nearring theory, group theory, semigroup theory, designs, and translation planes. Some of the material will be accessible to graduate students.
Semigroup theory and numerical approximation for equations in linear viscoelasticity
Fabiano, R. H.; Ito, K.
1990-01-01
A class of abstract integrodifferential equations used to model linear viscoelastic beams is investigated analytically, applying a Hilbert-space approach. The basic equation is rewritten as a Cauchy problem, and its well-posedness is demonstrated. Finite-dimensional subspaces of the state space and an estimate of the state operator are obtained; approximation schemes for the equations are constructed; and the convergence is proved using the Trotter-Kato theorem of linear semigroup theory. The actual convergence behavior of different approximations is demonstrated in numerical computations, and the results are presented in tables.
International Conference on Lattices, Semigroups, and Universal Algebra
Bordalo, Gabriela; Dwinger, Philip
1990-01-01
This volume contains papers which, for the most part, are based on talks given at an international conference on Lattices, Semigroups, and Universal Algebra that was held in Lisbon, Portugal during the week of June 20-24, 1988. The conference was dedicated to the memory of Professor Antonio Almeida Costa, a Portuguese mathematician who greatly contributed to the development of th algebra in Portugal, on the 10 anniversary of his death. The themes of the conference reflect some of his research interests and those of his students. The purpose of the conference was to gather leading experts in Lattices, Semigroups, and Universal Algebra and to promote a discussion of recent developments and trends in these areas. All three fields have grown rapidly during the last few decades with varying degrees of interaction. Lattice theory and Universal Algebra have historically evolved alongside with a large overlap between the groups of researchers in the two fields. More recently, techniques and ideas of these theories ha...
C0-semigroups of linear operators on some ultrametric Banach spaces
Directory of Open Access Journals (Sweden)
Toka Diagana
2006-01-01
Full Text Available C0-semigroups of linear operators play a crucial role in the solvability of evolution equations in the classical context. This paper is concerned with a brief conceptualization of C0-semigroups on (ultrametric free Banach spaces E. In contrast with the classical setting, the parameter of a given C0-semigroup belongs to a clopen ball Ωr of the ground field K. As an illustration, we will discuss the solvability of some homogeneous p-adic differential equations.
Star Products and Topological Quantum Groups
International Nuclear Information System (INIS)
Akhoumach, K.; Belbaraka, N.; Guedira, F.; Mansour, M.
2001-01-01
A well-behaved topological quantum algebra structure on a quantized enveloping topological algebra is given by a star product on the corresponding exact compact connected Poisson-Lie group of its triangular Lie bi-algebra. (author)
Neutrosophic Crisp Sets & Neutrosophic Crisp Topological Spaces
Directory of Open Access Journals (Sweden)
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.
An Optimal Dynamic Data Structure for Stabbing-Semigroup Queries
DEFF Research Database (Denmark)
Agarwal, Pankaj K.; Arge, Lars; Kaplan, Haim
2012-01-01
{R}$, the stabbing-semigroup query asks for computing $\\sum_{s \\in S(q)} \\omega(s)$. We propose a linear-size dynamic data structure, under the pointer-machine model, that answers queries in worst-case $O(\\log n)$ time and supports both insertions and deletions of intervals in amortized $O(\\log n)$ time....... It is the first data structure that attains the optimal $O(\\log n)$ bound for all three operations. Furthermore, our structure can easily be adapted to external memory, where we obtain a linear-size structure that answers queries and supports updates in $O(\\log_B n)$ I/Os, where B is the disk block size....... For the restricted case of a nested family of intervals (either every pair of intervals is disjoint or one contains the other), we present a simpler solution based on dynamic trees...
A Novel Approach toward Fuzzy Generalized Bi-Ideals in Ordered Semigroups
Directory of Open Access Journals (Sweden)
Faiz Muhammad Khan
2014-01-01
Full Text Available In several advanced fields like control engineering, computer science, fuzzy automata, finite state machine, and error correcting codes, the use of fuzzified algebraic structures especially ordered semigroups plays a central role. In this paper, we introduced a new and advanced generalization of fuzzy generalized bi-ideals of ordered semigroups. These new concepts are supported by suitable examples. These new notions are the generalizations of ordinary fuzzy generalized bi-ideals of ordered semigroups. Several fundamental theorems of ordered semigroups are investigated by the properties of these newly defined fuzzy generalized bi-ideals. Further, using level sets, ordinary fuzzy generalized bi-ideals are linked with these newly defined ideals which is the most significant part of this paper.
A novel approach toward fuzzy generalized bi-ideals in ordered semigroups.
Khan, Faiz Muhammad; Sarmin, Nor Haniza; Khan, Hidayat Ullah
2014-01-01
In several advanced fields like control engineering, computer science, fuzzy automata, finite state machine, and error correcting codes, the use of fuzzified algebraic structures especially ordered semigroups plays a central role. In this paper, we introduced a new and advanced generalization of fuzzy generalized bi-ideals of ordered semigroups. These new concepts are supported by suitable examples. These new notions are the generalizations of ordinary fuzzy generalized bi-ideals of ordered semigroups. Several fundamental theorems of ordered semigroups are investigated by the properties of these newly defined fuzzy generalized bi-ideals. Further, using level sets, ordinary fuzzy generalized bi-ideals are linked with these newly defined ideals which is the most significant part of this paper.
Semigroup Approach to Semilinear Partial Functional Differential Equations with Infinite Delay
Directory of Open Access Journals (Sweden)
Hassane Bouzahir
2007-02-01
Full Text Available We describe a semigroup of abstract semilinear functional differential equations with infinite delay by the use of the Crandall Liggett theorem. We suppose that the linear part is not necessarily densely defined but satisfies the resolvent estimates of the Hille-Yosida theorem. We clarify the properties of the phase space ensuring equivalence between the equation under investigation and the nonlinear semigroup.
Probability on compact Lie groups
Applebaum, David
2014-01-01
Probability theory on compact Lie groups deals with the interaction between “chance” and “symmetry,” a beautiful area of mathematics of great interest in its own sake but which is now also finding increasing applications in statistics and engineering (particularly with respect to signal processing). The author gives a comprehensive introduction to some of the principle areas of study, with an emphasis on applicability. The most important topics presented are: the study of measures via the non-commutative Fourier transform, existence and regularity of densities, properties of random walks and convolution semigroups of measures, and the statistical problem of deconvolution. The emphasis on compact (rather than general) Lie groups helps readers to get acquainted with what is widely seen as a difficult field but which is also justified by the wealth of interesting results at this level and the importance of these groups for applications. The book is primarily aimed at researchers working in probability, s...
Directory of Open Access Journals (Sweden)
Xue-song Li
2009-01-01
Full Text Available We study the strong convergence of two kinds of viscosity iteration processes for approximating common fixed points of the pseudocontractive semigroup in uniformly convex Banach spaces with uniformly Gâteaux differential norms. As special cases, we get the strong convergence of the implicit viscosity iteration process for approximating common fixed points of the nonexpansive semigroup in Banach spaces satisfying some conditions. The results presented in this paper extend and generalize some results concerned with the nonexpansive semigroup in (Chen and He, 2007 and the pseudocontractive mapping in (Zegeye et al., 2007 to the pseudocontractive semigroup in Banach spaces under different conditions.
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
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.
Covariant Schrödinger semigroups on Riemannian manifolds
Güneysu, Batu
2017-01-01
This monograph discusses covariant Schrödinger operators and their heat semigroups on noncompact Riemannian manifolds and aims to fill a gap in the literature, given the fact that the existing literature on Schrödinger operators has mainly focused on scalar Schrödinger operators on Euclidean spaces so far. In particular, the book studies operators that act on sections of vector bundles. In addition, these operators are allowed to have unbounded potential terms, possibly with strong local singularities. The results presented here provide the first systematic study of such operators that is sufficiently general to simultaneously treat the natural operators from quantum mechanics, such as magnetic Schrödinger operators with singular electric potentials, and those from geometry, such as squares of Dirac operators that have smooth but endomorphism-valued and possibly unbounded potentials. The book is largely self-contained, making it accessible for graduate and postgraduate students alike. Since it also inc...
The Collatz Problem in the Light of an Infinite Free Semigroup
Trümper, Manfred
2014-01-01
The Collatz (or 3m+1) problem is examined in terms of a free semigroup on which suitable diophantine and rational functions are defined. The elements of the semigroup, called T-words, comprise the information about the Collatz operations which relate an odd start number to an odd end number, the group operation being the concatenation of T-words. This view puts the concept of encoding vectors, first introduced in 1976 by Terras, in the proper mathematical context. A method is described which ...
Bounding the number of Fq-rational places in algebraic function fields using Weierstrass semigroups
DEFF Research Database (Denmark)
Geil, Hans Olav; Matsumoto, Ryutaroh
2009-01-01
We present a new bound on the number of Fq -rational places in an algebraic function field. It uses information about the generators of the Weierstrass semigroup related to a rational place. As we demonstrate, the bound has implications to the theory of towers of function fields....
Renardy, M.
1981-10-01
A semigroup approach to differential-delay equations is developed which seems more suitable for certain partial integro-differential equations than the standard theory. On a formal level, it is demonstrated that the stretching of filaments of viscoelastic liquids can be described by an equation of this form.
Functional calculus for C0-semigroups using infinite-dimensional systems theory
Schwenninger, F.L.; Zwart, Hans; Arendt, Wolfgang; Chill, Ralph; Tomilov, Yuri
2015-01-01
In this short note we use ideas from systems theory to define a functional calculus for infinitesimal generators of strongly continuous semigroups on a Hilbert space. Among others, we show how this leads to new proofs of (known) results in functional calculus.
The General Iterative Methods for Asymptotically Nonexpansive Semigroups in Banach Spaces
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Rabian Wangkeeree
2012-01-01
Full Text Available We introduce the general iterative methods for finding a common fixed point of asymptotically nonexpansive semigroups which is a unique solution of some variational inequalities. We prove the strong convergence theorems of such iterative scheme in a reflexive Banach space which admits a weakly continuous duality mapping. The main result extends various results existing in the current literature.
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.
Directory of Open Access Journals (Sweden)
Marat V. Markin
2004-01-01
Full Text Available In the class of scalar type spectral operators in a complex Banach space, a characterization of the generators of analytic C0-semigroups in terms of the analytic vectors of the operators is found.
Uniqueness of a pre-generator for $C_0$-semigroup on a general locally convex vector space
Lemle, Ludovic Dan; Wu, Liming
2007-01-01
The main purpose is to generalize a theorem of Arendt about uniqueness of $C_0$-semigroups from Banach space setting to the general locally convex vector spaces, more precisely, we show that cores are the only domains of uniqueness for $C_0$-semigroups on locally convex spaces. As an application, we find a necessary and sufficient condition for that the mass transport equation has one unique $L^1(\\R^d,dx)$ weak solution.
Aganagic, M; Marino, M; Vafa, C; Aganagic, Mina; Klemm, Albrecht; Marino, Marcos; Vafa, Cumrun
2005-01-01
We construct a cubic field theory which provides all genus amplitudes of the topological A-model for all non-compact Calabi-Yau toric threefolds. The topology of a given Feynman diagram encodes the topology of a fixed Calabi-Yau, with Schwinger parameters playing the role of Kahler classes of Calabi-Yau. We interpret this result as an operator computation of the amplitudes in the B-model mirror which is the Kodaira-Spencer quantum theory. The only degree of freedom of this theory is an unconventional chiral scalar on a Riemann surface. In this setup we identify the B-branes on the mirror Riemann surface as fermions related to the chiral boson by bosonization.
Characterizations of ordered semigroups in terms of (∈, ∈ ∨q)-fuzzy interior ideals.
Khan, Asghar; Jun, Young Bae; Abbas, Muhammad Zaheer
2012-04-01
In this paper, we give characterizations of ordered semigroups in terms of (∈, ∈ ∨q)-fuzzy interior ideals. We characterize different classes regular (resp. intra-regular, simple and semisimple) ordered semigroups in terms of (∈, ∈ ∨q)-fuzzy interior ideals (resp. (∈, ∈ ∨q)-fuzzy ideals). In this regard, we prove that in regular (resp. intra-regular and semisimple) ordered semigroups the concept of (∈, ∈ ∨q)-fuzzy ideals and (∈, ∈ ∨q)-fuzzy interior ideals coincide. We prove that an ordered semigroup S is simple if and only if it is (∈, ∈ ∨q)-fuzzy simple. We characterize intra-regular (resp. semisimple) ordered semigroups in terms of (∈, ∈ ∨q)-fuzzy ideals (resp. (∈, ∈ ∨q)-fuzzy interior ideals). Finally, we consider the concept of implication-based fuzzy interior ideals in an ordered semigroup, in particular, the implication operators in Lukasiewicz system of continuous-valued logic are discussed.
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...
Fixed point property for nonexpansive mappings and nonexpansive semigroups on the unit disk
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Luis Benítez-Babilonia
2015-06-01
Full Text Available For closed convex subsets D of a Banach spaces, in 2009, Tomonari Suzuki [11] proved that the fixed point property (FPP for nonexpansive mappings and the FPP for nonexpansive semigroups are equivalent. In this paper some relations between the aforementioned properties for mappings and semigroups defined on D, a closed convex subset of the hyperbolic metric space (D, ρ, are studied. This work arises as a generalization to the space (D, ρ of the study made by Suzuki. Resumen. Para subconjuntos D cerrados y convexos de espacios de Banach, Tomonari Suzuki [11] demostró en 2009 que la propiedad del punto fijo (PPF para funciones no expansivas y la PPF para semigrupos de funciones no expansivas son equivalentes. En este trabajo se estudian algunas relaciones entre dichas propiedades, cuando D es un subconjunto del espacio mético (D, ρ. Este trabajo surge como una generalización al espacio (D, ρ de los resultados de Suzuki.
Some problems on non-linear semigroups and the blow-up of integral solutions
International Nuclear Information System (INIS)
Pavel, N.H.
1983-07-01
After some introductory remarks, this highly mathematical document considers a unifying approach in the theory of non-linear semigroups. Then a brief survey is given on blow-up of mild solutions from the semilinear case. Finally, the global behavior of solutions to non-linear evolution equations is addressed; it is found that classical results on the behavior of the maximal solution u as t up-arrow tsub(max) hold also for integral solutions
On measuring unboundedness of the H∞-calculus for generators of analytic semigroups
Schwenninger, F.L.
We investigate the boundedness of the H$^\\infty$-calculus by estimating the bound b(ε) of the mapping H$^\\infty$→B(X): f→f(A)T(ε) for ε near zero. Here, −A generates the analytic semigroup T and H$^\\infty$ is the space of bounded analytic functions on a domain strictly containing the spectrum of A.
Inverse problem for the equation with n-times integrated semigroup
Orlovsky, D. G.
2017-12-01
We consider an abstract differential equation of the first order with unbounded linear operator u‧(t) = Au(t) + f(t) in a Banach space X. For this equation the Cauchy problem is studied with initial data u(0) = x at t = 0. We assume that the operator A generates an n-times integrated semigroup V(t). The inverse problem to determine the nonhomogeneous member is considered under the assumption that this term has the following representation f(t) = p, where p is an unknown element of the space X. This problem belongs to the class of inverse problems. Inverse problems for abstract differential equations was discussed initially with this inhomogeneous structure member but for equations with an operator generating a C 0-semigroup. An additional condition u(T) = y is specified for the determination of the unknown p, where y is a given element of the space X. Thus we get the two-point problem, which had not been considered previously for integrated semigroups. The question of existence and uniqueness of the classical solution of the inverse problem is studied. Sufficient conditions of correct solvability of the inverse problem are obtained. Explicit formula to determine the unknown element in the differential equation is given.
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...
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...
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
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.
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
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 ...
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...
THE SEMIGROUP OF METRIC MEASURE SPACES AND ITS INFINITELY DIVISIBLE PROBABILITY MEASURES.
Evans, Steven N; Molchanov, Ilya
2017-01-01
A metric measure space is a complete, separable metric space equipped with a probability measure that has full support. Two such spaces are equivalent if they are isometric as metric spaces via an isometry that maps the probability measure on the first space to the probability measure on the second. The resulting set of equivalence classes can be metrized with the Gromov-Prohorov metric of Greven, Pfaffelhuber and Winter. We consider the natural binary operation ⊞ on this space that takes two metric measure spaces and forms their Cartesian product equipped with the sum of the two metrics and the product of the two probability measures. We show that the metric measure spaces equipped with this operation form a cancellative, commutative, Polish semigroup with a translation invariant metric. There is an explicit family of continuous semicharacters that is extremely useful for, inter alia , establishing that there are no infinitely divisible elements and that each element has a unique factorization into prime elements. We investigate the interaction between the semigroup structure and the natural action of the positive real numbers on this space that arises from scaling the metric. For example, we show that for any given positive real numbers a , b , c the trivial space is the only space that satisfies a ⊞ b = c . We establish that there is no analogue of the law of large numbers: if X 1 , X 2 , … is an identically distributed independent sequence of random spaces, then no subsequence of [Formula: see text] converges in distribution unless each X k is almost surely equal to the trivial space. We characterize the infinitely divisible probability measures and the Lévy processes on this semigroup, characterize the stable probability measures and establish a counterpart of the LePage representation for the latter class.
Topological Structure of Vague Soft Sets
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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.
Applying Semigroup Property of Enhanced Chebyshev Polynomials to Anonymous Authentication Protocol
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Hong Lai
2012-01-01
Full Text Available We apply semigroup property of enhanced Chebyshev polynomials to present an anonymous authentication protocol. This paper aims at improving security and reducing computational and storage overhead. The proposed scheme not only has much lower computational complexity and cost in the initialization phase but also allows the users to choose their passwords freely. Moreover, it can provide revocation of lost or stolen smart card, which can resist man-in-the-middle attack and off-line dictionary attack together with various known attacks.
A semigroup approach to an integro-differential equation modeling slow erosion
Bressan, Alberto; Shen, Wen
2014-10-01
The paper is concerned with a scalar conservation law with nonlocal flux, providing a model for granular flow with slow erosion and deposition. While the solution u=u(t,x) can have jumps, the inverse function x=x(t,u) is always Lipschitz continuous; its derivative has bounded variation and satisfies a balance law with measure-valued sources. Using a backward Euler approximation scheme combined with a nonlinear projection operator, we construct a continuous semigroup whose trajectories are the unique entropy weak solutions to this balance law. Going back to the original variables, this yields the global well-posedness of the Cauchy problem for the granular flow model.
Bounding the number of points on a curve using a generalization of Weierstrass semigroups
DEFF Research Database (Denmark)
Beelen, Peter; Ruano, Diego
2013-01-01
In this article we use techniques from coding theory to derive upper bounds for the number of rational places of the function field of an algebraic curve defined over a finite field. The used techniques yield upper bounds if the (generalized) Weierstrass semigroup (J Pure Appl Algebra 207(2), 243......–260, 2006) for an n-tuple of places is known, even if the exact defining equation of the curve is not known. As shown in examples, this sometimes enables one to get an upper bound for the number of rational places for families of function fields. Our results extend results in (J Pure Appl Algebra 213...
On positive definite functions and representations of Clifford ω-semigroups
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Liliana Pavel
1995-11-01
Full Text Available It is known that a complex valued function f on a Clifford ω-semigroup, T=UnGn is positive definite if and only if its restriction fn to Gn, is positive definite for any positive integer n. Then, by the usual Gelfand-Naimark-Segal construction, f and fn (n\\in ℕ give rise to the representations πf of T, respectively πfn of Gn. In this note we study the relationship between the restriction of πf to Gn and the representation of πfn (n\\in ℕ .
Mappings with closed range and compactness
International Nuclear Information System (INIS)
Iyahen, S.O.; Umweni, I.
1985-12-01
The motivation for this note is the result of E.O. Thorp that a normed linear space E is finite dimensional if and only if every continuous linear map for E into any normed linear space has a closed range. Here, a class of Hausdorff topological groups is introduced; called r-compactifiable topological groups, they include compact groups, locally compact Abelian groups and locally convex linear topological spaces. It is proved that a group in this class which is separable, complete metrizable or locally compact, is necessarily compact if its image by a continuous group homomorphism is necessarily closed. It is deduced then that a Hausdorff locally convex is zero if its image by a continuous additive map is necessarily closed. (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
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.
Energy Technology Data Exchange (ETDEWEB)
Bazeia, D., E-mail: bazeia@fisica.ufpb.br [Departamento de Física, Universidade Federal da Paraíba, 58051-970 João Pessoa, PB (Brazil); Losano, L.; Marques, M.A. [Departamento de Física, Universidade Federal da Paraíba, 58051-970 João Pessoa, PB (Brazil); Menezes, R. [Departamento de Ciências Exatas, Universidade Federal da Paraíba, 58297-000 Rio Tinto, PB (Brazil); Departamento de Física, Universidade Federal de Campina Grande, 58109-970 Campina Grande, PB (Brazil); Rocha, R. da [Centro de Matemática, Computação e Cognição, Universidade Federal do ABC, 09210-580 Santo André (Brazil)
2016-07-10
In this work we deal with non-topological solutions of the Q-ball type in two space–time dimensions, in models described by a single complex scalar field that engenders global symmetry. The main novelty is the presence of stable Q-balls solutions that live in a compact interval of the real line and appear from a family of models controlled by two distinct parameters. We find analytical solutions and study their charge and energy, and show how to control the parameters to make the Q-balls classically and quantum mechanically stable.
Directory of Open Access Journals (Sweden)
Jiancai Huang
2012-01-01
Full Text Available We introduce an implicit and explicit iterative schemes for a finite family of nonexpansive semigroups with the Meir-Keeler-type contraction in a Banach space. Then we prove the strong convergence for the implicit and explicit iterative schemes. Our results extend and improve some recent ones in literatures.
Topological entropy for induced hyperspace maps
Energy Technology Data Exchange (ETDEWEB)
Canovas Pena, Jose S. [Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, 30203 Cartagena, Murcia (Spain)]. E-mail: Jose.canovas@upct.es; Lopez, Gabriel Soler [Departamento de Matematica Aplicada y Estadistica, Universidad Politecnica de Cartagena, 30203 Cartagena, Murcia (Spain)]. E-mail: Gabriel.soler@upct.es
2006-05-15
Let (X,d) be a compact metric space and let f:X->X be continuous. Let K(X) be the family of compact subsets of X endowed with the Hausdorff metric and define the extension f-bar :K(X)->K(X) by f-bar (K)=f(K) for any K-bar K(X). We prove that the topological entropy of f-bar is greater or equal than the topological entropy of f, and this inequality can be strict. On the other hand, we prove that the topological entropy of f is positive if and only if the topological entropy of f-bar is also positive.
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
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
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.).
Orbifolds, quantum cosmology, and nontrivial topology
International Nuclear Information System (INIS)
Fagundes, Helio V.; Vargas, Teofilo
2006-01-01
In order to include nontrivial topologies in the problem of quantum creation of a universe, it seems to be necessary to generalize the sum over compact, smooth 4-manifolds to a sum over finite-volume, compact 4-orbifolds. We consider in detail the case of a 4-spherical orbifold with a cone-point singularity. This allows for the inclusion of a nontrivial topology into the semiclassical path integral approach to quantum cosmology, in the context of a Robertson-Walker minisuperspace. (author)
The Entropy of Co-Compact Open Covers
Directory of Open Access Journals (Sweden)
Steven Bourquin
2013-06-01
Full Text Available Co-compact entropy is introduced as an invariant of topological conjugation for perfect mappings defined on any Hausdorff space (compactness and metrizability are not necessarily required. This is achieved through the consideration of co-compact covers of the space. The advantages of co-compact entropy include: (1 it does not require the space to be compact and, thus, generalizes Adler, Konheim and McAndrew’s topological entropy of continuous mappings on compact dynamical systems; and (2 it is an invariant of topological conjugation, compared to Bowen’s entropy, which is metric-dependent. Other properties of co-compact entropy are investigated, e.g., the co-compact entropy of a subsystem does not exceed that of the whole system. For the linear system, (R; f, defined by f(x = 2x, the co-compact entropy is zero, while Bowen’s entropy for this system is at least log 2. More generally, it is found that co-compact entropy is a lower bound of Bowen’s entropies, and the proof of this result also generates the Lebesgue Covering Theorem to co-compact open covers of non-compact metric spaces.
The character of free topological groups II
Directory of Open Access Journals (Sweden)
Peter Nickolas
2005-04-01
Full Text Available A systematic analysis is made of the character of the free and free abelian topological groups on metrizable spaces and compact spaces, and on certain other closely related spaces. In the first case, it is shown that the characters of the free and the free abelian topological groups on X are both equal to the “small cardinal” d if X is compact and metrizable, but also, more generally, if X is a non-discrete k!-space all of whose compact subsets are metrizable, or if X is a non-discrete Polish space. An example is given of a zero-dimensional separable metric space for which both characters are equal to the cardinal of the continuum. In the case of a compact space X, an explicit formula is derived for the character of the free topological group on X involving no cardinal invariant of X other than its weight; in particular the character is fully determined by the weight in the compact case. This paper is a sequel to a paper by the same authors in which the characters of the free groups were analysed under less restrictive topological assumptions.
NATO Advanced Study Institute on Structural Theory of Automata, Semigroups and Universal Algebra
Rosenberg, Ivo; Goldstein, Martin
2005-01-01
Several of the contributions to this volume bring forward many mutually beneficial interactions and connections between the three domains of the title. Developing them was the main purpose of the NATO ASI summerschool held in Montreal in 2003. Although some connections, for example between semigroups and automata, were known for a long time, developing them and surveying them in one volume is novel and hopefully stimulating for the future. Another aspect is the emphasis on the structural theory of automata that studies ways to contstruct big automata from small ones. The volume also has contributions on top current research or surveys in the three domains. One contribution even links clones of universal algebra with the computational complexity of computer science. Three contributions introduce the reader to research in the former East block.
Topological sigma B model in 4-dimensions
International Nuclear Information System (INIS)
Jun, Hyun-Keun; Park, Jae-Suk
2008-01-01
We propose a 4-dimensional version of topological sigma B-model, governing maps from a smooth compact 4-manifold M to a Calabi-Yau target manifold X. The theory depends on complex structure of X, while is independent of Kaehler metric of X. The theory is also a 4-dimensional topological field theory in the sense that the theory is independent of variation of Riemannian metric of the source 4-manifold M, potentially leading to new smooth invariant of 4-manifolds. We argue that the theory also comes with a topological family parametrized by the extended moduli space of complex structures.
The classification of 2-compact groups (talk summary)
Andersen, Kasper K. S.; Grodal, Jesper
2005-01-01
This is a summary of a talk given at the "Conference on Pure and Applied Topology", Isle of Skye, June 24, 2005. It contains an announcement and sketch of proof of the classification of 2-compact groups.
Quotient semigroups and extension semigroups
Indian Academy of Sciences (India)
Department of Mathematics, Teachers College of Qingdao University, Qingdao 266071, People's Republic of China; School of Mathematical Sciences, Ocean University of China, Qingdao 266100, People's Republic of China; School of Mathematical Sciences, Qufu Normal University, Qufu, Shandong 273165, People's ...
On quantum symmetries of compact metric spaces
Chirvasitu, Alexandru
2015-08-01
An action of a compact quantum group on a compact metric space (X , d) is (D)-isometric if the distance function is preserved by a diagonal action on X × X. In this study, we show that an isometric action in this sense has the following additional property: the corresponding action on the algebra of continuous functions on X by the convolution semigroup of probability measures on the quantum group contracts Lipschitz constants. In other words, it is isometric in another sense due to Li, Quaegebeur, and Sabbe, which partially answers a question posed by Goswami. We also introduce other possible notions of isometric quantum actions in terms of the Wasserstein p-distances between probability measures on X for p ≥ 1, which are used extensively in optimal transportation. Indeed, all of these definitions of quantum isometry belong to a hierarchy of implications, where the two described above lie at the extreme ends of the hierarchy. We conjecture that they are all equivalent.
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 ...
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.
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.
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.
Generated topology on infinite sets by ultrafilters
Directory of Open Access Journals (Sweden)
Alireza Bagheri Salec
2017-10-01
Full Text Available Let $X$ be an infinite set, equipped with a topology $tau$. In this paper we studied the relationship between $tau$, and ultrafilters on $X$. We can discovered, among other thing, some relations of the Robinson's compactness theorem, continuity and the separation axioms. It is important also, aspects of communication between mathematical concepts.
On cohomology theory for topological groups
Indian Academy of Sciences (India)
Home; Journals; Proceedings – Mathematical Sciences; Volume 122; Issue 2. On Cohomology ... Cohomology theory; group extension; locally compact groups; Lie groups. Abstract. We construct some new cohomology theories for topological groups and Lie groups and study some of its basic properties. For example, we ...
Tightness relative to some (co)reflections in topology | Ball ...
African Journals Online (AJOL)
This is a stronger result than the classical one, but not because of an increase in scope; after all, assuming weak choice principles, every compact regular locale is the topology of a compact Hausdorff space. The increased strength derives from the conclusion, for in general a space has many more sublocales than ...
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
On topological groups with remainder of character k
Directory of Open Access Journals (Sweden)
Maddalena Bonanzinga
2016-04-01
Full Text Available In [A.V. Arhangel'skii and J. van Mill, On topological groups with a first-countable remainder, Top. Proc. 42 (2013, 157-163] it is proved that the character of a non-locally compact topological group with a first countable remainder doesn't exceed $\\omega_1$ and a non-locally compact topological group of character $\\omega_1$ having a compactification whose reminder is first countable is given. We generalize these results in the general case of an arbitrary infinite cardinal k.
On a weaker form of countable compactness | Bonanzinga ...
African Journals Online (AJOL)
A star covering property which is equivalent to countable compactness for regular spaces and weaker than countable compactness for Hausdorff spaces is introduced and considered. Various kinds of irregularity of topological spaces are discussed. Quaestiones Mathematicae 30(2007), 407–415 ...
Energy Technology Data Exchange (ETDEWEB)
Bazeia, D.; Losano, L.; Marques, M.A.; Zafalan, I. [Universidade Federal da Paraiba, Departamento de Fisica, Joao Pessoa, PB (Brazil); Menezes, R. [Universidade Federal da Paraiba, Departamento de Ciencias Exatas, Rio Tinto, PB (Brazil); Universidade Federal de Campina Grande, Departamento de Fisica, Campina Grande, PB (Brazil)
2017-02-15
We study a family of Maxwell-Higgs models, described by the inclusion of a function of the scalar field that represent generalized magnetic permeability. We search for vortex configurations which obey first-order differential equations that solve the equations of motion. We first deal with the asymptotic behavior of the field configurations, and then implement a numerical study of the solutions, the energy density and the magnetic field. We work with the generalized permeability having distinct profiles, giving rise to new models, and we investigate how the vortices behave, compared with the solutions of the corresponding standard models. In particular, we show how to build compact vortices, that is, vortex solutions with the energy density and magnetic field vanishing outside a compact region of the plane. (orig.)
A Note on the G-Cyclic Operators over a Bounded Semigroup
International Nuclear Information System (INIS)
Hamada, Nuha H.; Jamil, Zeana Z.
2010-08-01
Let H be an infinite-dimensional separable complex Hilbert space, and B(H) be the Banach algebra of all linear bounded operators on H. Let S be a multiplication semigroup of C with 1, an operator T element of B(H) is called G-cyclic operator over S if there is a vector x in H such that {αT n x|α element of S, n ≥ 0} is dense in H. In this case x is called a G-cyclic vector for T over S. If T is G-cyclic operator and S = {1} then T is a hypercyclic operator. In this paper, we study the spectral properties of a G-cyclic operators over a bounded S under the condition that zero is not in the closure of S. We show that the class of all G-cyclic operators is contained in the norm-closure of the class of all hypercyclic operators. (author)
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
New forms of -compactness with respect to hereditary classes
Directory of Open Access Journals (Sweden)
Abdo Mohammed Qahis
2019-01-01
Full Text Available A hereditary class on a set X is a nonempty collection of subsets closed under heredity. The aim of this paper is to introduce and study strong forms of u-compactness in generalized topological spaces with respect to a hereditary class, called SuH-compactness and S- SuH-compactness. Also several of their properties are presented. Finally some eects of various kinds of functions on them are studied.
Compactly Generated de Morgan Lattices, Basic Algebras and Effect Algebras
Paseka, Jan; Riečanová, Zdenka
2010-12-01
We prove that a de Morgan lattice is compactly generated if and only if its order topology is compatible with a uniformity on L generated by some separating function family on L. Moreover, if L is complete then L is (o)-topological. Further, if a basic algebra L (hence lattice with sectional antitone involutions) is compactly generated then L is atomic. Thus all non-atomic Boolean algebras as well as non-atomic lattice effect algebras (including non-atomic MV-algebras and orthomodular lattices) are not compactly generated.
Crystalline metamaterials for topological properties at subwavelength scales.
Yves, Simon; Fleury, Romain; Berthelot, Thomas; Fink, Mathias; Lemoult, Fabrice; Lerosey, Geoffroy
2017-07-18
The exciting discovery of topological condensed matter systems has lately triggered a search for their photonic analogues, motivated by the possibility of robust backscattering-immune light transport. However, topological photonic phases have so far only been observed in photonic crystals and waveguide arrays, which are inherently physically wavelength scaled, hindering their application in compact subwavelength systems. In this letter, we tackle this problem by patterning the deep subwavelength resonant elements of metamaterials onto specific lattices, and create crystalline metamaterials that can develop complex nonlocal properties due to multiple scattering, despite their very subwavelength spatial scale that usually implies to disregard their structure. These spatially dispersive systems can support subwavelength topological phases, as we demonstrate at microwaves by direct field mapping. Our approach gives a straightforward tabletop platform for the study of photonic topological phases, and allows to envision applications benefiting the compactness of metamaterials and the amazing potential of topological insulators.
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
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.
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
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.
Quantum topological entropy: First steps of a 'pedestrian' approach
International Nuclear Information System (INIS)
Hudetz, T.
1991-01-01
We introduce a notion of topological entropy for automorphisms of arbitrary (noncommutative, but unital) nuclear C * -algebras A, generalizing the 'classical' topological entropy for a homeomorphism T: X → X of an arbitrary (possibly connected) compact Hausdorff space X, where the generalization is of course understood in the sense that the latter topological dynamical system (with Z-action) is equivalently viewed as the C * -dynamical system given by the T-induced automorphism of the Abelian C * -algebra A = C(X) of (complex-valued) continuous functions on X. As a simple but basic example, we calculate our quantum topological entropy for shift automorphisms on AF algebras A associated with topological Markov chains (i.e. 'quantum topological' Markov chains); and also a real physical interpretation of our simple 'quantum probabilistic' entropy functionals is discussed (already in the introduction, anticipating the later definitions and results). (author)
International Nuclear Information System (INIS)
Pomphrey, N.; Berry, L.A.; Boozer, A.H.
2001-01-01
Experimental devices to study the physics of high-beta (β>∼4%), low aspect ratio (A<∼4.5) stellarator plasmas require coils that will produce plasmas satisfying a set of physics goals, provide experimental flexibility, and be practical to construct. In the course of designing a flexible coil set for the National Compact Stellarator Experiment, we have made several innovations that may be useful in future stellarator design efforts. These include: the use of Singular Value Decomposition methods for obtaining families of smooth current potentials on distant coil winding surfaces from which low current density solutions may be identified; the use of a Control Matrix Method for identifying which few of the many detailed elements of the stellarator boundary must be targeted if a coil set is to provide fields to control the essential physics of the plasma; the use of Genetic Algorithms for choosing an optimal set of discrete coils from a continuum of potential contours; the evaluation of alternate coil topologies for balancing the tradeoff between physics objective and engineering constraints; the development of a new coil optimization code for designing modular coils, and the identification of a 'natural' basis for describing current sheet distributions. (author)
Pharmaceutical powder compaction technology
National Research Council Canada - National Science Library
Çelik, Metin
2011-01-01
... through the compaction formulation process and application. Compaction of powder constituents both active ingredient and excipients is examined to ensure consistent and reproducible disintegration and dispersion profiles...
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...
Topological fixed point theory of multivalued mappings
Górniewicz, Lech
1999-01-01
This volume presents a broad introduction to the topological fixed point theory of multivalued (set-valued) mappings, treating both classical concepts as well as modern techniques. A variety of up-to-date results is described within a unified framework. Topics covered include the basic theory of set-valued mappings with both convex and nonconvex values, approximation and homological methods in the fixed point theory together with a thorough discussion of various index theories for mappings with a topologically complex structure of values, applications to many fields of mathematics, mathematical economics and related subjects, and the fixed point approach to the theory of ordinary differential inclusions. The work emphasises the topological aspect of the theory, and gives special attention to the Lefschetz and Nielsen fixed point theory for acyclic valued mappings with diverse compactness assumptions via graph approximation and the homological approach. Audience: This work will be of interest to researchers an...
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 colourful approach to string topology
DEFF Research Database (Denmark)
Bargheer, Tarje
For M a compact, orientable manifold and N „ Rn1 a submanifold, we construct the cleavage operad that acts on MN through correspondences, analogous to the Cacti Operad acting on MS1 , formulating String Topology. For the unit sphere, N : Sn „ Rn1 we compute the cleavage operad...... apparent links between Knot Theory and String Topology.......For M a compact, orientable manifold and N „ Rn1 a submanifold, we construct the cleavage operad that acts on MN through correspondences, analogous to the Cacti Operad acting on MS1 , formulating String Topology. For the unit sphere, N : Sn „ Rn1 we compute the cleavage operad...... is obtained through an extension of the Cleavage Operad. Homotopically the extension is a simplication, and it adjoins a unit to the action on MSn. We nally give advantages of our geometric stance on generalizing String Topology even when N S1:We improve on equivariance of group actions on MSn, and provide...
Wavelength Selective 3D Topology Optimized Photonic Crystal Devices
DEFF Research Database (Denmark)
Frandsen, Lars Hagedorn; Elesin, Yuriy; Sigmund, Ole
2013-01-01
A compact photonic crystal drop filter has been designed using 3D topology optimization and fabricated in silicon-on-insulator material. Measurements and modeling are in excellent agreement showing a low-loss ~11nm 3dB bandwidth of the filter.......A compact photonic crystal drop filter has been designed using 3D topology optimization and fabricated in silicon-on-insulator material. Measurements and modeling are in excellent agreement showing a low-loss ~11nm 3dB bandwidth of the filter....
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.
The locally connected compact metric spaces embeddable in the plane
DEFF Research Database (Denmark)
Thomassen, Carsten
2004-01-01
We prove that a 2-connected, locally connected, compact topological space M is homeomorphic to a subset of the 2-sphere if and only if M is metrizable and contains none of the Kuratowski graphs K-5 and K-3,K-3.......We prove that a 2-connected, locally connected, compact topological space M is homeomorphic to a subset of the 2-sphere if and only if M is metrizable and contains none of the Kuratowski graphs K-5 and K-3,K-3....
African Journals Online (AJOL)
Petrophysical, Decompaction and Linear Regression techniques were used to investigate overpressure, degree of compaction and to derive a model compaction equation for. -1. -1 hydrostatic sandstones. Compaction coefficients obtained range from 0.0003 - 0.0005 m (averaging 0.0004 m ) and percentage compaction ...
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.
Ring-array processor distribution topology for optical interconnects
Li, Yao; Ha, Berlin; Wang, Ting; Wang, Sunyu; Katz, A.; Lu, X. J.; Kanterakis, E.
1992-01-01
The existing linear and rectangular processor distribution topologies for optical interconnects, although promising in many respects, cannot solve problems such as clock skews, the lack of supporting elements for efficient optical implementation, etc. The use of a ring-array processor distribution topology, however, can overcome these problems. Here, a study of the ring-array topology is conducted with an aim of implementing various fast clock rate, high-performance, compact optical networks for digital electronic multiprocessor computers. Practical design issues are addressed. Some proof-of-principle experimental results are included.
Bipolar soft connected, bipolar soft disconnected and bipolar soft compact spaces
Directory of Open Access Journals (Sweden)
Muhammad Shabir
2017-06-01
Full Text Available Bipolar soft topological spaces are mathematical expressions to estimate interpretation of data frameworks. Bipolar soft theory considers the core features of data granules. Bipolarity is important to distinguish between positive information which is guaranteed to be possible and negative information which is forbidden or surely false. Connectedness and compactness are the most important fundamental topological properties. These properties highlight the main features of topological spaces and distinguish one topology from another. Taking this into account, we explore the bipolar soft connectedness, bipolar soft disconnectedness and bipolar soft compactness properties for bipolar soft topological spaces. Moreover, we introduce the notion of bipolar soft disjoint sets, bipolar soft separation, and bipolar soft hereditary property and study on bipolar soft connected and disconnected spaces. By giving the detailed picture of bipolar soft connected and disconnected spaces we investigate bipolar soft compact spaces and derive some results related to this concept.
Energy Technology Data Exchange (ETDEWEB)
Kalb, Jeffrey L.; Lee, David S.
2008-01-01
Emerging high-bandwidth, low-latency network technology has made network-based architectures both feasible and potentially desirable for use in satellite payload architectures. The selection of network topology is a critical component when developing these multi-node or multi-point architectures. This study examines network topologies and their effect on overall network performance. Numerous topologies were reviewed against a number of performance, reliability, and cost metrics. This document identifies a handful of good network topologies for satellite applications and the metrics used to justify them as such. Since often multiple topologies will meet the requirements of the satellite payload architecture under development, the choice of network topology is not easy, and in the end the choice of topology is influenced by both the design characteristics and requirements of the overall system and the experience of the developer.
Real Topological Cyclic Homology
DEFF Research Database (Denmark)
Høgenhaven, Amalie
The main topics of this thesis are real topological Hochschild homology and real topological cyclic homology. If a ring or a ring spectrum is equipped with an anti-involution, then it induces additional structure on the topological Hochschild homology spectrum. The group O(2) acts on the spectrum......, where O(2) is the semi-direct product of T, the multiplicative group of complex number of modulus 1, by the group G=Gal(C/R). We refer to this O(2)-spectrum as the real topological Hochschild homology. This generalization leads to a G-equivariant version of topological cyclic homology, which we call...... real topological cyclic homology. The first part of the thesis computes the G-equivariant homotopy type of the real topological cyclic homology of spherical group rings at a prime p with anti-involution induced by taking inverses in the group. The second part of the thesis investigates the derived G...
Triple Point Topological Metals
Directory of Open Access Journals (Sweden)
Ziming Zhu
2016-07-01
Full Text Available Topologically protected fermionic quasiparticles appear in metals, where band degeneracies occur at the Fermi level, dictated by the band structure topology. While in some metals these quasiparticles are direct analogues of elementary fermionic particles of the relativistic quantum field theory, other metals can have symmetries that give rise to quasiparticles, fundamentally different from those known in high-energy physics. Here, we report on a new type of topological quasiparticles—triple point fermions—realized in metals with symmorphic crystal structure, which host crossings of three bands in the vicinity of the Fermi level protected by point group symmetries. We find two topologically different types of triple point fermions, both distinct from any other topological quasiparticles reported to date. We provide examples of existing materials that host triple point fermions of both types and discuss a variety of physical phenomena associated with these quasiparticles, such as the occurrence of topological surface Fermi arcs, transport anomalies, and topological Lifshitz transitions.
Topological entropy and chaos for maps induced on hyperspaces
International Nuclear Information System (INIS)
Kwietniak, Dominik; Oprocha, Piotr
2007-01-01
If f is a continuous selfmap of a compact metric space X then by the induced map we mean the map f-bar defined on the space of all nonempty closed subsets of X by f-bar(K)=f(K). The paper mainly deals with the topological entropy of induced maps. We show that under some nonrecurrence assumption the induced map f-bar is always topologically chaotic, that is, it has positive topological entropy. Additionally we characterize topological weak and strong mixing of f in terms of the omega limit set of induced map. This allows the description of the dynamics of the map f-bar induced by a transitive graph map f on the space of all subcontinua of a given graph G. It follows that in this case f-bar has the same topological entropy as f
Photonic Floquet topological insulators
Rechtsman, Mikael C.; Zeuner, Julia M.; Plotnik, Yonatan; Lumer, Yaakov; Podolsky, Daniel; Dreisow, Felix; Nolte, Stefan; Segev, Mordechai; Szameit, Alexander
2013-09-01
Topological insulators are a new phase of matter, with the striking property that conduction of electrons occurs only on the surface. In two dimensions, surface electrons in topological insulators do not scatter despite defects and disorder, providing robustness akin to superconductors. Topological insulators are predicted to have wideranging applications in fault-tolerant quantum computing and spintronics. Recently, large theoretical efforts were directed towards achieving topological insulation for electromagnetic waves. One-dimensional systems with topological edge states have been demonstrated, but these states are zero-dimensional, and therefore exhibit no transport properties. Topological protection of microwaves has been observed using a mechanism similar to the quantum Hall effect, by placing a gyromagnetic photonic crystal in an external magnetic field. However, since magnetic effects are very weak at optical frequencies, realizing photonic topological insulators with scatterfree edge states requires a fundamentally different mechanism - one that is free of magnetic fields. Recently, a number of proposals for photonic topological transport have been put forward. Specifically, one suggested temporally modulating a photonic crystal, thus breaking time-reversal symmetry and inducing one-way edge states. This is in the spirit of the proposed Floquet topological insulators, where temporal variations in solidstate systems induce topological edge states. Here, we propose and experimentally demonstrate the first external field-free photonic topological insulator with scatter-free edge transport: a photonic lattice exhibiting topologically protected transport of visible light on the lattice edges. Our system is composed of an array of evanescently coupled helical waveguides arranged in a graphene-like honeycomb lattice. Paraxial diffraction of light is described by a Schrödinger equation where the propagation coordinate acts as `time'. Thus the waveguides
Planck 2015 results. XVIII. Background geometry & topology
Ade, P.A.R.; Arnaud, M.; Ashdown, M.; Aumont, J.; Baccigalupi, C.; Banday, A.J.; Barreiro, R.B.; Bartolo, N.; Basak, S.; Battaner, E.; Benabed, K.; Benoît, A.; Benoit-Lévy, A.; Bernard, J.P.; Bersanelli, M.; Bielewicz, P.; Bock, J.J.; Bonaldi, A.; Bonavera, L.; Bond, J.R.; Borrill, J.; Bouchet, F.R.; Bucher, M.; Burigana, C.; Butler, R.C.; Calabrese, E.; Cardoso, J.F.; Catalano, A.; Challinor, A.; Chamballu, A.; Chiang, H.C.; Christensen, P.R.; Church, S.; Clements, D.L.; Colombi, S.; Colombo, L.P.L.; Combet, C.; Couchot, F.; Coulais, A.; Crill, B.P.; Curto, A.; Cuttaia, F.; Danese, L.; Davies, R.D.; Davis, R.J.; de Bernardis, P.; De Rosa, A.; De Zotti, G.; Delabrouille, J.; Désert, F.X.; Diego, J.M.; Dole, H.; Donzelli, S.; Doré, O.; Douspis, M.; Ducout, A.; Dupac, X.; Efstathiou, G.; Elsner, F.; Enßlin, T.A.; Eriksen, H.K.; Feeney, S.; Fergusson, J.; Finelli, F.; Forni, O.; Frailis, M.; Fraisse, A.A.; Franceschi, E.; Frejsel, A.; Galeotta, S.; Galli, S.; Ganga, K.; Giard, M.; Giraud-Héraud, Y.; Gjerløw, E.; González-Nuevo, J.; Górski, K.M.; Gratton, S.; Gregorio, A.; Gruppuso, A.; Gudmundsson, J.E.; Hansen, F.K.; Hanson, D.; Harrison, D.L.; Henrot-Versillé, S.; Hernández-Monteagudo, C.; Herranz, D.; Hildebrandt, S.R.; Hivon, E.; Hobson, M.; Holmes, W.A.; Hornstrup, A.; Hovest, W.; Huffenberger, K.M.; Hurier, G.; Jaffe, A.H.; Jaffe, T.R.; Jones, W.C.; Juvela, M.; Keihänen, E.; Keskitalo, R.; Kisner, T.S.; Knoche, J.; Kunz, M.; Kurki-Suonio, H.; Lagache, G.; Lähteenmäki, A.; Lamarre, J.M.; Lasenby, A.; Lattanzi, M.; Lawrence, C.R.; Leonardi, R.; Lesgourgues, J.; Levrier, F.; Liguori, M.; Lilje, P.B.; Linden-Vørnle, M.; López-Caniego, M.; Lubin, P.M.; Macías-Pérez, J.F.; Maggio, G.; Maino, D.; Mandolesi, N.; Mangilli, A.; Maris, M.; Martin, P.G.; Martínez-González, E.; Masi, S.; Matarrese, S.; McEwen, J.D.; McGehee, P.; Meinhold, P.R.; Melchiorri, A.; Mendes, L.; Mennella, A.; Migliaccio, M.; Mitra, S.; Miville-Deschênes, M.A.; Moneti, A.; Montier, L.; Morgante, G.; Mortlock, D.; Moss, A.; Munshi, D.; Murphy, J.A.; Naselsky, P.; Nati, F.; Natoli, P.; Netterfield, C.B.; Nørgaard-Nielsen, H.U.; Noviello, F.; Novikov, D.; Novikov, I.; Oxborrow, C.A.; Paci, F.; Pagano, L.; Pajot, F.; Paoletti, D.; Pasian, F.; Patanchon, G.; Peiris, H.V.; Perdereau, O.; Perotto, L.; Perrotta, F.; Pettorino, V.; Piacentini, F.; Piat, M.; Pierpaoli, E.; Pietrobon, D.; Plaszczynski, S.; Pogosyan, D.; Pointecouteau, E.; Polenta, G.; Popa, L.; Pratt, G.W.; Prézeau, G.; Prunet, S.; Puget, J.L.; Rachen, J.P.; Rebolo, R.; Reinecke, M.; Remazeilles, M.; Renault, C.; Renzi, A.; Ristorcelli, I.; Rocha, G.; Rosset, C.; Rossetti, M.; Roudier, G.; Rowan-Robinson, M.; Rubiño-Martín, J.A.; Rusholme, B.; Sandri, M.; Santos, D.; Savelainen, M.; Savini, G.; Scott, D.; Seiffert, M.D.; Shellard, E.P.S.; Spencer, L.D.; Stolyarov, V.; Stompor, R.; Sudiwala, R.; Sutton, D.; Suur-Uski, A.S.; Sygnet, J.F.; Tauber, J.A.; Terenzi, L.; Toffolatti, L.; Tomasi, M.; Tristram, M.; Tucci, M.; Tuovinen, J.; Valenziano, L.; Valiviita, J.; Tent, F. Van; Vielva, P.; Villa, F.; Wade, L.A.; Wandelt, B.D.; Wehus, I.K.; Yvon, D.; Zacchei, A.; Zonca, A.
2016-01-01
Full-sky CMB maps from the 2015 Planck release allow us to detect departures from global isotropy on the largest scales. We present the first searches using CMB polarization for correlations induced by a non-trivial topology with a fundamental domain intersecting, or nearly intersecting, the last scattering surface (at comoving distance $\\chi_{rec}$). We specialize to flat spaces with toroidal and slab topologies, finding that explicit searches for the latter are sensitive to other topologies with antipodal symmetry. These searches yield no detection of a compact topology at a scale below the diameter of the last scattering surface. The limits on the radius $R_i$ of the largest sphere inscribed in the topological domain (at log-likelihood-ratio $\\Delta\\ln{L}>-5$ relative to a simply-connected flat Planck best-fit model) are $R_i>0.97\\chi_{rec}$ for the cubic torus and $R_i>0.56\\chi_{rec}$ for the slab. The limit for the cubic torus from the matched-circles search is numerically equivalent, $R_i>0.97\\chi_{rec}...
Clay, Adam
2016-01-01
This book deals with the connections between topology and ordered groups. It begins with a self-contained introduction to orderable groups and from there explores the interactions between orderability and objects in low-dimensional topology, such as knot theory, braid groups, and 3-manifolds, as well as groups of homeomorphisms and other topological structures. The book also addresses recent applications of orderability in the studies of codimension-one foliations and Heegaard-Floer homology. The use of topological methods in proving algebraic results is another feature of the book. The book was written to serve both as a textbook for graduate students, containing many exercises, and as a reference for researchers in topology, algebra, and dynamical systems. A basic background in group theory and topology is the only prerequisite for the reader.
Compact Digital High Voltage Charger
Li, Ge
2005-01-01
The operation of classical resonant circuit developed for the pulse energizing is investigated. The HV pulse or generator is very compact by a soft switching circuit made up of IGBT working at over 30 kHZ. The frequencies of macro pulses andμpulses can be arbitrarily tuned below resonant frequency to digitalize the HV pulse power. Theμpulses can also be connected by filter circuit to get the HVDC power. The circuit topology is given and its novel control logic is analyzed by flowchart. The circuit is part of a system consisting of a AC or DC LV power supply, a pulse transformer, the pulse generator implemented by LV capacitor and leakage inductance of the transformer, a HV DC or pulse power supply and the charged HV capacitor of the modulators.
Critical types of Krasnoselskii fixed point theorems in weak topologies
African Journals Online (AJOL)
In this note, by means of the technique of measures of weak noncompactness, we establish a generalized form of fixed point theorem for the sum of T + S in weak topology setups of a metrizable locally convex space, where S is not weakly compact, I − T allows to be noninvertible, and T is not necessarily continuous.
On some properties of the superposition operator on topological manifolds
Directory of Open Access Journals (Sweden)
Janusz Dronka
2010-01-01
Full Text Available In this paper the superposition operator in the space of vector-valued, bounded and continuous functions on a topological manifold is considered. The acting conditions and criteria of continuity and compactness are established. As an application, an existence result for the nonlinear Hammerstein integral equation is obtained.
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)
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.
Topological Foundations of Electromagnetism
Barrett, Terrence W
2008-01-01
Topological Foundations of Electromagnetism seeks a fundamental understanding of the dynamics of electromagnetism; and marshals the evidence that in certain precisely defined topological conditions, electromagnetic theory (Maxwell's theory) must be extended or generalized in order to provide an explanation and understanding of, until now, unusual electromagnetic phenomena. Key to this generalization is an understanding of the circumstances under which the so-called A potential fields have physical effects. Basic to the approach taken is that the topological composition of electromagnetic field
Multipliers of Ap((0 ,((0 ,((0,∞)) with order convolution
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Introduction. The algebra Ap(G) of elements in L1(G) whose Fourier transforms belong to Lp( ˆG) and the multipliers for these algebras have been studied by various authors [1,7–9]. Let. I = (0, ∞) be the locally compact idempotent commutative topological semigroup with the usual topology and max multiplication and ˆI be ...
An algebra of absolutely continuous functions and its multipliers
Indian Academy of Sciences (India)
Introduction. Let I = [0, 1] be the compact topological semigroup with max multiplication and usual topology. C(I),Lp(I), 1 ≤ p ≤ ∞ are the associated Banach algebras. Larsen [5] obtained multipliers for the Banach algebra L1(I). Baker, Pym and Vasudeva [1] obtain characterizations of multipliers from Lp(I) to Lr(I), 1 ≤ r, ...
Morita, K
1989-01-01
Being an advanced account of certain aspects of general topology, the primary purpose of this volume is to provide the reader with an overview of recent developments.The papers cover basic fields such as metrization and extension of maps, as well as newly-developed fields like categorical topology and topological dynamics. Each chapter may be read independently of the others, with a few exceptions. It is assumed that the reader has some knowledge of set theory, algebra, analysis and basic general topology.
Topological Gyroscopic Metamaterials
Nash, Lisa Michelle
Topological materials are generally insulating in their bulk, with protected conducting states on their boundaries that are robust against disorder and perturbation of material property. The existence of these conducting edge states is characterized by an integer topological invariant. Though the phenomenon was first discovered in electronic systems, recent years have shown that topological states exist in classical systems as well. In this thesis we are primarily concerned with the topological properties of gyroscopic materials, which are created by coupling networks of fast-spinning objects. Through a series of simulations, numerical calculations, and experiments, we show that these materials can support topological edge states. We find that edge states in these gyroscopic metamaterials bear the hallmarks of topology related to broken time reversal symmetry: they transmit excitations unidirectionally and are extremely robust against experimental disorder. We also explore requirements for topology by studying several lattice configurations and find that topology emerges naturally in gyroscopic systems.A simple prescription can be used to create many gyroscopic lattices. Though many of our gyroscopic networks are periodic, we explore amorphous point-sets and find that topology also emerges in these networks.
General Topology of the Universe
Pandya, Aalok
2002-01-01
General topology of the universe is descibed. It is concluded that topology of the present universe is greater or stronger than the topology of the universe in the past and topology of the future universe will be stronger or greater than the present topology of the universe. Consequently, the universe remains unbounded.
Integrable topological billiards and equivalent dynamical systems
Vedyushkina, V. V.; Fomenko, A. T.
2017-08-01
We consider several topological integrable billiards and prove that they are Liouville equivalent to many systems of rigid body dynamics. The proof uses the Fomenko-Zieschang theory of invariants of integrable systems. We study billiards bounded by arcs of confocal quadrics and their generalizations, generalized billiards, where the motion occurs on a locally planar surface obtained by gluing several planar domains isometrically along their boundaries, which are arcs of confocal quadrics. We describe two new classes of integrable billiards bounded by arcs of confocal quadrics, namely, non-compact billiards and generalized billiards obtained by gluing planar billiards along non-convex parts of their boundaries. We completely classify non-compact billiards bounded by arcs of confocal quadrics and study their topology using the Fomenko invariants that describe the bifurcations of singular leaves of the additional integral. We study the topology of isoenergy surfaces for some non-convex generalized billiards. It turns out that they possess exotic Liouville foliations: the integral trajectories of the billiard that lie on some singular leaves admit no continuous extension. Such billiards appear to be leafwise equivalent to billiards bounded by arcs of confocal quadrics in the Minkowski metric.
International Nuclear Information System (INIS)
Bartolomaeus, G.; Wilhelm, J.
1983-01-01
Recently, based on the semigroup approach a new proof was presented of the existence of a unique solution of the non-stationary Boltzmann equation for the electron component of a collision dominated plasma. The proof underlies some restriction which should be overcome to extend the validity range to other problems of physical interest. One of the restrictions is the boundary condition applied. The choice of the boundary condition is essential for the proof because it determines the range of definition of the infinitesimal generator and thus the operator semigroup itself. The paper proves the existence of a unique solution for generalized boundary conditions, this solution takes non-negative values, which is necessary for a distribution function from the physical point of view. (author)
Modeling Internet Topology Dynamics
Haddadi, H.; Uhlig, S.; Moore, A.; Mortier, R.; Rio, M.
Despite the large number of papers on network topology modeling and inference, there still exists ambiguity about the real nature of the Internet AS and router level topology. While recent findings have illustrated the inaccuracies in maps inferred from BGP peering and traceroute measurements,
Topology optimization approaches
DEFF Research Database (Denmark)
Sigmund, Ole; Maute, Kurt
2013-01-01
Topology optimization has undergone a tremendous development since its introduction in the seminal paper by Bendsøe and Kikuchi in 1988. By now, the concept is developing in many different directions, including “density”, “level set”, “topological derivative”, “phase field”, “evolutionary...
Manufacturing tolerant topology optimization
DEFF Research Database (Denmark)
Sigmund, Ole
2009-01-01
(dilated) structures compared to the intended topology. Examples are MEMS devices manufactured using etching processes, nano-devices manufactured using e-beam lithography or laser micro-machining and macro structures manufactured using milling processes. In the suggested robust topology optimization...
Reconfigurable topological photonic crystal
Shalaev, Mikhail I.; Desnavi, Sameerah; Walasik, Wiktor; Litchinitser, Natalia M.
2018-02-01
Topological insulators are materials that conduct on the surface and insulate in their interior due to non-trivial topology of the band structure. The edge states on the interface between topological (non-trivial) and conventional (trivial) insulators are topologically protected from scattering due to structural defects and disorders. Recently, it was shown that photonic crystals (PCs) can serve as a platform for realizing a scatter-free propagation of light waves. In conventional PCs, imperfections, structural disorders, and surface roughness lead to significant losses. The breakthrough in overcoming these problems is likely to come from the synergy of the topological PCs and silicon-based photonics technology that enables high integration density, lossless propagation, and immunity to fabrication imperfections. For many applications, reconfigurability and capability to control the propagation of these non-trivial photonic edge states is essential. One way to facilitate such dynamic control is to use liquid crystals (LCs), which allow to modify the refractive index with external electric field. Here, we demonstrate dynamic control of topological edge states by modifying the refractive index of a LC background medium. Background index is changed depending on the orientation of a LC, while preserving the topology of the system. This results in a change of the spectral position of the photonic bandgap and the topological edge states. The proposed concept might be implemented using conventional semiconductor technology, and can be used for robust energy transport in integrated photonic devices, all-optical circuity, and optical communication systems.
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.
Interactive Topology Optimization
DEFF Research Database (Denmark)
Nobel-Jørgensen, Morten
Interactivity is the continuous interaction between the user and the application to solve a task. Topology optimization is the optimization of structures in order to improve stiffness or other objectives. The goal of the thesis is to explore how topology optimization can be used in applications...... in an interactive and intuitive way. By creating such applications with an intuitive and simple user interface we allow non-engineers like designers and architects to easily experiment with boundary conditions, design domains and other optimization settings. This is in contrast to commercial topology optimization...... software where the users are assumed to be well-educated both in the finite element method and topology optimization. This dissertation describes how various topology optimization methods have been used for creating cross-platform applications with high performance. The user interface design is based...
Topological String Theory and Enumerative Geometry
Energy Technology Data Exchange (ETDEWEB)
Song, Y. S
2003-05-19
In this thesis we investigate several problems which have their roots in both topological string theory and enumerative geometry. In the former case, underlying theories are topological field theories, whereas the latter case is concerned with intersection theories on moduli spaces. A permeating theme in this thesis is to examine the close interplay between these two complementary fields of study. The main problems addressed are as follows: In considering the Hurwitz enumeration problem of branched covers of compact connected Riemann surfaces, we completely solve the problem in the case of simple Hurwitz numbers. In addition, utilizing the connection between Hurwitz numbers and Hodge integrals, we derive a generating function for the latter on the moduli space {bar M}{sub g,2} of 2-pointed, genus-g Deligne-Mumford stable curves. We also investigate Givental's recent conjecture regarding semisimple Frobenius structures and Gromov-Witten invariants, both of which are closely related to topological field theories; we consider the case of a complex projective line P{sup 1} as a specific example and verify his conjecture at low genera. In the last chapter, we demonstrate that certain topological open string amplitudes can be computed via relative stable morphisms in the algebraic category.
Machine learning topological states
Deng, Dong-Ling; Li, Xiaopeng; Das Sarma, S.
2017-11-01
Artificial neural networks and machine learning have now reached a new era after several decades of improvement where applications are to explode in many fields of science, industry, and technology. Here, we use artificial neural networks to study an intriguing phenomenon in quantum physics—the topological phases of matter. We find that certain topological states, either symmetry-protected or with intrinsic topological order, can be represented with classical artificial neural networks. This is demonstrated by using three concrete spin systems, the one-dimensional (1D) symmetry-protected topological cluster state and the 2D and 3D toric code states with intrinsic topological orders. For all three cases, we show rigorously that the topological ground states can be represented by short-range neural networks in an exact and efficient fashion—the required number of hidden neurons is as small as the number of physical spins and the number of parameters scales only linearly with the system size. For the 2D toric-code model, we find that the proposed short-range neural networks can describe the excited states with Abelian anyons and their nontrivial mutual statistics as well. In addition, by using reinforcement learning we show that neural networks are capable of finding the topological ground states of nonintegrable Hamiltonians with strong interactions and studying their topological phase transitions. Our results demonstrate explicitly the exceptional power of neural networks in describing topological quantum states, and at the same time provide valuable guidance to machine learning of topological phases in generic lattice models.
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.
Partial Actions, Paradoxicality and Topological full Groups
DEFF Research Database (Denmark)
Scarparo, Eduardo
uniform Roe algebra is finite. In Article C, we analyze the C*-algebra generated by the Koopman representation of a topological full group, showing, in particular, that it is not AF andhas real rank zero. We also prove that if G is a finitely generated, elementary amenable group, and C*(G) has real rank......We study how paradoxicality properties affect the way groups partially acton topological spaces and C*-algebras. We also investigate the real rank zero and AF properties for certain classes of group C*-algebras. Specifically, in article A, we characterize supramenable groups in terms of existence...... of invariant probability measures for partial actions on compact Hausdorff spaces and existence of tracial states on partial crossed products. These characterizations show that, in general, one cannot decompose a partial crossed product of a C*-algebra by a semidirect product of groups as two iterated...
Topological excitations in U(1) -invariant theories
International Nuclear Information System (INIS)
Savit, R.
1977-01-01
A class of U(1) -invariant theories in d dimensions is introduced on a lattice. These theories are labeled by a simplex number s, with 1 < or = s < d. The case with s = 1 is the X-Y model; and s = 2 gives compact photodynamics. An exact duality transformation is applied to show that the U(1) -invariant theory in d dimensions with simplex number s is the same as a similar theory in d dimensions but which is Z /sub infinity/-invariant and has simplex number s = d-s. This dual theory describes the topological excitations of the original theory. These excitations are of dimension s - 1
Elements of differential topology
Shastri, Anant R
2011-01-01
Derived from the author's course on the subject, Elements of Differential Topology explores the vast and elegant theories in topology developed by Morse, Thom, Smale, Whitney, Milnor, and others. It begins with differential and integral calculus, leads you through the intricacies of manifold theory, and concludes with discussions on algebraic topology, algebraic/differential geometry, and Lie groups.The first two chapters review differential and integral calculus of several variables and present fundamental results that are used throughout the text. The next few chapters focus on smooth manifo
Signatures of topological superconductivity
Energy Technology Data Exchange (ETDEWEB)
Peng, Yang
2017-07-19
The prediction and experimental discovery of topological insulators brought the importance of topology in condensed matter physics into the limelight. Topology hence acts as a new dimension along which more and more new states of matter start to emerge. One of these topological states of matter, namely topological superconductors, comes into the focus because of their gapless excitations. These gapless excitations, especially in one dimensional topological superconductors, are Majorana zero modes localized at the ends of the superconductor and exhibit exotic nonabelian statistics, which can be potentially applied to fault-tolerant quantum computation. Given their highly interesting physical properties and potential applications to quantum computation, both theorists and experimentalists spend great efforts to realize topological supercondoctors and to detect Majoranas. In two projects within this thesis, we investigate the properties of Majorana zero modes in realistic materials which are absent in simple theoretical models. We find that the superconducting proximity effect, an essential ingredient in all existing platforms for topological superconductors, plays a significant role in determining the localization property of the Majoranas. Strong proximity coupling between the normal system and the superconducting substrate can lead to strongly localized Majoranas, which can explain the observation in a recent experiment. Motivated by experiments in Molenkamp's group, we also look at realistic quantum spin Hall Josephson junctions, in which charge puddles acting as magnetic impurities are coupled to the helical edge states. We find that with this setup, the junction generically realizes an exotic 8π periodic Josephson effect, which is absent in a pristine Josephson junction. In another two projects, we propose more pronounced signatures of Majoranas that are accessible with current experimental techniques. The first one is a transport measurement, which uses
2016-10-31
AFRL-AFOSR-UK-TR-2017-0002 Global Topology Optimisation Robert Jack UNIVERSITY OF BATH Final Report 10/31/2016 DISTRIBUTION A: Distribution approved...01 Aug 2015 to 31 Jul 2016 4. TITLE AND SUBTITLE Global Topology Optimisation 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA9550-15-1-0317 5c...future work. 15. SUBJECT TERMS EOARD, Topology Optimization, Non Convex 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT SAR 18
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.
Plasmonics in Topological Insulators
Directory of Open Access Journals (Sweden)
Yi-Ping Lai
2014-04-01
Full Text Available With strong spin-orbit coupling, topological insulators have an insulating bulk state, characterized by a band gap, and a conducting surface state, characterized by a Dirac cone. Plasmons in topological insulators show high frequency-tunability in the mid-infrared and terahertz spectral regions with transverse spin oscillations, also called “spin-plasmons”. This paper presents a discussion and review of the developments in this field from the fundamental theory of plasmons in bulk, thin-film, and surface-magnetized topological insulators to the techniques of plasmon excitation and future applications.
Sacramento, P. D.; Vieira, V. R.
2018-04-01
Mappings between models may be obtained by unitary transformations with preservation of the spectra but in general a change in the states. Non-canonical transformations in general also change the statistics of the operators involved. In these cases one may expect a change of topological properties as a consequence of the mapping. Here we consider some dualities resulting from mappings, by systematically using a Majorana fermion representation of spin and fermionic problems. We focus on the change of topological invariants that results from unitary transformations taking as examples the mapping between a spin system and a topological superconductor, and between different fermionic systems.
Barr, Stephen
1989-01-01
""A mathematician named KleinThought the Moebius band was divine.Said he: 'If you glueThe edges of two,You'll get a weird bottle like mine.' "" - Stephen BarrIn this lively book, the classic in its field, a master of recreational topology invites readers to venture into such tantalizing topological realms as continuity and connectedness via the Klein bottle and the Moebius strip. Beginning with a definition of topology and a discussion of Euler's theorem, Mr. Barr brings wit and clarity to these topics:New Surfaces (Orientability, Dimension, The Klein Bottle, etc.)The Shortest Moebius StripThe
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
Topologically massive supergravity
Directory of Open Access Journals (Sweden)
S. Deser
1983-01-01
Full Text Available The locally supersymmetric extension of three-dimensional topologically massive gravity is constructed. Its fermionic part is the sum of the (dynamically trivial Rarita-Schwinger action and a gauge-invariant topological term, of second derivative order, analogous to the gravitational one. It is ghost free and represents a single massive spin 3/2 excitation. The fermion-gravity coupling is minimal and the invariance is under the usual supergravity transformations. The system's energy, as well as that of the original topological gravity, is therefore positive.
Topological pregauge-pregeometry
International Nuclear Information System (INIS)
Akama, Keiichi; Oda, Ichiro.
1990-12-01
The pregauge-pregeometric action, i.e. the fundamental matter action whose quantum fluctuations give rise to the Einstein-Hilbert and the Yang-Mills actions is investigated from the viewpoint of the topological field theory. We show that the scalar pregauge-pregeometric action is a topological invariant for appropriate choices of the internal gauge group. This model realizes the picture that the gravitational and internal gauge theory at the low energy scale is induced as the quantum effects of the topological field theory at the Planck scale. (author)
Topological systems versus attachment relations | Guido ...
African Journals Online (AJOL)
... localification procedure introduced by S. Vickers for topological systems. Keywords: Adjoint functor, algebra, attachment relation, embedding functor, localification of topological systems, spatialization of topological systems, topological system, topological theory, variety of algebras. Quaestiones Mathematicae 37(2014), ...
Directory of Open Access Journals (Sweden)
Łukasz Rzepnicki
2013-01-01
Full Text Available Small vibrations of a nonhomogeneous string of length one with left end fixed and right one moving with damping are described by the one-dimensional wave equation \\[\\begin{cases} v_{tt}(x,t - \\frac{1}{\\rho}v_{xx}(x,t = 0, x \\in [0,1], t \\in [0, \\infty,\\\\ v(0,t = 0, v_x(1,t + hv_t(1,t = 0, \\\\ v(x,0 = v_0(x, v_t(x,0 = v_1(x,\\end{cases}\\] where \\(\\rho\\ is the density of the string and \\(h\\ is a complex parameter. This equation can be rewritten in an operator form as an abstract Cauchy problem for the closed, densely defined operator B acting on a certain energy space H. It is proven that the operator B generates the exponentially stable \\(C_0\\-semigroup of contractions in the space H under assumptions that \\(\\text{Re}\\; h \\gt 0\\ and the density function is of bounded variation satisfying \\(0 \\lt m \\leq \\rho(x\\ for a.e. \\(x \\in [0, 1]\\.
Extending Topological Abelian Groups by the Unit Circle
Directory of Open Access Journals (Sweden)
Hugo J. Bello
2013-01-01
Full Text Available A twisted sum in the category of topological Abelian groups is a short exact sequence 0→Y→X→Z→0 where all maps are assumed to be continuous and open onto their images. The twisted sum splits if it is equivalent to 0→Y→Y×Z→Z→0. We study the class STG of topological groups G for which every twisted sum 0→→X→G→0 splits. We prove that this class contains Hausdorff locally precompact groups, sequential direct limits of locally compact groups, and topological groups with ℒ∞ topologies. We also prove that it is closed by taking open and dense subgroups, quotients by dually embedded subgroups, and coproducts. As means to find further subclasses of STG, we use the connection between extensions of the form 0→→X→G→0 and quasi-characters on G, as well as three-space problems for topological groups. The subject is inspired on some concepts known in the framework of topological vector spaces such as the notion of -space, which were interpreted for topological groups by Cabello.
Topological Solitons in Physics.
Parsa, Zohreh
1979-01-01
A broad definition of solitons and a discussion of their role in physics is given. Vortices and magnetic monopoles which are examples of topological solitons in two and three spatial dimensions are described in some detail. (BB)
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.
Wilansky, Albert
2008-01-01
Three levels of examples and problems make this volume appropriate for students and professionals. Abundant exercises, ordered and numbered by degree of difficulty, illustrate important topological concepts. 1970 edition.
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.
Kurucuk, Nurses
2017-01-01
Soil compaction is widely applied in geotechnical engineering practice. It is used to maximise the dry density of soils to reduce subsequent settlement under working loads or to reduce the permeability of soils. The durability and stability of structures are highly related to the appropriate compaction achievement. The structural failure of roads and airfields, and the damage caused by foundation settlement can often be traced back to the failure in achieving adequate compaction. For that rea...
Okamura, Hajime; Ouchi, Masahiro
2003-01-01
Self-compacting concrete was first developed in 1988 to achieve durable concrete structures. Since then, various investigations have been carried out and this type of concrete has been used in practical structures in Japan, mainly by large construction companies. Investigations for establishing a rational mix-design method and self-compactability testing methods have been carried out from the viewpoint of making self-compacting concrete a standard concrete.
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
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
The refined topological vertex
International Nuclear Information System (INIS)
Iqbal, Amer; Kozcaz, Can; Vafa, Cumrun
2009-01-01
We define a refined topological vertex which depends in addition on a parameter, which physically corresponds to extending the self-dual graviphoton field strength to a more general configuration. Using this refined topological vertex we compute, using geometric engineering, a two-parameter (equivariant) instanton expansion of gauge theories which reproduce the results of Nekrasov. The refined vertex is also expected to be related to Khovanov knot invariants.
Manufacturing tolerant topology optimization
Sigmund, Ole
2009-01-01
In this paper we present an extension of the topology optimization method to include uncertainties during the fabrication of macro, micro and nano structures. More specifically, we consider devices that are manufactured using processes which may result in (uniformly) too thin (eroded) or too thick (dilated) structures compared to the intended topology. Examples are MEMS devices manufactured using etching processes, nano-devices manufactured using e-beam lithography or laser micro-machining an...
Noncommutative topological dynamics
International Nuclear Information System (INIS)
Ramos, C. Correia; Martins, Nuno; Severino, Ricardo; Ramos, J. Sousa
2006-01-01
We study noncommutative dynamical systems associated to unimodal and bimodal maps of the interval. To these maps we associate subshifts and the correspondent AF-algebras and Cuntz-Krieger algebras. As an example we consider systems having equal topological entropy log(1 + φ), where φ is the golden number, but distinct chaotic behavior and we show how a new numerical invariant allows to distinguish that complexity. Finally, we give a statistical interpretation to the topological numerical invariants associated to bimodal maps
Pharmaceutical powder compaction technology
National Research Council Canada - National Science Library
Çelik, Metin
2011-01-01
"Revised to reflect modern pharmaceutical compacting techniques, this Second Edition guides pharmaceutical engineers, formulation scientists, and product development and quality assurance personnel...
Compact Polarimetry Potentials
Truong-Loi, My-Linh; Dubois-Fernandez, Pascale; Pottier, Eric
2011-01-01
The goal of this study is to show the potential of a compact-pol SAR system for vegetation applications. Compact-pol concept has been suggested to minimize the system design while maximize the information and is declined as the ?/4, ?/2 and hybrid modes. In this paper, the applications such as biomass and vegetation height estimates are first presented, then, the equivalence between compact-pol data simulated from full-pol data and compact-pol data processed from raw data as such is shown. Finally, a calibration procedure using external targets is proposed.
Tunable Topological Phononic Crystals
Chen, Zeguo
2016-05-27
Topological insulators first observed in electronic systems have inspired many analogues in photonic and phononic crystals in which remarkable one-way propagation edge states are supported by topologically nontrivial band gaps. Such band gaps can be achieved by breaking the time-reversal symmetry to lift the degeneracy associated with Dirac cones at the corners of the Brillouin zone. Here, we report on our construction of a phononic crystal exhibiting a Dirac-like cone in the Brillouin zone center. We demonstrate that simultaneously breaking the time-reversal symmetry and altering the geometric size of the unit cell result in a topological transition that we verify by the Chern number calculation and edge-mode analysis. We develop a complete model based on the tight binding to uncover the physical mechanisms of the topological transition. Both the model and numerical simulations show that the topology of the band gap is tunable by varying both the velocity field and the geometric size; such tunability may dramatically enrich the design and use of acoustic topological insulators.
A framework of induced hyperspace dynamical systems equipped with the hit-or-miss topology
International Nuclear Information System (INIS)
Wang Yangeng; Wei Guo; Campbell, William H.; Bourquin, Steven
2009-01-01
For any dynamical system (E,d,f), where E is Hausdorff locally compact second countable (HLCSC), let F (resp., 2 E ) denote the space of all closed subsets (resp., non-empty closed subsets) of E equipped with the hit-or-miss topology τ f . Both F and 2 E are again HLCSC (F actually compact), thus metrizable. Let ρ be such a metric (three metrics available). The main purpose is to determine the conditions on f that ensure the continuity of the induced hyperspace maps 2 f :F→F and 2 f :2 E →2 E defined by 2 f (F)=f(F). With this setting, the induced hyperspace systems (F,ρ,2 f ) and (2 E ,ρ,2 f ) are compact and locally compact dynamical systems, respectively. Consequently, dynamical properties, particularly metric related dynamical properties, of the given system (E,d,f) can be explored through these hyperspace systems. In contrast, when the Vietoris topology τ v is equipped on 2 E , the space of the induced hyperspace topological dynamical system (2 E ,τ v ,2 f ) is not metrizable if E is not compact metrizable, e.g., E=R n , implying that metric related dynamical concepts cannot be defined for (2 E ,τ v ,2 f ). Moreover, two examples are provided to illustrate the advantages of the hit-or-miss topology as compared to the Vietoris topology.
Countable Fuzzy Topological Space and Countable Fuzzy Topological Vector Space
Directory of Open Access Journals (Sweden)
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.
Topological Schemas of Memory Spaces
Directory of Open Access Journals (Sweden)
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.
Ideal amenability of Banach algebras on locally compact groups
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
closed ideal of M(G) contained in right annihilators of M(G). Let G be a locally compact group and f ∈ CB(G), then the right orbit of f is given by. R ◦ (f ) = {rxf : x ∈ G} and let. AP (G) = {f ∈ CB(G): R ◦ (f ) is precompact in the norm topology},. W (G) = {f ∈ CB(G): R ◦ (f ) is precompact in the weak topology}. Theorem 1.4. There is ...
Localization and traces in open-closed topological Landau-Ginzburg models
International Nuclear Information System (INIS)
Herbst, Manfred; Lazaroiu, Calin-Iuliu
2005-01-01
We reconsider the issue of localization in open-closed B-twisted Landau-Ginzburg models with arbitrary Calabi-Yau target. Through careful analysis of zero-mode reduction, we show that the closed model allows for a one-parameter family of localization pictures, which generalize the standard residue representation. The parameter λ which indexes these pictures measures the area of worldsheets with S 2 topology, with the residue representation obtained in the limit of small area. In the boundary sector, we find a double family of such pictures, depending on parameters λ and μ which measure the area and boundary length of worldsheets with disk topology. We show that setting μ = 0 and varying λ interpolates between the localization picture of the B-model with a noncompact target space and a certain residue representation proposed recently. This gives a complete derivation of the boundary residue formula, starting from the explicit construction of the boundary coupling. We also show that the various localization pictures are related by a semigroup of homotopy equivalences
International Nuclear Information System (INIS)
Izaurieta, F.; Rodriguez, E.; Salgado, P.
2008-01-01
A new Lagrangian realizing the symmetry of the M-algebra in eleven-dimensional space-time is presented. By means of the novel technique of Abelian semigroup expansion, a link between the M-algebra and the orthosymplectic algebra osp(32 vertical stroke 1) is established, and an M-algebra-invariant symmetric tensor of rank six is computed. This symmetric invariant tensor is a key ingredient in the construction of the new Lagrangian. The gauge-invariant Lagrangian is displayed in an explicitly Lorentz-invariant way by means of a subspace separation method based on the extended Cartan homotopy formula. (orig.)
Directory of Open Access Journals (Sweden)
Liu Min
2010-01-01
Full Text Available In this paper, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a system of mixed equilibrium problems, the set of common fixed points for a nonexpansive semigroup and the set of solutions of the quasi-variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in a Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extend some recent results in the literature.
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.
Introduction to topological groups
Husain, Taqdir
2018-01-01
Concise treatment covers semitopological groups, locally compact groups, Harr measure, and duality theory and some of its applications. The volume concludes with a chapter that introduces Banach algebras. 1966 edition.
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 optimized microbioreactors
DEFF Research Database (Denmark)
Schäpper, Daniel; Lencastre Fernandes, Rita; Eliasson Lantz, Anna
2011-01-01
This article presents the fusion of two hitherto unrelated fields—microbioreactors and topology optimization. The basis for this study is a rectangular microbioreactor with homogeneously distributed immobilized brewers yeast cells (Saccharomyces cerevisiae) that produce a recombinant protein....... Topology optimization is then used to change the spatial distribution of cells in the reactor in order to optimize for maximal product flow out of the reactor. This distribution accounts for potentially negative effects of, for example, by-product inhibition. We show that the theoretical improvement...... in productivity is at least fivefold compared with the homogeneous reactor. The improvements obtained by applying topology optimization are largest where either nutrition is scarce or inhibition effects are pronounced....
Architecture, Drawing, Topology
DEFF Research Database (Denmark)
This book presents contributions of drawing and text along with their many relationalities from ontology to history and vice versa in a range of reflections on architecture, drawing and topology. We hope to thereby indicate the potential of the theme in understanding not only the architecture...... of today, but – perhaps most importantly – also creating and producing architecture that is contemporaneous and reacts to the radical changes of the physical world which surrounds us in the increasingly artificial measures of new materialities and understandings thereof. The contributions range from...... the intricate issues of the imagination and the moving ratio in the topological culture, over urban topology, diagrammatisation, mediality and dynamics of transduction in the contemporary artificial environment....
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...
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...
Filters in topology optimization
DEFF Research Database (Denmark)
Bourdin, Blaise
1999-01-01
In this article, a modified (``filtered'') version of the minimum compliance topology optimization problem is studied. The direct dependence of the material properties on its pointwise density is replaced by a regularization of the density field using a convolution operator. In this setting...... it is possible to establish the existence of solutions. Moreover, convergence of an approximation by means of finite elements can be obtained. This is illustrated through some numerical experiments. The ``filtering'' technique is also shown to cope with two important numerical problems in topology optimization...
Differential topology first steps
Wallace, Andrew H
1968-01-01
Keeping mathematical prerequisites to a minimum, this undergraduate-level text stimulates students' intuitive understanding of topology while avoiding the more difficult subtleties and technicalities. Its focus is the method of spherical modifications and the study of critical points of functions on manifolds.No previous knowledge of topology is necessary for this text, which offers introductory material regarding open and closed sets and continuous maps in the first chapter. Succeeding chapters discuss the notions of differentiable manifolds and maps and explore one of the central topics of d
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.
Monastyrsky, M I
2006-01-01
This book reports new results in condensed matter physics for which topological methods and ideas are important. It considers, on the one hand, recently discovered systems such as carbon nanocrystals and, on the other hand, new topological methods used to describe more traditional systems such as the Fermi surfaces of normal metals, liquid crystals and quasicrystals. The authors of the book are renowned specialists in their fields and present the results of ongoing research, some of it obtained only very recently and not yet published in monograph form.
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
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
Topological field theories and duality
International Nuclear Information System (INIS)
Stephany, J.; Universidad Simon Bolivar, Caracas
1996-05-01
Topologically non trivial effects appearing in the discussion of duality transformations in higher genus manifold are discussed in a simple example, and their relation with the properties of Topological Field Theories is established. (author). 16 refs
Topology optimization of viscoelastic rectifiers
DEFF Research Database (Denmark)
Jensen, Kristian Ejlebjærg; Szabo, Peter; Okkels, Fridolin
2012-01-01
An approach for the design of microfluidic viscoelastic rectifiers is presented based on a combination of a viscoelastic model and the method of topology optimization. This presumption free approach yields a material layout topologically different from experimentally realized rectifiers...
Coherence Multiplex System Topologies
Meijerink, Arjan; Taniman, R.O.; Heideman, G.H.L.M.; van Etten, Wim
2007-01-01
Coherence multiplexing is a potentially inexpensive form of optical code-division multiple access, which is particularly suitable for short-range applications with moderate bandwidth requirements, such as access networks, LANs, or interconnects. Various topologies are known for constructing an
Architecture, Drawing, Topology
DEFF Research Database (Denmark)
This book presents contributions of drawing and text along with their many relationalities from ontology to history and vice versa in a range of reflections on architecture, drawing and topology. We hope to thereby indicate the potential of the theme in understanding not only the architecture...
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.
Slope constrained Topology Optimization
DEFF Research Database (Denmark)
Petersson, J.; Sigmund, Ole
1998-01-01
The problem of minimum compliance topology optimization of an elastic continuum is considered. A general continuous density-energy relation is assumed, including variable thickness sheet models and artificial power laws. To ensure existence of solutions, the design set is restricted by enforcing...
Steen, Lynn Arthur
1978-01-01
Over 140 examples, preceded by a succinct exposition of general topology and basic terminology. Each example treated as a whole. Over 25 Venn diagrams and charts summarize properties of the examples, while discussions of general methods of construction and change give readers insight into constructing counterexamples. Includes problems and exercises, correlated with examples. Bibliography. 1978 edition.
LHCb Topological Trigger Reoptimization
INSPIRE-00400931; Ilten, Philip; Khairullin, Egor; Rogozhnikov, Alex; Ustyuzhanin, Andrey; Williams, Michael
2015-12-23
The main b-physics trigger algorithm used by the LHCb experiment is the so-called topological trigger. The topological trigger selects vertices which are a) detached from the primary proton-proton collision and b) compatible with coming from the decay of a b-hadron. In the LHC Run 1, this trigger, which utilized a custom boosted decision tree algorithm, selected a nearly 100% pure sample of b-hadrons with a typical efficiency of 60-70%; its output was used in about 60% of LHCb papers. This talk presents studies carried out to optimize the topological trigger for LHC Run 2. In particular, we have carried out a detailed comparison of various machine learning classifier algorithms, e.g., AdaBoost, MatrixNet and neural networks. The topological trigger algorithm is designed to select all "interesting" decays of b-hadrons, but cannot be trained on every such decay. Studies have therefore been performed to determine how to optimize the performance of the classification algorithm on decays not used in the training. ...
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.
Topological Trigger Developments
Likhomanenko, Tatiana
2015-01-01
The main b-physics trigger algorithm used by the LHCb experiment is the so-called topological trigger. The topological trigger selects vertices which are a) detached from the primary proton-proton collision and b) compatible with coming from the decay of a b-hadron. In the LHC Run 1, this trigger utilized a custom boosted decision tree algorithm, selected an almost 100% pure sample of b-hadrons with a typical efficiency of 60-70%, and its output was used in about 60% of LHCb papers. This talk presents studies carried out to optimize the topological trigger for LHC Run 2. In particular, we have carried out a detailed comparison of various machine learning classifier algorithms, e.g., AdaBoost, MatrixNet and uBoost. The topological trigger algorithm is designed to select all "interesting" decays of b-hadrons, but cannot be trained on every such decay. Studies have therefore been performed to determine how to optimize the performance of the classification algorithm on decays not used in the training. These inclu...
Rendering the Topological Spines
Energy Technology Data Exchange (ETDEWEB)
Nieves-Rivera, D. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2015-05-05
Many tools to analyze and represent high dimensional data already exits yet most of them are not flexible, informative and intuitive enough to help the scientists make the corresponding analysis and predictions, understand the structure and complexity of scientific data, get a complete picture of it and explore a greater number of hypotheses. With this in mind, N-Dimensional Data Analysis and Visualization (ND²AV) is being developed to serve as an interactive visual analysis platform with the purpose of coupling together a number of these existing tools that range from statistics, machine learning, and data mining, with new techniques, in particular with new visualization approaches. My task is to create the rendering and implementation of a new concept called topological spines in order to extend ND²AV's scope. Other existing visualization tools create a representation preserving either the topological properties or the structural (geometric) ones because it is challenging to preserve them both simultaneously. Overcoming such challenge by creating a balance in between them, the topological spines are introduced as a new approach that aims to preserve them both. Its render using OpenGL and C++ and is currently being tested to further on be implemented on ND²AV. In this paper I will present what are the Topological Spines and how they are rendered.
Adjoint entropy vs topological entropy
Giordano Bruno, Anna
2012-01-01
Recently the adjoint algebraic entropy of endomorphisms of abelian groups was introduced and studied. We generalize the notion of adjoint entropy to continuous endomorphisms of topological abelian groups. Indeed, the adjoint algebraic entropy is defined using the family of all finite-index subgroups, while we take only the subfamily of all open finite-index subgroups to define the topological adjoint entropy. This allows us to compare the (topological) adjoint entropy with the known topologic...
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…
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.
Topological Properties of Superconducting Junctions
Pikulin, D.I.; Nazarov, Y.V.
Motivated by recent developments in the field of one-dimensional topological superconductors, we investigate the topological properties of s-matrix of generic superconducting junctions where dimension should not play any role. We argue that for a finite junction the s-matrix is always topologically
Stoop, B.T.J.; Larbi, J.A.; Heijnen, W.M.M.
1996-01-01
It is shown that it is possible to produce compacted gypsum with a low porosity and a high strength on a laboratory scale by uniaxial compaction of flue gas desulphurization (FGD-) gypsum powder. Compacted FGD-gypsum cylinders were produced at a compaction pres-sure between 50 and 500 MPa yielding
A Cp-theory problem book compactness in function spaces
Tkachuk, Vladimir V
2015-01-01
This third volume in Vladimir Tkachuk's series on Cp-theory problems applies all modern methods of Cp-theory to study compactness-like properties in function spaces and introduces the reader to the theory of compact spaces widely used in Functional Analysis. The text is designed to bring a dedicated reader from basic topological principles to the frontiers of modern research covering a wide variety of topics in Cp-theory and general topology at the professional level. The first volume, Topological and Function Spaces © 2011, provided an introduction from scratch to Cp-theory and general topology, preparing the reader for a professional understanding of Cp-theory in the last section of its main text. The second volume, Special Features of Function Spaces © 2014, continued from the first, giving reasonably complete coverage of Cp-theory, systematically introducing each of the major topics and providing 500 carefully selected problems and exercises with complete solutions. This third volume is self-contained...
Topology optimized permanent magnet systems
DEFF Research Database (Denmark)
Bjørk, Rasmus; Bahl, Christian; Insinga, Andrea Roberto
2017-01-01
Topology optimization of permanent magnet systems consisting of permanent magnets, high permeability iron and air is presented. An implementation of topology optimization for magnetostatics is discussed and three examples are considered. The Halbach cylinder is topology optimized with iron...... and an increase of 15% in magnetic efficiency is shown. A topology optimized structure to concentrate a homogeneous field is shown to increase the magnitude of the field by 111%. Finally, a permanent magnet with alternating high and low field regions is topology optimized and a ΛcoolΛcool figure of merit of 0...
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.
Undergraduate topology a working textbook
McCluskey, Aisling
2014-01-01
This textbook offers an accessible, modern introduction at undergraduate level to an area known variously as general topology, point-set topology or analytic topology with a particular focus on helping students to build theory for themselves. It is the result of several years of the authors' combined university teaching experience stimulated by sustained interest in advanced mathematical thinking and learning, alongside established research careers in analytic topology. Point-set topology is a discipline that needs relatively little background knowledge, but sufficient determination to grasp i
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.
Floquet topological insulators for sound
Fleury, Romain; Khanikaev, Alexander B.; Alù, Andrea
2016-06-01
The unique conduction properties of condensed matter systems with topological order have recently inspired a quest for the similar effects in classical wave phenomena. Acoustic topological insulators, in particular, hold the promise to revolutionize our ability to control sound, allowing for large isolation in the bulk and broadband one-way transport along their edges, with topological immunity against structural defects and disorder. So far, these fascinating properties have been obtained relying on moving media, which may introduce noise and absorption losses, hindering the practical potential of topological acoustics. Here we overcome these limitations by modulating in time the acoustic properties of a lattice of resonators, introducing the concept of acoustic Floquet topological insulators. We show that acoustic waves provide a fertile ground to apply the anomalous physics of Floquet topological insulators, and demonstrate their relevance for a wide range of acoustic applications, including broadband acoustic isolation and topologically protected, nonreciprocal acoustic emitters.
Proceedings – Mathematical Sciences | Indian Academy of Sciences
Indian Academy of Sciences (India)
Home; Journals; Proceedings – Mathematical Sciences. A GHAFFARI. Articles written in Proceedings – Mathematical Sciences. Volume 127 Issue 4 September 2017 pp 689-705 Research Article. Involutions and trivolutions on second dual of algebras related to locally compact groups and topological semigroups.
Computational differential topology
Directory of Open Access Journals (Sweden)
Denis Blackmore
2007-04-01
Full Text Available Some of the more differential aspects of the nascent field of computational topology are introduced and treated in considerable depth. Relevant categories based upon stratified geometric objects are proposed, and fundamental problems are identified and discussed in the context of both differential topology and computer science. New results on the triangulation of objects in the computational differential categories are proven, and evaluated from the perspective of effective computability (algorithmic solvability. In addition, the elements of innovative, effectively computable approaches for analyzing and obtaining computer generated representations of geometric objects based upon singularity/stratification theory and obstruction theory are formulated. New methods for characterizing complicated intersection sets are proven using differential analysis and homology theory. Also included are brief descriptions of several implementation aspects of some of the approaches described, as well as applications of the results in such areas as virtual sculpting, virtual surgery, modeling of heterogeneous biomaterials, and high speed visualizations.
DEFF Research Database (Denmark)
Ekman, Ulrik
2015-01-01
This article discusses the issue of approaching the design of the ubiquitous city as a matter of topology. The general context here is the design of contemporary global urbanity in the form of u-cities, smart cities, or intelligent cities emerging with the second phase of network societies...... that increasingly develop mixed reality environments with context-aware out-of-the-box computing as well as the soci-ocultural and experiental horizon of a virtually and physically mobile citizenry. Design here must meet an ongoing and exceedingly complex interactivity among environmental, technical, social...... and personal multiplicities of urban nodes on the move. This chapter focuses on the design of a busy traffic intersection in the South Korean u-city Songdo. Hence, the discussion whether and how Songdo may be approached via design as topology primarily considers the situation, event, and experience in which...
Quist, Daniel A [Los Alamos, NM; Gavrilov, Eugene M [Los Alamos, NM; Fisk, Michael E [Jemez, NM
2008-01-15
A method enables the topology of an acyclic fully propagated network to be discovered. A list of switches that comprise the network is formed and the MAC address cache for each one of the switches is determined. For each pair of switches, from the MAC address caches the remaining switches that see the pair of switches are located. For each pair of switches the remaining switches are determined that see one of the pair of switches on a first port and the second one of the pair of switches on a second port. A list of insiders is formed for every pair of switches. It is determined whether the insider for each pair of switches is a graph edge and adjacent ones of the graph edges are determined. A symmetric adjacency matrix is formed from the graph edges to represent the topology of the data link network.
Monastyrsky, Michail Ilych
2007-01-01
The book presents a class of new results in molecular biology for which topological methods and ideas are important. These include: the large-scale conformation properties of DNA; computational methods (Monte Carlo) allowing the simulation of large-scale properties of DNA; the tangle model of DNA recombination and other applications of Knot theory; dynamics of supercoiled DNA and biocatalitic properties of DNA; the structure of proteins; and other very recent problems in molecular biology. The text also provides a short course of modern topology intended for the broad audience of biologists and physicists. The authors are renowned specialists in their fields and some of the new results presented here are documented for the first time in monographic form.
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...
Operator algebras and topology
International Nuclear Information System (INIS)
Schick, T.
2002-01-01
These notes, based on three lectures on operator algebras and topology at the 'School on High Dimensional Manifold Theory' at the ICTP in Trieste, introduce a new set of tools to high dimensional manifold theory, namely techniques coming from the theory of operator algebras, in particular C*-algebras. These are extensively studied in their own right. We will focus on the basic definitions and properties, and on their relevance to the geometry and topology of manifolds. A central pillar of work in the theory of C*-algebras is the Baum-Connes conjecture. This is an isomorphism conjecture, as discussed in the talks of Luck, but with a certain special flavor. Nevertheless, it has important direct applications to the topology of manifolds, it implies e.g. the Novikov conjecture. In the first chapter, the Baum-Connes conjecture will be explained and put into our context. Another application of the Baum-Connes conjecture is to the positive scalar curvature question. This will be discussed by Stephan Stolz. It implies the so-called 'stable Gromov-Lawson-Rosenberg conjecture'. The unstable version of this conjecture said that, given a closed spin manifold M, a certain obstruction, living in a certain (topological) K-theory group, vanishes if and only M admits a Riemannian metric with positive scalar curvature. It turns out that this is wrong, and counterexamples will be presented in the second chapter. The third chapter introduces another set of invariants, also using operator algebra techniques, namely L 2 -cohomology, L 2 -Betti numbers and other L 2 -invariants. These invariants, their basic properties, and the central questions about them, are introduced in the third chapter. (author)
Topological confinement and superconductivity
Energy Technology Data Exchange (ETDEWEB)
Al-hassanieh, Dhaled A [Los Alamos National Laboratory; Batista, Cristian D [Los Alamos National Laboratory
2008-01-01
We derive a Kondo Lattice model with a correlated conduction band from a two-band Hubbard Hamiltonian. This mapping allows us to describe the emergence of a robust pairing mechanism in a model that only contains repulsive interactions. The mechanism is due to topological confinement and results from the interplay between antiferromagnetism and delocalization. By using Density-Matrix-Renormalization-Group (DMRG) we demonstrate that this mechanism leads to dominant superconducting correlations in aID-system.
DEFF Research Database (Denmark)
Schwerdtfeger, Peter; Wirz, Lukas; Avery, James Emil
2014-01-01
Fullerenes are carbon molecules that form polyhedral cages. Their bond structures are exactly the planar cubic graphs that have only pentagon and hexagon faces. Strikingly, a number of chemical properties of a fullerene can be derived from its graph structure. A rich mathematics of cubic planar g....... In this paper, we present a general overview of recent topological and graph theoretical developments in fullerene research over the past two decades, describing both solved and open problems....
Technologies for converter topologies
Energy Technology Data Exchange (ETDEWEB)
Zhou, Yan; Zhang, Haiyu
2017-02-28
In some embodiments of the disclosed inverter topologies, an inverter may include a full bridge LLC resonant converter, a first boost converter, and a second boost converter. In such embodiments, the first and second boost converters operate in an interleaved manner. In other disclosed embodiments, the inverter may include a half-bridge inverter circuit, a resonant circuit, a capacitor divider circuit, and a transformer.
Topological Substituent Descriptors
Directory of Open Access Journals (Sweden)
Mircea V. DIUDEA
2002-12-01
Full Text Available Motivation. Substituted 1,3,5-triazines are known as useful herbicidal substances. In view of reducing the cost of biological screening, computational methods are carried out for evaluating the biological activity of organic compounds. Often a class of bioactives differs only in the substituent attached to a basic skeleton. In such cases substituent descriptors will give the same prospecting results as in case of using the whole molecule description, but with significantly reduced computational time. Such descriptors are useful in describing steric effects involved in chemical reactions. Method. Molecular topology is the method used for substituent description and multi linear regression analysis as a statistical tool. Results. Novel topological descriptors, XLDS and Ws, based on the layer matrix of distance sums and walks in molecular graphs, respectively, are proposed for describing the topology of substituents linked on a chemical skeleton. They are tested for modeling the esterification reaction in the class of benzoic acids and herbicidal activity of 2-difluoromethylthio-4,6-bis(monoalkylamino-1,3,5-triazines. Conclusions. Ws substituent descriptor, based on walks in graph, satisfactorily describes the steric effect of alkyl substituents behaving in esterification reaction, with good correlations to the Taft and Charton steric parameters, respectively. Modeling the herbicidal activity of the seo of 1,3,5-triazines exceeded the models reported in literature, so far.
Charged topological black hole pair creation
International Nuclear Information System (INIS)
Mann, R.B.
1998-01-01
I examine the pair creation of black holes in space-times with a cosmological constant of either sign. I consider cosmological C-metrics and show that the conical singularities in this metric vanish only for three distinct classes of black hole metric, two of which have compact event horizons on each spatial slice. One class is a generalization of the Reissner-Nordstroem (anti-)de Sitter black holes in which the event horizons are the direct product of a null line with a 2-surface with topology of genus g. The other class consists of neutral black holes whose event horizons are the direct product of a null conoid with a circle. In the presence of a domain wall, black hole pairs of all possible types will be pair created for a wide range of mass and charge, including even negative mass black holes. I determine the relevant instantons and Euclidean actions for each case. (orig.)
Inhomogeneous compact extra dimensions
Energy Technology Data Exchange (ETDEWEB)
Bronnikov, K.A. [Center of Gravity and Fundamental Metrology, VNIIMS, 46 Ozyornaya st., Moscow 119361 (Russian Federation); Budaev, R.I.; Grobov, A.V.; Dmitriev, A.E.; Rubin, Sergey G., E-mail: kb20@yandex.ru, E-mail: buday48@mail.ru, E-mail: alexey.grobov@gmail.com, E-mail: alexdintras@mail.ru, E-mail: sergeirubin@list.ru [National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), 115409 Moscow (Russian Federation)
2017-10-01
We show that an inhomogeneous compact extra space possesses two necessary features— their existence does not contradict the observable value of the cosmological constant Λ{sub 4} in pure f ( R ) theory, and the extra dimensions are stable relative to the 'radion mode' of perturbations, the only mode considered. For a two-dimensional extra space, both analytical and numerical solutions for the metric are found, able to provide a zero or arbitrarily small Λ{sub 4}. A no-go theorem has also been proved, that maximally symmetric compact extra spaces are inconsistent with 4D Minkowski space in the framework of pure f ( R ) gravity.
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
Indian Academy of Sciences (India)
The classification of real compact surfaces is a main result which is at the same time easy to understand and non- trivial, simple in formulation and rich in consequences. The aim of this article is to explain the theorem by means of many drawings. It is an invitation to a visual approach of mathematics. First Definitions and ...
Indian Academy of Sciences (India)
physics pp. 817–825. Hadrons in compact stars. DEBADES BANDYOPADHYAY. Saha Institute of Nuclear Physics, 1/AF Bidhan Nagar, Kolkata 700 064, India ... There is a growing interplay between the physics of dense matter in relativistic .... Kaplan and Nelson [7] first showed in a chiral SU(3)L × SU(3)R model that.
Topological imprint for periodic orbits
International Nuclear Information System (INIS)
Martín, Jesús San; Moscoso, Ma José; Gómez, A González
2012-01-01
The more self-crossing points an orbit has the more complex it is. We introduce the topological imprint to characterize crossing points and focus on the period-doubling cascade. The period-doubling cascade topological imprint determines the topological imprint for orbits in chaotic bands. In addition, there is a closer link between this concept and the braids studied by Lettelier et al (2000 J. Phys. A: Math. Gen. 33 1809–25). (paper)
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
Lynch, Mark
2012-01-01
We continue our study of topological X-rays begun in Lynch ["Topological X-rays and MRI's," iJMEST 33(3) (2002), pp. 389-392]. We modify our definition of a topological magnetic resonance imaging and give an affirmative answer to the question posed there: Can we identify a closed set in a box by defining X-rays to probe the interior and without…
Topological Order in Silicon Photonics
2017-02-07
AFRL-AFOSR-VA-TR-2017-0037 Topological orders in Silicon photonics Mohammad Hafezi MARYLAND UNIV COLLEGE PARK 3112 LEE BLDG COLLEGE PARK, MD 20742...15 SEP 2016 4. TITLE AND SUBTITLE Topological Order in Silicon Photonics 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA-9550-14-1-0267 5c. PROGRAM...matter to ultra cold gases. Recently, photonic systems have been under investigation to explore various types of topological orders and to potentially
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.
Topologically clean distance fields.
Gyulassy, Attila; Duchaineau, Mark; Natarajan, Vijay; Pascucci, Valerio; Bringa, Eduardo; Higginbotham, Andrew; Hamann, Bernd
2007-01-01
Analysis of the results obtained from material simulations is important in the physical sciences. Our research was motivated by the need to investigate the properties of a simulated porous solid as it is hit by a projectile. This paper describes two techniques for the generation of distance fields containing a minimal number of topological features, and we use them to identify features of the material. We focus on distance fields defined on a volumetric domain considering the distance to a given surface embedded within the domain. Topological features of the field are characterized by its critical points. Our first method begins with a distance field that is computed using a standard approach, and simplifies this field using ideas from Morse theory. We present a procedure for identifying and extracting a feature set through analysis of the MS complex, and apply it to find the invariants in the clean distance field. Our second method proceeds by advancing a front, beginning at the surface, and locally controlling the creation of new critical points. We demonstrate the value of topologically clean distance fields for the analysis of filament structures in porous solids. Our methods produce a curved skeleton representation of the filaments that helps material scientists to perform a detailed qualitative and quantitative analysis of pores, and hence infer important material properties. Furthermore, we provide a set of criteria for finding the "difference" between two skeletal structures, and use this to examine how the structure of the porous solid changes over several timesteps in the simulation of the particle impact.
Lieb polariton topological insulators
Li, Chunyan; Ye, Fangwei; Chen, Xianfeng; Kartashov, Yaroslav V.; Ferrando, Albert; Torner, Lluis; Skryabin, Dmitry V.
2018-02-01
We predict that the interplay between the spin-orbit coupling, stemming from the transverse electric-transverse magnetic energy splitting, and the Zeeman effect in semiconductor microcavities supporting exciton-polariton quasiparticles, results in the appearance of unidirectional linear topological edge states when the top microcavity mirror is patterned to form a truncated dislocated Lieb lattice of cylindrical pillars. Periodic nonlinear edge states are found to emerge from the linear ones. They are strongly localized across the interface and they are remarkably robust in comparison to their counterparts in honeycomb lattices. Such robustness makes possible the existence of nested unidirectional dark solitons that move steadily along the lattice edge.
Architecture, Drawing, Topology
DEFF Research Database (Denmark)
Meldgaard, Morten
This book presents contributions of drawing and text along with their many relationalities from ontology to history and vice versa in a range of reflections on architecture, drawing and topology. We hope to thereby indicate the potential of the theme in understanding not only the architecture...... of today, but – perhaps most importantly – also creating and producing architecture that is contemporaneous and reacts to the radical changes of the physical world which surrounds us in the increasingly artificial measures of new materialities and understandings thereof. The contributions range from...
Introduction to generalized topological spaces
Directory of Open Access Journals (Sweden)
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.
Topological approach to the generalized n-centre problem
Bolotin, S. V.; Kozlov, V. V.
2017-06-01
This paper considers a natural Hamiltonian system with two degrees of freedom and Hamiltonian H=\\Vert p\\Vert^2/2+V(q). The configuration space M is a closed surface (for non-compact M certain conditions at infinity are required). It is well known that if the potential energy V has n>2χ(M) Newtonian singularities, then the system is not integrable and has positive topological entropy on the energy level H=h>\\sup V. This result is generalized here to the case when the potential energy has several singular points a_j of type V(q)∼ -\\operatorname{dist}(q,a_j)-α_j. Let A_k=2-2k-1, k\\in{N}, and let n_k be the number of singular points with A_k≤slant α_jk+1. It is proved that if \\displaystyle \\sum2≤slant k≤slant∞n_kA_k>2χ(M), then the system has a compact chaotic invariant set of collision-free trajectories on any energy level H=h>\\sup V. This result is purely topological: no analytical properties of the potential energy are used except the presence of singularities. The proofs are based on the generalized Levi-Civita regularization and elementary topology of coverings. As an example, the plane n-centre problem is considered. Bibliography: 29 titles.
Topological fixed point theory for singlevalued and multivalued mappings and applications
Ben Amar, Afif
2016-01-01
This is a monograph covering topological fixed point theory for several classes of single and multivalued maps. The authors begin by presenting basic notions in locally convex topological vector spaces. Special attention is then devoted to weak compactness, in particular to the theorems of Eberlein–Šmulian, Grothendick and Dunford–Pettis. Leray–Schauder alternatives and eigenvalue problems for decomposable single-valued nonlinear weakly compact operators in Dunford–Pettis spaces are considered, in addition to some variants of Schauder, Krasnoselskii, Sadovskii, and Leray–Schauder type fixed point theorems for different classes of weakly sequentially continuous operators on general Banach spaces. The authors then proceed with an examination of Sadovskii, Furi–Pera, and Krasnoselskii fixed point theorems and nonlinear Leray–Schauder alternatives in the framework of weak topologies and involving multivalued mappings with weakly sequentially closed graph. These results are formulated in terms of ax...
A Compact Three-Phase Single-Input/Dual-Output Matrix Converter
DEFF Research Database (Denmark)
Liu, Xiong; Wang, Peng; Loh, Poh Chiang
2012-01-01
This paper presents a novel matrix converter with one ac input and two ac outputs. The presented topology is based on the traditional indirect matrix converter, but with its rear-end six-switch inverter replaced by a compact nine-switch inverter. With only three extra switches added, the proposed...
Weakly compact operators and interpolation
Maligranda, Lech
1992-01-01
The class of weakly compact operators is, as well as the class of compact operators, a fundamental operator ideal. They were investigated strongly in the last twenty years. In this survey, we have collected and ordered some of this (partly very new) knowledge. We have also included some comments, remarks and examples. The class of weakly compact operators is, as well as the class of compact operators, a fundamental operator ideal. They were investigated strongly in the last twenty years. I...
1997-01-01
The origins of this volume can be traced back to a conference on "Ethics, Economic and Business" organized by Columbia Busi ness School in March of 1993, and held in the splendid facilities of Columbia's Casa Italiana. Preliminary versions of several of the papers were presented at that meeting. In July 1994 the Fields Institute of Mathematical Sciences sponsored a workshop on "Geometry, Topology and Markets": additional papers and more refined versions of the original papers were presented there. They were published in their present versions in Social Choice and Wel fare, volume 14, number 2, 1997. The common aim of these workshops and this volume is to crystallize research in an area which has emerged rapidly in the last fifteen years, the area of topological approaches to social choice and the theory of games. The area is attracting increasing interest from social choice theorists, game theorists, mathematical econ omists and mathematicians, yet there is no authoritative collection of papers in the a...
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.
Directory of Open Access Journals (Sweden)
L. Baulieu
2016-11-01
Full Text Available We extend to a possibly infinite chain the conformally invariant mechanical system that was introduced earlier as a toy model for understanding the topological Yang–Mills theory. It gives a topological quantum model that has interesting and computable zero modes and topological invariants. It confirms the recent conjecture by several authors that supersymmetric quantum mechanics may provide useful tools for understanding robotic mechanical systems (Vitelli et al. and condensed matter properties (Kane et al., where trajectories are allowed or not by the conservation of topological indices. The absences of ground state and mass gaps are special features of such systems.
Analysis of laboratory compaction methods of roller compacted concrete
Trtík, Tomáš; Chylík, Roman; Bílý, Petr; Fládr, Josef
2017-09-01
Roller-Compacted Concrete (RCC) is an ordinary concrete poured and compacted with machines typically used for laying of asphalt road layers. One of the problems connected with this technology is preparation of representative samples in the laboratory. The aim of this work was to analyse two methods of preparation of RCC laboratory samples with bulk density as the comparative parameter. The first method used dynamic compaction by pneumatic hammer. The second method of compaction had a static character. The specimens were loaded by precisely defined force in laboratory loading machine to create the same conditions as during static rolling (in the Czech Republic, only static rolling is commonly used). Bulk densities obtained by the two compaction methods were compared with core drills extracted from real RCC structure. The results have shown that the samples produced by pneumatic hammer tend to overestimate the bulk density of the material. For both compaction methods, immediate bearing index test was performed to verify the quality of compaction. A fundamental difference between static and dynamic compaction was identified. In static compaction, initial resistance to penetration of the mandrel was higher, after exceeding certain limit the resistance was constant. This means that the samples were well compacted just on the surface. Specimens made by pneumatic hammer actively resisted throughout the test, the whole volume was uniformly compacted.
Energy Technology Data Exchange (ETDEWEB)
Placidi, M.; Jung, J. -Y.; Ratti, A.; Sun, C.
2014-07-25
This paper describes beam distribution schemes adopting a novel implementation based on low amplitude vertical deflections combined with horizontal ones generated by Lambertson-type septum magnets. This scheme offers substantial compactness in the longitudinal layouts of the beam lines and increased flexibility for beam delivery of multiple beam lines on a shot-to-shot basis. Fast kickers (FK) or transverse electric field RF Deflectors (RFD) provide the low amplitude deflections. Initially proposed at the Stanford Linear Accelerator Center (SLAC) as tools for beam diagnostics and more recently adopted for multiline beam pattern schemes, RFDs offer repetition capabilities and a likely better amplitude reproducibility when compared to FKs, which, in turn, offer more modest financial involvements both in construction and operation. Both solutions represent an ideal approach for the design of compact beam distribution systems resulting in space and cost savings while preserving flexibility and beam quality.
Energy Technology Data Exchange (ETDEWEB)
Placidi, M.; Jung, J.-Y.; Ratti, A.; Sun, C., E-mail: csun@lbl.gov
2014-12-21
This paper describes beam distribution schemes adopting a novel implementation based on low amplitude vertical deflections combined with horizontal ones generated by Lambertson-type septum magnets. This scheme offers substantial compactness in the longitudinal layouts of the beam lines and increased flexibility for beam delivery of multiple beam lines on a shot-to-shot basis. Fast kickers (FK) or transverse electric field RF Deflectors (RFD) provide the low amplitude deflections. Initially proposed at the Stanford Linear Accelerator Center (SLAC) as tools for beam diagnostics and more recently adopted for multiline beam pattern schemes, RFDs offer repetition capabilities and a likely better amplitude reproducibility when compared to FKs, which, in turn, offer more modest financial involvements both in construction and operation. Both solutions represent an ideal approach for the design of compact beam distribution systems resulting in space and cost savings while preserving flexibility and beam quality.
Compact stellarators as reactors
International Nuclear Information System (INIS)
Lyon, J.F.; Valanju, P.; Zarnstorff, M.C.; Hirshman, S.; Spong, D.A.; Strickler, D.; Williamson, D.E.; Ware, A.
2001-01-01
Two types of compact stellarators are examined as reactors: two- and three-field-period (M=2 and 3) quasi-axisymmetric devices with volume-average =4-5% and M=2 and 3 quasi-poloidal devices with =10-15%. These low-aspect-ratio stellarator-tokamak hybrids differ from conventional stellarators in their use of the plasma-generated bootstrap current to supplement the poloidal field from external coils. Using the ARIES-AT model with B max =12T on the coils gives Compact Stellarator reactors with R=7.3-8.2m, a factor of 2-3 smaller R than other stellarator reactors for the same assumptions, and neutron wall loadings up to 3.7MWm -2 . (author)
CERN. Geneva
2015-01-01
Fusion research is currently to a large extent focused on tokamak (ITER) and inertial confinement (NIF) research. In addition to these large international or national efforts there are private companies performing fusion research using much smaller devices than ITER or NIF. The attempt to achieve fusion energy production through relatively small and compact devices compared to tokamaks decreases the costs and building time of the reactors and this has allowed some private companies to enter the field, like EMC2, General Fusion, Helion Energy, Lawrenceville Plasma Physics and Lockheed Martin. Some of these companies are trying to demonstrate net energy production within the next few years. If they are successful their next step is to attempt to commercialize their technology. In this presentation an overview of compact fusion reactor concepts is given.
Winkler, A.; Harazim, S.; Collins, D.J.; Br?nig, R.; Schmidt, H.; Menzel, S.B.
2017-01-01
In this work, we discuss and demonstrate the principle features of surface acoustic wave (SAW) aerosol generation, based on the properties of the fluid supply, the acoustic wave field and the acoustowetting phenomena. Furthermore, we demonstrate a compact SAW-based aerosol generator amenable to mass production fabricated using simple techniques including photolithography, computerized numerical control (CNC) milling and printed circuit board (PCB) manufacturing. Using this device, we present ...
Topological arguments for Kolmogorov complexity
Directory of Open Access Journals (Sweden)
Alexander Shen
2012-08-01
Full Text Available We present several application of simple topological arguments in problems of Kolmogorov complexity. Basically we use the standard fact from topology that the disk is simply connected. It proves to be enough to construct strings with some nontrivial algorithmic properties.
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
A Course on Topological Groups
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 2; Issue 8. A Course on Topological Groups - A Pellucid Little Book on Topological Groups. K Parthasarathy. Book Review Volume 2 Issue 8 August 1997 pp 82-83. Fulltext. Click here to view fulltext PDF. Permanent link:
Topology optimization of turbulent flows
DEFF Research Database (Denmark)
Dilgen, Cetin B.; Dilgen, Sumer B.; Fuhrman, David R.
2018-01-01
The aim of this work is to present a fast and viable approach for taking into account turbulence in topology optimization of complex fluid flow systems, without resorting to any simplifying assumptions in the derivation of discrete adjoints. Topology optimization is an iterative gradient...
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.
Topological phases of quantum matter
Indian Academy of Sciences (India)
Although first to mention topological phases, not really the first Nobel prize for topological phases. First - 1982 Nobel to Klaus von Klitzing for `discovery of quantised. Hall effect '. Second - 1998 Nobel to RobertLaughlin, Horst Stormer and. Daniel Tsui for `discovery of a new form of quantum fluid with fractionally charged ...
Cartography – morphology – topology
DEFF Research Database (Denmark)
Dinesen, Cort Ross; Peder Pedersen, Claus
I 2004 a Summer School was established on the Greek island of Hydra. The was to be the basis of research-based morphological and topological studies, which have since taken place for 4 weeks of every year. Starting with Hydra’s topography different ways of considering topology were developed...
Topology optimized RF MEMS switches
DEFF Research Database (Denmark)
Philippine, M. A.; Zareie, H.; Sigmund, Ole
2013-01-01
Topology optimization is a rigorous and powerful method that should become a standard MEMS design tool - it can produce unique and non-intuitive designs that meet complex objectives and can dramatically improve the performance and reliability of MEMS devices. We present successful uses of topolog...
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.
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.
Solving equations by topological methods
Directory of Open Access Journals (Sweden)
Lech Górniewicz
2005-01-01
Full Text Available In this paper we survey most important results from topological fixed point theory which can be directly applied to differential equations. Some new formulations are presented. We believe that our article will be useful for analysts applying topological fixed point theory in nonlinear analysis and in differential equations.
A method for manufacturing compacts
International Nuclear Information System (INIS)
Baschwitz, Robert; Raymond, Jean.
1974-01-01
Description is given of a method for preparing compacts with high matrix density. The method is characterized by the steps of forming the mixture by simultaneously pouring the components directly into a compacting matrix comprising coated particles and a graphite binder mixture in the granular form, then compressing the compact after having brought the material to be compacted to a temperature at which the binder is in the fluid state. The method can be applied to the manufacture of compacts for high temperature nuclear reactors [fr
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.
Combined Shape and Topology Optimization
DEFF Research Database (Denmark)
Christiansen, Asger Nyman
Shape and topology optimization seeks to compute the optimal shape and topology of a structure such that one or more properties, for example stiffness, balance or volume, are improved. The goal of the thesis is to develop a method for shape and topology optimization which uses the Deformable...... Simplicial Complex (DSC) method. Consequently, we present a novel method which combines current shape and topology optimization methods. This method represents the surface of the structure explicitly and discretizes the structure into non-overlapping elements, i.e. a simplicial complex. An explicit surface...... representation usually limits the optimization to minor shape changes. However, the DSC method uses a single explicit representation and still allows for large shape and topology changes. It does so by constantly applying a set of mesh operations during deformations of the structure. Using an explicit instead...
Streamline topology of axisymmetric flows
DEFF Research Database (Denmark)
Brøns, Morten
Topological fluid mechanics in the sense of the present paper is the study and classification of flow patterns close to a critical point. Here we discuss the topology of steady viscous incompressible axisymmetric flows in the vicinity of the axis. Following previous studies the velocity field $v...... to the authors knowledge has not been used systematically to high orders in topological fluid mechanics. We compare the general results with experimental and computational results on the Vogel-Ronneberg flow. We show that the topology changes observed when recirculating bubbles on the vortex axis are created...... and interact follow the topological classification and that the complete set of patterns found is contained in a codimension-4 unfolding of the most simple singular configuration....
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...
Diffusion through statically compacted clay
International Nuclear Information System (INIS)
Ho, C.L.; Shebl, M.A.A.
1994-01-01
This paper presents experimental work on the effect of compaction on contaminant flow through clay liners. The experimental program included evaluation of soil properties, compaction, permeability and solute diffusion. A permeameter was built of non reactive materials to test samples compacted at different water contents and compactive efforts. The flow of a permeating solute, LiCl, was monitored. Effluent samples were collected for solute concentration measurements. The concentrations were measured by performing atomic adsorption tests. The analyzed results showed different diffusion characteristics when compaction conditions changed. At each compactive effort, permeability decreased as molding water content increased. Consequently, transit time (measured at relative concentration 50%) increased and diffusivity decreased. As compactive effort increased for soils compacted dry of optimum, permeability and diffusion decreased. On the other hand, as compactive effort increased for soils compacted wet of optimum, permeability and diffusivity increased. Tortuosity factor was indirectly measured from the diffusion and retardation rate. Tortuosity factor also decreased as placement water content was increased from dry of optimum to wet of optimum. Then decreases were more pronounced for low compactive effort tests. 27 refs., 7 figs., 5 tabs
Transportation Network Topologies
Alexandrov, Natalia (Editor)
2004-01-01
The existing U.S. hub-and-spoke air transportation system is reaching saturation. Major aspects of the current system, such as capacity, safety, mobility, customer satisfaction, security, communications, and ecological effects, require improvements. The changing dynamics - increased presence of general aviation, unmanned autonomous vehicles, military aircraft in civil airspace as part of homeland defense - contributes to growing complexity of airspace. The system has proven remarkably resistant to change. NASA Langley Research Center and the National Institute of Aerospace conducted a workshop on Transportation Network Topologies on 9-10 December 2003 in Williamsburg, Virginia. The workshop aimed to examine the feasibility of traditional methods for complex system analysis and design as well as potential novel alternatives in application to transportation systems, identify state-of-the-art models and methods, conduct gap analysis, and thus to lay a foundation for establishing a focused research program in complex systems applied to air transportation.
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)
From bosonic topological transition to symmetric fermion mass generation
You, Yi-Zhuang; He, Yin-Chen; Vishwanath, Ashvin; Xu, Cenke
2018-03-01
A bosonic topological transition (BTT) is a quantum critical point between the bosonic symmetry-protected topological phase and the trivial phase. In this work, we investigate such a transition in a (2+1)-dimensional lattice model with the maximal microscopic symmetry: an internal SO (4 ) symmetry. We derive a description for this transition in terms of compact quantum electrodynamics (QED) with four fermion flavors (Nf=4 ). Within a systematic renormalization group analysis, we identify the critical point with the desired O (4 ) emergent symmetry and all expected deformations. By lowering the microscopic symmetry, we recover the previous Nf=2 noncompact QED description of the BTT. Finally, by merging two BTTs we recover a previously discussed theory of symmetric mass generation, as an SU (2 ) quantum chromodynamics-Higgs theory with Nf=4 flavors of SU (2 ) fundamental fermions and one SU (2 ) fundamental Higgs boson. This provides a consistency check on both theories.
Cultural Topology of Creativity
Directory of Open Access Journals (Sweden)
L. M. Andryukhina
2012-01-01
Full Text Available The man in the modern culture faces the challenge of either being creative or forced to leave the stage, which reflects the essential basics of life. The price of lost opportunities, caused by mental stereotypes and encapsulation, is gradually rising. The paper reveals the socio-cultural conditions and the necessary cultural topology of creativity development, as well as the man’s creative potential in the 21st century. The content of the creativity concept is specified along with the phenomenon of its fast expansion in the modern discourse. That results from the global spreading of numerous creative practices in various spheres of life, affecting the progress directions in economics, business, industrial technologies, labor, employment and social stratification. The author emphasizes the social features of creativity, the rising number of, so called, creative class, and outlines the two opposing strategies influencing the topology modification of the social and cultural environment. The first one, applied by the developed countries, facilitates the development of the creative human potential, whereas the other one, inherent in our country, holds that a creative person is able to make progress by himself. However, for solving the urgent problem of innovative development, the creative potential of modern Russia is not sufficient, and following the second strategy will result in unrealized social opportunities and ever lasting social and cultural situation demanding further investment. According to the author, to avoid such a perspective, it is necessary to overcome the three deeply rooted archetypes: the educational disciplinary centrism, organizational absolutism and cultural ostracism.
Litinski, Daniel; Kesselring, Markus S.; Eisert, Jens; von Oppen, Felix
2017-07-01
We present a scalable architecture for fault-tolerant topological quantum computation using networks of voltage-controlled Majorana Cooper pair boxes and topological color codes for error correction. Color codes have a set of transversal gates which coincides with the set of topologically protected gates in Majorana-based systems, namely, the Clifford gates. In this way, we establish color codes as providing a natural setting in which advantages offered by topological hardware can be combined with those arising from topological error-correcting software for full-fledged fault-tolerant quantum computing. We provide a complete description of our architecture, including the underlying physical ingredients. We start by showing that in topological superconductor networks, hexagonal cells can be employed to serve as physical qubits for universal quantum computation, and we present protocols for realizing topologically protected Clifford gates. These hexagonal-cell qubits allow for a direct implementation of open-boundary color codes with ancilla-free syndrome read-out and logical T gates via magic-state distillation. For concreteness, we describe how the necessary operations can be implemented using networks of Majorana Cooper pair boxes, and we give a feasibility estimate for error correction in this architecture. Our approach is motivated by nanowire-based networks of topological superconductors, but it could also be realized in alternative settings such as quantum-Hall-superconductor hybrids.
Equivariant topological quantum field theory and symmetry protected topological phases
Energy Technology Data Exchange (ETDEWEB)
Kapustin, Anton [Division of Physics, California Institute of Technology,1200 E California Blvd, Pasadena, CA, 91125 (United States); Turzillo, Alex [Simons Center for Geometry and Physics, State University of New York,Stony Brook, NY, 11794 (United States)
2017-03-01
Short-Range Entangled topological phases of matter are closely related to Topological Quantum Field Theory. We use this connection to classify Symmetry Protected Topological phases in low dimensions, including the case when the symmetry involves time-reversal. To accomplish this, we generalize Turaev’s description of equivariant TQFT to the unoriented case. We show that invertible unoriented equivariant TQFTs in one or fewer spatial dimensions are classified by twisted group cohomology, in agreement with the proposal of Chen, Gu, Liu and Wen. We also show that invertible oriented equivariant TQFTs in spatial dimension two or fewer are classified by ordinary group cohomology.
U(1) lattice gauge theory with a topological action
Akerlund, Oscar
2015-01-01
We investigate the phase diagram of the compact $U(1)$ lattice gauge theory in four dimensions using a non-standard action which is invariant under continuous deformations of the plaquette angles. Just as for the Wilson action, we find a weakly first order transition, separating a confining phase where magnetic monopoles condense, and a Coulomb phase where monopoles are dilute. We also find a third phase where monopoles are completely absent. The topological action offers an algorithmic advantage for the computation of the free energy.
Compact synchrotron radiation source
International Nuclear Information System (INIS)
Liu, N.; Wang, T.; Tian, J.; Lin, Y.; Chen, S.; He, W.; Hu, Y.; Li, Q.
1985-01-01
A compact 800 MeV synchrotron radiation source is discussed. The storage ring has a circumference of 30.3 m, two 90 degree and four 45 degree bending magnet sections, two long straight sections and four short straight sections. The radius of the bending magnet is 2.224m. The critical wave length is 24A. The injector is a 15 Mev Microtron Electrons are accelerated from 15 Mev to 800 Mev by ramping the field of the ring. The expected stored current will be around 100 ma
International Nuclear Information System (INIS)
Madhavi, V.; Phatak, P.R.; Bahadur, C.; Bayala, A.K.; Jakati, R.K.; Sathian, V.
2003-01-01
Full text: A compact size neutron flux monitor has been developed incorporating standard boards developed for smart radiation monitors. The sensitivity of the monitors is 0.4cps/nV. It has been tested up to 2075 nV flux with standard neutron sources. It shows convincing results even in high flux areas like 6m away from the accelerator in RMC (Parel) for 106/107 nV. These monitors have a focal and remote display, alarm function with potential free contacts for centralized control and additional provision of connectivity via RS485/Ethernet. This paper describes the construction, working and results of the above flux monitor
Compact synchrotron light sources
Weihreter, Ernst
1996-01-01
This book covers a new niche in circular accelerator design, motivated by the promising industrial prospects of recent micromanufacturing methods - X-ray lithography, synchrotron radiation-based micromachining and microanalysis techniques. It describes the basic concepts and the essential challenges for the development of compact synchrotron radiation sources from an accelerator designer's point of view and gives an outline of the actual state of the art. The volume is intended as an introduction and as a reference for physicists, engineers and managers involved in this rapidly developing fiel
Fissioning universe: Topological inflation and Kaluza-Klein cosmologies
Energy Technology Data Exchange (ETDEWEB)
Kaku, Michio; Lykken, J.
1986-05-05
We propose a Kaluza-Klein cosmology by reversing the usual scenario: instead of starting with a flat 4+N dimensional universe in which N of the dimensions curl up into a compact manifold, we start with a compact 3+N dimensional manifold in which 3 of the dimensions are allowed to peel off and expand into the known universe. We reverse the usual ''spontaneous compactification'' scenario begin with a closed manifold Msup(3+N) which undergoes ''spontaneous fissioning'' into a product manifold M/sup 3/xMsup(N). Remarkably, the 3-dimensional universe M/sup 3/ can undergo a rapid de Sitter expansion large enough to solve the horizon and flatness problem. We call this ''topological inflation'', which we propose as an alternative to the usual GUT inflation. The inflationary phase automatically terminates into a big bang phase. (orig.).
The fissioning universe: Topological inflation and Kaluza-Klein cosmologies
International Nuclear Information System (INIS)
Kaku, Michio; Lykken, J.
1986-01-01
We propose a Kaluza-Klein cosmology by reversing the usual scenario: instead of starting with a flat 4+N dimensional universe in which N of the dimensions curl up into a compact manifold, we start with a compact 3+N dimensional manifold in which 3 of the dimensions are allowed to peel off and expand into the known universe. We reverse the usual ''spontaneous compactification'' scenario begin with a closed manifold Msup(3+N) which undergoes ''spontaneous fissioning'' into a product manifold M 3 xMsup(N). Remarkably, the 3-dimensional universe M 3 can undergo a rapid de Sitter expansion large enough to solve the horizon and flatness problem. We call this ''topological inflation'', which we propose as an alternative to the usual GUT inflation. The inflationary phase automatically terminates into a big bang phase. (orig.)
Various notions of amenability for not necessarily locally compact groupoids
Directory of Open Access Journals (Sweden)
Mădălina Roxana Buneci
2014-08-01
Full Text Available We start with a groupoid G endowed with a family W of subsets mimicking the properties of a neighborhood basis of the unit space (of a topological groupoid with paracompact unit space. Using the family W we endow each G-space with a uniform structure. The uniformities of the G-spaces allow us to define various notions of amenability for the G-equivariant maps. As in [C. Anantharaman-Delaroche and J. Renault, Amenable Groupoids. Monographie de L'Enseignement Mathematique No 36, Geneve, 2000], the amenability of the groupoid G is defined as the amenability of its range map. If the groupoid G is a group, all notions of amenability that we introduce coincide with the classical notion of amenability for topological (not necessarily locally-compact groups.
Topological and non-topological soliton solutions to some time ...
Indian Academy of Sciences (India)
topological soliton solutions to some time-fractional differential equations. M MIRZAZADEH ... Biswas et al [21,23–27] obtained optical solitons and soliton ..... nonlinear fractional partial differential equations in mathematical and physical sciences.
Spherical Orbifolds for Cosmic Topology
International Nuclear Information System (INIS)
Kramer, Peter
2012-01-01
Harmonic analysis is a tool to infer cosmic topology from the measured astrophysical cosmic microwave background CMB radiation. For overall positive curvature, Platonic spherical manifolds are candidates for this analysis. We combine the specific point symmetry of the Platonic manifolds with their deck transformations. This analysis in topology leads from manifolds to orbifolds. We discuss the deck transformations of the orbifolds and give eigenmodes for the harmonic analysis as linear combinations of Wigner polynomials on the 3-sphere. These provide new tools for detecting cosmic topology from the CMB radiation.
Topology optimised wavelength dependent splitters
DEFF Research Database (Denmark)
Hede, K. K.; Burgos Leon, J.; Frandsen, Lars Hagedorn
A photonic crystal wavelength dependent splitter has been constructed by utilising topology optimisation1. The splitter has been fabricated in a silicon-on-insulator material (Fig. 1). The topology optimised wavelength dependent splitter demonstrates promising 3D FDTD simulation results....... This complex photonic crystal structure is very sensitive against small fabrication variations from the expected topology optimised design. A wavelength dependent splitter is an important basic building block for high-performance nanophotonic circuits. 1J. S. Jensen and O. Sigmund, App. Phys. Lett. 84, 2022...
Topology optimization for coated structures
DEFF Research Database (Denmark)
Clausen, Anders; Andreassen, Erik; Sigmund, Ole
2015-01-01
This paper presents new results within the design of three-dimensional (3D) coated structures using topology optimization.The work is an extension of a recently published two-dimensional (2D) method for including coatedstructures into the minimum compliance topology optimization problem. The high...... level of control over key parameters demonstrated for the 2D model can likewise be achieved in 3D. The effectiveness of the approach isdemonstrated with numerical examples, which for the 3D problems have been solved using a parallel topology optimization implementation based on the PETSc toolkit....
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...
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.
Scalable Nonlinear Compact Schemes
Energy Technology Data Exchange (ETDEWEB)
Ghosh, Debojyoti [Argonne National Lab. (ANL), Argonne, IL (United States); Constantinescu, Emil M. [Univ. of Chicago, IL (United States); Brown, Jed [Univ. of Colorado, Boulder, CO (United States)
2014-04-01
In this work, we focus on compact schemes resulting in tridiagonal systems of equations, specifically the fifth-order CRWENO scheme. We propose a scalable implementation of the nonlinear compact schemes by implementing a parallel tridiagonal solver based on the partitioning/substructuring approach. We use an iterative solver for the reduced system of equations; however, we solve this system to machine zero accuracy to ensure that no parallelization errors are introduced. It is possible to achieve machine-zero convergence with few iterations because of the diagonal dominance of the system. The number of iterations is specified a priori instead of a norm-based exit criterion, and collective communications are avoided. The overall algorithm thus involves only point-to-point communication between neighboring processors. Our implementation of the tridiagonal solver differs from and avoids the drawbacks of past efforts in the following ways: it introduces no parallelization-related approximations (multiprocessor solutions are exactly identical to uniprocessor ones), it involves minimal communication, the mathematical complexity is similar to that of the Thomas algorithm on a single processor, and it does not require any communication and computation scheduling.
Performance assessment of topologically diverse power systems subjected to hurricane events
International Nuclear Information System (INIS)
Winkler, James; Duenas-Osorio, Leonardo; Stein, Robert; Subramanian, Devika
2010-01-01
Large tropical cyclones cause severe damage to major cities along the United States Gulf Coast annually. A diverse collection of engineering and statistical models are currently used to estimate the geographical distribution of power outage probabilities stemming from these hurricanes to aid in storm preparedness and recovery efforts. Graph theoretic studies of power networks have separately attempted to link abstract network topology to transmission and distribution system reliability. However, few works have employed both techniques to unravel the intimate connection between network damage arising from storms, topology, and system reliability. This investigation presents a new methodology combining hurricane damage predictions and topological assessment to characterize the impact of hurricanes upon power system reliability. Component fragility models are applied to predict failure probability for individual transmission and distribution power network elements simultaneously. The damage model is calibrated using power network component failure data for Harris County, TX, USA caused by Hurricane Ike in September of 2008, resulting in a mean outage prediction error of 15.59% and low standard deviation. Simulated hurricane events are then applied to measure the hurricane reliability of three topologically distinct transmission networks. The rate of system performance decline is shown to depend on their topological structure. Reliability is found to correlate directly with topological features, such as network meshedness, centrality, and clustering, and the compact irregular ring mesh topology is identified as particularly favorable, which can influence regional lifeline policy for retrofit and hardening activities to withstand hurricane events.
Performance assessment of topologically diverse power systems subjected to hurricane events
Energy Technology Data Exchange (ETDEWEB)
Winkler, James, E-mail: jwinkler@rice.ed [Rice University, Department of Civil and Environmental Engineering, 6100 Main Street, Houston, TX 77005 (United States); Duenas-Osorio, Leonardo, E-mail: leonardo.duenas-osorio@rice.ed [Rice University, Department of Civil and Environmental Engineering, 6100 Main Street, Houston, TX 77005 (United States); Stein, Robert, E-mail: stein@rice.ed [Rice University, Department of Political Science, 6100 Main Street, Houston, TX 77005 (United States); Subramanian, Devika, E-mail: devika@rice.ed [Rice University, Department of Computer Science, 6100 Main Street, Houston, TX 77005 (United States); Rice University, Department of Electrical Engineering, 6100 Main Street, Houston, TX 77005 (United States)
2010-04-15
Large tropical cyclones cause severe damage to major cities along the United States Gulf Coast annually. A diverse collection of engineering and statistical models are currently used to estimate the geographical distribution of power outage probabilities stemming from these hurricanes to aid in storm preparedness and recovery efforts. Graph theoretic studies of power networks have separately attempted to link abstract network topology to transmission and distribution system reliability. However, few works have employed both techniques to unravel the intimate connection between network damage arising from storms, topology, and system reliability. This investigation presents a new methodology combining hurricane damage predictions and topological assessment to characterize the impact of hurricanes upon power system reliability. Component fragility models are applied to predict failure probability for individual transmission and distribution power network elements simultaneously. The damage model is calibrated using power network component failure data for Harris County, TX, USA caused by Hurricane Ike in September of 2008, resulting in a mean outage prediction error of 15.59% and low standard deviation. Simulated hurricane events are then applied to measure the hurricane reliability of three topologically distinct transmission networks. The rate of system performance decline is shown to depend on their topological structure. Reliability is found to correlate directly with topological features, such as network meshedness, centrality, and clustering, and the compact irregular ring mesh topology is identified as particularly favorable, which can influence regional lifeline policy for retrofit and hardening activities to withstand hurricane events.
A compact codimension-two braneworld with precisely one brane
International Nuclear Information System (INIS)
Akerblom, Nikolas; Cornelissen, Gunther
2010-01-01
Building on earlier work on football-shaped extra dimensions, we construct a compact codimension-two braneworld with precisely one brane. The two extra dimensions topologically represent a 2-torus which is stabilized by a bulk cosmological constant and magnetic flux. The torus has positive constant curvature almost everywhere, except for a single conical singularity at the location of the brane. In contradistinction to the football-shaped case, there is no fine-tuning required for the brane tension. We also present some plausibility arguments why the model should not suffer from serious stability issues.
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
Topological characteristics of model gels
International Nuclear Information System (INIS)
Miller, Mark A; Hansen, Jean-Pierre; Blaak, Ronald
2010-01-01
The Euler characteristic of an object is a topological invariant determined by the number of handles and holes that it contains. Here, we use the Euler characteristic to profile the topology of model three-dimensional gel-forming fluids as a function of increasing length scale. These profiles act as a 'topological fingerprint' of the structure, and can be interpreted in terms of three types of topological events. As model fluids we have considered a system of dipolar dumbbells, and suspensions of adhesive hard spheres with isotropic and patchy interactions in turn. The correlation between the percolation threshold and the length scale on which the Euler characteristic passes through zero is examined and found to be system-dependent. A scheme for the efficient calculation of the Euler characteristic with and without periodic boundary conditions is described.
Intuitive concepts in elementary topology
Arnold, BH
2011-01-01
Classroom-tested and much-cited, this concise text is designed for undergraduates. It offers a valuable and instructive introduction to the basic concepts of topology, taking an intuitive rather than an axiomatic viewpoint. 1962 edition.
Topology Based Domain Search (TBDS)
National Research Council Canada - National Science Library
Manning, William
2002-01-01
This effort will explore radical changes in the way Domain Name System (DNS) is used by endpoints in a network to improve the resilience of the endpoint and its applications in the face of dynamically changing infrastructure topology...
A topological quantum optics interface.
Barik, Sabyasachi; Karasahin, Aziz; Flower, Christopher; Cai, Tao; Miyake, Hirokazu; DeGottardi, Wade; Hafezi, Mohammad; Waks, Edo
2018-02-09
The application of topology in optics has led to a new paradigm in developing photonic devices with robust properties against disorder. Although considerable progress on topological phenomena has been achieved in the classical domain, the realization of strong light-matter coupling in the quantum domain remains unexplored. We demonstrate a strong interface between single quantum emitters and topological photonic states. Our approach creates robust counterpropagating edge states at the boundary of two distinct topological photonic crystals. We demonstrate the chiral emission of a quantum emitter into these modes and establish their robustness against sharp bends. This approach may enable the development of quantum optics devices with built-in protection, with potential applications in quantum simulation and sensing. Copyright © 2018 The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. No claim to original U.S. Government Works.
Topology optimized electrothermal polysilicon microgrippers
DEFF Research Database (Denmark)
Sardan Sukas, Özlem; Petersen, Dirch Hjorth; Mølhave, Kristian
2008-01-01
This paper presents the topology optimized design procedure and fabrication of electrothermal polysilicon microgrippers for nanomanipulation purposes. Performance of the optimized microactuators is compared with a conventional three-beam microactuator design through finite element analysis...
Two-dimensional topological photonics
Khanikaev, Alexander B.; Shvets, Gennady
2017-12-01
Originating from the studies of two-dimensional condensed-matter states, the concept of topological order has recently been expanded to other fields of physics and engineering, particularly optics and photonics. Topological photonic structures have already overturned some of the traditional views on wave propagation and manipulation. The application of topological concepts to guided wave propagation has enabled novel photonic devices, such as reflection-free sharply bent waveguides, robust delay lines, spin-polarized switches and non-reciprocal devices. Discrete degrees of freedom, widely used in condensed-matter physics, such as spin and valley, are now entering the realm of photonics. In this Review, we summarize the latest advances in this highly dynamic field, with special emphasis on the experimental work on two-dimensional photonic topological structures.
Topological gravity with minimal matter
International Nuclear Information System (INIS)
Li Keke
1991-01-01
Topological minimal matter, obtained by twisting the minimal N = 2 supeconformal field theory, is coupled to two-dimensional topological gravity. The free field formulation of the coupled system allows explicit representations of BRST charge, physical operators and their correlation functions. The contact terms of the physical operators may be evaluated by extending the argument used in a recent solution of topological gravity without matter. The consistency of the contact terms in correlation functions implies recursion relations which coincide with the Virasoro constraints derived from the multi-matrix models. Topological gravity with minimal matter thus provides the field theoretic description for the multi-matrix models of two-dimensional quantum gravity. (orig.)
Renormalization of topological field theory
International Nuclear Information System (INIS)
Birmingham, D.; Rakowski, M.; Thompson, G.
1988-11-01
One loop corrections to topological field theory in three and four dimensions are presented. By regularizing determinants, we compute the effective action and β-function in four dimensional topological Yang-Mills theory and find that the BRST symmetry is preserved. Moreover, the minima of the effective action still correspond to instanton configurations. In three dimensions, an analysis of the Chern-Simons theory shows that the topological nature of the theory is also preserved to this order. In addition, we find that this theory possesses an extra supersymmetry when quantized in the Landau gauge. Using dimensional regularization, we then study the Ward identities of the extended BRST symmetry in the three dimensional topological Yang-Mills-Higgs model. (author). 22 refs
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 ...
Advances in compact torus research
International Nuclear Information System (INIS)
1986-05-01
A compact torus is a low aspect ratio, axisymmetric, closed magnetic field line configuration with no vessel wall or magnetic field coils linking the hole in the plasma toroid. This concept offers reactor advantages such as simplicity, high β, and the possibility of translation. Several methods have been used to generate compact toroids, including plasma guns, high energy particle rings, and field-reversed theta pinches. This document summarizes the results of recent work on compact toroids, presented at the first IAEA Technical Committee Meeting on Compact Torus Research held in Sydney, Australia from 4 to 7 March 1985
Boundedly controlled topology foundations of algebraic topology and simple homotopy theory
Anderson, Douglas R
1988-01-01
Several recent investigations have focused attention on spaces and manifolds which are non-compact but where the problems studied have some kind of "control near infinity". This monograph introduces the category of spaces that are "boundedly controlled" over the (usually non-compact) metric space Z. It sets out to develop the algebraic and geometric tools needed to formulate and to prove boundedly controlled analogues of many of the standard results of algebraic topology and simple homotopy theory. One of the themes of the book is to show that in many cases the proof of a standard result can be easily adapted to prove the boundedly controlled analogue and to provide the details, often omitted in other treatments, of this adaptation. For this reason, the book does not require of the reader an extensive background. In the last chapter it is shown that special cases of the boundedly controlled Whitehead group are strongly related to lower K-theoretic groups, and the boundedly controlled theory is compared to Sie...
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.
Topology Optimized Photonic Wire Splitters
DEFF Research Database (Denmark)
Frandsen, Lars Hagedorn; Borel, Peter Ingo; Jensen, Jakob Søndergaard
2006-01-01
Photonic wire splitters have been designed using topology optimization. The splitters have been fabricated in silicon-on-insulator material and display broadband low-loss 3dB splitting in a bandwidth larger than 100 nm.......Photonic wire splitters have been designed using topology optimization. The splitters have been fabricated in silicon-on-insulator material and display broadband low-loss 3dB splitting in a bandwidth larger than 100 nm....
Topology Optimization of Nanophotonic Devices
DEFF Research Database (Denmark)
Yang, Lirong
This thesis explores the various aspects of utilizing topology optimization in designing nanophotonic devices. Either frequency-domain or time-domain methods is used in combination with the optimization algorithms, depending on various aims of the designing problems. The frequency-domain methods...... lengthscale and flexible pulse delay are addressed to demonstrate time-domain based topology optimization’s potential in designing complicated photonic structures with specifications on the time characteristics of pulses....
Symmetry and topology in evolution
International Nuclear Information System (INIS)
Lukacs, B.; Berczi, S.; Molnar, I.; Paal, G.
1991-10-01
This volume contains papers of an interdisciplinary symposium on evolution. The aim of this symposium, held in Budapest, Hungary, 28-29 May 1991, was to clear the role of symmetry and topology at different levels of the evolutionary processes. 21 papers were presented, their topics included evolution of the Universe, symmetry of elementary particles, asymmetry of the Earth, symmetry and asymmetry of biomolecules, symmetry and topology of lining objects, human asymmetry etc. (R.P.)
Topological Fidelity in Sensor Networks
Chintakunta, Harish; Krim, Hamid
2011-01-01
Sensor Networks are inherently complex networks, and many of their associated problems require analysis of some of their global characteristics. These are primarily affected by the topology of the network. We present in this paper, a general framework for a topological analysis of a network, and develop distributed algorithms in a generalized combinatorial setting in order to solve two seemingly unrelated problems, 1) Coverage hole detection and Localization and 2) Worm hole attack detection ...
Topological excitations in semiconductor heterostructures
International Nuclear Information System (INIS)
Koushik, R.; Mukerjee, Subroto; Ghosh, Arindam; Baenninger, Matthias; Narayan, Vijay; Pepper, Michael; Farrer, Ian; Ritchie, David A.
2013-01-01
Topological defects play an important role in the melting phenomena in two-dimensions. In this work, we report experimental observation of topological defect induced melting in two-dimensional electron systems (2DES) in the presence of strong Coulomb interaction and disorder. The phenomenon is characterised by measurement of conductivity which goes to zero in a Berezinskii-Kosterlitz-Thouless like transition. Further evidence is provided via low-frequency conductivity noise measurements
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.
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)
Topology change and quantum physics
International Nuclear Information System (INIS)
Balachandran, A.P.; Marmo, G.; Simoni, A.
1995-03-01
The role of topology in elementary quantum physics is discussed in detail. It is argued that attributes of classical spatial topology emerge from properties of state vectors with suitably smooth time evolution. Equivalently, they emerge from considerations on the domain of the quantum Hamiltonian, this domain being often specified by boundary conditions in elementary quantum physics. Several examples are presented where classical topology is changed by smoothly altering the boundary conditions. When the parameters labelling the latter are treated as quantum variables, quantum states need not give a well-defined classical topology, instead they can give a quantum superposition of such topologies. An existing argument of Sorkin based on the spin-statistics connection and indicating the necessity of topology change in quantum gravity is recalled. It is suggested therefrom and our results here that Einstein gravity and its minor variants are effective theories of a deeper description with additional novel degrees of freedom. Other reasons for suspecting such a microstructure are also summarized. (author). 22 refs, 3 figs
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
Continuous-variable topological codes
Morimae, Tomoyuki
2013-10-01
Topological code is a stabilizer quantum error correcting code whose generators are local but logical operators are topologically nontrivial and nonlocal. It offers interesting features such as the homological deformations of string operators and anyonic excitations on it. Topological codes are also closely related to the “topological order,” which has been an important concept in condensed-matter physics. In this paper, we consider continuous-variable versions of topological codes, including the toric code by Kitaev [A. Y. Kitaev, Ann. Phys.APNYA60003-491610.1016/S0003-4916(02)00018-0 303, 2 (2003)] with a single type of stabilizer on the checkerboard lattice, and the color code by Bombin and Martin-Delgado [H. Bombin and M. A. Martin-Delgado, Phys. Rev. Lett.PRLTAO0031-900710.1103/PhysRevLett.97.180501 97, 180501 (2006)]. We show that it is possible to consider continuous-variable analog of these topological codes.
Galois conjugates of topological phases
Freedman, M. H.; Gukelberger, J.; Hastings, M. B.; Trebst, S.; Troyer, M.; Wang, Z.
2012-01-01
Galois conjugation relates unitary conformal field theories and topological quantum field theories (TQFTs) to their nonunitary counterparts. Here we investigate Galois conjugates of quantum double models, such as the Levin-Wen model. While these Galois-conjugated Hamiltonians are typically non-Hermitian, we find that their ground-state wave functions still obey a generalized version of the usual code property (local operators do not act on the ground-state manifold) and hence enjoy a generalized topological protection. The key question addressed in this paper is whether such nonunitary topological phases can also appear as the ground states of Hermitian Hamiltonians. Specific attempts at constructing Hermitian Hamiltonians with these ground states lead to a loss of the code property and topological protection of the degenerate ground states. Beyond this, we rigorously prove that no local change of basis can transform the ground states of the Galois-conjugated doubled Fibonacci theory into the ground states of a topological model whose Hermitian Hamiltonian satisfies Lieb-Robinson bounds. These include all gapped local or quasilocal Hamiltonians. A similar statement holds for many other nonunitary TQFTs. One consequence is that these nonunitary TQFTs do not describe physical realizations of topological phases. In particular, this implies that the “Gaffnian” wave function can not be the ground state of a gapped fractional quantum Hall state.
High Impact Technology Compact Combustion (HITCC) Compact Core Technologies
2016-01-01
were combusted in a vitiated stream. The molecular weight and hydrogen -to-carbon ratios of these fuels were measured by Princeton University [17...AFRL-RQ-WP-TR-2016-0010 HIGH IMPACT TECHNOLOGY COMPACT COMBUSTION (HITCC) COMPACT CORE TECHNOLOGIES Andrew W. Caswell Combustion ...ANDREW W. CASWELL CHARLES J. CROSS, Branch Chief Program Engineer Combustion Branch Combustion Branch Turbine Engine Division Turbine
Isometric coactions of compact quantum groups on compact ...
Indian Academy of Sciences (India)
We propose a notion of isometric coaction of a compact quantum group on a compact quantum metric space in the framework of Rieffel, where the metric structure is given by a Lipnorm. Within this setting we study the problem of the existence of a quantum isometry group.
International Nuclear Information System (INIS)
Schmidt, J.
1987-01-01
The author discusses his lab's plan for completing the Compact Ignition Tokamak (CIT) conceptual design during calendar year 1987. Around July 1 they froze the subsystem envelopes on the device to continue with the conceptual design. They did this by formalizing a general requirements document. They have been developing the management plan and submitted a version to the DOE July 10. He describes a group of management activities. They released the vacuum vessel Request For Proposals (RFP) on August 5. An RFP to do a major part of the system engineering on the device is being developed. They intend to assemble the device outside of the test cell, then move it into the the test cell, install it there, and bring to the test cell many of the auxiliary facilities from TFTR, for example, power supplies
International Nuclear Information System (INIS)
Wachter, W.J.
1988-01-01
A method and apparatus for compacting spent fuel rods comprises transferring the rods from a nuclear fuel rod assembly into a different nuclear fuel rod container having a smaller cross section than the assembly. The individual rods are moved from a fuel assembly and through a transition funnel by movable grippers at opposite ends of the funnel. One movable gripper reciprocates between gripping and release positions in a gap between the fuel assembly and the transition funnel. All of the fuel rods are withdrawn concurrently and are merged towards one another into a tighter array within the transition funnel and emerge as a bundle. A movable and a stationary bundle gripper are provided between the funnel and the storage container to advance the bundle of fuel rods into the container. (author)
Compact cryocooler heat exchangers
International Nuclear Information System (INIS)
Luna, J.; Frederking, T.H.K.
1991-01-01
Compact heat exchangers are subject to different constraints as a room temperature gas is cooled down by a cold stream returning from a JT valve (or a similar cryoprocess component). In particular, the optimization of exchangers for liquid helium systems has to cover a wide range in temperature and density of the fluid. In the present work we address the following thermodynamic questions: 1. The optimization of intermediate temperatures which optimize stage operation (a stage is assumed to have a constant cross section); 2. The optimum temperature difference available for best overall economic performance values. The results are viewed in the context of porous media concepts applied to rather low speeds of fluid flow in narrow passages. In this paper examples of fluid/solid constraints imposed in this non-classical low temperature area are presented
Energy Technology Data Exchange (ETDEWEB)
Elizondo-Decanini, Juan M.
2017-08-29
A compact particle accelerator having an input portion configured to receive power to produce particles for acceleration, where the input portion includes a switch, is provided. In a general embodiment, a vacuum tube receives particles produced from the input portion at a first end, and a plurality of wafer stacks are positioned serially along the vacuum tube. Each of the plurality of wafer stacks include a dielectric and metal-oxide pair, wherein each of the plurality of wafer stacks further accelerate the particles in the vacuum tube. A beam shaper coupled to a second end of the vacuum tube shapes the particles accelerated by the plurality of wafer stacks into a beam and an output portion outputs the beam.
Compact vacuum insulation embodiments
Benson, D.K.; Potter, T.F.
1992-04-28
An ultra-thin compact vacuum insulation panel is comprised of two hard, but bendable metal wall sheets closely spaced apart from each other and welded around the edges to enclose a vacuum chamber. Glass or ceramic spacers hold the wall sheets apart. The spacers can be discrete spherical beads or monolithic sheets of glass or ceramic webs with nodules protruding therefrom to form essentially point' or line' contacts with the metal wall sheets. In the case of monolithic spacers that form line' contacts, two such spacers with the line contacts running perpendicular to each other form effectively point' contacts at the intersections. Corrugations accommodate bending and expansion, tubular insulated pipes and conduits, and preferred applications are also included. 26 figs.
Benson, D.K.; Potter, T.F.
1993-01-05
An ultra-thin compact vacuum insulation panel is comprised of two hard, but bendable metal wall sheets closely spaced apart from each other and welded around the edges to enclose a vacuum chamber. Glass or ceramic spacers hold the wall sheets apart. The spacers can be discrete spherical beads or monolithic sheets of glass or ceramic webs with nodules protruding therefrom to form essentially point'' or line'' contacts with the metal wall sheets. In the case of monolithic spacers that form line'' contacts, two such spacers with the line contacts running perpendicular to each other form effectively point'' contacts at the intersections. Corrugations accommodate bending and expansion, tubular insulated pipes and conduits, and preferred applications are also included.
Yu, Siyuan; Lourtioz, Jean-Michel
2014-01-01
This book brings together in a single volume a unique contribution by the top experts around the world in the field of compact semiconductor lasers to provide a comprehensive description and analysis of the current status as well as future directions in the field of micro- and nano-scale semiconductor lasers. It is organized according to the various forms of micro- or nano-laser cavity configurations with each chapter discussing key technical issues, including semiconductor carrier recombination processes and optical gain dynamics, photonic confinement behavior and output coupling mechanisms, carrier transport considerations relevant to the injection process, and emission mode control. Required reading for those working in and researching the area of semiconductors lasers and micro-electronics.
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.
International Nuclear Information System (INIS)
Lake, Matthew; Thomas, Steven; Ward, John
2010-01-01
We propose a mechanism for the creation of cosmic string loops with dynamically stabilised windings in the internal space. Assuming a velocity correlations regime in the post-inflationary epoch, such windings are seen to arise naturally in string networks prior to loop formation. The angular momentum of the string in the compact space may then be sufficient to ensure that the windings remain stable after the loop chops off from the network, even if the internal manifold is simply connected. For concreteness we embed our model in the Klebanov-Strassler geometry, which provides a natural mechanism for brane inflation, as well a being one of the best understood compactification schemes in type IIB string theory. We see that the interaction of angular momentum with the string tension causes the loop to oscillate between phases of expansion and contraction. This, in principle, should give rise to a distinct gravitational wave signature, the future detection of which could provide indirect evidence for the existence of extra dimensions
COMPACTION CHARACTERISTICS OF IGUMALE SHALE
African Journals Online (AJOL)
*
In 1933 Proctor first conducted tests on compaction for application to construction of earth fill dams in California. Results published by. Proctor (1933) showed that with a given amount of compaction, there exists for each soil a moisture content, termed the optimum moisture content (OMC) at which a maximum dry density.
Roller-compacted concrete pavements.
2010-09-01
Roller-compacted concrete (RCC) gets its name from the heavy vibratory steel drum and rubber-tired rollers used to help compact it into its final form. RCC has similar strength properties and consists of the same basic ingredients as conventional con...
Mirror symmetry, toric branes and topological string amplitudes as polynomials
International Nuclear Information System (INIS)
Alim, Murad
2009-01-01
The central theme of this thesis is the extension and application of mirror symmetry of topological string theory. The contribution of this work on the mathematical side is given by interpreting the calculated partition functions as generating functions for mathematical invariants which are extracted in various examples. Furthermore the extension of the variation of the vacuum bundle to include D-branes on compact geometries is studied. Based on previous work for non-compact geometries a system of differential equations is derived which allows to extend the mirror map to the deformation spaces of the D-Branes. Furthermore, these equations allow the computation of the full quantum corrected superpotentials which are induced by the D-branes. Based on the holomorphic anomaly equation, which describes the background dependence of topological string theory relating recursively loop amplitudes, this work generalizes a polynomial construction of the loop amplitudes, which was found for manifolds with a one dimensional space of deformations, to arbitrary target manifolds with arbitrary dimension of the deformation space. The polynomial generators are determined and it is proven that the higher loop amplitudes are polynomials of a certain degree in the generators. Furthermore, the polynomial construction is generalized to solve the extension of the holomorphic anomaly equation to D-branes without deformation space. This method is applied to calculate higher loop amplitudes in numerous examples and the mathematical invariants are extracted. (orig.)
Mirror symmetry, toric branes and topological string amplitudes as polynomials
Energy Technology Data Exchange (ETDEWEB)
Alim, Murad
2009-07-13
The central theme of this thesis is the extension and application of mirror symmetry of topological string theory. The contribution of this work on the mathematical side is given by interpreting the calculated partition functions as generating functions for mathematical invariants which are extracted in various examples. Furthermore the extension of the variation of the vacuum bundle to include D-branes on compact geometries is studied. Based on previous work for non-compact geometries a system of differential equations is derived which allows to extend the mirror map to the deformation spaces of the D-Branes. Furthermore, these equations allow the computation of the full quantum corrected superpotentials which are induced by the D-branes. Based on the holomorphic anomaly equation, which describes the background dependence of topological string theory relating recursively loop amplitudes, this work generalizes a polynomial construction of the loop amplitudes, which was found for manifolds with a one dimensional space of deformations, to arbitrary target manifolds with arbitrary dimension of the deformation space. The polynomial generators are determined and it is proven that the higher loop amplitudes are polynomials of a certain degree in the generators. Furthermore, the polynomial construction is generalized to solve the extension of the holomorphic anomaly equation to D-branes without deformation space. This method is applied to calculate higher loop amplitudes in numerous examples and the mathematical invariants are extracted. (orig.)
Test fields on compact spacetimes: Problems, some partial results and speculations
International Nuclear Information System (INIS)
Yurtsever, U.
1989-09-01
In this paper we study some basic aspects of (Lorentzian) field theory on compact Lorentz manifolds. All compact spacetimes are acausal, i.e. possess closed timelike curves; this makes them a useful testbed in analyzing some new notions of causality that we will introduce for more general acausal spacetimes. In addition, studying compact spacetimes in their own right raises a wide range of fascinating mathematical problems some of which we will explore. We will see that it is reasonable to expect Lorentzian field theory on a compact spacetime to provide information on the topology of the underlying manifold; if this is true, then this information is likely to be ''orthogonal'' (or complementary) to the information obtained through the study of Euclidean field theory. (author). 45 refs, 2 figs
Topological strings from quantum mechanics
Energy Technology Data Exchange (ETDEWEB)
Grassi, Alba; Marino, Marcos [Geneve Univ. (Switzerland). Dept. de Physique Theorique et Section de Mathematique; Hatsuda, Yasuyuki [Deutsches Elektronen-Synchrotron (DESY), Hamburg (Germany). Theory Group
2014-12-15
We propose a general correspondence which associates a non-perturbative quantum-mechanical operator to a toric Calabi-Yau manifold, and we conjecture an explicit formula for its spectral determinant in terms of an M-theoretic version of the topological string free energy. As a consequence, we derive an exact quantization condition for the operator spectrum, in terms of the vanishing of a generalized θ function. The perturbative part of this quantization condition is given by the Nekrasov-Shatashvili limit of the refined topological string, but there are non-perturbative corrections determined by the conventional topological string. We analyze in detail the cases of local P{sup 2}, local P{sup 1} x P{sup 1} and local F{sub 1}. In all these cases, the predictions for the spectrum agree with the existing numerical results. We also show explicitly that our conjectured spectral determinant leads to the correct spectral traces of the corresponding operators, which are closely related to topological string theory at orbifold points. Physically, our results provide a Fermi gas picture of topological strings on toric Calabi-Yau manifolds, which is fully non-perturbative and background independent. They also suggest the existence of an underlying theory of M2 branes behind this formulation. Mathematically, our results lead to precise, surprising conjectures relating the spectral theory of functional difference operators to enumerative geometry.
Magnonic topological insulators in antiferromagnets
Nakata, Kouki; Kim, Se Kwon; Klinovaja, Jelena; Loss, Daniel
2017-12-01
Extending the notion of symmetry protected topological phases to insulating antiferromagnets (AFs) described in terms of opposite magnetic dipole moments associated with the magnetic N e ´el order, we establish a bosonic counterpart of topological insulators in semiconductors. Making use of the Aharonov-Casher effect, induced by electric field gradients, we propose a magnonic analog of the quantum spin Hall effect (magnonic QSHE) for edge states that carry helical magnons. We show that such up and down magnons form the same Landau levels and perform cyclotron motion with the same frequency but propagate in opposite direction. The insulating AF becomes characterized by a topological Z2 number consisting of the Chern integer associated with each helical magnon edge state. Focusing on the topological Hall phase for magnons, we study bulk magnon effects such as magnonic spin, thermal, Nernst, and Ettinghausen effects, as well as the thermomagnetic properties of helical magnon transport both in topologically trivial and nontrivial bulk AFs and establish the magnonic Wiedemann-Franz law. We show that our predictions are within experimental reach with current device and measurement techniques.
Braiding knots with topological strings
International Nuclear Information System (INIS)
Gu, Jie
2015-08-01
For an arbitrary knot in a three-sphere, the Ooguri-Vafa conjecture associates to it a unique stack of branes in type A topological string on the resolved conifold, and relates the colored HOMFLY invariants of the knot to the free energies on the branes. For torus knots, we use a modified version of the topological recursion developed by Eynard and Orantin to compute the free energies on the branes from the Aganagic-Vafa spectral curves of the branes, and find they are consistent with the known colored HOMFLY knot invariants a la the Ooguri-Vafa conjecture. In addition our modified topological recursion can reproduce the correct closed string free energies, which encode the information of the background geometry. We conjecture the modified topological recursion is applicable for branes associated to hyperbolic knots as well, encouraged by the observation that the modified topological recursion yields the correct planar closed string free energy from the Aganagic-Vafa spectral curves of hyperbolic knots. This has implications for the knot theory concerning distinguishing mutant knots with colored HOMFLY invariants. Furthermore, for hyperbolic knots, we present methods to compute colored HOMFLY invariants in nonsymmetric representations of U(N). The key step in this computation is computing quantum 6j-symbols in the quantum group U q (sl N ).
Topological strings from quantum mechanics
International Nuclear Information System (INIS)
Grassi, Alba; Marino, Marcos; Hatsuda, Yasuyuki
2014-12-01
We propose a general correspondence which associates a non-perturbative quantum-mechanical operator to a toric Calabi-Yau manifold, and we conjecture an explicit formula for its spectral determinant in terms of an M-theoretic version of the topological string free energy. As a consequence, we derive an exact quantization condition for the operator spectrum, in terms of the vanishing of a generalized θ function. The perturbative part of this quantization condition is given by the Nekrasov-Shatashvili limit of the refined topological string, but there are non-perturbative corrections determined by the conventional topological string. We analyze in detail the cases of local P 2 , local P 1 x P 1 and local F 1 . In all these cases, the predictions for the spectrum agree with the existing numerical results. We also show explicitly that our conjectured spectral determinant leads to the correct spectral traces of the corresponding operators, which are closely related to topological string theory at orbifold points. Physically, our results provide a Fermi gas picture of topological strings on toric Calabi-Yau manifolds, which is fully non-perturbative and background independent. They also suggest the existence of an underlying theory of M2 branes behind this formulation. Mathematically, our results lead to precise, surprising conjectures relating the spectral theory of functional difference operators to enumerative geometry.
Effective Topological Charge Cancelation Mechanism.
Mesarec, Luka; Góźdź, Wojciech; Iglič, Aleš; Kralj, Samo
2016-06-01
Topological defects (TDs) appear almost unavoidably in continuous symmetry breaking phase transitions. The topological origin makes their key features independent of systems' microscopic details; therefore TDs display many universalities. Because of their strong impact on numerous material properties and their significant role in several technological applications it is of strong interest to find simple and robust mechanisms controlling the positioning and local number of TDs. We present a numerical study of TDs within effectively two dimensional closed soft films exhibiting in-plane orientational ordering. Popular examples of such class of systems are liquid crystalline shells and various biological membranes. We introduce the Effective Topological Charge Cancellation mechanism controlling localised positional assembling tendency of TDs and the formation of pairs {defect, antidefect} on curved surfaces and/or presence of relevant "impurities" (e.g. nanoparticles). For this purpose, we define an effective topological charge Δmeff consisting of real, virtual and smeared curvature topological charges within a surface patch Δς identified by the typical spatially averaged local Gaussian curvature K. We demonstrate a strong tendency enforcing Δmeff → 0 on surfaces composed of Δς exhibiting significantly different values of spatially averaged K. For Δmeff ≠ 0 we estimate a critical depinning threshold to form pairs {defect, antidefect} using the electrostatic analogy.
Topological Strings and Integrable Hierarchies
Aganagic, M; Klemm, A D; Marino, M; Vafa, C; Aganagic, Mina; Dijkgraaf, Robbert; Klemm, Albrecht; Marino, Marcos; Vafa, Cumrun
2006-01-01
We consider the topological B-model on local Calabi-Yau geometries. We show how one can solve for the amplitudes by using W-algebra symmetries which encodes the symmetries of holomorphic diffeomorphisms of the Calabi-Yau. In the highly effective fermionic/brane formulation this leads to a free fermion description of the amplitudes. Furthermore we argue that topological strings on Calabi-Yau geometries provide a unifying picture connecting non-critical (super)strings, integrable hierarchies, and various matrix models. In particular we show how the ordinary matrix model, the double scaling limit of matrix models, and Kontsevich-like matrix model are all related and arise from studying branes in specific local Calabi-Yau three-folds. We also show how A-model topological string on P^1 and local toric threefolds (and in particular the topological vertex) can be realized and solved as B-model topological string amplitudes on a Calabi-Yau manifold.
Compact Dexterous Robotic Hand
Lovchik, Christopher Scott (Inventor); Diftler, Myron A. (Inventor)
2001-01-01
A compact robotic hand includes a palm housing, a wrist section, and a forearm section. The palm housing supports a plurality of fingers and one or more movable palm members that cooperate with the fingers to grasp and/or release an object. Each flexible finger comprises a plurality of hingedly connected segments, including a proximal segment pivotally connected to the palm housing. The proximal finger segment includes at least one groove defining first and second cam surfaces for engagement with a cable. A plurality of lead screw assemblies each carried by the palm housing are supplied with power from a flexible shaft rotated by an actuator and output linear motion to a cable move a finger. The cable is secured within a respective groove and enables each finger to move between an opened and closed position. A decoupling assembly pivotally connected to a proximal finger segment enables a cable connected thereto to control movement of an intermediate and distal finger segment independent of movement of the proximal finger segment. The dexterous robotic hand closely resembles the function of a human hand yet is light weight and capable of grasping both heavy and light objects with a high degree of precision.
Leung, Ka-Ngo; Lou, Tak Pui
2005-03-22
A compact neutron generator has at its outer circumference a toroidal shaped plasma chamber in which a tritium (or other) plasma is generated. A RF antenna is wrapped around the plasma chamber. A plurality of tritium ion beamlets are extracted through spaced extraction apertures of a plasma electrode on the inner surface of the toroidal plasma chamber and directed inwardly toward the center of neutron generator. The beamlets pass through spaced acceleration and focusing electrodes to a neutron generating target at the center of neutron generator. The target is typically made of titanium tubing. Water is flowed through the tubing for cooling. The beam can be pulsed rapidly to achieve ultrashort neutron bursts. The target may be moved rapidly up and down so that the average power deposited on the surface of the target may be kept at a reasonable level. The neutron generator can produce fast neutrons from a T-T reaction which can be used for luggage and cargo interrogation applications. A luggage or cargo inspection system has a pulsed T-T neutron generator or source at the center, surrounded by associated gamma detectors and other components for identifying explosives or other contraband.
Benson, D.K.; Potter, T.F.
1992-10-27
Improved compact insulation panel is provided which is comprised of two adjacent metal sheets spaced close together with a plurality of spherical, or other discretely shaped, glass or ceramic beads optimally positioned between the sheets to provide support and maintain the spacing between the metal sheets when the gases there between are evacuated to form a vacuum. These spherical glass beads provide the maximum support while minimizing thermal conductance. In its preferred embodiment; these two metal sheets are textured with ribs or concave protrusions in conjunction with the glass beads to maximize the structural integrity of the panels while increasing the spacing between beads, thereby reducing the number of beads and the number of thermal conduction paths. Glass or porcelain-enameled liners in combination with the glass spacers and metal sidewalls effectively decrease thermal conductivity, and various laminates, including wood, porcelain-enameled metal, and others effectively increase the strength and insulation capabilities of the panels. Also, a metal web is provided to hold the spacers in place, and strategic grooves are shown to accommodate expansion and contraction or shaping of the panels. 35 figs.
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.
Aeroelastic Wingbox Stiffener Topology Optimization
Stanford, Bret K.
2017-01-01
This work considers an aeroelastic wingbox model seeded with run-out blade stiffeners along the skins. Topology optimization is conducted within the shell webs of the stiffeners, in order to add cutouts and holes for mass reduction. This optimization is done with a global-local approach in order to moderate the computational cost: aeroelastic loads are computed at the wing-level, but the topology and sizing optimization is conducted at the panel-level. Each panel is optimized separately under stress, buckling, and adjacency constraints, and periodically reassembled to update the trimmed aeroelastic loads. The resulting topology is baselined against a design with standard full-depth solid stiffener blades, and found to weigh 7.43% less.
Topology of helical fluid flow
DEFF Research Database (Denmark)
Andersen, Morten; Brøns, Morten
2014-01-01
Phys. Fluids 25, 1949–1952) contains an infinite sum of modified Bessel functions. Using the approach by Okulov (Okulov, V. L. 1995 Russ. J. Eng. Thermophys. 5, 63–75) we obtain a closed-form approximation which is considerably easier to analyse. Critical points of the stream function can be found from...... function for the topology of the streamline pattern in incompressible flows. On this basis, we perform a comprehensive study of the topology of the flow field generated by a helical vortex filament in an ideal fluid. The classical expression for the stream function obtained by Hardin (Hardin, J. C. 1982...... the zeroes of a single real function of one variable, and we show that three different flow topologies can occur, depending on a single dimensionless parameter. By including the self-induced velocity on the vortex filament by a localised induction approximation, the stream function is slightly modified...
Topology optimization of flexoelectric structures
Nanthakumar, S. S.; Zhuang, Xiaoying; Park, Harold S.; Rabczuk, Timon
2017-08-01
We present a mixed finite element formulation for flexoelectric nanostructures that is coupled with topology optimization to maximize their intrinsic material performance with regards to their energy conversion potential. Using Barium Titanate (BTO) as the model flexoelectric material, we demonstrate the significant enhancement in energy conversion that can be obtained using topology optimization. We also demonstrate that non-smooth surfaces can play a key role in the energy conversion enhancements obtained through topology optimization. Finally, we examine the relative benefits of flexoelectricity, and surface piezoelectricity on the energy conversion efficiency of nanobeams. We find that the energy conversion efficiency of flexoelectric nanobeams is comparable to the energy conversion efficiency obtained from nanobeams whose electromechanical coupling occurs through surface piezoelectricity, but are ten times thinner. Overall, our results not only demonstrate the utility and efficiency of flexoelectricity as a nanoscale energy conversion mechanism, but also its relative superiority as compared to piezoelectric or surface piezoelectric effects.
Development of Active External Network Topology Module for Floodlight SDN Controller
Directory of Open Access Journals (Sweden)
A. A. Noskov
2015-01-01
Full Text Available Traditional network architecture is inflexible and complicated. This observation has led to a paradigm shift towards software-defined networking (SDN, where network management level is separated from data forwarding level. This change was made possible by control plane transfer from the switching equipment to software modules that run on a dedicated server, called the controller (or network operating system, or network applications, that work with this controller. Methods of representation, storage and communication interfaces with network topology elements are the most important aspects of network operating systems available to SDN user because performance of some key controller modules is heavily dependent on internal representation of the network topology. Notably, firewall and routing modules are examples of such modules. This article describes the methods used for presentation and storage of network topologies, as well as interface to the corresponding Floodlight modules. An alternative algorithm has been suggested and developed for message exchange conveying network topology alterations between the controller and network applications. Proposed algorithm makes implementation of module alerting based on subscription to the relevant events. API for interaction between controller and network applications has been developed. This algorithm and API formed the base for Topology Tracker module capable to inform network applications about the changes that had occurred in the network topology and also stores compact representation of the network to speed up the interaction process.
Topological Characterization of Fractured Coal
Jing, Yu; Armstrong, Ryan T.; Ramandi, Hamed L.; Mostaghimi, Peyman
2017-12-01
Coal transport properties are highly dependent on the underlying fractured network, known as cleats, which are characterized by geometrical and topological properties. X-ray microcomputed tomography (micro-CT) has been widely applied to obtain 3-D digital representations of the cleat network. However, segmentation of 3-D data is often problematic due to image noise, which will result in inaccurate estimation of coal properties (e.g., porosity and specific surface area). To circumvent this issue, a discrete fracture network (DFN) model is proposed. We develop a characterization framework to determine if the developed DFN models can preserve the topological properties of the coal cleat network found in micro-CT data. We compute the Euler characteristic, fractal dimension, and percolation quantities to analyze the topology locally and globally and compare the results between micro-CT data (before denoising), filtered micro-CT data (after denoising), and the DFN model. We find that micro-CT data with noise have extensive connectivity while filtered micro-CT data and DFN models have similar topology both globally and locally. It is concluded that the topology of the DFN models are closer to that of the realistic cleat network that do not have segmentation-induced pores. In addition, micro-CT imaging always struggles with the trade-off between sample size and resolution, while the presented DFN models are not restricted by imaging resolution and thus can be constructed with extended domain size. Overall, the presented DFN model is a reliable alternative with realistic cleat topology, extended domain size and favorable data format for direct numerical simulations.
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
Good environmental performance from Compact
International Nuclear Information System (INIS)
Kinnunen, L.
1996-01-01
For Rovaniemi and the designers of the town's new Suosiola power plant, it was clear from the start that it would be based on atmospheric-pressurized fluidized bed technology. In a bid to keep environmental emissions to a minimum, the decision fell to Foster Wheeler's new Compact CFB boiler. Work on developing the Compact boiler has been carried out since 1989. Flow models and cold air and hot air tests were completed in 1990. The first Compact boiler, an 18 MW unit, was commissioned at Kuhmo in 1993; this was followed by one at Kokkola in 1994
The United Nations Global Compact
DEFF Research Database (Denmark)
Rasche, Andreas; Waddock, Sandra; McIntosh, Malcolm
2013-01-01
This article reviews the interdisciplinary literature on the UN Global Compact. The review identifies three research perspectives, which scholars have used to study the UN Global Compact so far: a historical perspective discussing the Global Compact in the context of UN-business relations......, an operational perspective discussing the composition and impact of its participants, as well as a governance perspective discussing the constraints and opportunities of the initiative as an institutionalized arena for addressing global governance gaps. The authors contrast these three perspectives and identify...
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
Topological insulators fundamentals and perspectives
Ortmann, Frank; Valenzuela, Sergio O
2015-01-01
There are only few discoveries and new technologies in physical sciences that have the potential to dramatically alter and revolutionize our electronic world. Topological insulators are one of them. The present book for the first time provides a full overview and in-depth knowledge about this hot topic in materials science and condensed matter physics. Techniques such as angle-resolved photoemission spectrometry (ARPES), advanced solid-state Nuclear Magnetic Resonance (NMR) or scanning-tunnel microscopy (STM) together with key principles of topological insulators such as spin-locked electronic
Improving Topology Optimization using Games
DEFF Research Database (Denmark)
Nobel-Jørgensen, Morten; Christiansen, Asger Nyman; Bærentzen, J. Andreas
structures. Consequently, we have created a game, the TopOptGame, which improves the player's topology optimization intuition in a fun and engaging way while collecting data about the users performance. Technically, the TopOptGame builds on the TopOptApp [1] - an interactive topology optimization application...... designed for hand-held devices. The TopOptApp solves the 2D minimum compliance problem with interactive control of loads, supports and volume fraction, and thus the TopOptApp allows the user to change the problem on the y and watch the design evolve to a new optimum in real time. TopOptApp is available...
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.
Topology optimization of flow problems
DEFF Research Database (Denmark)
Gersborg, Allan Roulund
2007-01-01
transport in 2D Stokes flow. Using Stokes flow limits the range of applications; nonetheless, the thesis gives a proof-of-concept for the application of the method within fluid dynamic problems and it remains of interest for the design of microfluidic devices. Furthermore, the thesis contributes...... of the computed topology design using standard, credible analysis tools with a body-fitted mesh. Also, the thesis encompasses work on how to utilize the finite volume method (FVM) in the topology optimization context. This is motivated by the momentous position the FVM has in the fluid dynamics community...
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.
Topological phases of topological-insulator thin films
Asmar, Mahmoud M.; Sheehy, Daniel E.; Vekhter, Ilya
2018-02-01
We study the properties of a thin film of topological insulator material. We treat the coupling between helical states at opposite surfaces of the film in the properly-adapted tunneling approximation, and show that the tunneling matrix element oscillates as a function of both the film thickness and the momentum in the plane of the film for Bi2Se3 and Bi2Te3 . As a result, while the magnitude of the matrix element at the center of the surface Brillouin zone gives the gap in the energy spectrum, the sign of the matrix element uniquely determines the topological properties of the film, as demonstrated by explicitly computing the pseudospin textures and the Chern number. We find a sequence of transitions between topological and nontopological phases, separated by semimetallic states, as the film thickness varies. In the topological phase, the edge states of the film always exist but only carry a spin current if the edge potentials break particle-hole symmetry. The edge states decay very slowly away from the boundary in Bi2Se3 , making Bi2Te3 , where this scale is shorter, a more promising candidate for the observation of these states. Our results hold for free-standing films as well as heterostructures with large-gap insulators.
Compact instantaneous water heater
Energy Technology Data Exchange (ETDEWEB)
Azevedo, Jorge G.W.; Machado, Antonio R.; Ferraz, Andre D.; Rocha, Ivan C.C. da; Konishi, Ricardo [Companhia de Gas de Santa Catarina (SCGAS), Florianopolis, SC (Brazil); Lehmkuhl, Willian A.; Francisco Jr, Roberto W.; Hatanaka, Ricardo L.; Pereira, Fernando M.; Oliveira, Amir A.M. [Universidade Federal de Santa Catarina (UFSC), Florianopolis, SC (Brazil)
2012-07-01
This paper presents an experimental study of combustion in an inert porous medium in a liquid heating device application. This project aims to increase efficiency in the application of natural gas in residential and commercial sectors with the use of advanced combustion and heat transfer. The goal is to facilitate the development of a high performance compact water heater allowing hot water supply for up to two simultaneous showers. The experiment consists in a cylindrical porous burner with an integrated annular water heat exchanger. The reactants were injected radially into the burner and the flame stabilizes within the porous matrix. The water circulates in a coiled pipe positioned at the center of the burner. This configuration allows for heat transfer by conduction and radiation from the solid matrix to the heat exchanger. This article presented preliminary experimental results of a new water heater based on an annular porous burner. The range of equivalence ratios tested varied from 0.65 to 0.8. The power range was varied from 3 to 5 kW. Increasing the equivalence ratio or decreasing the total power input of the burner resulted in increased thermal efficiencies of the water heater. Thermal efficiencies varying from 60 to 92% were obtained. The condition for the goal of a comfortable bath was 20 deg C for 8-12 L/min. This preliminary prototype has achieved water temperature of 11deg C for 5 L/min. Further optimizations will be necessary in order to achieve intense heating with high thermal efficiency. (author)
What Is Business's Social Compact?
Avishai, Bernard
1994-01-01
Under the "new" social compact, businesses must focus on continuous learning and thus have both an obligation to support teaching and an opportunity to profit from it. Learning organizations must also be teaching organizations. (SK)
Compact, Ultrasensitive Formaldehyde Monitor Project
National Aeronautics and Space Administration — The Small Business Innovative Research Phase II proposal seeks to develop a compact UV laser ?based sensor for Earth science and planetary atmosphere exploration....
A New Numerical Method for Z2 Topological Insulators with Strong Disorder
Akagi, Yutaka; Katsura, Hosho; Koma, Tohru
2017-12-01
We propose a new method to numerically compute the Z2 indices for disordered topological insulators in Kitaev's periodic table. All of the Z2 indices are derived from the index formulae which are expressed in terms of a pair of projections introduced by Avron, Seiler, and Simon. For a given pair of projections, the corresponding index is determined by the spectrum of the difference between the two projections. This difference exhibits remarkable and useful properties, as it is compact and has a supersymmetric structure in the spectrum. These properties enable highly efficient numerical calculation of the indices of disordered topological insulators. The method, which we propose, is demonstrated for the Bernevig-Hughes-Zhang and Wilson-Dirac models whose topological phases are characterized by a Z2 index in two and three dimensions, respectively.
Topological string on elliptic CY 3-folds and the ring of Jacobi forms
Energy Technology Data Exchange (ETDEWEB)
Huang, Min-xin [Interdisciplinary Center for Theoretical Study,University of Science and Technology of China, Hefei, Anhui 230026 (China); Katz, Sheldon [Department of Mathematics, University of Illinois at Urbana-Champaign,1409 W. Green St., Urbana, IL 6180 (United States); Klemm, Albrecht [Bethe Center for Theoretical Physics (BCTP),Physikalisches Institut, Universität Bonn, 53115 Bonn (Germany)
2015-10-20
We give evidence that the all genus amplitudes of topological string theory on compact elliptically fibered Calabi-Yau manifolds can be written in terms of meromorphic Jacobi forms whose weight grows linearly and whose index grows quadratically with the base degree. The denominators of these forms have a simple universal form with the property that the poles of the meromorphic form lie only at torsion points. The modular parameter corresponds to the fibre class while the rôle of the string coupling is played by the elliptic parameter. As a consequence the topological string amplitudes are modular and quasi periodic in the string coupling. This leads to very strong all genus results on these geometries, which are checked against results from curve counting. The structure can be viewed as an indication that an N=2 analog of the reciprocal of the Igusa cusp form exists that might govern the topological string theory on these Calabi-Yau manifolds completely.
Topological phases: Wormholes in quantum matter
Schoutens, K.
2009-01-01
Proliferation of so-called anyonic defects in a topological phase of quantum matter leads to a critical state that can be visualized as a 'quantum foam', with topology-changing fluctuations on all length scales.
Compaction with Automatic Jog Introduction
1986-11-01
conserve area. For these reasons, compaction algorithms have gained widespread attention in the VLSI literature S ,[4, 5, 9, 111, and have been incorporated...graph is (V,E), then Dijkstra’s algorithm runs in time 6 (IEl - IVI log IV!) using Fibonacci heaps [3]. In contrast, the longest- path algorithm of...however, so that hierarchical compaction can alleviate much of the resource -. 33 pa. .1 N’, problem. It also may be suited to use in channel routing
Topological freeness for Hilbert bimodules
DEFF Research Database (Denmark)
Kwasniewski, Bartosz
2014-01-01
It is shown that topological freeness of Rieffel’s induced representation functor implies that any C*-algebra generated by a faithful covariant representation of a Hilbert bimodule X over a C*-algebra A is canonically isomorphic to the crossed product A ⋊ X ℤ. An ideal lattice description and a s...
Topological Insulator Nanowires and Nanoribbons
Kong, Desheng
2010-01-13
Recent theoretical calculations and photoemission spectroscopy measurements on the bulk Bi2Se3 material show that it is a three-dimensional topological insulator possessing conductive surface states with nondegenerate spins, attractive for dissipationless electronics and spintronics applications. Nanoscale topological insulator materials have a large surface-to-volume ratio that can manifest the conductive surface states and are promising candidates for devices. Here we report the synthesis and characterization of high quality single crystalline Bi2Se5 nanomaterials with a variety of morphologies. The synthesis of Bi 2Se5 nanowires and nanoribbons employs Au-catalyzed vapor-liquid-solid (VLS) mechanism. Nanowires, which exhibit rough surfaces, are formed by stacking nanoplatelets along the axial direction of the wires. Nanoribbons are grown along [1120] direction with a rectangular cross-section and have diverse morphologies, including quasi-one-dimensional, sheetlike, zigzag and sawtooth shapes. Scanning tunneling microscopy (STM) studies on nanoribbons show atomically smooth surfaces with ∼ 1 nm step edges, indicating single Se-Bi-Se-Bi-Se quintuple layers. STM measurements reveal a honeycomb atomic lattice, suggesting that the STM tip couples not only to the top Se atomic layer, but also to the Bi atomic layer underneath, which opens up the possibility to investigate the contribution of different atomic orbitais to the topological surface states. Transport measurements of a single nanoribbon device (four terminal resistance and Hall resistance) show great promise for nanoribbons as candidates to study topological surface states. © 2010 American Chemical Society.
Topological Aspects of Quantum Chromodynamics
Hooft, G. 't
2000-01-01
Absolute confinement of its color charges is a natural property of gauge theories such as quantum chromodynamics. On the one hand, it can be attributed to the existence of color-magnetic monopoles, a topological feature of the theory, but one can also maintain that all non-Abelian gauge theories
Structural Topology Optimization with Eigenvalues
Czech Academy of Sciences Publication Activity Database
Achtziger, W.; Kočvara, Michal
2007-01-01
Roč. 18, č. 4 (2007), s. 1129-1164 ISSN 1052-6234 R&D Projects: GA AV ČR IAA1075402 Institutional research plan: CEZ:AV0Z10750506 Keywords : Topology optimization * Vibration of structures * Optimization of Eigenvalues Subject RIV: BA - General Mathematics Impact factor: 1.554, year: 2007
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.
Algebraic topology of spin glasses
International Nuclear Information System (INIS)
Koma, Tohru
2011-01-01
We study the topology of frustration in d-dimensional Ising spin glasses with d ≥ 2 with nearest-neighbor interactions. We prove the following. For any given spin configuration, the domain walls on the unfrustration network are all transverse to a frustrated loop on the unfrustration network, where a domain wall is defined to be a connected element of the collection of all the (d - 1)-cells which are dual to the bonds having an unfavorable energy, and the unfrustration network is the collection of all the unfrustrated plaquettes. These domain walls are topologically nontrivial because they are all related to the global frustration of a loop on the unfrustration network. Taking account of the thermal stability for the domain walls, we can explain the numerical results that three- or higher-dimensional systems exhibit a spin glass phase, whereas two-dimensional ones do not. Namely, in two dimensions, the thermal fluctuations of the topologically nontrivial domain walls destroy the order of the frozen spins on the unfrustration network, whereas they do not in three or higher dimensions. This may be interpreted as a global topological effect of the frustrations.
Independent Study Project, Topic: Topology.
Notre Dame High School, Easton, PA.
Using this guide and the four popular books noted in it, a student, working independently, will learn about some of the classical ideas and problems of topology: the Meobius strip and Klein bottle, the four color problem, genus of a surface, networks, Euler's formula, and the Jordan Curve Theorem. The unit culminates in a project of the students'…
Topology of molecular interaction networks
Winterbach, W.; Van Mieghem, P.; Reinders, M.; Wang, H.; De Ridder, D.
2013-01-01
Molecular interactions are often represented as network models which have become the common language of many areas of biology. Graphs serve as convenient mathematical representations of network models and have themselves become objects of study. Their topology has been intensively researched over
Magnetic Field Topology in Jets
Gardiner, T. A.; Frank, A.
2000-01-01
We present results on the magnetic field topology in a pulsed radiative. jet. For initially helical magnetic fields and periodic velocity variations, we find that the magnetic field alternates along the, length of the jet from toroidally dominated in the knots to possibly poloidally dominated in the intervening regions.
Approximate Reanalysis in Topology Optimization
DEFF Research Database (Denmark)
Amir, Oded; Bendsøe, Martin P.; Sigmund, Ole
2009-01-01
In the nested approach to structural optimization, most of the computational effort is invested in the solution of the finite element analysis equations. In this study, the integration of an approximate reanalysis procedure into the framework of topology optimization of continuum structures...
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...
Classical topology and quantum states
Indian Academy of Sciences (India)
We argue that there are indeed such axioms involving observables with smooth time evolution: they contain commutative subalgebras from which the spatial slice of spacetime with its topology (and with further reﬁnements of the axiom, its - and ∞ - structures) can be reconstructed using Gel'fand–Naimark theory and ...
Topology optimization of microfluidic mixers
DEFF Research Database (Denmark)
Andreasen, Casper Schousboe; Gersborg, Allan Roulund; Sigmund, Ole
2009-01-01
This paper demonstrates the application of the topology optimization method as a general and systematic approach for microfluidic mixer design. The mixing process is modeled as convection dominated transport in low Reynolds number incompressible flow. The mixer performance is maximized by altering...
Topology optimization for acoustic problems
DEFF Research Database (Denmark)
Dühring, Maria Bayard
2006-01-01
In this paper a method to control acoustic properties in a room with topology optimization is presented. It is shown how the squared sound pressure amplitude in a certain part of a room can be minimized by distribution of material in a design domain along the ceiling in 2D and 3D. Nice 0-1 designs...
Phantom stars and topology change
International Nuclear Information System (INIS)
DeBenedictis, Andrew; Garattini, Remo; Lobo, Francisco S. N.
2008-01-01
In this work, we consider time-dependent dark-energy star models, with an evolving parameter ω crossing the phantom divide ω=-1. Once in the phantom regime, the null energy condition is violated, which physically implies that the negative radial pressure exceeds the energy density. Therefore, an enormous negative pressure in the center may, in principle, imply a topology change, consequently opening up a tunnel and converting the dark-energy star into a wormhole. The criteria for this topology change are discussed and, in particular, we consider a Casimir energy approach involving quasilocal energy difference calculations that may reflect or measure the occurrence of a topology change. We denote these exotic geometries consisting of dark-energy stars (in the phantom regime) and phantom wormholes as phantom stars. The final product of this topological change, namely, phantom wormholes, have far-reaching physical and cosmological implications, as in addition to being used for interstellar shortcuts, an absurdly advanced civilization may manipulate these geometries to induce closed timelike curves, consequently violating causality.
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.
Wave Manipulation by Topology Optimization
DEFF Research Database (Denmark)
Andkjær, Jacob Anders
topology optimization can be used to design structures for manipulation of the electromagnetic and acoustic waves. The wave problems considered here fall within three classes. The first class concerns the design of cloaks, which when wrapped around an object will render the object undetectable...
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.
Topology Optimization for Convection Problems
DEFF Research Database (Denmark)
Alexandersen, Joe
2011-01-01
.This is done by the use of a self-programmed FORTRAN-code, which builds on an existing 2D-plane thermomechanical nite element code implementing during the course `41525 FEM-Heavy'. The topology optimizationfeatures have been implemented from scratch, and allows the program to optimize elastostatic mechanical...
Topological excitations in magnetic materials
Energy Technology Data Exchange (ETDEWEB)
Bazeia, D., E-mail: bazeia@fisica.ufpb.br [Departamento de Física, Universidade Federal da Paraíba, 58051-970 João Pessoa, PB (Brazil); Doria, M.M. [Instituto de Física, Universidade Federal do Rio de Janeiro, Rio de Janeiro (Brazil); Dipartimento di Fisica, Università di Camerino, I-62032 Camerino (Italy); Rodrigues, E.I.B. [Departamento de Física, Universidade Federal da Paraíba, 58051-970 João Pessoa, PB (Brazil)
2016-05-20
In this work we propose a new route to describe topological excitations in magnetic systems through a single real scalar field. We show here that spherically symmetric structures in two spatial dimensions, which map helical excitations in magnetic materials, admit this formulation and can be used to model skyrmion-like structures in magnetic materials.
Topological visual mapping in robotics.
Romero, Anna; Cazorla, Miguel
2012-08-01
A key problem in robotics is the construction of a map from its environment. This map could be used in different tasks, like localization, recognition, obstacle avoidance, etc. Besides, the simultaneous location and mapping (SLAM) problem has had a lot of interest in the robotics community. This paper presents a new method for visual mapping, using topological instead of metric information. For that purpose, we propose prior image segmentation into regions in order to group the extracted invariant features in a graph so that each graph defines a single region of the image. Although others methods have been proposed for visual SLAM, our method is complete, in the sense that it makes all the process: it presents a new method for image matching; it defines a way to build the topological map; and it also defines a matching criterion for loop-closing. The matching process will take into account visual features and their structure using the graph transformation matching (GTM) algorithm, which allows us to process the matching and to remove out the outliers. Then, using this image comparison method, we propose an algorithm for constructing topological maps. During the experimentation phase, we will test the robustness of the method and its ability constructing topological maps. We have also introduced new hysteresis behavior in order to solve some problems found building the graph.
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
Topology Discovery Using Cisco Discovery Protocol
Rodriguez, Sergio R.
2009-01-01
In this paper we address the problem of discovering network topology in proprietary networks. Namely, we investigate topology discovery in Cisco-based networks. Cisco devices run Cisco Discovery Protocol (CDP) which holds information about these devices. We first compare properties of topologies that can be obtained from networks deploying CDP versus Spanning Tree Protocol (STP) and Management Information Base (MIB) Forwarding Database (FDB). Then we describe a method of discovering topology ...
SATA II - Stochastic Algebraic Topology and Applications
2017-01-30
AFRL-AFOSR-UK-TR-2017-0018 SATA II - Stochastic Algebraic Topology and Applications 150032 Robert Adler TECHNION ISRAEL INSTITUTE OF TECHNOLOGY Final...REPORT TYPE Final 3. DATES COVERED (From - To) 15 Dec 2014 to 14 Dec 2016 4. TITLE AND SUBTITLE SATA II - Stochastic Algebraic Topology and Applications... Topology and Applications Continuation of, and associated with SATA: Stochastic Algebraic Topology and Applications FA8655-11-1-3039, 09/1/2011–08/31/2014
Jakob Nielsen and His Contributions to Topology
DEFF Research Database (Denmark)
Hansen, Vagn Lundsgaard
1999-01-01
The Danish mathematician Jakob Nielsen won international recognition as one of the developers of combinatorial group theory and the topology of surfaces. This article describes the life and work of Jakob Nielsen with emphasis on his contributions to topology.......The Danish mathematician Jakob Nielsen won international recognition as one of the developers of combinatorial group theory and the topology of surfaces. This article describes the life and work of Jakob Nielsen with emphasis on his contributions to topology....
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 ...
Excitations in Topological Superfluids and Superconductors
Wu, Hao
In this thesis I present the theoretical work on Fermionic surface states, and %the bulk Bosonic collective excitations in topological superfluids and superconductors. Broken symmetries %Bulk-edge correspondence in topological condensed matter systems have implications for the spectrum of Fermionic excitations confined on surfaces or topological defects. (Abstract shortened by ProQuest.).
Invertibility in L-Topological Spaces
Directory of Open Access Journals (Sweden)
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.
Dual Feynman rules - topological asymptotic freedom
International Nuclear Information System (INIS)
Chew, G.F.; Levinson, M.; California Univ., Berkeley
1983-01-01
Feynman-graph rules are formulated for the strong - interaction components of the topological expansion - defined as those graphs all of whose vertices are zero - entropy connected parts. These rules imply a ''topological asymptotic freedom'' and admit a corresponding perturbative evaluation where the zeroth order exhibits topological supersymmetry. (orig.)
Topological analysis of telecommunications networks
Directory of Open Access Journals (Sweden)
Milojko V. Jevtović
2011-01-01
Full Text Available A topological analysis of the structure of telecommunications networks is a very interesting topic in the network research, but also a key issue in their design and planning. Satisfying multiple criteria in terms of locations of switching nodes as well as their connectivity with respect to the requests for capacity, transmission speed, reliability, availability and cost are the main research objectives. There are three ways of presenting the topology of telecommunications networks: table, matrix or graph method. The table method is suitable for a network of a relatively small number of nodes in relation to the number of links. The matrix method involves the formation of a connection matrix in which its columns present source traffic nodes and its rows are the switching systems that belong to the destination. The method of the topology graph means that the network nodes are connected via directional or unidirectional links. We can thus easily analyze the structural parameters of telecommunications networks. This paper presents the mathematical analysis of the star-, ring-, fully connected loop- and grid (matrix-shaped topology as well as the topology based on the shortest path tree. For each of these topologies, the expressions for determining the number of branches, the middle level of reliability, the medium length and the average length of the link are given in tables. For the fully connected loop network with five nodes the values of all topological parameters are calculated. Based on the topological parameters, the relationships that represent integral and distributed indicators of reliability are given in this work as well as the values of the particular network. The main objectives of the topology optimization of telecommunications networks are: achieving the minimum complexity, maximum capacity, the shortest path message transfer, the maximum speed of communication and maximum economy. The performance of telecommunications networks is
Constructing a logical, regular axis topology from an irregular topology
Faraj, Daniel A.
2014-07-01
Constructing a logical regular topology from an irregular topology including, for each axial dimension and recursively, for each compute node in a subcommunicator until returning to a first node: adding to a logical line of the axial dimension a neighbor specified in a nearest neighbor list; calling the added compute node; determining, by the called node, whether any neighbor in the node's nearest neighbor list is available to add to the logical line; if a neighbor in the called compute node's nearest neighbor list is available to add to the logical line, adding, by the called compute node to the logical line, any neighbor in the called compute node's nearest neighbor list for the axial dimension not already added to the logical line; and, if no neighbor in the called compute node's nearest neighbor list is available to add to the logical line, returning to the calling compute node.
Energy Technology Data Exchange (ETDEWEB)
Smith, David A. [Univ. of Colorado, Boulder, CO (United States)
1998-11-01
In November of 1993, mysterious signals recorded by a satellite-borne broadband VHF radio science experiment called Blackboard led to a completely unexpected discovery. Prior to launch of the ALEXIS satellite, it was thought that its secondary payload, Blackboard, would most often detect the radio emissions from lightning when its receiver was not overwhelmed by noise from narrowband communication carriers. Instead, the vast majority of events that triggered the instrument were isolated pairs of pulses that were one hundred times more energetic than normal thunderstorm electrical emissions. The events, which came to be known as TIPPs (for transionospheric pulse pairs), presented a true mystery to the geophysics community. At the time, it was not even known whether the events had natural or anthropogenic origins. After two and one half years of research into the unique signals, two ground-based receiver arrays in New Mexico first began to detect and record thunderstorm radio emissions that were consistent with the Blackboard observations. On two occasions, the ground-based systems and Blackboard even recorded emissions that were produced by the same exact events. From the ground based observations, it has been determined that TIPP events areproduced by brief, singular, isolated, intracloud electrical discharges that occur in intense regions of thunderstorms. These discharges have been dubbed CIDS, an acronym for compact intracloud discharges. During the summer of 1996, ground-based receiver arrays were used to record the electric field change signals and broadband HF emissions from hundreds of CIDS. Event timing that was accurate to within a few microseconds made possible the determination of source locations using methods of differential time of arrival. Ionospheric reflections of signals were recorded in addition to groundwave/line-of-sight signals and were used to determine accurate altitudes for the discharges. Twenty-four CIDS were recorded from three
On type-2 m-topological spaces
Directory of Open Access Journals (Sweden)
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.
Topological data analysis for scientific visualization
Tierny, Julien
2017-01-01
Combining theoretical and practical aspects of topology, this book delivers a comprehensive and self-contained introduction to topological methods for the analysis and visualization of scientific data. Theoretical concepts are presented in a thorough but intuitive manner, with many high-quality color illustrations. Key algorithms for the computation and simplification of topological data representations are described in details, and their application is carefully illustrated in a chapter dedicated to concrete use cases. With its fine balance between theory and practice, "Topological Data Analysis for Scientific Visualization" constitutes an appealing introduction to the increasingly important topic of topological data analysis, for lecturers, students and researchers.
Compact magnetic confinement fusion: Spherical torus and compact torus
Directory of Open Access Journals (Sweden)
Zhe Gao
2016-05-01
Full Text Available The spherical torus (ST and compact torus (CT are two kinds of alternative magnetic confinement fusion concepts with compact geometry. The ST is actually a sub-category of tokamak with a low aspect ratio; while the CT is a toroidal magnetic configuration with a simply-connected geometry including spheromak and field reversed pinch. The ST and CT have potential advantages for ultimate fusion reactor; while at present they can also provide unique fusion science and technology contributions for mainstream fusion research. However, some critical scientific and technology issues should be extensively investigated.
Co-compact Gabor Systems on Locally Compact Abelian Groups
DEFF Research Database (Denmark)
Jakobsen, Mads Sielemann; Lemvig, Jakob
2016-01-01
In this work we extend classical structure and duality results in Gabor analysis on the euclidean space to the setting of second countable locally compact abelian (LCA) groups. We formulate the concept of rationally oversampling of Gabor systems in an LCA group and prove corresponding characteriz......In this work we extend classical structure and duality results in Gabor analysis on the euclidean space to the setting of second countable locally compact abelian (LCA) groups. We formulate the concept of rationally oversampling of Gabor systems in an LCA group and prove corresponding...
String Topology for Lie Groups
DEFF Research Database (Denmark)
A. Hepworth, Richard
2010-01-01
In 1999 Chas and Sullivan showed that the homology of the free loop space of an oriented manifold admits the structure of a Batalin-Vilkovisky algebra. In this paper we give a direct description of this Batalin-Vilkovisky algebra in the case that the manifold is a compact Lie group G. Our answer ...
Symmetric Topological Phases and Tensor Network States
Jiang, Shenghan
Classification and simulation of quantum phases are one of main themes in condensed matter physics. Quantum phases can be distinguished by their symmetrical and topological properties. The interplay between symmetry and topology in condensed matter physics often leads to exotic quantum phases and rich phase diagrams. Famous examples include quantum Hall phases, spin liquids and topological insulators. In this thesis, I present our works toward a more systematically understanding of symmetric topological quantum phases in bosonic systems. In the absence of global symmetries, gapped quantum phases are characterized by topological orders. Topological orders in 2+1D are well studied, while a systematically understanding of topological orders in 3+1D is still lacking. By studying a family of exact solvable models, we find at least some topological orders in 3+1D can be distinguished by braiding phases of loop excitations. In the presence of both global symmetries and topological orders, the interplay between them leads to new phases termed as symmetry enriched topological (SET) phases. We develop a framework to classify a large class of SET phases using tensor networks. For each tensor class, we can write down generic variational wavefunctions. We apply our method to study gapped spin liquids on the kagome lattice, which can be viewed as SET phases of on-site symmetries as well as lattice symmetries. In the absence of topological order, symmetry could protect different topological phases, which are often referred to as symmetry protected topological (SPT) phases. We present systematic constructions of tensor network wavefunctions for bosonic symmetry protected topological (SPT) phases respecting both onsite and spatial symmetries.
Cartography – morphology – topology
DEFF Research Database (Denmark)
Dinesen, Cort Ross; Peder Pedersen, Claus
. The work was approached from a new angle every year through a series of associated questions, resulting in an extensive body of drawings describing the various discourses raised. The developed observational forms reflected in the collected body of drawings constitute a topological landscape with a great...... and developing topological emergence as a passage between cartographic appropriation and creative becoming while simultaneously lifting the material out of its mimetic reference, makes room for the of a movement towards a production of meaning as well as a basis for initiating architectonic practices. We seek...... to provoke a level of operation between the real and the virtual from this body holding the sensing body as its pivot along with the phenomenology of the object; omnipresently considering and shaping virtual constructions. This questioning of architectonic discourse is capable of instrumentalizing ambiguity...
Magnetic topology, nonequilibrium, and dissipation
International Nuclear Information System (INIS)
Parker, E.N.
1985-01-01
Static equilibrium of a magnetic field throughout a large volume of highly conducting fluid requires a degree of topological symmetry that is generally lacking in nature. The dynamical nonequilibrium of the magnetic topologies in the real world forms current sheets across which there is active reconnection of the field, dissipating the energy of the magnetic strains and reducing the fields toward simpler forms. The magnetic fields in astronomical settings are generally subject to continual straining by the convection within their parent body. The work done on the field by the convection appears in the energy of the small-scale strains, and is soon dissipated by the reconnection. The intense heating of the tenuous outer atmosphere of stars by this mechanism appears to be responsible for most of the X-ray emission of ordinary stars
Effective Topology from Spacetime Tomography
International Nuclear Information System (INIS)
Wallden, Petros
2007-01-01
We recover the effective topology of spacetime using the notion of record from the decoherent histories approach to Quantum Theory. From a series of (gedanken) experiments, we obtain the set of possible events, grouped into sub-sets that corresponds to histories, but with no other information such as (causal) order or any notion of proximity. This corresponds to tomography of the 'effective' spacetime, that is done in an operational way. Making certain assumptions about these records, and using the existence of upper bound in the speed of transfer of matter and information, we recover the full partial (causal) order up to certain ambiguities. The partially ordered set of events corresponds to an 'effective' causal set which is a discretized version of spacetime with the causal relation as defining feature. We conclude with a derivation of the topology of this effective discretized spacetime
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.
Topological 2-dimensional quantum mechanics
International Nuclear Information System (INIS)
Dasnieres de Veigy, A.; Ouvry, S.
1992-12-01
A Chern-Simons Lagrangian is defined for a system of planar particles topologically interacting at a distance. The anyon model appears as a particular case where all the particles are identical. Exact N-body eigenstates are proposed and a perturbative algorithm is set up. The case where some particles are fixed on a lattice, is discussed, and curved manifolds are considered. (author) 14 refs
Performance of Topological Insulator Interconnects
Philip, Timothy M.; Hirsbrunner, Mark R.; Park, Moon Jip; Gilbert, Matthew J.
2016-01-01
The poor performance of copper interconnects at the nanometer scale calls for new material solutions for continued scaling of integrated circuits. We propose the use of three dimensional time-reversal-invariant topological insulators (TIs), which host backscattering-protected surface states, for this purpose. Using semiclassical methods, we demonstrate that nanoscale TI interconnects have a resistance 1-3 orders of magnitude lower than copper interconnects and graphene nanoribbons at the nano...
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....
Topological Insulator Nanowires and Nanoribbons
Energy Technology Data Exchange (ETDEWEB)
Kong, D.S.
2010-06-02
Recent theoretical calculations and photoemission spectroscopy measurements on the bulk Bi{sub 2}Se{sub 3} material show that it is a three-dimensional topological insulator possessing conductive surface states with nondegenerate spins, attractive for dissipationless electronics and spintronics applications. Nanoscale topological insulator materials have a large surface-to-volume ratio that can manifest the conductive surface states and are promising candidates for devices. Here we report the synthesis and characterization of high quality single crystalline Bi{sub 2}Se{sub 3} nanomaterials with a variety of morphologies. The synthesis of Bi{sub 2}Se{sub 3} nanowires and nanoribbons employs Au-catalyzed vapor-liquid-solid (VLS) mechanism. Nanowires, which exhibit rough surfaces, are formed by stacking nanoplatelets along the axial direction of the wires. Nanoribbons are grown along [11-20] direction with a rectangular crosssection and have diverse morphologies, including quasi-one-dimensional, sheetlike, zigzag and sawtooth shapes. Scanning tunneling microscopy (STM) studies on nanoribbons show atomically smooth surfaces with {approx}1 nm step edges, indicating single Se-Bi-Se-Bi-Se quintuple layers. STM measurements reveal a honeycomb atomic lattice, suggesting that the STM tip couples not only to the top Se atomic layer, but also to the Bi atomic layer underneath, which opens up the possibility to investigate the contribution of different atomic orbitals to the topological surface states. Transport measurements of a single nanoribbon device (four terminal resistance and Hall resistance) show great promise for nanoribbons as candidates to study topological surface states.
Topological K-Kolmogorov groups
International Nuclear Information System (INIS)
Abd El-Sattar, A. Dabbour.
1987-07-01
The idea of the K-groups was used to define K-Kolmogorov homology and cohomology (over pairs of coefficient groups) which are descriptions of certain modifications of the Kolmogorov groups. The present work is devoted to the study of the topological properties of the K-Kolmogorov groups which lie at the root of the group duality based essentially upon Pontrjagin's concept of group multiplication. 14 refs
Membrane topology of hedgehog acyltransferase.
Matevossian, Armine; Resh, Marilyn D
2015-01-23
Hedgehog acyltransferase (Hhat) is a multipass transmembrane enzyme that mediates the covalent attachment of the 16-carbon fatty acid palmitate to the N-terminal cysteine of Sonic Hedgehog (Shh). Palmitoylation of Shh by Hhat is critical for short and long range signaling. Knowledge of the topological organization of Hhat transmembrane helices would enhance our understanding of Hhat-mediated Shh palmitoylation. Bioinformatics analysis of transmembrane domains within human Hhat using 10 different algorithms resulted in highly consistent predictions in the C-terminal, but not in the N-terminal, region of Hhat. To empirically determine the topology of Hhat, we designed and exploited Hhat constructs containing either terminal or 12 different internal epitope tags. We used selective permeabilization coupled with immunofluorescence as well as a protease protection assay to demonstrate that Hhat contains 10 transmembrane domains and 2 re-entrant loops. The invariant His and highly conserved Asp residues within the membrane-bound O-acyltransferase (MBOAT) homology domain are segregated on opposite sides of the endoplasmic reticulum membrane. The localization of His-379 on the lumenal membrane surface is consistent with a role for this invariant residue in catalysis. Analysis of the activity and stability of the Hhat constructs revealed that the C-terminal MBOAT domain is especially sensitive to manipulation. Moreover, there was remarkable similarity in the overall topological organization of Hhat and ghrelin O-acyltransferase, another MBOAT family member. Knowledge of the topological organization of Hhat could serve as an important tool for further design of selective Hhat inhibitors. © 2015 by The American Society for Biochemistry and Molecular Biology, Inc.
Topological defects in extended inflation
International Nuclear Information System (INIS)
Copeland, E.J.; Kolb, E.W.; Chicago Univ., IL; Liddle, A.R.
1990-04-01
We consider the production of topological defects, especially cosmic strings, in extended inflation models. In extended inflation, the Universe passes through a first-order phase transition via bubble percolation, which naturally allows defects to form at the end of inflation. The correlation length, which determines the number density of the defects, is related to the mean size of bubbles when they collide. This mechanism allows a natural combination of inflation and large-scale structure via cosmic strings. 18 refs
Topological defects in extended inflation
International Nuclear Information System (INIS)
Copeland, E.J.; Kolb, E.W.; Liddle, A.R.
1990-01-01
We consider the production of topological defects, especially cosmic strings, in extended-inflation models. In extended inflation, the Universe passes through a first-order phase transition via bubble percolation, which naturally allows defects to form at the end of inflation. The correlation length, which determines the number density of the defects, is related to the mean size of the bubbles when they collide. This mechanism allows a natural combination of inflation and large-scale structure via cosmic strings
Lectures on the Topological Vertex
Mariño, M
2008-01-01
In this lectures, I will summarize the approach to Gromov–Witten invariants on toric Calabi–Yau threefolds based on large N dualities. Since the large N duality/topological vertex approach computes Gromov–Witten invariants in terms of Chern–Simons knot and link invariants, Sect. 2 is devoted to a review of these. Section 3 reviews topological strings and Gromov–Witten invariants, and gives some information about the open string case. Section 4 introduces the class of geometries we will deal with, namely toric (noncompact) Calabi–Yau manifolds, and we present a useful graphical way to represent these manifolds which constitutes the geometric core of the theory of the topological vertex. Finally, in Sect. 5, we define the vertex and present some explicit formulae for it and some simple applications. A brief Appendix contains useful information about symmetric polynomials. It has not been possible to present all the relevant background and physical derivations in this set of lectures. However, these...
Review of possible SICAM topologies
Energy Technology Data Exchange (ETDEWEB)
Ljusev, P.
2002-12-15
In this report some possible topologies and approaches towards construction of a SIngle Conversion stage AMpli er - SICAM are explored. Operation of such amplifier from a single phase voltage grid - AC mains, imposes some stringent limitations over the audio amplifier construction and possible topologies. It will be shown that these restrictions will necessitate the use of reactive energy storage elements at the SICAM input, still making some kind of a power supply needed. Therefore, SICAM should be conceived not as a single stage, but as a sophisticated interconnection of two dedicated stages, that are optimised and designed for the best performance in the audio range, leading to better efficiency, lower losses, reduced volume and cost of the integrated components. Several topologies will be presented, starting with the straightforward AC to AC conversion, continuing with DC-AC and ending with DC to DC conversion. Extensions, advantages, drawbacks and trade-offs will be thoroughly investigated, leading to conclusions for the direction of future research and development. (au)
Algebraic topology a first course
Fulton, William
1995-01-01
To the Teacher. This book is designed to introduce a student to some of the important ideas of algebraic topology by emphasizing the re lations of these ideas with other areas of mathematics. Rather than choosing one point of view of modem topology (homotopy theory, simplicial complexes, singular theory, axiomatic homology, differ ential topology, etc.), we concentrate our attention on concrete prob lems in low dimensions, introducing only as much algebraic machin ery as necessary for the problems we meet. This makes it possible to see a wider variety of important features of the subject than is usual in a beginning text. The book is designed for students of mathematics or science who are not aiming to become practicing algebraic topol ogists-without, we hope, discouraging budding topologists. We also feel that this approach is in better harmony with the historical devel opment of the subject. What would we like a student to know after a first course in to pology (assuming we reject the answer: ...
Topological qubit design and leakage
Energy Technology Data Exchange (ETDEWEB)
Ainsworth, R; Slingerland, J K, E-mail: robert.ainsworth@nuim.ie, E-mail: joost@thphys.nuim.ie [Department of Mathematical Physics, National University of Ireland Maynooth, Co. Kildare (Ireland)
2011-06-15
We examine how best to design qubits for use in topological quantum computation. These qubits are topological Hilbert spaces associated with small groups of anyons. Operations are performed on these by exchanging the anyons. One might argue that in order to have as many simple single-qubit operations as possible, the number of anyons per group should be maximized. However, we show that there is a maximal number of particles per qubit, namely 4, and more generally a maximal number of particles for qudits of dimension d. We also look at the possibility of having topological qubits for which one can perform two-qubit gates without leakage into non-computational states. It turns out that the requirement that all two-qubit gates are leakage free is very restrictive and this property can only be realized for two-qubit systems related to Ising-like anyon models, which do not allow for universal quantum computation by braiding. Our results follow directly from the representation theory of braid groups, which implies that they are valid for all anyon models. We also make some remarks about generalizations to other exchange groups.