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1

Pikul, Piotr. "Locally ordered topological spaces." Reports on Mathematical Logic 55 (2020): 113–41. http://dx.doi.org/10.4467/20842589rm.20.006.12438.

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2

Polyrakis, Ioannis A. "Schauder bases in locally solid lattice Banach spaces." Mathematical Proceedings of the Cambridge Philosophical Society 101, no. 1 (January 1987): 91–105. http://dx.doi.org/10.1017/s0305004100066433.

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Schauder bases in Banach spaces are studied in [5].In ordered Banach spaces a special type of Schauder bases, the O.P. Schauder bases, are studied because then the properties of ordered spaces can be used.
3

BEZHANISHVILI, GURAM, NICK BEZHANISHVILI, JOEL LUCERO-BRYAN, and JAN VAN MILL. "THE MCKINSEY–TARSKI THEOREM FOR LOCALLY COMPACT ORDERED SPACES." Bulletin of Symbolic Logic 27, no. 2 (April 29, 2021): 187–211. http://dx.doi.org/10.1017/bsl.2021.16.

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AbstractWe prove that the modal logic of a crowded locally compact generalized ordered space is $\textsf {S4}$ . This provides a version of the McKinsey–Tarski theorem for generalized ordered spaces. We then utilize this theorem to axiomatize the modal logic of an arbitrary locally compact generalized ordered space.
4

Reiland, Thomas W. "Nonsmooth analysis and optimization on partially ordered vector spaces." International Journal of Mathematics and Mathematical Sciences 15, no. 1 (1992): 65–81. http://dx.doi.org/10.1155/s0161171292000085.

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Interval-Lipschitz mappings between topological vector spaces are defined and compared with other Lipschitz-type operators. A theory of generalized gradients is presented when both spaces are locally convex and the range space is an order complete vector lattice. Sample applications to the theory of nonsmooth optimization are given.
5

Roth, Walter. "Hahn-Banach Type Theorems for Locally Convex Cones." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 68, no. 1 (February 2000): 104–25. http://dx.doi.org/10.1017/s1446788700001609.

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AbstractWe prove Hahn-Banach type theorems for linear functionals with values in R∪{+∞} on ordered cones, Using the concept of locally convex cones, we provide a sandwich theorem involving sub- and superlinear functionals which are allowed to attain infinite values. It render general versions of well-known extension and separation results. We describe the range of all linear functionals sandwiched between given sub- and superlinear functionals on an ordered cone. The results are of interest even in vector spaces, since we consider sublinear functionals that may attain the value +∞.
6

KELLERER, HANS G., and G. WINKLER. "RANDOM DYNAMICAL SYSTEMS ON ORDERED TOPOLOGICAL SPACES." Stochastics and Dynamics 06, no. 03 (September 2006): 255–300. http://dx.doi.org/10.1142/s0219493706001797.

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Let (Xn, n ≥ 0) be a random dynamical system and its state space be endowed with a reasonable topology. Instead of completing the structure as common by some linearity, this study stresses — motivated in particular by economic applications — order aspects. If the underlying random transformations are supposed to be order-preserving, this results in a fairly complete theory. First of all, the classical notions of and familiar criteria for recurrence and transience can be extended from discrete Markov chain theory. The most important fact is provided by the existence and uniqueness of a locally finite-invariant measure for recurrent systems. It allows to derive ergodic theorems as well as to introduce an attract or in a natural way. The classification is completed by distinguishing positive and null recurrence corresponding, respectively, to the case of a finite or infinite invariant measure; equivalently, this amounts to finite or infinite mean passage times. For positive recurrent systems, moreover, strengthened versions of weak convergence as well as generalized laws of large numbers are available.
7

Flum, Jörg, and Juan Carlos Martinez. "On topological spaces equivalent to ordinals." Journal of Symbolic Logic 53, no. 3 (September 1988): 785–95. http://dx.doi.org/10.2307/2274571.

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AbstractLet L be one of the topological languages Lt, (L∞ω)t and (Lκω)t. We characterize the topological spaces which are models of the L-theory of the class of ordinals equipped with the order topology. The results show that the role played in classical model theory by the property of being well-ordered is taken over in the topological context by the property of being locally compact and scattered.
8

Zhou, Zhi-Ang. "The Relationship between Two Kinds of Generalized Convex Set-Valued Maps in Real Ordered Linear Spaces." Abstract and Applied Analysis 2013 (2013): 1–4. http://dx.doi.org/10.1155/2013/105617.

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A new notion of the ic-cone convexlike set-valued map characterized by the algebraic interior and the vector closure is introduced in real ordered linear spaces. The relationship between the ic-cone convexlike set-valued map and the nearly cone subconvexlike set-valued map is established. The results in this paper generalize some known results in the literature from locally convex spaces to linear spaces.
9

DANILENKO, ALEXANDRE I. "STRONG ORBIT EQUIVALENCE OF LOCALLY COMPACT CANTOR MINIMAL SYSTEMS." International Journal of Mathematics 12, no. 01 (February 2001): 113–23. http://dx.doi.org/10.1142/s0129167x0100068x.

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We study minimal self-homeomorphisms of zero dimensional metrizable locally compact non-compact Hausdorff spaces. For this class of systems, we show that the ordered cohomology group is a complete invariant for strong orbit equivalence, i.e. topological orbit equivalence with continuous orbit cocycles. This is an "infinite" counterpart of a well known result of Giordano, Putnam and Skau about compact Cantor systems.
10

Mlaiki, Nabil, Jamshaid Ahmad, and Abdullah Eqal Al-Mazrooei. "Endpoints of Generalized Contractions in F -Metric Spaces with Application to Integral Equations." Journal of Function Spaces 2022 (June 6, 2022): 1–9. http://dx.doi.org/10.1155/2022/3739382.

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The purpose of this article is to introduce locally α - ζ -multivalued contraction and rational Ćirić type α - ζ -multivalued contraction in the context of F -metric spaces and prove some endpoint results. We provide a nontrivial example to show the authenticity of our main result. Our results generalize some well-known results of literature. We also present some endpoint results in both graphic F -metric spaces and ordered F -metric spaces. As an application of our main result, we investigate the solution of an integral equation.
11

Gupta, Manjul, and Kalika Kaushal. "Topological properties and matrix transformations of certain ordered generalized sequence spaces." International Journal of Mathematics and Mathematical Sciences 18, no. 2 (1995): 341–56. http://dx.doi.org/10.1155/s0161171295000433.

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In this note, we carry out investigations related to the mixed impact of ordering and topological structure of a locally convex solid Riesz space(X,τ)and a scalar valued sequence spaceλ, on the vector valued sequence spaceλ(X)which is formed and topologized with the help ofλandX, and vice versa. Besides,we also characterizeo-matrix transformations fromc(X),ℓ∞(X)to themselves,cs(X)toc(X)and derive necessary conditions for a matrix of linear operators to transformℓ1(X)into a simple ordered vector valued sequence spaceΛ(X).
12

Shoaib, Abdullah, Muhammad Arshad, and Jamshaid Ahmad. "Fixed Point Results of Locally Contractive Mappings in Ordered Quasi-Partial Metric Spaces." Scientific World Journal 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/194897.

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Fixed point results for a self-map satisfying locally contractive conditions on a closed ball in an ordered 0-complete quasi-partial metric space have been established. Instead of monotone mapping, the notion of dominated mappings is applied. We have used weaker metric, weaker contractive conditions, and weaker restrictions to obtain unique fixed points. An example is given which shows that how this result can be used when the corresponding results cannot. Our results generalize, extend, and improve several well-known conventional results.
13

Tri, Vo, and Erdal Karapinar. "A fixed point theorem and an application for the Cauchy problem in the scale of Banach spaces." Filomat 34, no. 13 (2020): 4387–98. http://dx.doi.org/10.2298/fil2013387t.

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The main aim of this paper is to prove the existence of the fixed point of the sum of two operators in setting of the cone-normed spaces with the values of cone-norm belonging to an ordered locally convex space. We apply this result to prove the existence of global solution of the Cauchy problem with perturbation of the form (x?(t) = f[t,x(t)] + g[t,x(t)], t ? [0,?), x(0) = x0? F1, in a scale of Banach spaces {(Fs,||.||) : s ? (0, 1]}.
14

Postolica, Vasile. "New existence results for efficient points in locally convex spaces ordered by supernormal cones." Journal of Global Optimization 3, no. 2 (1993): 233–42. http://dx.doi.org/10.1007/bf01096741.

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15

CHOLEWA, JAN W., and ANÍBAL RODRÍGUEZ-BERNAL. "EXTREMAL EQUILIBRIA FOR DISSIPATIVE PARABOLIC EQUATIONS IN LOCALLY UNIFORM SPACES." Mathematical Models and Methods in Applied Sciences 19, no. 11 (November 2009): 1995–2037. http://dx.doi.org/10.1142/s0218202509004029.

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We consider a reaction diffusion equation ut = Δu + f(x, u) in ℝN with initial data in the locally uniform space [Formula: see text], q ∈ [1, ∞), and with dissipative nonlinearities satisfying s f(x, s) ≤ C(x)s2 + D(x) |s|, where [Formula: see text] and [Formula: see text] for certain [Formula: see text]. We construct a global attractor [Formula: see text] and show that [Formula: see text] is actually contained in an ordered interval [φm, φM], where [Formula: see text] is a pair of stationary solutions, minimal and maximal respectively, that satisfy φm ≤ lim inft→∞ u(t; u0) ≤ lim supt→∞ u(t; u0) ≤ φM uniformly for u0 in bounded subsets of [Formula: see text]. A sufficient condition concerning the existence of minimal positive steady state, asymptotically stable from below, is given. Certain sufficient conditions are also discussed ensuring the solutions to be asymptotically small as |x| → ∞. In this case the solutions are shown to enter, asymptotically, Lebesgue spaces of integrable functions in ℝN, the attractor attracts in the uniform convergence topology in ℝN and is a bounded subset of W2,r(ℝN) for some r > N/2. Uniqueness and asymptotic stability of positive solutions are also discussed. Applications to some model problems, including some from mathematical biology are given.
16

Shoaib, Abdullah, Poom Kumam, and Kanokwan Sitthithakerngkiet. "Interpolative Hardy Roger's type contraction on a closed ball in ordered dislocated metric spaces and some results." AIMS Mathematics 7, no. 8 (2022): 13821–31. http://dx.doi.org/10.3934/math.2022762.

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<abstract><p>The aim of this paper is to find out fixed point results with interpolative contractive conditions for pairs of generalized locally dominated mappings on closed balls in ordered dislocated metric spaces. We have explained our main result with an example. Our results generalize the result of Karapınar et al. (Symmetry 2018, 11, 8).</p></abstract>
17

Arshad, Muhammad, Abdullah Shoaib, and Pasquale Vetro. "Common Fixed Points of a Pair of Hardy Rogers Type Mappings on a Closed Ball in Ordered Dislocated Metric Spaces." Journal of Function Spaces and Applications 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/638181.

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Common fixed point results for mappings satisfying locally contractive conditions on a closed ball in an ordered complete dislocated metric space have been established. The notion of dominated mappings is applied to approximate the unique solution of nonlinear functional equations. Our results improve several well-known conventional results.
18

Rasham, Tahair, Muhammad Nazam, Hassen Aydi, and Ravi P. Agarwal. "Existence of Common Fixed Points of Generalized ∆-Implicit Locally Contractive Mappings on Closed Ball in Multiplicative G-Metric Spaces with Applications." Mathematics 10, no. 18 (September 16, 2022): 3369. http://dx.doi.org/10.3390/math10183369.

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In this paper, we introduce a generalized Δ-implicit locally contractive condition and give some examples to support it and show its significance in fixed point theory. We prove that the mappings satisfying the generalized Δ-implicit locally contractive condition admit a common fixed point, where the ordered multiplicative GM-metric space is chosen as the underlying space. The obtained fixed point theorems generalize many earlier fixed point theorems on implicit locally contractive mappings. In addition, some nontrivial and interesting examples are provided to support our findings. To demonstrate the originality of our new main result, we apply it to show the existence of solutions to a system of nonlinear—Volterra type—integral equations.
19

Howroyd, J. D. "A Domain-Theoretic Approach to Integration in Hausdorff Spaces." LMS Journal of Computation and Mathematics 3 (2000): 229–73. http://dx.doi.org/10.1112/s1461157000000292.

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AbstractIn this paper we generalize the construction of a domain-theoretic integral, introduced by Professor Abbas Edalat, in locally compact separable Hausdorff spaces, to general Hausdorff spaces embedded in a domain. Our main example of such spaces comprises general metric spaces embedded in the rounded ideal completion of the partially ordered set of formal balls. We go on to discuss analytic subsets of a general Hausdorff space, and give a sufficient condition for a measure supported on an analytic set to be approximated by a sequence of simple valuations. In particular, this condition is always satisfied in a metric space embedded in the rounded ideal completion of its formal ball space. We finish with a comments section, where we highlight some potential areas for future research and discuss some questions of computability.
20

Kendall, Wilfrid S., and Jesper Møller. "Perfect simulation using dominating processes on ordered spaces, with application to locally stable point processes." Advances in Applied Probability 32, no. 03 (September 2000): 844–65. http://dx.doi.org/10.1017/s0001867800010284.

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In this paper we investigate the application of perfect simulation, in particular Coupling from the Past (CFTP), to the simulation of random point processes. We give a general formulation of the method of dominated CFTP and apply it to the problem of perfect simulation of general locally stable point processes as equilibrium distributions of spatial birth-and-death processes. We then investigate discrete-time Metropolis-Hastings samplers for point processes, and show how a variant which samples systematically from cells can be converted into a perfect version. An application is given to the Strauss point process.
21

Kendall, Wilfrid S., and Jesper Møller. "Perfect simulation using dominating processes on ordered spaces, with application to locally stable point processes." Advances in Applied Probability 32, no. 3 (September 2000): 844–65. http://dx.doi.org/10.1239/aap/1013540247.

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In this paper we investigate the application of perfect simulation, in particular Coupling from the Past (CFTP), to the simulation of random point processes. We give a general formulation of the method of dominated CFTP and apply it to the problem of perfect simulation of general locally stable point processes as equilibrium distributions of spatial birth-and-death processes. We then investigate discrete-time Metropolis-Hastings samplers for point processes, and show how a variant which samples systematically from cells can be converted into a perfect version. An application is given to the Strauss point process.
22

Polyrakis, Ioannis A. "Strongly exposed points in bases for the positive cone of ordered Banach spaces and characterizations of l1(Г)". Proceedings of the Edinburgh Mathematical Society 29, № 2 (червень 1986): 271–82. http://dx.doi.org/10.1017/s0013091500017648.

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The study of extreme, strongly exposed points of closed, convex and bounded sets in Banach spaces has been developed especially by the interconnection of the Radon–Nikodým property with the geometry of closed, convex and bounded subsets of Banach spaces [5],[2] . In the theory of ordered Banach spaces as well as in the Choquet theory, [4], we are interested in the study of a special type of convex sets, not necessarily bounded, namely the bases for the positive cone. In [7] the geometry (extreme points, dentability) of closed and convex subsets K of a Banach space X with the Radon-Nikodým property is studied and special emphasis has been given to the case where K is a base for acone P of X. In [6, Theorem 1], it is proved that an infinite-dimensional, separable, locally solid lattice Banach space is order-isomorphic to l1 if, and only if, X has the Krein–Milman property and its positive cone has a bounded base.
23

DE JEU, MARCEL, and MARTEN WORTEL. "POSITIVE REPRESENTATIONS OF FINITE GROUPS IN RIESZ SPACES." International Journal of Mathematics 23, no. 07 (June 27, 2012): 1250076. http://dx.doi.org/10.1142/s0129167x12500760.

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In this paper, which is part of a study of positive representations of locally compact groups in Banach lattices, we initiate the theory of positive representations of finite groups in Riesz spaces. If such a representation has only the zero subspace and possibly the space itself as invariant principal bands, then the space is Archimedean and finite-dimensional. Various notions of irreducibility of a positive representation are introduced and, for a finite group acting positively in a space with sufficiently many projections, these are shown to be equal. We describe the finite-dimensional positive Archimedean representations of a finite group and establish that, up to order equivalence, these are order direct sums, with unique multiplicities, of the order indecomposable positive representations naturally associated with transitive G-spaces. Character theory is shown to break down for positive representations. Induction and systems of imprimitivity are introduced in an ordered context, where the multiplicity formulation of Frobenius reciprocity turns out not to hold.
24

Błaszczyszyn, Bartłomiej, and D. Yogeshwaran. "Directionally convex ordering of random measures, shot noise fields, and some applications to wireless communications." Advances in Applied Probability 41, no. 03 (September 2009): 623–46. http://dx.doi.org/10.1017/s0001867800003499.

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Directionally convex ordering is a useful tool for comparing the dependence structure of random vectors, which also takes into account the variability of the marginal distributions. It can be extended to random fields by comparing all finite-dimensional distributions. Viewing locally finite measures as nonnegative fields of measure values indexed by the bounded Borel subsets of the space, in this paper we formulate and study directionally convex ordering of random measures on locally compact spaces. We show that the directionally convex order is preserved under some of the natural operations considered on random measures and point processes, such as deterministic displacement of points, independent superposition, and thinning, as well as independent, identically distributed marking. Further operations on Cox point processes such as position-dependent marking and displacement of points are shown to preserve the order. We also examine the impact of the directionally convex order on the second moment properties, in particular on clustering and on Palm distributions. Comparisons of Ripley's functions and pair correlation functions, as well as examples, seem to indicate that point processes higher in the directionally convex order cluster more. In our main result we show that nonnegative integral shot noise fields with respect to the directionally convex ordered random measures inherit this ordering from the measures. Numerous applications of this result are shown, in particular to comparison of various Cox processes and some performance measures of wireless networks, in both of which shot noise fields appear as key ingredients. We also mention a few pertinent open questions.
25

Błaszczyszyn, Bartłomiej, and D. Yogeshwaran. "Directionally convex ordering of random measures, shot noise fields, and some applications to wireless communications." Advances in Applied Probability 41, no. 3 (September 2009): 623–46. http://dx.doi.org/10.1239/aap/1253281057.

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Directionally convex ordering is a useful tool for comparing the dependence structure of random vectors, which also takes into account the variability of the marginal distributions. It can be extended to random fields by comparing all finite-dimensional distributions. Viewing locally finite measures as nonnegative fields of measure values indexed by the bounded Borel subsets of the space, in this paper we formulate and study directionally convex ordering of random measures on locally compact spaces. We show that the directionally convex order is preserved under some of the natural operations considered on random measures and point processes, such as deterministic displacement of points, independent superposition, and thinning, as well as independent, identically distributed marking. Further operations on Cox point processes such as position-dependent marking and displacement of points are shown to preserve the order. We also examine the impact of the directionally convex order on the second moment properties, in particular on clustering and on Palm distributions. Comparisons of Ripley's functions and pair correlation functions, as well as examples, seem to indicate that point processes higher in the directionally convex order cluster more. In our main result we show that nonnegative integral shot noise fields with respect to the directionally convex ordered random measures inherit this ordering from the measures. Numerous applications of this result are shown, in particular to comparison of various Cox processes and some performance measures of wireless networks, in both of which shot noise fields appear as key ingredients. We also mention a few pertinent open questions.
26

Yamamuro, Sadayuki. "Absolute values in orthogonally decomposable spaces." Bulletin of the Australian Mathematical Society 31, no. 2 (April 1985): 215–33. http://dx.doi.org/10.1017/s0004972700004706.

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In an ordered Banach space which is orthogonally decomposable, we define the absolute value and its general properties are given. The results are used to study the properties of linear operators which satisfy Kato's inequality and the locality condition.
27

Gill, Ramandeep, and Jonathan Granot. "Temporal evolution of prompt GRB polarization." Monthly Notices of the Royal Astronomical Society 504, no. 2 (April 12, 2021): 1939–58. http://dx.doi.org/10.1093/mnras/stab1013.

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ABSTRACT The dominant radiation mechanism that produces the prompt emission in gamma-ray bursts (GRBs) remains a major open question. Spectral information alone has proven insufficient in elucidating its nature. Time-resolved linear polarization has the potential to distinguish between popular emission mechanisms, e.g. synchrotron radiation from electrons with a power-law energy distribution or inverse Compton scattering of soft seed thermal photons, which can yield the typical GRB spectrum but produce different levels of polarization. Furthermore, it can be used to learn about the outflow’s composition (i.e. whether it is kinetic-energy-dominated or Poynting-flux-dominated) and angular structure. For synchrotron emission, it is a powerful probe of the magnetic field geometry. Here, we consider synchrotron emission from a thin ultrarelativistic outflow, with bulk Lorentz factor Γ(R) = Γ0(R/R0)−m/2 ≫ 1, that radiates a Band-function spectrum in a single (multiple) pulse(s) over a range of radii, R0 ≤ R ≤ R0 + ΔR. Pulse profiles and polarization evolution at a given energy are presented for a coasting (m = 0) and accelerating (m = −2/3) thin spherical shell and for different viewing angles for a top-hat jet with sharp as well as smooth edges in emissivity. Four different magnetic field configurations are considered, such as a locally ordered field coherent over angular scales θB ≳ 1/Γ, a tangled field (B⊥) in the plane transverse to the radial direction, an ordered field (B∥) aligned in the radial direction, and a globally ordered toroidal field (Btor). All field configurations produce distinct polarization evolution with single (for B⊥ and B∥) and double (for Btor) 90○ changes in the polarization position angle.
28

Chen, Michael Chun-Yuan, James Di Francesco, Jaime E. Pineda, Stella S. R. Offner, and Rachel K. Friesen. "Turbulence and Accretion: A High-resolution Study of the B5 Filaments." Astrophysical Journal 935, no. 1 (August 1, 2022): 57. http://dx.doi.org/10.3847/1538-4357/ac7d4a.

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Abstract High-resolution observations of the Perseus B5 “core” have previously revealed that this subsonic region actually consists of several filaments that are likely in the process of forming a quadruple stellar system. Since subsonic filaments are thought to be produced at the ∼0.1 pc sonic scale by turbulent compression, a detailed kinematic study is crucial to test such a scenario in the context of core and star formation. Here we present a detailed kinematic follow-up study of the B5 filaments at a 0.009 pc resolution using the VLA and GBT combined observations fitted with multicomponent spectral models. Using precisely identified filament spines, we find a remarkable resemblance between the averaged width profiles of each filament and Plummer-like functions, with filaments possessing FWHM widths of ∼0.03 pc. The velocity dispersion profiles of the filaments also show decreasing trends toward the filament spines. Moreover, the velocity gradient field in B5 appears to be locally well ordered (∼0.04 pc) but globally complex, with kinematic behaviors suggestive of inhomogeneous turbulent accretion onto filaments and longitudinal flows toward a local overdensity along one of the filaments.
29

O’Brien, Michael J., Blakesley Burkhart, and Michael J. Shelley. "Studying Interstellar Turbulence Driving Scales Using the Bispectrum." Astrophysical Journal 930, no. 2 (May 1, 2022): 149. http://dx.doi.org/10.3847/1538-4357/ac6502.

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Abstract We demonstrate the utility of the bispectrum, the Fourier three-point correlation function, for studying driving scales of magnetohydrodynamic (MHD) turbulence in the interstellar medium. We calculate the bispectrum by implementing a parallelized Monte Carlo direct measurement method, which we have made publicly available. In previous works, the bispectrum has been used to identify nonlinear scaling correlations and break degeneracies in lower-order statistics like the power spectrum. We find that the bicoherence, a related statistic which measures phase coupling of Fourier modes, identifies turbulence-driving scales using density and column density fields. In particular, it shows that the driving scale is phase-coupled to scales present in the turbulent cascade. We also find that the presence of an ordered magnetic field at large scales enhances phase coupling as compared to a pure hydrodynamic case. We therefore suggest the bispectrum and bicoherence as tools for searching for non-locality for wave interactions in MHD turbulence.
30

Ayaß, Ruth. "Doing Waiting: An Ethnomethodological Analysis." Journal of Contemporary Ethnography 49, no. 4 (January 24, 2020): 419–55. http://dx.doi.org/10.1177/0891241619897413.

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Waiting is an activity that is virtually carried out by everybody at every time and everywhere. In contrast to other occupations, such as playing the piano, it does not require painstaking training efforts. Notwithstanding, we do possess methodically employed techniques of indicating to others that we are waiting—that is, we make our waiting recognizable as such. Many forms of waiting in everyday life are bound to specific places: waiting shelters, waiting rooms, waiting halls. The waiting person is thus visible and frequently forms a waiting community with fellow waiting people. Moreover, many forms of waiting take a specific form (a queue). But also in situations where such recognizable social formations are not possible (e.g., when waiting alone), people make clear to themselves and to others that they are waiting. Primarily people waiting in publicly accessible spaces demonstrate to each other and to others what they are doing—that is, waiting. They do so in a methodical way and thus make their actions accountable for themselves and others as an ordered structure. Hence, there is a sense in which waiting people wait competently, making their waiting visible to others as a “doing”—a “doing waiting” in the sense of ethnomethodology. The essay pursues the question of waiting people’s particular handling of the space they are in and the material available to them: which spatial resources are made available to them by the specific locality? Which material resources are provided? In what ways do waiting people make use of this space and the objects to which they have access? How do they use other elements of the physical environment? Which additional resources are brought along? The article addresses these questions by using empirical data of natural situations of waiting (ethnographic fieldnotes, photographs, drawings, and video recordings).
31

"Periodic point and fixed point results for monotone mappings in complete ordered locally convex spaces with application to differential equations." Advances in Fixed Point Theory, 2019. http://dx.doi.org/10.28919/afpt/4185.

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32

Hollinshead, Keith, and Vannsy Kuon. "Culture Dynamics across the World Today: Tourism and the Palette of Imagination." Journal of Geographical Research 4, no. 4 (November 9, 2021). http://dx.doi.org/10.30564/jgr.v4i4.3488.

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In general,this manuscript critiques the contemporary dynamisms of the formation/deformation of the cultural sphere under the increased mobilisations of globalization.In particular,it inspects the symphysis [SYMPHYSIS] between 'tourism' and 'culture',where the latter stands as an immense portmanteau phenomenon embracing many different things (under the vicissitudes of globalisation/glocalisation) across the protean realms of race, gender, entertainment, consumerism, meaning-making, et cetera.Critiquing Jamal and Robinson's recent attempt at panoramic coverage of the geography of tourism/tourism studies), it argues that tourism is regularly implicated in cultural practices relating to power-exercises in/across society. Then, in synthesising Bauman’s vision of contemporary society as that moving from seemingly well-ordered stabilities to a geographic realm where change is the-only-permanence and uncertainty the-onlycertainty, the manuscript generates five lead propositions calling for 'plural knowability',viz.,for a deeper/richer palette-of-imagination on the teeming multiplicities and throbbing provisionalities of culture as it emerges/unfolds or otherwise gets recast under the destabilising 'nomadic logics' of our time. In viewing culture as a vehicle of both 'impermanence' and 'seduction nowadays, the paper notes how in so many places and spaces, individuals are less inclined to be engaged locally/regionally/nationally as culture —partly through the volatile iterability of travel/tourism — has become an ever-widening polylogue.
33

Ayaseh, D., та A. Ranjbari. "Порядково борнологические локально выпуклые решеточные конусы". Владикавказский математический журнал, № 3(3) (18 вересня 2017). http://dx.doi.org/10.23671/vnc.2017.3.7109.

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In this paper, we introduce the concepts of $us$-lattice cones and order bornological locally convex lattice cones. In the special case of locally convex solid Riesz spaces, these concepts reduce to the known concepts of seminormed Riesz spaces and order bornological Riesz spaces, respectively. We define solid sets in locally convex cones and present some characterizations for order bornological locally convex lattice cones.
34

Sarazin, Matthieu X. B., Julie Victor, David Medernach, Jérémie Naudé, and Bruno Delord. "Online Learning and Memory of Neural Trajectory Replays for Prefrontal Persistent and Dynamic Representations in the Irregular Asynchronous State." Frontiers in Neural Circuits 15 (July 8, 2021). http://dx.doi.org/10.3389/fncir.2021.648538.

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In the prefrontal cortex (PFC), higher-order cognitive functions and adaptive flexible behaviors rely on continuous dynamical sequences of spiking activity that constitute neural trajectories in the state space of activity. Neural trajectories subserve diverse representations, from explicit mappings in physical spaces to generalized mappings in the task space, and up to complex abstract transformations such as working memory, decision-making and behavioral planning. Computational models have separately assessed learning and replay of neural trajectories, often using unrealistic learning rules or decoupling simulations for learning from replay. Hence, the question remains open of how neural trajectories are learned, memorized and replayed online, with permanently acting biological plasticity rules. The asynchronous irregular regime characterizing cortical dynamics in awake conditions exerts a major source of disorder that may jeopardize plasticity and replay of locally ordered activity. Here, we show that a recurrent model of local PFC circuitry endowed with realistic synaptic spike timing-dependent plasticity and scaling processes can learn, memorize and replay large-size neural trajectories online under asynchronous irregular dynamics, at regular or fast (sped-up) timescale. Presented trajectories are quickly learned (within seconds) as synaptic engrams in the network, and the model is able to chunk overlapping trajectories presented separately. These trajectory engrams last long-term (dozen hours) and trajectory replays can be triggered over an hour. In turn, we show the conditions under which trajectory engrams and replays preserve asynchronous irregular dynamics in the network. Functionally, spiking activity during trajectory replays at regular timescale accounts for both dynamical coding with temporal tuning in individual neurons, persistent activity at the population level, and large levels of variability consistent with observed cognitive-related PFC dynamics. Together, these results offer a consistent theoretical framework accounting for how neural trajectories can be learned, memorized and replayed in PFC networks circuits to subserve flexible dynamic representations and adaptive behaviors.
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Di Nola, Antonio, Giacomo Lenzi, and Luca Spada. "Sheaf representations and locality of Riesz spaces with order unit." Journal of Logic and Analysis 13 (May 11, 2021). http://dx.doi.org/10.4115/jla.2021.13.2.

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We present an algebraic study of Riesz spaces (=real vector lattices) with a (strong) order unit. We exploit a categorical equivalence between those structures and a variety of algebras called RMV-algebras. We prove two different sheaf representations for Riesz spaces with order unit: the first represents them as sheaves of linearly ordered Riesz spaces over a spectral space, the second represent them as sheaves of "local" Riesz spaces over a compact Hausdorff space. Motivated by the latter representation we study the class of local RMV-algebras. We study the algebraic properties of local RMV-algebra and provide a characterisation of them as special retracts of the real interval [0,1]. Finally, we prove that the category of local RMV-algebras is equivalent to the category of all Riesz spaces.
36

Bayes, Chantelle. "The Cyborg Flâneur: Reimagining Urban Nature through the Act of Walking." M/C Journal 21, no. 4 (October 15, 2018). http://dx.doi.org/10.5204/mcj.1444.

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The concept of the “writer flâneur”, as developed by Walter Benjamin, sought to make sense of the seemingly chaotic nineteenth century city. While the flâneur provided a way for new urban structures to be ordered, it was also a transgressive act that involved engaging with urban spaces in new ways. In the contemporary city, where spaces are now heavily controlled and ordered, some members of the city’s socio-ecological community suffer as a result of idealistic notions of who and what belongs in the city, and how we must behave as urban citizens. Many of these ideals emerge from nineteenth century conceptions of the city in contrast to the country (Williams). However, a reimagining of the flâneur can allow for new transgressions of urban space and result in new literary imaginaries that capture the complexity of urban environments, question some of the more damaging processes and systems, offer new ways of connecting with the city, and propose alternative ways of living with the non-human in such places. With reference to the work of Debra Benita Shaw, Rob Shields and Donna Haraway, I will examine how the urban walking figure might be reimagined as cyborg, complicating boundaries between the real and imagined, the organic and inorganic, and between the human and non-human (Haraway Cyborgs). I will argue that the cyborg flâneur allows for new ways of writing and reading the urban and can work to reimagine the city as posthuman multispecies community. As one example of cyborg flânerie, I look to the app Story City to show how a writer can develop new environmental imaginaries in situ as an act of resistance against the anthropocentric ordering of the city. This article intends to begin a conversation about the ethical, political and epistemological potential of cyborg flânerie and leads to several questions which will require further research.Shaping the City: Environmental ImaginariesIn a sense, the flâneur is the product of a utopian imaginary of the city. According to Shields, Walter Benjamin used the flâneur as a literary device to make sense of the changing modern city of Paris: The flâneur is a hero who excels under the stress of coming to terms with a changing ‘social spatialisation’ of everyday social and economic relations which in the nineteenth century increasingly extended the world of the average person further and further to include rival mass tourism destinations linked by railroad, news of other European powers and distant colonies. This expanding spatialization took the form of economic realities such as changing labour markets and commodity prices and social encounters with strangers and foreigners which impinged on the life world of Europeans. (Fancy Footwork 67)Through his writing, these new spaces and inhabitants were made familiar again to those that lived there. In consequence, the flâneur was seen as a heroic figure who approached the city like a wilderness to be studied and tamed:Even to early 20th-century sociologists the flâneur was a heroic everyman—masculine, controlled and as in tune with his environment as James Fenimore Cooper’s Mohican braves were in their native forests. Anticipating the hardboiled hero of the detective novel, the flâneur pursued clues to the truth of the metropolis, attempting to think through its historical specificity, to inhabit it, even as the truth of empire and commodity capitalism was hidden from him. (Shields Flanerie 210)In this way, the flâneur was a stabilising force, categorising and therefore ordering the city. However, flânerie was also a transgressive act as the walker engaged in eccentric and idle wandering against the usual purposeful walking practices of the time (Coates). Drawing on this aspect, flânerie has increasingly been employed in the humanities and social sciences as a practice of resistance as Jamie Coates has shown. This makes the flâneur, albeit in a refigured form, a useful tool for transgressing strict socio-ecological conventions that affect the contemporary city.Marginalised groups are usually the most impacted by the strict control and ordering of contemporary urban spaces in response to utopian imaginaries of who and what belong. Marginalised people are discouraged and excluded from living in particular areas of the city through urban policy and commercial practices (Shaw 7). Likewise, certain non-human others, like birds, are allowed to inhabit our cities while those that don’t fit ideal urban imaginaries, like bats or snakes, are controlled, excluded or killed (Low). Defensive architecture, CCTV, and audio deterrents are often employed in cities to control public spaces. In London, the spiked corridor of a shop entrance designed to keep homeless people from sleeping there (Andreou; Borromeo) mirrors the spiked ledges that keep pigeons from resting on buildings (observed 2012/2014). On the Gold Coast youths are deterred from loitering in public spaces with classical music (observed 2013–17), while in Brisbane predatory bird calls are played near outdoor restaurants to discourage ibis from pestering customers (Hinchliffe and Begley). In contrast, bright lights, calming music and inviting scents are used to welcome orderly consumers into shopping centres while certain kinds of plants are cultivated in urban parks and gardens to attract acceptable wildlife like butterflies and lorikeets (Wilson; Low). These ways of managing public spaces are built on utopian conceptions of the city as a “civilising” force—a place of order, consumption and safety.As environmental concerns become more urgent, it is important to re-examine these conceptions of urban environments and the assemblage of environmental imaginaries that interact and continue to shape understandings of and attitudes towards human and non-human nature. The network of goods, people and natural entities that feed into and support the city mean that imaginaries shaped in urban areas influence both urban and surrounding peoples and ecologies (Braun). Local ecologies also become threatened as urban structures and processes continue to encompass more of the world’s populations and locales, often displacing and damaging entangled natural/cultural entities in the process. Furthermore, conceptions and attitudes shaped in the city often feed into global systems and as such can have far reaching implications for the way local ecologies are governed, built, and managed. There has already been much research, including work by Lawrence Buell and Ursula Heise, on the contribution that art and literature can make to the development of environmental imaginaries, whether intentional or unintentional, and resulting in both positive and negative associations with urban inhabitants (Yusoff and Gabrys; Buell; Heise). Imaginaries might be understood as social constructs through which we make sense of the world and through which we determine cultural and personal values, attitudes and beliefs. According to Neimanis et al., environmental imaginaries help us to make sense of the way physical environments shape “one’s sense of social belonging” as well as how we “formulate—and enact—our values and attitudes towards ‘nature’” (5). These environmental imaginaries underlie urban structures and work to determine which aspects of the city are valued, who is welcomed into the city, and who is excluded from participation in urban systems and processes. The development of new narrative imaginaries can question some of the underlying assumptions about who or what belongs in the city and how we might settle conflicts in ecologically diverse communities. The reimagined flâneur then might be employed to transgress traditional notions of belonging in the city and replace this with a sense of “becoming” in relation with the myriad of others inhabiting the city (Haraway The Trouble). Like the Benjaminian flâneur, the postmodern version enacts a similar transgressive walking practice. However, the postmodern flâneur serves to resist dominant narratives, with a “greater focus on the tactile and grounded qualities of walking” than the traditional flâneur—and, as opposed to the lone detached wanderer, postmodern flâneur engage in a network of social relationships and may even wander in groups (Coates 32). By employing the notion of the postmodern flâneur, writers might find ways to address problematic urban imaginaries and question dominant narratives about who should and should not inhabit the city. Building on this and in reference to Haraway (Cyborgs), the notion of a cyborg flâneur might take this resistance one step further, not only seeking to counter the dominant social narratives that control urban spaces but also resisting anthropocentric notions of the city. Where the traditional flâneur walked a pet tortoise on a leash, the cyborg flâneur walks with a companion species (Shields Fancy Footwork; Haraway Companion Species). The distinction is subtle. The traditional flâneur walks a pet, an object of display that showcases the eccentric status of the owner. The cyborg flâneur walks in mutual enjoyment with a companion (perhaps a domestic companion, perhaps not); their path negotiated together, tracked, and mapped via GPS. The two acts may at first appear the same, but the difference is in the relationship between the human, non-human, and the multi-modal spaces they occupy. As Coates argues, not everyone who walks is a flâneur and similarly, not everyone who engages in relational walking is a cyborg flâneur. Rather a cyborg flâneur enacts a deliberate practice of walking in relation with naturecultures to transgress boundaries between human and non-human, cultural and natural, and the virtual, material and imagined spaces that make up a place.The Posthuman City: Cyborgs, Hybrids, and EntanglementsIn developing new environmental imaginaries, posthuman conceptions of the city can be drawn upon to readdress urban space as complex, questioning utopian notions of the city particularly as they relate to the exclusion of certain others, and allowing for diverse socio-ecological communities. The posthuman city might be understood in opposition to anthropocentric notions where the non-human is seen as something separate to culture and in need of management and control within the human sphere of the city. Instead, the posthuman city is a complex entanglement of hybrid non-human, cultural and technological entities (Braun; Haraway Companion Species). The flâneur who experiences the city through a posthuman lens acknowledges the human as already embodied and embedded in the non-human world. Key to re-imagining the city is recognising the myriad ways in which non-human nature also acts upon us and influences decisions on how we live in cities (Schliephake 140). This constitutes a “becoming-with each other”, in Haraway’s terms, which recognises the interdependency of urban inhabitants (The Trouble 3). In re-considering the city as a negotiated process between nature and culture rather than a colonisation of nature by culture, the agency of non-humans to contribute to the construction of cities and indeed environmental imaginaries must be acknowledged. Living in the posthuman city requires us humans to engage with the city on multiple levels as we navigate the virtual, corporeal, and imagined spaces that make up the contemporary urban experience. The virtual city is made up of narratives projected through media productions such as tourism campaigns, informational plaques, site markers, and images on Google map locations, all of which privilege certain understandings of the city. Virtual narratives serve to define the city through a network of historical and spatially determined locales. Closely bound up with the virtual is the imagined city that draws on urban ideals, potential developments, mythical or alternative versions of particular cities as well as literary interpretations of cities. These narratives are overlaid on the places that we engage with in our everyday lived experiences. Embodied encounters with the city serve to reinforce or counteract certain virtual and imagined versions while imagined and virtual narratives enhance locales by placing current experience within a temporal narrative that extends into the past as well as the future. Walking the City: The Cyber/Cyborg FlâneurThe notion of the cyber flâneur emerged in the twenty-first century from the practices of idly surfing the Internet, which in many ways has become an extension of the cityscape. In the contemporary world where we exist in both physical and digital spaces, the cyber flâneur (and indeed its cousin the virtual flâneur) have been employed to make sense of new digital sites of connection, voyeurism, and consumption. Metaphors that evoke the city have often been used to describe the experience of the digital including “chat rooms”, “cyber space”, and “home pages” while new notions of digital tourism, the rise of online shopping, and meeting apps have become substitutes for engaging with the physical sites of cities such as shopping malls, pubs, and attractions. The flâneur and cyberflâneur have helped to make sense of the complexities and chaos of urban life so that it might become more palatable to the inhabitants, reducing anxieties about safety and disorder. However, as with the concept of the flâneur, implicit in the cyberflâneur is a reinforcement of traditional urban hierarchies and social structures. This categorising has also worked to solidify notions of who belongs and who does not. Therefore, as Debra Benita Shaw argues, the cyberflâneur is not able to represent the complexities of “how we inhabit and experience the hybrid spaces of contemporary cities” (3). Here, Shaw suggests that Haraway’s cyborg might be used to interrupt settled boundaries and to reimagine the urban walking figure. In both Shaw and Shields (Flanerie), the cyborg is invoked as a solution to the problematic figure of the flâneur. While Shaw presents these figures in opposition and proposes that the flâneur be laid to rest as the cyborg takes its place, I argue that the idea of the flâneur may still have some use, particularly when applied to new multi-modal narratives. As Shields demonstrates, the cyborg operates in the virtual space of simulation rather than at the material level (217). Instead of setting up an opposition between the cyborg and flâneur, these figures might be merged to bring the cyborg into being through the material practice of flânerie, while refiguring the flâneur as posthuman. The traditional flâneur sought to define space, but the cyborg flâneur might be seen to perform space in relation to an entangled natural/cultural community. By drawing on this notion of the cyborg, it becomes possible to circumvent some of the traditional associations with the urban walking figure and imagine a new kind of flâneur, one that walks the streets as an act to complicate rather than compartmentalise urban space. As we emerge into a post-truth world where facts and fictions blur, creative practitioners can find opportunities to forge new ways of knowing, and new ways of connecting with the city through the cyborg flâneur. The development of new literary imaginaries can reconstruct natural/cultural relationships and propose alternative ways of living in a posthuman and multispecies community. The rise of smart-phone apps like Story City provides cyborg flâneurs with the ability to create digital narratives overlaid on real places and has the potential to encourage real connections with urban environments. While these apps are by no means the only activity that a cyborg flâneur might participate in, they offer the writer a platform to engage audiences in a purposeful and transgressive practice of cyborg flânerie. Such narratives produced through cyborg flânerie would conflate virtual, corporeal, and imagined experiences of the city and allow for new environmental imaginaries to be created in situ. The “readers” of these narratives can also become cyborg flâneurs as the traditional urban wanderer is combined with the virtual and imagined space of the contemporary city. As opposed to wandering the virtual city online, readers are encouraged to physically walk the city and engage with the narrative in situ. For example, in one narrative, readers are directed to walk a trail along the Brisbane river or through the CBD to chase a sea monster (Wilkins and Diskett). The reader can choose different pre-set paths which influence the outcome of each story and embed the story in a physical location. In this way, the narrative is layered onto the real streets and spaces of the cityscape. As the reader is directed to walk particular routes through the city, the narratives which unfold are also partly constructed by the natural/cultural entities which make up those locales establishing a narrative practice which engages with the urban on a posthuman level. The murky water of the Brisbane River could easily conceal monsters. Occasional sightings of crocodiles (Hall), fish that leap from the water, and shadows cast by rippling waves as the City Cat moves across the surface impact the experience of the story (observed 2016–2017). Potential exists to capitalise on this narrative form and develop new environmental imaginaries that pay attention to the city as a posthuman place. For example, a narrative might direct the reader’s attention to the networks of water that hydrate people and animals, allow transportation, and remove wastes from the city. People may also be directed to explore their senses within place, be encouraged to participate in sensory gardens, or respond to features of the city in new ways. The cyborg flâneur might be employed in much the same way as the flâneur, to help the “reader” make sense of the posthuman city, where boundaries are shifted, and increasing rates of social and ecological change are transforming contemporary urban sites and structures. Shields asks whether the cyborg might also act as “a stabilising figure amidst the collapse of dualisms, polluted categories, transgressive hybrids, and unstable fluidity” (Flanerie 211). As opposed to the traditional flâneur however, this “stabilising” figure doesn’t sort urban inhabitants into discrete categories but maps the many relations between organisms and technologies, fictions and realities, and the human and non-human. The cyborg flâneur allows for other kinds of “reading” of the city to take place—including those by women, families, and non-Western inhabitants. As opposed to the nineteenth century reader-flâneur, those who read the city through the Story City app are also participants in the making of the story, co-constructing the narrative along with the author and locale. I would argue this participation is a key feature of the cyborg flâneur narrative along with the transience of the narratives which may alter and eventually expire as urban structures and environments change. Not all those who engage with these narratives will necessarily enact a posthuman understanding and not all writers of these narratives will do so as cyborg flâneurs. Nevertheless, platforms such as Story City provide writers with an opportunity to engage participants to question dominant narratives of the city and to reimagine themselves within a multispecies community. In addition, by bringing readers into contact with the human and non-human entities that make up the city, there is potential for real relationships to be established. Through new digital platforms such as apps, writers can develop new environmental imaginaries that question urban ideals including conceptions about who belongs in the city and who does not. The notion of the cyborg is a useful concept through which to reimagine the city as a negotiated process between nature and culture, and to reimagine the flâneur as performer who becomes part of the posthuman city as they walk the streets. This article provides one example of cyborg flânerie in smart-phone apps like Story City that allow writers to construct new urban imaginaries, bring the virtual and imagined city into the physical spaces of the urban environment, and can act to re-place the reader in diverse socio-ecological communities. The reader then becomes both product and constructer of urban space, a cyborg flâneur in the cyborg city. This conversation raises further questions about the cyborg flâneur, including: how might cyborg flânerie be enacted in other spaces (rural, virtual, more-than-human)? What other platforms and narrative forms might cyborg flâneurs use to share their posthuman narratives? How might cyborg flânerie operate in other cities, other cultures and when adopted by marginalised groups? In answering these questions, the potential and limitations of the cyborg flâneur might be refined. The hope is that one day the notion of a cyborg flâneur will no longer necessary as the posthuman city becomes a space of negotiation rather than exclusion. ReferencesAndreou, Alex. “Anti-Homeless Spikes: ‘Sleeping Rough Opened My Eyes to the City’s Barbed Cruelty.’” The Guardian 19 Feb. 2015. 25 Aug. 2017 <https://www.theguardian.com/society/2015/feb/18/defensive-architecture-keeps-poverty-undeen-and-makes-us-more-hostile>.Borromeo, Leah. “These Anti-Homeless Spikes Are Brutal. We Need to Get Rid of Them.” The Guardian 23 Jul. 2015. 25 Aug. 2017 <https://www.theguardian.com/commentisfree/2015/jul/23/anti-homeless-spikes-inhumane-defensive-architecture>.Braun, Bruce. “Environmental Issues: Writing a More-than-Human Urban Geography.” Progress in Human Geography 29.5 (2005): 635–50. Buell, Lawrence. The Future of Environmental Criticism: Environmental Crisis and Literary Imagination. Malden: Blackwell, 2005.Coates, Jamie. “Key Figure of Mobility: The Flâneur.” Social Anthropology 25.1 (2017): 28–41.Hall, Peter. “Crocodiles Spotted in Queensland: A Brief History of Sightings and Captures in the Southeast.” The Courier Mail 4 Jan. 2017. 20 Aug. 2017 <http://www.couriermail.com.au/news/queensland/crocodiles-spotted-in-queensland-a-brief-history-of-sightings-and-captures-in-the-southeast/news-story/5fbb2d44bf3537b8a6d1f6c8613e2789>.Haraway, Donna J. Staying with the Trouble: Making Kin in the Chthulucene. Durham: Duke UP, 2016.———. The Companion Species Manifesto: Dogs, People, and Significant Otherness. Vol. 1. Chicago: Prickly Paradigm Press, 2003.———. Simians, Cyborgs, and Women: The Reinvention of Nature. Oxon: Routledge, 1991.Heise, Ursula K. Sense of Place and Sense of Planet: The Environmental Imagination of the Global. Oxford: Oxford UP, 2008. Hinchliffe, Jessica, and Terri Begley. “Brisbane’s Angry Birds: Recordings No Deterrent for Nosey Ibis at South Bank.” ABC News 2 Jun. 2015. 25 Aug. 2017 <http://www.abc.net.au/news/2015-02-06/recorded-bird-noise-not-detering-south-banks-angry-birds/6065610>.Low, Tim. The New Nature: Winners and Losers in Wild Australia. London: Penguin, 2002.Neimanis, Astrid, Cecilia Asberg, and Suzi Hayes. “Posthumanist Imaginaries.” Research Handbook on Climate Governance. Eds. K. Bäckstrand and E. Lövbrand. Massachusetts: Edward Elgar Publishing, 2015. 480–90.Schliephake, Christopher. Urban Ecologies: City Space, Material Agency, and Environmental Politics in Contemporary Culture. Maryland: Lexington Books, 2014.Shaw, Debra Benita. “Streets for Cyborgs: The Electronic Flâneur and the Posthuman City.” Space and Culture 18.3 (2015): 230–42.Shields, Rob. “Fancy Footwork: Walter Benjamin’s Notes on Flânerie.” The Flâneur. Ed. Keith Tester. London: Routledge, 2014. 61–80.———. “Flânerie for Cyborgs.” Theory, Culture & Society 23.7-8 (2006): 209–20.Yusoff, Kathryn, and Jennifer Gabrys. “Climate Change and the Imagination.” Wiley Interdisciplinary Reviews: Climate Change 2.4 (2011): 516–34.Wilkins, Kim, and Joseph Diskett. 9 Fathom Deep. Brisbane: Story City, 2014. Williams, Raymond. The Country and the City. New York: Oxford UP, 1975.Wilson, Alexander. The Culture of Nature: North American Landscape from Disney to the Exxon Valdez. Toronto: Between the Lines, 1991.
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Haupt, Adam. "Queering Hip-Hop, Queering the City: Dope Saint Jude’s Transformative Politics." M/C Journal 19, no. 4 (August 31, 2016). http://dx.doi.org/10.5204/mcj.1125.

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This paper argues that artist Dope Saint Jude is transforming South African hip-hop by queering a genre that has predominantly been male and heteronormative. Specifically, I analyse the opening skit of her music video “Keep in Touch” in order to unpack the ways which she revives Gayle, a gay language that adopted double-coded forms of speech during the apartheid era—a context in which homosexuals were criminalised. The use of Gayle and spaces close to the city centre of Cape Town (such as Salt River and Woodstock) speaks to the city as it was before it was transformed by the decline of industries due to the country’s adoption of neoliberal economics and, more recently, by the gentrification of these spaces. Dope Saint Jude therefore reclaims these city spaces through her use of gay modes of speech that have a long history in Cape Town and by positioning her work as hip-hop, which has been popular in the city for well over two decades. Her inclusion of transgender MC and DJ Angel Ho pushes the boundaries of hegemonic and binary conceptions of gender identity even further. In essence, Dope Saint Jude is transforming local hip-hop in a context that is shaped significantly by US cultural imperialism. The artist is also transforming our perspective of spaces that have been altered by neoliberal economics.Setting the SceneDope Saint Jude (DSJ) is a queer MC from Elsies River, a working class township located on Cape Town's Cape Flats in South Africa. Elsies River was defined as a “coloured” neighbourhood under the apartheid state's Group Areas Act, which segregated South Africans racially. With the aid of the Population Registration Act, citizens were classified, not merely along the lines of white, Asian, or black—black subjects were also divided into further categories. The apartheid state also distinguished between black and “coloured” subjects. Michael MacDonald contends that segregation “ordained blacks to be inferior to whites; apartheid cast them to be indelibly different” (11). Apartheid declared “African claims in South Africa to be inferior to white claims” and effectively claimed that black subjects “belonged elsewhere, in societies of their own, because their race was different” (ibid). The term “coloured” defined people as “mixed race” to separate communities that might otherwise have identified as black in the broad and inclusive sense (Erasmus 16). Racial categorisation was used to create a racial hierarchy with white subjects at the top of that hierarchy and those classified as black receiving the least resources and benefits. This frustrated attempts to establish broad alliances of black struggles against apartheid. It is in this sense that race is socially and politically constructed and continues to have currency, despite the fact that biologically essentialist understandings of race have been discredited (Yudell 13–14). Thanks to apartheid town planning and resource allocation, many townships on the Cape Flats were poverty-stricken and plagued by gang violence (Salo 363). This continues to be the case because post-apartheid South Africa's embrace of neoliberal economics failed to address racialised class inequalities significantly (Haupt, Static 6–8). This is the '90s context in which socially conscious hip-hop crews, such as Prophets of da City or Black Noise, came together. They drew inspiration from Black Consciousness philosophy via their exposure to US hip-hop crews such as Public Enemy in order to challenge apartheid policies, including their racial interpellation as “coloured” as distinct from the more inclusive category, black (Haupt, “Black Thing” 178). Prophets of da City—whose co-founding member, Shaheen Ariefdien, also lived in Elsies River—was the first South African hip-hop outfit to record an album. Whilst much of their work was performed in English, they quickly transformed the genre by rapping in non-standard varieties of Afrikaans and by including MCs who rap in African languages (ibid). They therefore succeeded in addressing key issues related to race, language, and class disparities in relation to South Africa's transition to democracy (Haupt, “Black Thing”; Haupt, Stealing Empire). However, as is the case with mainstream US hip-hop, specifically gangsta rap (Clay 149), South African hip-hop has been largely dominated by heterosexual men. This includes the more commercial hip-hop scene, which is largely perceived to be located in Johannesburg, where male MCs like AKA and Cassper Nyovest became celebrities. However, certain female MCs have claimed the genre, notably EJ von Lyrik and Burni Aman who are formerly of Godessa, the first female hip-hop crew to record and perform locally and internationally (Haupt, Stealing Empire 166; Haupt, “Can a Woman in Hip-Hop”). DSJ therefore presents the exception to a largely heteronormative and male-dominated South African music industry and hip-hop scene as she transforms it with her queer politics. While queer hip-hop is not new in the US (Pabón and Smalls), this is new territory for South Africa. Writing about the US MC Jean Grae in the context of a “male-dominated music industry and genre,” Shanté Paradigm Smalls contends,Heteronormativity blocks the materiality of the experiences of Black people. Yet, many Black people strive for a heteronormative effect if not “reality”. In hip hop, there is a particular emphasis on maintaining the rigidity of categories, even if those categories fail [sic]. (87) DSJ challenges these rigid categories. Keep in TouchDSJ's most visible entry onto the media landscape to date has been her appearance in an H&M recycling campaign with British Sri Lankan artist MIA (H&M), some fashion shoots, her new EP—Reimagine (Dope Saint Jude)—and recent Finnish, US and French tours as well as her YouTube channel, which features her music videos. As the characters’ theatrical costumes suggest, “Keep in Touch” is possibly the most camp and playful music video she has produced. It commences somewhat comically with Dope Saint Jude walking down Salt River main road to a public telephone, where she and a young woman in pig tails exchange dirty looks. Salt River is located at the foot of Devil's Peak not far from Cape Town's CBD. Many factories were located there, but the area is also surrounded by low-income housing, which was designated a “coloured” area under apartheid. After apartheid, neighbourhoods such as Salt River, Woodstock, and the Bo-Kaap became increasingly gentrified and, instead of becoming more inclusive, many parts of Cape Town continued to be influenced by policies that enable racialised inequalities. Dope Saint Jude calls Angel Ho: DSJ: Awêh, Angie! Yoh, you must check this kak sturvy girl here by the pay phone. [Turns to the girl, who walks away as she bursts a chewing gum bubble.] Ja, you better keep in touch. Anyway, listen here, what are you wys?Angel Ho: Ah, just at the salon getting my hair did. What's good? DSJ: Wanna catch on kak today?Angel Ho: Yes, honey. But, first, let me Gayle you this. By the jol by the art gallery, this Wendy, nuh. This Wendy tapped me on the shoulder and wys me, “This is a place of decorum.”DSJ: What did she wys?Angel Ho: De-corum. She basically told me this is not your house. DSJ: I know you told that girl to keep in touch!Angel Ho: Yes, Mama! I'm Paula, I told that bitch, “Keep in touch!” [Points index finger in the air.](Saint Jude, Dope, “Keep in Touch”)Angel Ho's name is a play on the male name Angelo and refers to the trope of the ho (whore) in gangsta rap lyrics and in music videos that present objectified women as secondary to male, heterosexual narratives (Sharpley-Whiting 23; Collins 27). The queering of Angelo, along with Angel Ho’s non-binary styling in terms of hair, make-up, and attire, appropriates a heterosexist, sexualised stereotype of women in order to create room for a gender identity that operates beyond heteronormative male-female binaries. Angel Ho’s location in a hair salon also speaks to stereotypical associations of salons with women and gay subjects. In a discussion of gender stereotypes about hair salons, Kristen Barber argues that beauty work has traditionally been “associated with women and with gay men” and that “the body beautiful has been tightly linked to the concept of femininity” (455–56). During the telephonic exchange, Angel Ho and Dope Saint Jude code-switch between standard and non-standard varieties of English and Afrikaans, as the opening appellation, “Awêh,” suggests. In this context, the term is a friendly greeting, which intimates solidarity. “Sturvy” means pretentious, whilst “kak” means shit, but here it is used to qualify “sturvy” and means that the girl at the pay phone is very pretentious or “full of airs.” To be “wys” means to be wise, but it can also mean that you are showing someone something or educating them. The meanings of these terms shift, depending on the context. The language practices in this skit are in line with the work of earlier hip-hop crews, such as Prophets of da City and Brasse vannie Kaap, to validate black, multilingual forms of speech and expression that challenge the linguistic imperialism of standard English and Afrikaans in South Africa, which has eleven official languages (Haupt, “Black Thing”; Haupt, Stealing Empire; Williams). Henry Louis Gates’s research on African American speech varieties and literary practices emerging from the repressive context of slavery is essential to understanding hip-hop’s language politics. Hip-hop artists' multilingual wordplay creates parallel discursive universes that operate both on the syntagmatic axis of meaning-making and the paradigmatic axis (Gates 49; Haupt, “Stealing Empire” 76–77). Historically, these discursive universes were those of the slave masters and the slaves, respectively. While white hegemonic meanings are produced on the syntagmatic axis (which is ordered and linear), black modes of speech as seen in hip-hop word play operate on the paradigmatic axis, which is connotative and non-linear (ibid). Distinguishing between Signifyin(g) / Signification (upper case, meaning black expression) and signification (lower case, meaning white dominant expression), he argues that “the signifier ‘Signification’ has remained identical in spelling to its white counterpart to demonstrate [. . .] that a simultaneous, but negated, parallel discursive (ontological, political) universe exists within the larger white discursive universe” (Gates 49). The meanings of terms and expressions can change, depending on the context and manner in which they are used. It is therefore the shared experiences of speech communities (such as slavery or racist/sexist oppression) that determine the negotiated meanings of certain forms of expression. Gayle as a Parallel Discursive UniverseDSJ and Angel Ho's performance of Gayle takes these linguistic practices further. Viewers are offered points of entry into Gayle via the music video’s subtitles. We learn that Wendy is code for a white person and that to keep in touch means exactly the opposite. Saint Jude explains that Gayle is a very fun queer language that was used to kind of mask what people were saying [. . .] It hides meanings and it makes use of women's names [. . . .] But the thing about Gayle is it's constantly changing [. . .] So everywhere you go, you kind of have to pick it up according to the context that you're in. (Ovens, Saint Jude and Haupt)According to Kathryn Luyt, “Gayle originated as Moffietaal [gay language] in the coloured gay drag culture of the Western Cape as a form of slang amongst Afrikaans-speakers which over time, grew into a stylect used by gay English and Afrikaans-speakers across South Africa” (Luyt 8; Cage 4). Given that the apartheid state criminalised homosexuals, Gayle was coded to evade detection and to seek out other members of this speech community (Luyt 8). Luyt qualifies the term “language” by arguing, “The term ‘language’ here, is used not as a constructed language with its own grammar, syntax, morphology and phonology, but in the same way as linguists would discuss women’s language, as a way of speaking, a kind of sociolect” (Luyt 8; Cage 1). However, the double-coded nature of Gayle allows one to think of it as creating a parallel discursive universe as Gates describes it (49). Whereas African American and Cape Flats discursive practices function parallel to white, hegemonic discourses, gay modes of speech run parallel to heteronormative communication. Exclusion and MicroaggressionsThe skit brings both discursive practices into play by creating room for one to consider that DSJ queers a male-dominated genre that is shaped by US cultural imperialism (Haupt, Stealing Empire 166) as a way of speaking back to intersectional forms of marginalisation (Crenshaw 1244), which are created by “white supremacist capitalist patriarchy” (hooks 116). This is significant in South Africa where “curative rape” of lesbians and other forms of homophobic violence are prominent (cf. Gqola; Hames; Msibi). Angel Ho's anecdote conveys a sense of the extent to which black individuals are subject to scrutiny. Ho's interpretation of the claim that the gallery “is a place of decorum” is correct: it is not Ho's house. Black queer subjects are not meant to feel at home or feel a sense of ownership. This functions as a racial microaggression: “subtle insults (verbal, nonverbal, and/or visual) directed toward people of color, often automatically or unconsciously” (Solorzano, Ceja, and Yosso 60). This speaks to DSJ's use of Salt River, Woodstock, and Bo-Kaap for the music video, which features black queer bodies in performance—all of these spaces are being gentrified, effectively pushing working class people of colour out of the city (cf. Didier, Morange, and Peyroux; Lemanski). Gustav Visser explains that gentrification has come to mean a unit-by-unit acquisition of housing which replaces low-income residents with high-income residents, and which occurs independent of the structural condition, architecture, tenure or original cost level of the housing (although it is usually renovated for or by the new occupiers). (81–82) In South Africa this inequity plays out along racial lines because its neoliberal economic policies created a small black elite without improving the lives of the black working class. Instead, the “new African bourgeoisie, because it shares racial identities with the bulk of the poor and class interests with white economic elites, is in position to mediate the reinforcing cleavages between rich whites and poor blacks without having to make more radical changes” (MacDonald 158). In a news article about a working class Salt River family of colour’s battle against an eviction, Christine Hogg explains, “Gentrification often means the poor are displaced as the rich move in or buildings are upgraded by new businesses. In Woodstock and Salt River both are happening at a pace.” Angel Ho’s anecdote, as told from a Woodstock hair salon, conveys a sense of what Woodstock’s transformation from a coloured, working class Group Area to an upmarket, trendy, and arty space would mean for people of colour, including black, queer subjects. One could argue that this reading of the video is undermined by DSJ’s work with global brand H&M. Was she was snared by neoliberal economics? Perhaps, but one response is that the seeds of any subculture’s commercial co-option lie in the fact it speaks through commodities (for example clothing, make-up, CDs, vinyl, or iTunes / mp3 downloads (Hebdige 95; Haupt, Stealing Empire 144–45). Subcultures have a window period in which to challenge hegemonic ideologies before they are delegitimated or commercially co-opted. Hardt and Negri contend that the means that extend the reach of corporate globalisation could be used to challenge it from within it (44–46; Haupt, Stealing Empire 26). DSJ utilises her H&M work, social media, the hip-hop genre, and international networks to exploit that window period to help mainstream black queer identity politics.ConclusionDSJ speaks back to processes of exclusion from the city, which was transformed by apartheid and, more recently, gentrification, by claiming it as a creative and playful space for queer subjects of colour. She uses Gayle to lay claim to the city as it has a long history in Cape Town. In fact, she says that she is not reviving Gayle, but is simply “putting it on a bigger platform” (Ovens, Saint Jude, and Haupt). The use of subtitles in the video suggests that she wants to mainstream queer identity politics. Saint Jude also transforms hip-hop heteronormativity by queering the genre and by locating her work within the history of Cape hip-hop’s multilingual wordplay. ReferencesBarber, Kristin. “The Well-Coiffed Man: Class, Race, and Heterosexual Masculinity in the Hair Salon.” Gender and Society 22.4 (2008): 455–76.Cage, Ken. “An Investigation into the Form and Function of Language Used by Gay Men in South Africa.” Rand Afrikaans University: MA thesis, 1999.Clay, Andreana. “‘I Used to Be Scared of the Dick’: Queer Women of Color and Hip-Hop Masculinity.” Home Girls Make Some Noise: Hip Hop Feminism Anthology. Ed. Gwendolyn D. Pough, Elain Richardson, Aisha Durham, and Rachel Raimist. California: Sojourns, 2007.Collins, Patricia Hill. Black Sexual Politics: African Americans, Gender, and the New Racism. New York: Routledge, 2005. Crenshaw, Kimberle. “Mapping the Margins: Intersectionality, Identity Politics, and Violence against Women of Color”. 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New York: New York UP, 2007.Smalls, Shanté Paradigm. “‘The Rain Comes Down’: Jean Grae and Hip Hop Heteronormativity.” American Behavioral Scientist 55.1 (2011): 86–95.Visser, Gustav. “Gentrification: Prospects for Urban South African Society?” Acta Academica Supplementum 1 (2003): 79–104.Williams, Quentin E. “Youth Multilingualism in South Africa’s Hip-Hop Culture: a Metapragmatic Analysis.” Sociolinguistic Studies 10.1 (2016): 109–33.Yudell, Michael. “A Short History of the Race Concept.” Race and the Genetic Revolution: Science, Myth, and Culture. Ed. Sheldon Krimsky and Kathleen Sloan. New York: Columbia UP, 2011.InterviewsOvens, Neil, Dope Saint Jude, and Adam Haupt. One FM Radio interview. Cape Town. 21 Apr. 2016.VideosSaint Jude, Dope. “Keep in Touch.” YouTube. 23 Feb. 2015. <https://www.youtube.com/watch?v=w2ux9R839lE>. H&M. “H&M World Recycle Week Featuring M.I.A.” YouTube. 11 Apr. 2016. <https://www.youtube.com/watch?v=f7MskKkn2Jg>. MusicSaint Jude, Dope. Reimagine. 15 June 2016. <https://dopesaintjude.bandcamp.com/album/reimagine>.

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