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Добірка наукової літератури з теми "Locally ordered spaces"

Автор: Grafiati

Опубліковано: 28 вересня 2022

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Статті в журналах з теми "Locally ordered spaces"

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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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.

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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.

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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.

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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 +∞.

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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.

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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.

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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.

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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.

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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.

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Більше джерел

Дисертації з теми "Locally ordered spaces"

Coursolle, Pierre-Yves. "A framework for locally structured spaces - application to geometric models of concurrency." Thesis, Institut polytechnique de Paris, 2022. https://tel.archives-ouvertes.fr/tel-03789652.

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L'utilisation de méthodes provenant de la topologie algébrique dans l'étude des processus concurrents ont été introduites en 1998. L'un des ingrédients clef est la réalisation des ensembles précubiques dans la catégories des espaces localement ordonnés. Cependant la formalisation du concept d'espace localement ordonné n'est pas consensuelle : plusieurs définitions non équivalentes ont été proposées dans la littérature. C'est un inconvénient majeur puisque, comme on le montre dans le chapitre 3, les colimites d'espaces localement ordonnés sont très sensibles à des changements apparemment mineurs dans les définitions. Il existe ainsi une pléthore de notions mathématiques similaires mais non équivalentes, toutes basées sur la topologie, qui essaient de formaliser la même idée.Dans cette thèse, on construit un cadre commun pour pouvoir comparer ces notions. L'idée clef est de remplacer, pour chaque ensemble X, l'ensemble des parties de X ordonné par inclusion par un ensemble préordonné T(X). Intuitivement, les membres de T(X) correspondent à des parties de X équipées d'une structure supplémentaire et on impose que les inclusions tiennent compte de ces structures. T étant fixé, on peut définir les espaces T-topologiques et les application T-continues en remplaçant les sous-ensembles par les membres des T(X) dans les définitions classiques des espaces topologiques et des applications continues en termes de bases de topologie. En imposant des axiomes appropriés aux T(X), on obtient une catégorie concrète. On montre que beaucoup de notions standard de topologie, comme la convergence, la compacité ou la topologie initiale, peuvent être étendues à ce cadre. Ainsi T est une sorte de template qui fixe la forme des espaces qui lui sont associés, pour cette raison, on appelle théorie topologique un tel T.Dans le chapitre 7, on développe une généralisation naturelle des streams de Krishnan comme des espaces T-topologiques vérifiant une simple propriété de stabilité supplémentaire. En effet, pour un T bien choisi, on retrouve alors les streams usuels
The usage of methods from Algebraic Topology in the study of concurrent processes was initiated in 1998. One of its key ingredient is the realization of precubical sets in the category of locally ordered spaces. Nevertheless, the formalization of the concept of a locally ordered space is not firmly set: various non-equivalent definitions have indeed appeared in the literature. This is a serious drawback, as we see in the third chapte, because the colimits of locally ordered spaces are extremely sensitive to seemingly anodyne modification in their definition. We end up with plethora of similar yet non-equivalent mathematical notions, all grounded on topology, intended to formalize the same idea.In this thesis, we design a unified framework to compare these notions. The key idea is to replace, for every set X, the powerset of X ordered by inclusion by a mere preordered set T(X). Intuitively, the members of T(X) are to be thought as parts of X endowed with an additional structure and we require that inclusions take these structures into account. Given T, we can define T-topological spaces and T-continuous maps by replacing the subsets by the members of the T(X) in the classic definitions of topological spaces and of continuous maps in terms of topological bases. By fixing the appropriate axioms on the T(X), we obtain a concrete category. We show that many standard notions of topology, like convergence, compactness, or initial topology, can be extended to this framework. Thus T is a kind of template which fix the form of the spaces associated to it, that is why such a T is called a topological theory.In the seventh chapter, we develop a natural generalization of Krishnan’s streams as T-topological spaces satisfying a simple additional stability property. Indeed, for a well choosen T, we recover standard streams

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Sommaro, Silvia. "Groups of principal homogeneous spaces for some Hopf orders arising from formal groups." Thesis, University of Exeter, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.368366.

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Brauer, Uwe, and Lavi Karp. "Local existence of classical solutions for the Einstein-Euler system using weighted Sobolev spaces of fractional order." Universität Potsdam, 2006. http://opus.kobv.de/ubp/volltexte/2009/3017/.

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We prove the existence of a class of local in time solutions, including static solutions, of the Einstein-Euler system. This result is the relativistic generalisation of a similar result for the Euler-Poisson system obtained by Gamblin [8]. As in his case the initial data of the density do not have compact support but fall off at infinity in an appropriate manner. An essential tool in our approach is the construction and use of weighted Sobolev spaces of fractional order. Moreover, these new spaces allow us to improve the regularity conditions for the solutions of evolution equations. The details of this construction, the properties of these spaces and results on elliptic and hyperbolic equations will be presented in a forthcoming article.

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Menezes, Filipe [Verfasser], and Hans-Joachim [Akademischer Betreuer] Werner. "A local complete active space 2nd-order perturbation theory method / Filipe Menezes ; Betreuer: Hans-Joachim Werner." Stuttgart : Universitätsbibliothek der Universität Stuttgart, 2016. http://d-nb.info/1124000100/34.

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Papafitsoros, Konstantinos. "Novel higher order regularisation methods for image reconstruction." Thesis, University of Cambridge, 2015. https://www.repository.cam.ac.uk/handle/1810/246692.

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In this thesis we study novel higher order total variation-based variational methods for digital image reconstruction. These methods are formulated in the context of Tikhonov regularisation. We focus on regularisation techniques in which the regulariser incorporates second order derivatives or a sophisticated combination of first and second order derivatives. The introduction of higher order derivatives in the regularisation process has been shown to be an advantage over the classical first order case, i.e., total variation regularisation, as classical artifacts such as the staircasing effect are significantly reduced or totally eliminated. Also in image inpainting the introduction of higher order derivatives in the regulariser turns out to be crucial to achieve interpolation across large gaps. First, we introduce, analyse and implement a combined first and second order regularisation method with applications in image denoising, deblurring and inpainting. The method, numerically realised by the split Bregman algorithm, is computationally efficient and capable of giving comparable results with total generalised variation (TGV), a state of the art higher order method. An additional experimental analysis is performed for image inpainting and an online demo is provided on the IPOL website (Image Processing Online). We also compute and study properties of exact solutions of the one dimensional total generalised variation problem with L^{2} data fitting term, for simple piecewise affine data functions, with or without jumps . This gives an insight on how this type of regularisation behaves and unravels the role of the TGV parameters. Finally, we introduce, study and analyse a novel non-local Hessian functional. We prove localisations of the non-local Hessian to the local analogue in several topologies and our analysis results in derivative-free characterisations of higher order Sobolev and BV spaces. An alternative formulation of a non-local Hessian functional is also introduced which is able to produce piecewise affine reconstructions in image denoising, outperforming TGV.

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Debroux, Noémie. "Mathematical modelling of image processing problems : theoretical studies and applications to joint registration and segmentation." Thesis, Normandie, 2018. http://www.theses.fr/2018NORMIR02/document.

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Dans cette thèse, nous nous proposons d'étudier et de traiter conjointement plusieurs problèmes phares en traitement d'images incluant le recalage d'images qui vise à apparier deux images via une transformation, la segmentation d'images dont le but est de délimiter les contours des objets présents au sein d'une image, et la décomposition d'images intimement liée au débruitage, partitionnant une image en une version plus régulière de celle-ci et sa partie complémentaire oscillante appelée texture, par des approches variationnelles locales et non locales. Les relations étroites existant entre ces différents problèmes motivent l'introduction de modèles conjoints dans lesquels chaque tâche aide les autres, surmontant ainsi certaines difficultés inhérentes au problème isolé. Le premier modèle proposé aborde la problématique de recalage d'images guidé par des résultats intermédiaires de segmentation préservant la topologie, dans un cadre variationnel. Un second modèle de segmentation et de recalage conjoint est introduit, étudié théoriquement et numériquement puis mis à l'épreuve à travers plusieurs simulations numériques. Le dernier modèle présenté tente de répondre à un besoin précis du CEREMA (Centre d'Études et d'Expertise sur les Risques, l'Environnement, la Mobilité et l'Aménagement) à savoir la détection automatique de fissures sur des images d'enrobés bitumineux. De part la complexité des images à traiter, une méthode conjointe de décomposition et de segmentation de structures fines est mise en place, puis justifiée théoriquement et numériquement, et enfin validée sur les images fournies
In this thesis, we study and jointly address several important image processing problems including registration that aims at aligning images through a deformation, image segmentation whose goal consists in finding the edges delineating the objects inside an image, and image decomposition closely related to image denoising, and attempting to partition an image into a smoother version of it named cartoon and its complementary oscillatory part called texture, with both local and nonlocal variational approaches. The first proposed model addresses the topology-preserving segmentation-guided registration problem in a variational framework. A second joint segmentation and registration model is introduced, theoretically and numerically studied, then tested on various numerical simulations. The last model presented in this work tries to answer a more specific need expressed by the CEREMA (Centre of analysis and expertise on risks, environment, mobility and planning), namely automatic crack recovery detection on bituminous surface images. Due to the image complexity, a joint fine structure decomposition and segmentation model is proposed to deal with this problem. It is then theoretically and numerically justified and validated on the provided images

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De, Wet Johan Pieter. "Local properties of graphs." Thesis, 2016. http://hdl.handle.net/10500/22278.

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We say a graph is locally P if the induced graph on the neighbourhood of every vertex has the property P. Specically, a graph is locally traceable (LT) or locally hamiltonian (LH) if the induced graph on the neighbourhood of every vertex is traceable or hamiltonian, respectively. A locally locally hamiltonian (L2H) graph is a graph in which the graph induced by the neighbourhood of each vertex is an LH graph. This concept is generalized to an arbitrary degree of nesting, to make it possible to work with LkH graphs. This thesis focuses on the global cycle properties of LT, LH and LkH graphs. Methods are developed to construct and combine such graphs to create others with desired properties. It is shown that with the exception of three graphs, LT graphs with maximum degree no greater than 5 are fully cycle extendable (and hence hamiltonian), but the Hamilton cycle problem for LT graphs with maximum degree 6 is NP-complete. Furthermore, the smallest nontraceable LT graph has order 10, and the smallest value of the maximum degree for which LT graphs can be nontraceable is 6. It is also shown that LH graphs with maximum degree 6 are fully cycle extendable, and that there exist nonhamiltonian LH graphs with maximum degree 9 or less for all orders greater than 10. The Hamilton cycle problem is shown to be NP-complete for LH graphs with maximum degree 9. The construction of r-regular nonhamiltonian graphs is demonstrated, and it is shown that the number of vertices in a longest path in an LH graph can contain a vanishing fraction of the vertices of the graph. NP-completeness of the Hamilton cycle problem for LkH graphs for higher values of k is also investigated.
Mathematical Sciences
D. Phil. (Mathematics)

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Ting, Hsu Kuang, and 許光廷. "The Order of Power／Space in a Locality－Take Ta-Lin’s Protest against the Placement of an Incinerator as an Example." Thesis, 2002. http://ndltd.ncl.edu.tw/handle/13719165754007092613.

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碩士
南華大學
環境與藝術研究所
90
Abstract Traditional farming settlement had been the most typical kind of settlement for the Chinese people who migrated to Taiwan for hundreds of years. The present study, which choose Ta-Lin as the research subject, is an inter-disciplinary approach to understand the different spatial significances formulated over the ages in such a settlement, especially the sacred and the profane ones, and their conflicts over a public affair today. This study includes three primary sections: （1） Over the past centuries, the religious tradition of Taoism played the key role in formulating the spatial organization and spatial significances in the traditional Chinese settlement. This study has discussed Ta-Lin’s local religious beliefs, and the spatial organization and significances upheld by the residents. （2） But since the age of Japanese colonialism, Ta-Lin experienced abrupt transformation of their social and political organization under the imperialist regime. As a result, the spatial ordering of their place had been dominated and reformulated according to the non-religious, profane political power. This study reveals how a centralized political power came to impose itself to the local people, through inserting a new spatial/geographical ordering system. This scenario even lasted through the Kuo-ming Tang Nationalist government, wherein modernist urban planning laws were generally enforced, and in the making of public policy, modern economic development for the place dispersed any consideration of local religious sentiment. （3） In the case of a high profile protest launched by the residents of Ta-Lin against the placement of an incinerator, the so-called 大林抗爭事件, we find that in the present day, most interestingly, the religious significance of the place and the corresponding spatial praxis in the traditional settlement still reflect the most deep-seated value of the local residents. The protest itself, which gained national media attention, in the end was a conflict between the sacred and the profane systems of spatial ordering. Keywords: Settlement、Sacred Space、Locality Consciousness、Power／Space

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Книги з теми "Locally ordered spaces"

Choquet order and simplices: With applications in probabilistic models. Berlin: Springer-Verlag, 1985.

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Peterlini, Hans Karl, and Jasmin Donlic, eds. Jahrbuch Migration und Gesellschaft / Yearbook Migration and Society 2020/2021. Bielefeld, Germany: transcript Verlag, 2021. http://dx.doi.org/10.14361/9783839455913.

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Migration is not a state of emergency, but a basic existential experience of humanity. It shapes contemporary societies by challenging established orders, creating transnational spaces beyond national hegemonies, creating new economies, influencing urban and communal ways of life, making inequality and precariousness visible locally and globally. Migration research as a social science does not narrow the focus to 'the migrants', but investigates the conditions for living together and shaping life between ethnicization and pluralization, discrimination and empowerment, division and participation. The Yearbook Migration and Society repeatedly turns the prism of narrative anew. The 2020/2021 edition focuses on the topic "Beyond Borders".

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Caramello, Olivia. Examples of theories of presheaf type. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198758914.003.0011.

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This chapter discusses several classical as well as new examples of theories of presheaf type from the perspective of the theory developed in the previous chapters. The known examples of theories of presheaf type that are revisited in the course of the chapter include the theory of intervals (classified by the topos of simplicial sets), the theory of linear orders, the theory of Diers fields, the theory of abstract circles (classified by the topos of cyclic sets) and the geometric theory of finite sets. The new examples include the theory of algebraic (or separable) extensions of a given field, the theory of locally finite groups, the theory of vector spaces with linear independence predicates and the theory of lattice-ordered abelian groups with strong unit.

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Berger, Tobias. Translating Practices and Normative Orders. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198807865.003.0007.

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This chapter analyses, firstly, the translation of a key practice of the rule of law—the formal documentation of court proceedings in writing. It shows how the grassroots-level NGO fieldworkers do not use the official paperwork provided by the project to neutrally record village court sessions. Instead, they use the documents as symbolic capital that allows marginalized people to access local elites they could have otherwise not have accessed. Secondly, the employees of the local NGOs also translate the normative vocabularies in which the rule of law is justified. Instead of advocating access to village court justice in the secular registers of human rights and the rule of law, the fieldworkers draw on Islam and Islamic law to enhance participatory spaces in non-state courts, particularly for women. This, however, leads to contestations with established religious authorities over competing interpretations of Islam and Islamic law.

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Santos, Milton. The Nature of Space. Translated by Brenda Baletti. Duke University Press, 2021. http://dx.doi.org/10.1215/9781478021704.

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In The Nature of Space, pioneering Afro-Brazilian geographer Milton Santos attends to globalization writ large and how local and global orders intersect in the construction of space. Santos offers a theory of human space based on relationships between time and ontology. He argues that when geographers consider the inseparability of time and space, they can then transcend fragmented realities and partial truths without trying to theorize their way around them. Based on these premises, Santos examines the role of space, which he defines as indissoluble systems of objects and systems of actions in social processes, while providing a geographic contribution to the production of a critical social theory.

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Ng, Wing Chung. The State, Public Order, and Local Theater in South China. University of Illinois Press, 2017. http://dx.doi.org/10.5406/illinois/9780252039119.003.0006.

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This chapter explores the theater as a site of chaos and unruly behavior, and examines the role of the state in managing the Cantonese opera theater as a public space. It considers the many scars of physical violence borne by the opera community, some inflicted from the outside, and others occasioned by eruptions of factionalism. The division from within became chronic especially in the mid-1920s when politics in Guangzhou took a radical turn. This development was no small irony in an age of state-building when different government authorities—including the British in colonial Hong Kong, the successive warlord regimes in control of South China, and the Chinese Nationalist government after 1927—all, to various degrees, sought to police the theater and assert control in the interest of mobilization, discipline, and order.

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Labrador, Roderick N. “What’s so p/funny?”. University of Illinois Press, 2017. http://dx.doi.org/10.5406/illinois/9780252038808.003.0003.

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This chapter critiques the idea of Hawaiʻi as a “multicultural paradise” and the production of Local by examining the popular practice of ethnic humor. It argues that Hawaiʻi ethnic humor is a space for the production of “Local knowledge(s)” and ideologies where identities are constructed and social order and racial hierarchy are enacted. It draws attention to the production of Local as a nonimmigrant identity, especially the ways in which Local comedians appropriate the voice of immigrant Filipinos through the use of Mock Filipino (or speaking English with a “Filipino accent”). Although understood as “innocent” and “harmless” joking in which “we can laugh at ourselves,” Hawaiʻi ethnic humor in general, and Mock Filipino in particular, simultaneously produce racially demeaning or “racially interested” discourses that uphold the positive self-image of Locals, especially their membership in Hawaiʻi's “racial paradise,” while lowering that of immigrant Filipinos.

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Thornton, Niamh, and Miriam Haddu, eds. Legacies of the Past. Edinburgh University Press, 2020. http://dx.doi.org/10.3366/edinburgh/9781474480536.001.0001.

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Riven with unresolved traumas the past haunts spaces in Mexican film and visual culture, because the political process has attempted to erase or appropriate their significance. Without consensus and/or a clearly defined narrative, these events act like spectres haunting the present. In order to comprehend how they manifest, this collection looks at a selection of traumas that haunt the present and consider how filmmakers and visual artists have found ways of understanding the haunted spaces. Their explorations, imaginings, and counter-imaginings of the past bring the spectres to the foreground and create new narratives and, thus, propose new histories. This book explores the (audio)visual representations of several heightened events in Mexican history in order to comprehend how storytelling and narrative matters for a shared understanding of ourselves. This book considers the ways memory and trauma dominate Mexican visual and screen cultures and how their ghosts are attached to specific locales and moments.

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Edmunds, D. E., and W. D. Evans. Second-Order Differential Operators on Arbitrary Open Sets. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198812050.003.0007.

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In this chapter, three different methods are described for obtaining nice operators generated in some L2 space by second-order differential expressions and either Dirichlet or Neumann boundary conditions. The first is based on sesquilinear forms and the determination of m-sectorial operators by Kato’s First Representation Theorem; the second produces an m-accretive realization by a technique due to Kato using his distributional inequality; the third has its roots in the work of Levinson and Titchmarsh and gives operators T that are such that iT is m-accretive. The class of such operators includes the self-adjoint operators, even ones that are not bounded below. The essential self-adjointness of Schrödinger operators whose potentials have strong local singularities are considered, and the quantum-mechanical interpretation of essential self-adjointness is discussed.

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Churchill, David. Policing the City. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198797845.003.0005.

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This chapter assesses the impact of policing on urban order. It argues that the nineteenth-century police forces were especially attentive to local perceptions of nuisance and improvement in their efforts to tame urban popular culture and to sanitize urban public space. Police efforts to impose public order were modified by structural constraints, exercise of discretion in law enforcement, and resistance on the part of the public. And yet, the psychological repercussions of street order policing were profound, as large sections of the urban population came under an unprecedented level of official scrutiny. Hence, this chapter argues that—faced with a highly officious and, at times, repressive form of police authority—the urban public became ‘police-conscious’ in the nineteenth century.

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Частини книг з теми "Locally ordered spaces"

Bridges, Douglas S. "The Arrow-Hahn Construction in a Locally Compact Metric Space." In Mathematical Topics on Representations of Ordered Structures and Utility Theory, 281–99. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-34226-5_15.

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Xiao, Ti-Jun, and Jin Liang. "Laplace transforms and operator families in locally convex spaces." In The Cauchy Problem for Higher Order Abstract Differential Equations, 1–44. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/978-3-540-49479-9_1.

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Spagnolo, Sergio, and Giovanni Taglialatela. "Local in Space Energy Estimates for Second-order Hyperbolic Equations." In Evolution Equations of Hyperbolic and Schrödinger Type, 301–13. Basel: Springer Basel, 2012. http://dx.doi.org/10.1007/978-3-0348-0454-7_16.

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Parhi, Sanjaya Kumar, and Debasis Sharma. "On the Local Convergence of a Sixth-Order Iterative Scheme in Banach Spaces." In Advances in Intelligent Systems and Computing, 79–88. Singapore: Springer Singapore, 2021. http://dx.doi.org/10.1007/978-981-16-1402-6_7.

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Müller, A., and J. M. Rico. "Mobility and Higher Order Local Analysis of the Configuration Space of Single-Loop Mechanisms." In Advances in Robot Kinematics: Analysis and Design, 215–24. Dordrecht: Springer Netherlands, 2008. http://dx.doi.org/10.1007/978-1-4020-8600-7_23.

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Papacchini, Fabio, Cláudia Nalon, Ullrich Hustadt, and Clare Dixon. "Efficient Local Reductions to Basic Modal Logic." In Automated Deduction – CADE 28, 76–92. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-79876-5_5.

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AbstractWe present novel reductions of the propositional modal logics "Image missing" , "Image missing" , "Image missing" , "Image missing" and "Image missing" to Separated Normal Form with Sets of Modal Levels. The reductions result in smaller formulae than the well-known reductions by Kracht and allow us to use the local reasoning of the prover "Image missing" to determine the satisfiability of modal formulae in these logics. We show experimentally that the combination of our reductions with the prover "Image missing" performs well when compared with a specialised resolution calculus for these logics and with the b̆uilt-in reductions of the first-order prover SPASS.

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Mosseri, R., and J. F. Sadoc. "Curved Space Approach to the Relation between Long Range Disorder and Local Order in Amorphous Tetracoordinated Semiconductors." In Structure and Bonding in Noncrystalline Solids, 45–76. Boston, MA: Springer US, 1986. http://dx.doi.org/10.1007/978-1-4615-9477-2_4.

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To Figueras, Lluís. "Drapers and tailors. Fashion and consumption in medieval Catalonia." In La moda come motore economico: innovazione di processo e prodotto, nuove strategie commerciali, comportamento dei consumatori / Fashion as an economic engine: process and product innovation, commercial strategies, consumer behavior, 25–44. Florence: Firenze University Press, 2022. http://dx.doi.org/10.36253/978-88-5518-565-3.05.

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The range of textiles available in markets across the western Mediterranean expanded significantly during the thirteenth century. Cloth retailers, or drapers, constituted a fundamental link between merchants and consumers, using a network of local markets with specific spaces for selling cloth. They were able to sell a wide range of commodities, including Flemish and French woollens, to satisfy a growing demand. Between 1250 and 1350, there were also tailors almost everywhere, some at the permanent service of an aristocratic court, such as the kings of Aragon, but most of them worked as independent entrepreneurs offering their services in exchange for specific payments. Therefore both drapers and tailors formed small partnerships and frequently used credit in order to reach all levels of medieval society.

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Lejeune, Catherine, Delphine Pagès-El Karoui, Camille Schmoll, and Hélène Thiollet. "Migration, Urbanity and Cosmopolitanism in a Globalized World: An Introduction." In IMISCOE Research Series, 1–13. Cham: Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-67365-9_1.

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AbstractGlobalization and migration have generated acute and often contradictory changes: they have increased social diversity while inducing global homogenization; they have sharpened differentiation of spaces and statuses while accelerating and amplifying communication and circulations; they have induced more complex social stratification while enriching individual and collective identities. These changes happen to be strikingly visible in cities. Urban contexts, indeed, offer privileged sites of inquiry to understanding the social dynamics of globalization, informal belonging and local citizenships, transient and multi-layered identities, symbolic orders and exclusionary practices. But cities are also material sites and they create multisensorial scapes that shape experiences of globalization and social change. They operate through multiple scales, connecting horizontal extensions and vertical layers of the city with generic, landmark, interstitial and neglected places. Far from being mere contexts, cities are both changing and being changed by migration and globalization.

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Theobald, Maryanne, Gillian Busch, Ilana Mushin, Lyndal O’Gorman, Cathy Nielson, Janet Watts, and Susan Danby. "Making Culture Visible: Telling Small Stories in Busy Classrooms." In Storytelling Practices in Home and Educational Contexts, 123–48. Singapore: Springer Nature Singapore, 2022. http://dx.doi.org/10.1007/978-981-16-9955-9_8.

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AbstractClassrooms are busy institutional settings in which conversational agendas are typically ordered by teachers due to the focus on curriculum content. Opportunities for extended storytelling, outside of focussed literacy times, may occur infrequently. This chapter investigates how children engage with each other and with curriculum concepts referred to as “culture”, through telling stories. The data are video recordings of young children (aged 4–5 years) telling stories during their everyday classroom activities. The data are drawn from a study on what intercultural competence “looks like” in the everyday interactions of preschool classrooms in inner-city Queensland, Australia. An ethnomethodological approach using conversation analysis highlights three fragments where children tell something about themselves. As they tell stories about aspects of their lives outside the classroom, children make their “culture” visible to other children and co-construct a local peer culture. The implications of the study’s findings point to how classrooms can be conversational spaces where children practise and build culture in action. The children share aspects of their everyday lives that are sometimes tangentially aligned with curriculum, but always available as a resource for making cultural connections. The children themselves do not name these activities as culture, but their association to what is known about how culture is defined, shows that they are orienting to these aspects.

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Тези доповідей конференцій з теми "Locally ordered spaces"

"MULTISPECTRAL TEXTURE ANALYSIS USING LOCAL BINARY PATTERN ON TOTALLY ORDERED VECTORIAL SPACES." In International Conference on Computer Vision Theory and Applications. SciTePress - Science and and Technology Publications, 2010. http://dx.doi.org/10.5220/0002828700370043.

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Pan, Jinsong, Yao Xiao, and Hanyang Gu. "Numerical Investigation of Spacer Effects on Heat Transfer Enhancement in a Vertical Annular Channel at Supercritical Pressure." In 2017 25th International Conference on Nuclear Engineering. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/icone25-66911.

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Supercritical water-cooled reactor (SCWR) is one of the Gen-IV reactors, which shows higher economy and safety. Reactor core of a SCWR employs a tight lattice in order to efficiently remove heat from nuclear fuels. In the narrow sub-channels of a tight lattice reactor core, a spacer has been used as a turbulence generator and a space-keeper between the fuel rods. Meanwhile, the spacer has significant influences on the heat transfer of the fuel rods. In order to investigate the effects of simple spacers on heat transfer to upwardly flowing supercritical fluid in a vertical annular channel, an experiment is underway at the supercritical model fluid thermal hydraulics test facility (SMOTH) with supercritical R134A. The equivalent diameter of the annular channel is 6 mm. The outer metal circular tube of the annular channel test section is electrically-heated. The blockage ratio of the simple spacers ranges from 0.2 to 0.4. Based on the geometry parameters of the test section, preliminary numerical investigations were carried out for the effects of simple spacer on the local heat transfer performance of supercritical R134A using commercial CFD code FLUENT. Heat transfer characteristics in the spacer downstream were analyzed with respect to the variations of heat flux, mass flux, pressure, blockage ratio and local enthalpy. And the reason for the different heat transfer enhancement under different conditions is given preliminarily. Finally, existing empirical correlations were selected to be compared with the results of CFD numerical simulation. The applicability of conventional subcritical heat transfer enhancement correlations for spacer grids to supercritical fluid was discussed.

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Müller, Andreas. "Higher-Order Local Analysis of Kinematic Singularities of Lower Pair Linkages." In ASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2017. http://dx.doi.org/10.1115/detc2017-67039.

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Kinematic singularities of linkages are configurations where the differential mobility changes. Constraint singularities are critical points of the constraint mapping defining the loop closure constraints. Configuration space (c-space) singularities are points where the c-space ceases to be a smooth manifold. These singularity types are not identical. C-space singularities are reflected by the c-space geometry. Identifying kinematic singularities amounts to locally analyze the set of critical points. The local geometry of the set of critical points is best approximated by its tangent cone (an algebraic variety). The latter is defined in this paper in a form that allows for its computational determination using the Jacobian minors. An explicit closed form expression for the derivatives of the minors is presented in terms of Lie brackets of joint screws. A computational method is proposed to determine a polynomial system defining the tangent cone. This finally allows for identifying c-space and kinematic singularities.

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Müller, Andreas. "Local Analysis of Closed-Loop Linkages: Mobility, Singularities, and Shakiness." In ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. American Society of Mechanical Engineers, 2015. http://dx.doi.org/10.1115/detc2015-47485.

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The mobility of a linkage is determined by the constraints imposed on its members. The constraints define the configuration space (c-space) variety as the geometric entity in which the finite mobility of a linkage is encoded. The instantaneous motions are determined by the constraints, rather than by the c-space geometry. Shaky linkages are prominent examples that exhibit a higher instantaneous than finite DOF even in regular configurations. Inextricably connected to the mobility are kinematic singularities that are reflected in a change of the instantaneous DOF. The local analysis of a linkage, aiming at determining the instantaneous and finite mobility in a given configuration, hence needs to consider the c-space geometry as well as the constraint system. A method for the local analysis is presented based on a higher-order local approximation of the c-space adopting the concept of the tangent cone to a variety. The latter is the best local approximation of the c-space in a general configuration. It thus allows for investigating the mobility in regular as well as singular configurations. Therewith the c-space is locally represented as an algebraic variety whose degree is the necessary approximation order. In regular configurations the tangent cone is the tangent space. The method is generally applicable and computationally simple. It allows for a classification of linkages as overconstrained and underconstrained, and to identify singularities.

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Chen, Cheng-Hung, Marco P. Schoen, and Ken W. Bosworth. "A Condensed Hybrid Optimization Algorithm Using Enhanced Continuous Tabu Search and Particle Swarm Optimization." In ASME 2009 Dynamic Systems and Control Conference. ASMEDC, 2009. http://dx.doi.org/10.1115/dscc2009-2526.

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A novel Condensed Hybrid Optimization (CHO) algorithm using Enhanced Continuous Tabu Search (ECTS) and Particle Swarm Optimization (PSO) is proposed. The proposed CHO algorithm combines the respective strengths of ECTS and PSO. The ECTS is a modified Tabu Search (TS), which has good search capabilities on large search spaces. In this study, ECTS is utilized to define smaller search spaces, which are used in a second stage by the basic PSO to find the respective local optimum. The ECTS covers the global search space by using a TS concept called diversification and then selects the most promising areas in the search space. Once the promising regions in the search space are defined, the proposed CHO algorithm employs another TS concept called intensification in order to search the promising area thoroughly. The proposed CHO algorithm is tested with the multi-dimensional Hyperbolic and Rosenbrock problems. Compared to other four algorithms, the simulations results indicate that the accuracy and effectiveness of the proposed CHO algorithm.

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Ramkumar, Barathram, Marco P. Schoen, Feng Lin, and Brian G. Williams. "Hybrid Optimization Algorithm Using Enhanced Continuous Tabu Search and Genetic Algorithm for Parameter Estimation." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-13374.

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A new algorithm using Enhanced Continuous Tabu Search (ECTS) and genetic algorithm (GA) is proposed for parameter estimation problems. The proposed algorithm combines the respective strengths of ECTS and GA. The ECTS is a modified Tabu Search (TS), which has good search capabilities for large search spaces. In this work, the ECTS is used to define smaller search spaces, which are used in a second stage by a GA to find the respective local minima. The ECTS covers the global search space by using a TS concept called diversification and then selects the most promising regions in the search space. Once the promising areas in the search space are identified, the proposed algorithm employs another TS concept called intensification in order to search the promising area thoroughly. The proposed algorithm is tested with benchmark multimodal functions for which the global minimum is known. In addition, the novel algorithm is used for parameter estimation problems, where standard estimation algorithms encounter problems estimating the parameters in an un-biased fashion. The simulation results indicate the effectiveness of the proposed hybrid algorithm.

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Gibała-Kapecka, Beata, and Tomasz Kapecki. "The real city - the mental city." In Virtual City and Territory. Barcelona: Centre de Política de Sòl i Valoracions, 2016. http://dx.doi.org/10.5821/ctv.8108.

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The search for relationships and dependencies between the real city and its mental image, may prove to be a key to understanding and reading the needs of the residents, primarily related to safety and comfort of living, as well as the location of places conducive to the development of social bonds. One of the important elements in the structure of a city is the public space. Reproduced on the mental maps, it is the most distinctive and recurring element in its image. Not adapted to new needs and neglected, it disintegrates the local community. Erased from memory, it leaves an empty space in the notional image of the city. Students from three Kraków-based universities have been dealing with the issue of the repair of public spaces (at the stage of creation of conceptual designs) for several years, forming interdisciplinary design teams made up of architects, interior designers, sociologists and aesthetes. Practical sociological studies are employed in order to create an image of the needs of the local inhabitants, which is then translated into design visions of various types of public spaces, conducive to the realization of their needs.

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Rippel, Markus, Seung-Kyum Choi, Farrokh Mistree, and Janet K. Allen. "A Simulation-Based Robust Concept Exploration Method." In ASME 2010 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2010. http://dx.doi.org/10.1115/detc2010-28767.

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In early stages of the engineering design process it is necessary to explore the design space to find a feasible range or point that satisfies the design requirements. When robustness of the system is among the requirements, the Robust Concept Exploration Method (RCEM) can be used. In RCEM a metamodel such as a global response surface of the entire design space is used. Based on this surrogate model the robustness of the system is evaluated. In nonlinear or multimodal design spaces a very detailed metamodel such as a very high order response surface might be required to reflect accurately the characteristics of the model. For large design spaces this is computationally very expensive. In this paper, using the Probabilistic Collocation Method (PCM) for generating local response models at the points of interest, a Simulation-Based RCEM is proposed as a very efficient and flexible robust concept exploration method. We believe that using the PCM with other design exploration methods would be equally effective.

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Singh Sidhu, Balraj, and J. S. Dhillon. "Higher Order Optimal Stable Digital IIR Filter Design Using Heuristic Optimization." In InSITE 2015: Informing Science + IT Education Conferences: USA. Informing Science Institute, 2015. http://dx.doi.org/10.28945/2222.

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This paper proposes the innovative methodologies for the robust and stable design of optimal stable digital infinite impulse response (IIR) filters using different mutation variants of hybrid differential evolution (HDE). A multivariable optimization is employed as the design criterion to obtain the optimal stable IIR filter that satisfies the different performance requirements like minimizing the magnitude approximation error and minimizing the ripple magnitude. HDE method is undertaken as a global search technique and exploratory search is exploited as a local search technique. The proposed different mutation variants of HDE method enhance the capability to explore and exploit the search space locally as well globally to obtain the optimal filter design parameters. The chance of starting with better solution is improved by comparing the opposite solution. Here HDE has been effectively applied for the design of higher order optimal stable band-pass, and band-stop digital IIR filters. The experimental results depict that proposed HDE methods are superior or at least comparable to other algorithms and can be efficiently applied for higher order IIR filter design.

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Bokor, Peter, Johannes Kinder, Marco Serafini, and Neeraj Suri. "Supporting domain-specific state space reductions through local partial-order reduction." In 2011 26th IEEE/ACM International Conference on Automated Software Engineering (ASE). IEEE, 2011. http://dx.doi.org/10.1109/ase.2011.6100044.

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Звіти організацій з теми "Locally ordered spaces"

Ron, Amos. Approximation Orders of and Approximation Maps from Local Principal Shift-Invariant Spaces. Fort Belvoir, VA: Defense Technical Information Center, May 1993. http://dx.doi.org/10.21236/ada265038.

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Cliffe, Emma. Local Humanitarian Leadership Index: A snapshot of progress towards local humanitarian leadership outcomes in the humanitarian coordination architecture in Jordan, Lebanon and Syria. Oxfam, July 2022. http://dx.doi.org/10.21201/2022.9141.

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This index outlines what needs to change in order to achieve local humanitarian leadership in the Syria crisis response. It summarizes research undertaken on the engagement of local and national actors in the international humanitarian coordination architecture in Jordan, Lebanon and Syria, and is accompanied by three country case studies. The index is designed to support local and national non-government organizations to advocate for reforms so they can increase their engagement within the humanitarian coordination system, and use these spaces to advocate for their desired changes in the response. Donors, UN agencies and INGOs bear the main responsibility for enabling those reforms. The recommendations in each section provide practical solutions to address the barriers and challenges identified in the research.

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Woodruffe, Paul. Suburban Interventions: Understanding the Values of Place and Belonging Through Collaboration. Unitec ePress, May 2012. http://dx.doi.org/10.34074/ocds.12012.

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How can a socially defined project facilitate meaningful knowledge transfer between community, corporate, and institution? In order to address this question, this paper focuses on an ongoing live project in suburban Auckland New Zealand began in 2010, undertaken by a post-graduate student and researcher collective. The collective currently creates subtle interventions sited within local cyberspace, and through this current project will employ impermanent and small-scale design to advocate for a series of neglected and disputed sites. It explores the impact and value the presence of artists and designers working within local communities can have, and “champions the role of the artist in the development of the public realm, and their intuitive response to spaces, places, people and wildlife” (Wood 2009, p.26). The significance of this project is that it promotes a collaborative and multidisciplinary methodology that works with community groups to advocate to corporate entities for a wider social and environmental awareness of specific sites. This paper aims to explain the processes and findings of the project to date through both its successes and failures. It also proposes the possibility of the methodology being transferred to undergraduate and post-graduate study as a tool to promote multi-disciplined collaborate project briefs that focus on community well being.

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Woodruffe, Paul. Suburban Interventions: Understanding the Values of Place and Belonging Through Collaboration. Unitec ePress, May 2012. http://dx.doi.org/10.34074/ocds.12012.

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How can a socially defined project facilitate meaningful knowledge transfer between community, corporate and institution? In order to address this question, this paper focuses on an ongoing live project in suburban Auckland New Zealand begun in 2010, undertaken by a post-graduate student and researcher collective. The collective currently creates subtle interventions sited within local cyberspace, and through this current project will employ impermanent and small-scale design to advocate for a series of neglected and disputed sites. It explores the impact and value the presence of artists and designers working within local communities can have, and “champions the role of the artist in the development of the public realm, and their intuitive response to spaces, places, people and wildlife” (Wood 2009, p.26). The significance of this project is that it promotes a collaborative and multidisciplinary methodology that works with community groups to advocate to corporate entities for a wider social and environmental awareness of specific sites. This paper aims to explain the processes and findings of the project to date through both its successes and failures. It also proposes the possibility of the methodology being transferred to undergraduate and post-graduate study as a tool to promote multi-disciplined collaborate project briefs that focus on community well being.

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Mouat, Beth, Mike Bergh, Richard Shelmerdine, and Kobus Leach. Scottish Inshore Fisheries Integrated Data System (SIFIDS): Work package 1 final report: Review and optimisation of shellfish data collection strategies for Scottish inshore waters. Edited by Hannah Ladd-Jones and Mark James. Marine Alliance for Science and Technology for Scotland (MASTS), 2018. http://dx.doi.org/10.15664/10023.23379.

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[Extract from Executive Summary] The collection of additional data to facilitate fisheries management has been identified as a priority at the national level via the Scottish Inshore Fisheries Strategy, and at the local level in the management plans of Regional Inshore Fisheries Groups. Data collection implemented by industry offers a potentially cost effective means by which to provide additional information to enhance current stock assessment programmes, and to produce empirical indicators to inform fisheries management. The fundamental driver for data collection should be the purpose for which it is required; however, the regionalisation of fisheries management and increased, and often competing, demands, on our marine space mean that there are many potential uses for industry derived data. This report presents the findings of a single work package in the wider prototypic Scottish Inshore Fisheries Integrated Data System (SIFIDS) project; looking at ways in which inshore fisheries data collection can be improved on. The propose of this work package was to review and evaluate current inshore (shellfish) fisheries data collection and stock assessments in order to determine where it might be possible for industry derived data collection to provide a positive contribution. For the purposes of this work package the focus was limited to brown crab, lobsters, and scallops.

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Hall, Mark, and Neil Price. Medieval Scotland: A Future for its Past. Society of Antiquaries of Scotland, September 2012. http://dx.doi.org/10.9750/scarf.09.2012.165.

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The main recommendations of the panel report can be summarised under five key headings. Underpinning all five areas is the recognition that human narratives remain crucial for ensuring the widest access to our shared past. There is no wish to see political and economic narratives abandoned but the need is recognised for there to be an expansion to more social narratives to fully explore the potential of the diverse evidence base. The questions that can be asked are here framed in a national context but they need to be supported and improved a) by the development of regional research frameworks, and b) by an enhanced study of Scotland’s international context through time. 1. From North Britain to the Idea of Scotland: Understanding why, where and how ‘Scotland’ emerges provides a focal point of research. Investigating state formation requires work from Medieval Scotland: a future for its past ii a variety of sources, exploring the relationships between centres of consumption - royal, ecclesiastical and urban - and their hinterlands. Working from site-specific work to regional analysis, researchers can explore how what would become ‘Scotland’ came to be, and whence sprang its inspiration. 2. Lifestyles and Living Spaces: Holistic approaches to exploring medieval settlement should be promoted, combining landscape studies with artefactual, environmental, and documentary work. Understanding the role of individual sites within wider local, regional and national settlement systems should be promoted, and chronological frameworks developed to chart the changing nature of Medieval settlement. 3. Mentalities: The holistic understanding of medieval belief (particularly, but not exclusively, in its early medieval or early historic phase) needs to broaden its contextual understanding with reference to prehistoric or inherited belief systems and frames of reference. Collaborative approaches should draw on international parallels and analogues in pursuit of defining and contrasting local or regional belief systems through integrated studies of portable material culture, monumentality and landscape. 4. Empowerment: Revisiting museum collections and renewing the study of newly retrieved artefacts is vital to a broader understanding of the dynamics of writing within society. Text needs to be seen less as a metaphor and more as a technological and social innovation in material culture which will help the understanding of it as an experienced, imaginatively rich reality of life. In archaeological terms, the study of the relatively neglected cultural areas of sensory perception, memory, learning and play needs to be promoted to enrich the understanding of past social behaviours. 5. Parameters: Multi-disciplinary, collaborative, and cross-sector approaches should be encouraged in order to release the research potential of all sectors of archaeology. Creative solutions should be sought to the challenges of transmitting the importance of archaeological work and conserving the resource for current and future research.

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Shaping the COVID decade: addressing the long-term societal impacts of COVID-19. The British Academy, 2021. http://dx.doi.org/10.5871/bac19stf/9780856726590.001.

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In September 2020, the British Academy was asked by the Government Office for Science to produce an independent review to address the question: What are the long-term societal impacts of COVID-19? This short but substantial question led us to a rapid integration of evidence and an extensive consultation process. As history has shown us, the effects of a pandemic are as much social, cultural and economic as they are about medicine and health. Our aim has been to deliver an integrated view across these areas to start understanding the long-term impacts and how we address them. Our evidence review – in our companion report, The COVID decade – concluded that there are nine interconnected areas of long-term societal impact arising from the pandemic which could play out over the coming COVID decade, ranging from the rising importance of local communities, to exacerbated inequalities and a renewed awareness of education and skills in an uncertain economic climate. From those areas of impact we identified a range of policy issues for consideration by actors across society, about how to respond to these social, economic and cultural challenges beyond the immediate short-term crisis. The challenges are interconnected and require a systemic approach – one that also takes account of dimensions such as place (physical and social context, locality), scale (individual, community, regional, national) and time (past, present, future; short, medium and longer term). History indicates that times of upheaval – such as the pandemic – can be opportunities to reshape society, but that this requires vision and for key decisionmakers to work together. We find that in many places there is a need to start afresh, with a more systemic view, and where we should freely consider whether we might organise life differently in the future. In order to consider how to look to the future and shape the COVID decade, we suggest seven strategic goals for policymakers to pursue: build multi-level governance; improve knowledge, data and information linkage and sharing; prioritise digital infrastructure; reimagine urban spaces; create an agile education and training system; strengthen community-led social infrastructure; and promote a shared social purpose. These strategic goals are based on our evidence review and our analysis of the nine areas of long-term societal impact identified. We provide a range of illustrative policy opportunities for consideration in each of these areas in the report that follows.

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