10,595 research outputs found

    Richness of dynamics and global bifurcations in systems with a homoclinic figure-eight

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    We consider 2D flows with a homoclinic figure-eight to a dissipative saddle. We study the rich dynamics that such a system exhibits under a periodic forcing. First, we derive the bifurcation diagram using topological techniques. In particular, there is a homoclinic zone in the parameter space with a non-smooth boundary. We provide a complete explanation of this phenomenon relating it to primary quadratic homoclinic tangency curves which end up at some cubic tangency (cusp) points. We also describe the possible attractors that exist (and may coexist) in the system. A main goal of this work is to show how the previous qualitative description can be complemented with quantitative global information. To this end, we introduce a return map model which can be seen as the simplest one which is 'universal' in some sense. We carry out several numerical experiments on the model, to check that all the objects predicted to exist by the theory are found in the model, and also to investigate new properties of the system

    On periodic Ambrosetti-Prodi-type problems

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    This work presents a discussion of Ambrosetti-Prodi-type second-order periodic problems. In short, the existence, non-existence, and multiplicity of solutions will be discussed on the parameter λ \lambda . The arguments rely on a Nagumo condition, to guarantee an apriori bound on the first derivative, lower and upper-solutions method, and the Leray-Schauder's topological degree theory. There are two types of new results based on the parameter's variation: An existence and non-existence theorem and a multiplicity theorem, proving the existence of a bifurcation point. An application to a damped and forced pendulum is studied, suggesting a method to estimate the critical values of the parameter

    3d mirror symmetry of braided tensor categories

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    We study the braided tensor structure of line operators in the topological A and B twists of abelian 3d N=4\mathcal{N}=4 gauge theories, as accessed via boundary vertex operator algebras (VOA's). We focus exclusively on abelian theories. We first find a non-perturbative completion of boundary VOA's in the B twist, which start out as certain affine Lie superalebras; and we construct free-field realizations of both A and B-twist VOA's, finding an interesting interplay with the symmetry fractionalization group of bulk theories. We use the free-field realizations to establish an isomorphism between A and B VOA's related by 3d mirror symmetry. Turning to line operators, we extend previous physical classifications of line operators to include new monodromy defects and bound states. We also outline a mechanism by which continuous global symmetries in a physical theory are promoted to higher symmetries in a topological twist -- in our case, these are infinite one-form symmetries, related to boundary spectral flow, which structure the categories of lines and control abelian gauging. Finally, we establish the existence of braided tensor structure on categories of line operators, viewed as non-semisimple categories of modules for boundary VOA's. In the A twist, we obtain the categories by extending modules of symplectic boson VOA's, corresponding to gauging free hypermultiplets; in the B twist, we instead extend Kazhdan-Lusztig categories for affine Lie superalgebras. We prove braided tensor equivalences among the categories of 3d-mirror theories. All results on VOA's and their module categories are mathematically rigorous; they rely strongly on recently developed techniques to access non-semisimple extensions.Comment: 158 pages, comments welcome

    The interpretation of Islam and nationalism by the elite through the English language media in Pakistan.

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    The media is constructed and interpreted through what people 'know'. That knowledge is, forthe most part, created through day to day experiences. In Pakistan, Islam and nationalism aretwo components of this social knowledge which are intrinsically tied to the experiences of thePakistani people. Censorship and selection are means through which this knowledge isarticulated and interpreted.General conceptions of partially shared large scale bodies of knowledge and ideas reinforce,and are reinforced by, general medium of mass communication: the print and electronic media.Focusing on the govermnent, media institutions and Pakistani elites, I describe and analyse thedifferent, sometimes conflicting, interpretations of Islam and Pakistani nationalism manifest inand through media productions presented in Pakistan.The media means many things, not least of which is power. It is the media as a source ofpower that is so frequently controlled, directed and manipulated. The terminology may beslightly different according to the context within which one is talking - propaganda, selection,etc. - but ultimately it comes down to the same thing - censorship. Each of the three groups:government, media institutions and Pakistani elites - have the power to interpret and censormedia content and consideration must be taken of each of the other power holders consequentlyrestricting the power of each group in relation to the other two. The processes of thismanipulation and their consequences form the major themes of this thesis

    How to Be a God

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    When it comes to questions concerning the nature of Reality, Philosophers and Theologians have the answers. Philosophers have the answers that can’t be proven right. Theologians have the answers that can’t be proven wrong. Today’s designers of Massively-Multiplayer Online Role-Playing Games create realities for a living. They can’t spend centuries mulling over the issues: they have to face them head-on. Their practical experiences can indicate which theoretical proposals actually work in practice. That’s today’s designers. Tomorrow’s will have a whole new set of questions to answer. The designers of virtual worlds are the literal gods of those realities. Suppose Artificial Intelligence comes through and allows us to create non-player characters as smart as us. What are our responsibilities as gods? How should we, as gods, conduct ourselves? How should we be gods

    UFO: Unified Foundational Ontology

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    The Unified Foundational Ontology (UFO) was developed over the last two decades by consistently putting together theories from areas such as formal ontology in philosophy, cognitive science, linguistics, and philosophical logics. It comprises a number of micro-theories addressing fundamental conceptual modeling notions, including entity types and relationship types. The aim of this paper is to summarize the current state of UFO, presenting a formalization of the ontology, along with the analysis of a number of cases to illustrate the application of UFO and facilitate its comparison with other foundational ontologies in this special issue. (The cases originate from the First FOUST Workshop – the Foundational Stance, an international forum dedicated to Foundational Ontology research.

    The gauge-invariant I-method for Yang-Mills

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    We prove global well-posedness of the 3d 3d Yang-Mills equation in the temporal gauge in Hσ H^{\sigma} for σ>56 \sigma > \frac{5}{6} . Unlike related equations, Yang-Mills is not directly amenable to the method of almost conservation laws (I-method) in its Fourier and global version. We propose a modified energy which: 1) Is gauge-invariant and easy to localize 2) Provides local gauges which give control of local Sobolev norms (through an Uhlenbeck-type lemma for fractional regularities) 3) Is slightly smoother in time compared to the classical I-method energy for related systems. The spatial smoothing is realized via the Yang-Mills heat flow instead of the multiplier II. Due to the temporal condition and its finite speed of propagation, the local gauge selection is compatible with recent initial data extension results. Therefore, smoothened energy differences can be partitioned into local pieces whose (appropriately extended) bounds can be square summed. After revealing the null structure within the trilinear integrals, these can be estimated using known methods. In an appendix we show how an invariant modified energy for Maxwell-Klein-Gordon can extend previous results to regularities σ>56 \sigma > \frac{5}{6}

    The syntax of negative polarity items in Syrian Arabic based on the dialect of Deir Ezzor

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    Negative Polarity Items (NPIs) are pervasive among languages. Cross-linguistic examination of NPIs continues to shed light on the complexity of this phenomenon. One unfortunate fact is that NPIs in Arabic dialects have seen relatively little examination in comparison with NPIs in other languages, such as English, Dutch, and Greek. The present study aims at contributing to filling this lacuna in research. It is a descriptive and analytical study of the syntax of negative polarity items in the Arabic dialect of Deir Ezzor, a city on the Euphrates in the north-eastern part of Syria; this Arabic dialect is Mesopotamian and not Levantine. This thesis contributes to the study of NPIs by providing an extensive inventory of these items in an Arabic dialect and a deeper analysis of these items' behaviour and licensing conditions. This study moves beyond the already known negative polarity pronouns and determiners to discuss negative polarity auxiliary verbs and negative polarity lexical verbs. It also expands the discussion of the idiomatic NPIs by discussing minimisers and maximisers. This thesis discusses the largest number of NPIs in any Arabic dialect. It also sheds light on areas where a contribution is needed, such as a thorough examination of the licensing contexts, e.g., the subjunctive and comparatives. This study examines the licensing proposals and concludes that Giannakidou’s nonveridicality theory offers the needed account. This study proposes new ways to examine the contexts where the licensing is possible, e.g., considering the details of comparative structures and what makes them licensing environments for NPIs. This study concludes that further research is needed and that researchers should not limit their exploration to testing the proposals that account for the licensing problem. Details do matter, and the details are what we should be looking for

    Constructing and classifying five-dimensional black holes using integrability

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    In this thesis we look at the problem of nding and classifying stationary and biaxisymmetric solutions in ve-dimensional theories of gravity, using particular hidden symmetries. We consider three theories: the electrostatic sector of Einstein-Maxwell, vacuum gravity and minimal supergravity (Einstein-Maxwell gravity with a Chern-Simons term). For electrostatic solutions to Einstein-Maxwell theory, the equations on the metric and Maxwell eld possess a SL(2;R) symmetry. This allows one to derive transformations which either charge a solution or immerse it in an electric Melvin background. By considering a neutral static black lens seed and performing these two transformations with appropriately tuned transformation parameters, we construct the rst example of a regular black lens in Einstein Maxwell theory with topologically trivial asymptotics. For vacuum gravity we consider asymptotically at solutions. The vacuum Einstein equations are integrable in the sense that they can be reformulated as the integrability condition for an auxiliary linear system of PDEs. Taking these PDEs, one can integrate them over the event horizons, the axes of symmetry and in nity. By carefully considering continuity conditions between these solutions, one may actually solve for metric data on the horizons and the axes in terms of some geometrically de ned moduli, subject to a set of polynomial constraints. This represents a very useful tool for answering the existence problem, reducing it to the much more tractable question of whether a particular system of polynomials (subject to some inequalities) has any solutions. Using this polynomial system we provide a constructive uniqueness proof for the Kerr (using analogous four-dimensional results), Myers-Perry and black ring solutions. We also prove, through a combination of analytic and numerical methods, that the \simplest" L(n; 1) black lens cannot exist by showing that it must possess a conical singularity on one of the axes. Finally we consider the case of asymptotically at solutions in minimal supergravity. As with the vacuum, this is an integrable theory and so a similar analysis can be performed with exactly analogous results, although with rather more complicated polynomial systems determining the existence of solutions. A notable feature of minimal supergravity, not present in the vacuum theory, is the existence of regular solitons - in this context these are non-trivial solutions without black hole regions. We begin the exploration of the moduli space of these solitons by rst studying the case of at space

    Generalized Schur-Weyl dualities for quantum affine symmetric pairs and orientifold KLR algebras

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    We define a boundary analogue of the Kang-Kashiwara-Kim-Oh generalized Schur-Weyl dualities between quantum affine algebras and Khovanov-Lauda-Rouquier (KLR) algebras. Let g\mathfrak{g} be a complex simple Lie algebra and UqLgU_qL\mathfrak{g} the corresponding quantum affine algebra. We construct a functor θF{}^{\theta}{\sf F} between finite-dimensional modules over a quantum symmetric pair of affine type UqkUqLgU_q\mathfrak{k}\subset U_qL{\mathfrak{g}} and an orientifold KLR (ooKLR) algebra arising from a framed quiver with a contravariant involution, whose nodes are indexed by finite-dimensional UqLgU_qL{\mathfrak{g}}-modules. With respect to the Kang-Kashiwara-Kim-Oh construction, our combinatorial model is further enriched with the poles of the trigonometric K-matrices (that is trigonometric solutions of a generalized reflection equation) intertwining the action of UqkU_q\mathfrak{k} on finite-dimensional UqLgU_qL{\mathfrak{g}}-modules. By construction, θF{}^{\theta}{\sf F} is naturally compatible with the Kang-Kashiwara-Kim-Oh functor in that, while the latter is a functor of monoidal categories, θF{}^{\theta}{\sf F} is a functor of module categories. Relying on an isomorphism between suitable completions of ooKLR algebras and affine Hecke algebras of type C\sf C, we prove that θF{}^{\theta}{\sf F} recovers the Schur-Weyl dualities due to Fan-Lai-Li-Luo-Wang-Watanabe in quasi-split type AIII\sf AIII. Finally, we construct spectral K-matrices for orientifold KLR algebras, yielding a meromorphic braiding on its category of finite-dimensional representations. We prove that, in the case of the A{\sf A}_{\infty} quiver with no fixed points and no framing, the functor θF{}^{\theta}{\sf F} is exact, factors through a suitable localization, and takes values in a boundary analogue of the Hernandez-Leclerc category.Comment: 61 page
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