Relevant bibliographies by topics / Real singularity theory

Academic literature on the topic 'Real singularity theory'

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Published: 1 September 2023

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Journal articles on the topic "Real singularity theory"

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Xiong, Gang, Wenxian Yu, and Shuning Zhang. "Dynamic Singularity Spectrum Distribution of Sea Clutter." Fluctuation and Noise Letters 14, no. 01 (December 25, 2014): 1550004. http://dx.doi.org/10.1142/s0219477515500042.

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The fractal and multifractal theory have provided new approaches for radar signal processing and target-detecting under the background of ocean. However, the related research mainly focuses on fractal dimension or multifractal spectrum (MFS) of sea clutter. In this paper, a new dynamic singularity analysis method of sea clutter using MFS distribution is developed, based on moving detrending analysis (DMA-MFSD). Theoretically, we introduce the time information by using cyclic auto-correlation of sea clutter. For transient correlation series, the instantaneous singularity spectrum based on multifractal detrending moving analysis (MF-DMA) algorithm is calculated, and the dynamic singularity spectrum distribution of sea clutter is acquired. In addition, we analyze the time-varying singularity exponent ranges and maximum position function in DMA-MFSD of sea clutter. For the real sea clutter data, we analyze the dynamic singularity spectrum distribution of real sea clutter in level III sea state, and conclude that the radar sea clutter has the non-stationary and time-varying scale characteristic and represents the time-varying singularity spectrum distribution based on the proposed DMA-MFSD method. The DMA-MFSD will also provide reference for nonlinear dynamics and multifractal signal processing.
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Baker, Gregory, Russel E. Caflisch, and Michael Siegel. "Singularity formation during Rayleigh–Taylor instability." Journal of Fluid Mechanics 252 (July 1993): 51–78. http://dx.doi.org/10.1017/s0022112093003660.

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During the motion of a fluid interface undergoing Rayleigh-Taylor instability, vorticity is generated on the interface baronclinically. This vorticity is then subject to Kelvin-Helmholtz instability. For the related problem of evolution of a nearly flat vortex sheet without density stratification (and with viscosity and surface tension neglected), Kelvin-Helmholtz instability has been shown to lead to development of curvature singularities in the sheet. In this paper, a simple approximate theory is developed for Rayleigh-Taylor instability as a generalization of Moore's approximation for vortex sheets. For the approximate theory, a family of exact solutions is found for which singularities develop on the fluid interface. The resulting predictions for the time and type of the singularity are directly verified by numerical computation of the full equations. These computations are performed using a point vortex method, and singularities for the numerical solution are detected using a form fit for the Fourier components at high wavenumber. Excellent agreement between the theoretical predictions and the numerical results is demonstrated for small to medium values of the Atwood number A, i.e. for A between 0 and approximately 0.9. For A near 1, however, the singularities actually slow down when close to the real axis. In particular, for A = 1, the numerical evidence suggests that the singularities do not reach the real axis in finite time.
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Dubrulle, Bérengère. "Multi-Fractality, Universality and Singularity in Turbulence." Fractal and Fractional 6, no. 10 (October 20, 2022): 613. http://dx.doi.org/10.3390/fractalfract6100613.

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In most geophysical flows, vortices (or eddies) of all sizes are observed. In 1941, Kolmogorov devised a theory to describe the hierarchical organization of such vortices via a homogeneous self-similar process. This theory correctly explains the universal power-law energy spectrum observed in all turbulent flows. Finer observations however prove that this picture is too simplistic, owing to intermittency of energy dissipation and high velocity derivatives. In this review, we discuss how such intermittency can be explained and fitted into a new picture of turbulence. We first discuss how the concept of multi-fractality (invented by Parisi and Frisch in 1982) enables to generalize the concept of self-similarity in a non-homogeneous environment and recover a universality in turbulence. We further review the local extension of this theory, and show how it enables to probe the most irregular locations of the velocity field, in the sense foreseen by Lars Onsager in 1949. Finally, we discuss how the multi-fractal theory connects to possible singularities, in the real or in the complex plane, as first investigated by Frisch and Morf in 1981.
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Kaneko, Akira. "On the analyticity of the locus of singularity of real analytic solutions with minimal dimension." Nagoya Mathematical Journal 104 (December 1986): 63–84. http://dx.doi.org/10.1017/s0027763000022686.

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Let P(x, D) be a linear partial differential operator with real analytic coefficients and let C ⊂ Rn be a germ of closed subset, say at the origin. We say that C is (the locus of) an irremovable singularity of a real analytic solution u of P(x, D)u = 0 if u is defined outside C on a neighborhood Ω of 0 but cannot be extended to the whole neighborhood Ω even as a hyperfunction solution of P(x, D)u = 0. This usage of the word “singularity” is the same as the one for the analytic functions in complex analysis, and is different of the usual usage of “singularities of solutions” in the theory of partial differential equations.
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Yau, Stephen T., and Letian Zhang. "An upper estimate of integral points in real simplices with an application to singularity theory." Mathematical Research Letters 13, no. 6 (2006): 911–21. http://dx.doi.org/10.4310/mrl.2006.v13.n6.a6.

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Klehn, Oliver. "Real and complex indices of vector fields on complete intersection curves with isolated singularity." Compositio Mathematica 141, no. 02 (February 10, 2005): 525–40. http://dx.doi.org/10.1112/s0010437x04000958.

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Shalaby, Abouzeid M. "Effective action study of the 𝒫𝒯-symmetric (iϕ3)6−𝜖 theory and the Yang–Lee edge singularity." International Journal of Modern Physics A 34, no. 17 (June 20, 2019): 1950090. http://dx.doi.org/10.1142/s0217751x19500908.

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We use the effective potential method to study the [Formula: see text]-symmetric [Formula: see text] field theory in [Formula: see text] space–time dimensions. For [Formula: see text], we obtained the first two energy levels which are real as well as reflecting the stability of the spectrum. [Formula: see text]-symmetry breaking occurs at [Formula: see text] where the two levels merge and beyond this critical point they have complex values. Since there exist no results in the literature to compare with, we extracted the critical exponents of the theory to test the accuracy of our calculations where we find them agree with exact results from the literature. We showed that the critical point is in fact a Yang–Lee edge singularity which is the first time to link [Formula: see text]-symmetry breaking to the existence of a Yang–Lee edge singularity. For [Formula: see text], the fixed point is nontrivial and exists for negative [Formula: see text] values as expected from Yang–Lee theory for ferromagnetic systems.
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Zhai, Liang-Jun, Huai-Yu Wang, and Guang-Yao Huang. "Scaling of the Berry Phase in the Yang-Lee Edge Singularity." Entropy 21, no. 9 (August 26, 2019): 836. http://dx.doi.org/10.3390/e21090836.

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We study the scaling behavior of the Berry phase in the Yang-Lee edge singularity (YLES) of the non-Hermitian quantum system. A representative model, the one-dimensional quantum Ising model in an imaginary longitudinal field, is selected. For this model, the dissipative phase transition (DPT), accompanying a parity-time (PT) symmetry-breaking phase transition, occurs when the imaginary field changes through the YLES. We find that the real and imaginary parts of the complex Berry phase show anomalies around the critical points of YLES. In the overlapping critical regions constituted by the (0 + 1)D YLES and (1 + 1)D ferromagnetic-paramagnetic phase transition (FPPT), we find that the real and imaginary parts of the Berry phase can be described by both the (0 + 1)D YLES and (1 + 1)D FPPT scaling theory. Our results demonstrate that the complex Berry phase can be used as a universal order parameter for the description of the critical behavior and the phase transition in the non-Hermitian systems.
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Loudon, Rodney. "One-dimensional hydrogen atom." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2185 (January 2016): 20150534. http://dx.doi.org/10.1098/rspa.2015.0534.

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The theory of the one-dimensional (1D) hydrogen atom was initiated by a 1952 paper but, after more than 60 years, it remains a topic of debate and controversy. The aim here is a critique of the current status of the theory and its relation to relevant experiments. A 1959 solution of the Schrödinger equation by the use of a cut-off at x = a to remove the singularity at the origin in the 1/| x | form of the potential is clarified and a mistaken approximation is identified. The singular atom is not found in the real world but the theory with cut-off has been applied successfully to a range of four practical three-dimensional systems confined towards one dimension, particularly their observed large increases in ground state binding energy. The true 1D atom is in principle restored when the short distance a tends to zero but it is sometimes claimed that the solutions obtained by the limiting procedure differ from those obtained by solution of the basic Schrödinger equation without any cut-off in the potential. The treatment of the singularity by a limiting procedure for applications to practical systems is endorsed.
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Sinclair, GB. "Stress singularities in classical elasticity—II: Asymptotic identification." Applied Mechanics Reviews 57, no. 5 (September 1, 2004): 385–439. http://dx.doi.org/10.1115/1.1767846.

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This review article (Part II) is a sequel to an earlier one (Part I) that dealt with means of removal and interpretation of stress singularities in elasticity, as well as their asymptotic and numerical analysis. It reviews contributions to the literature that have actually effected asymptotic identifications of possible stress singularities for specific configurations. For the most part, attention is focused on 2D elastostatic configurations with constituent materials being homogeneous and isotropic. For such configurations, the following types of stress singularity are identified: power singularities with both real and complex exponents, logarithmic intensification of power singularities with real exponents, pure logarithmic singularities, and log-squared singularities. These identifications are reviewed for the in-plane loading of angular elastic plates comprised of a single material in Section 2, and for such plates comprised of multiple materials in Section 3. In Section 4, singularity identifications are examined for the out-of-plane shear of elastic wedges comprised of single and multiple materials, and for the out-of-plane bending of elastic plates within the context of classical and higher-order theory. A review of stress singularities identified for other geometries is given in Section 5, axisymmetric and 3D configurations being considered. A limited examination of the stress singularities identified for other field equations is given as well in Section 5. The paper closes with an overview of the status of singularity identification within elasticity. This Part II of the review has 227 references.
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Dissertations / Theses on the topic "Real singularity theory"

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Oudrane, M'hammed. "Projections régulières, structure de Lipschitz des ensembles définissables et faisceaux de Sobolev." Electronic Thesis or Diss., Université Côte d'Azur, 2023. http://www.theses.fr/2023COAZ4034.

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Dans cette thèse, nous abordons des questions autour de la structure métrique des ensembles définissables dans les structures o-minimales.Dans la première partie, nous étudions les projections régulières au sens de Mostowski, nous prouvons que ces projections n'existent que pour les structures polynomialement bornées, nous utilisons les projections régulières pour refaire la preuve de Parusinski de l'existence des recouvrements réguliers. Dans la deuxième partie de cette thèse, nous étudions les faisceaux de Sobolev (au sens de Lebeau). Pour les fonctions de Sobolev de régularité entière positive, nous construisons ces faisceaux sur le site définissable d'une surface en nous basant sur des observations de base des domaines définissables dans le plan
In this thesis we address questions around the metric structure of definable sets in o-minimal structures. In the first part we study regular projections in the sense of Mostowski, we prove that these projections exists only for polynomially bounded structures, we use regular projections to re perform Parusinski's proof of the existence of regular covers. In the second part of this thesis, we study Sobolev sheaves (in the sense of Lebeau). For Sobolev functions of positive integer regularity, we construct these sheaves on the definable site of a surface based on basic observations of definable domains in the plane
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Books on the topic "Real singularity theory"

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Roque, Tatiana. The role of genericity in the history of dynamical systems theory. Edited by Karine Chemla, Renaud Chorlay, and David Rabouin. Oxford University Press, 2017. http://dx.doi.org/10.1093/oxfordhb/9780198777267.013.10.

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This article examines the role of genericity in the development of dynamical systems theory. In his memoir ‘Sur les courbes définies par une équation différentielle’, published in four parts between 1881 and 1886, Henri Poincaré studied the behavior of curves that are solutions for certain types of differential equations. He successfully classified them by focusing on singular points, described the trajectories’ behavior in important particular cases and provided new methods that proved to be extremely useful. This article begins with a discussion of singularity theory and its influence on the first definitions of genericity, along with the application of the notions of structural stability and genericity to understand dynamical systems. It also analyzes the Smale conjecture and how it was proven wrong and concludes with an overview of changes in the definitions of genericity meant to describe the ‘dark realm of dynamics’.
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Keats, Jonathon. Virtual Words. Oxford University Press, 2010. http://dx.doi.org/10.1093/oso/9780195398540.001.0001.

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The technological realm provides an unusually active laboratory not only for new ideas and products but also for the remarkable linguistic innovations that accompany and describe them. How else would words like qubit (a unit of quantum information), crowdsourcing (outsourcing to the masses), or in vitro meat (chicken and beef grown in an industrial vat) enter our language? In Virtual Words: Language on the Edge of Science and Technology, Jonathon Keats, author of Wired Magazine's monthly Jargon Watch column, investigates the interplay between words and ideas in our fast-paced tech-driven use-it-or-lose-it society. In 28 illuminating short essays, Keats examines how such words get coined, what relationship they have to their subject matter, and why some, like blog, succeed while others, like flog, fail. Divided into broad categories--such as commentary, promotion, and slang, in addition to scientific and technological neologisms--chapters each consider one exemplary word, its definition, origin, context, and significance. Examples range from microbiome (the collective genome of all microbes hosted by the human body) and unparticle (a form of matter lacking definite mass) to gene foundry (a laboratory where artificial life forms are assembled) and singularity (a hypothetical future moment when technology transforms the whole universe into a sentient supercomputer). Together these words provide not only a survey of technological invention and its consequences, but also a fascinating glimpse of novel language as it comes into being. No one knows this emerging lexical terrain better than Jonathon Keats. In writing that is as inventive and engaging as the language it describes, Virtual Words offers endless delights for word-lovers, technophiles, and anyone intrigued by the essential human obsession with naming.
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Book chapters on the topic "Real singularity theory"

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Abacı, Uygar. "Kant’s ‘Only Possible Argument’, Possibility and Necessity." In Kant's Revolutionary Theory of Modality, 104–32. Oxford University Press, 2019. http://dx.doi.org/10.1093/oso/9780198831556.003.0004.

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This chapter offers a reconstruction and analysis of Kant’s reformed ontological argument, moving from the actualist principle (AP) that every real possibility must be grounded in actuality to the conclusion that there exists a unique really necessary being, grounding all real possibility. This argument turns on a distinction between real modality, i.e. possibility and necessity of existence, and logical modality, i.e. possibility and necessity of thought. The existing literature on the argument focuses on the problem that the singularity of the ground of all real possibility is not warranted by the premises of the argument. There is, however, an even more fundamental problem: what grounds the actualist principle? The principle can be interpreted ontologically, as expressing the conditions of real possibility per se, or epistemologically, expressing the conditions of our cognition of real possibility. The precritical Kant adopts the ontological interpretation, but does not provide a justification for it.
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Stewart, Ian. "6. Physical infinity." In Infinity: A Very Short Introduction, 91–102. Oxford University Press, 2017. http://dx.doi.org/10.1093/actrade/9780198755234.003.0007.

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‘Physical infinity’ moves from mathematics to the real world and tackles questions such as ‘is space infinite?’ In many areas of physics, the presence of an infinite quantity (often called a singularity) is construed as a warning that the theory is losing touch with reality. For instance, according to classical ray optics, the intensity of light at the focus of a lens is infinite. The physical resolution of this difficulty involves replacing light rays by waves. Singularities are discussed in three physical contexts: optics, Newtonian gravity, and Albert Einstein’s relativity. However, there’s one area of physics in which an actual infinity—physical, not conceptual—is presented as a possible truth: cosmology.
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Kourelis, Kostis. "Style and Real Estate." In Redirecting Ethnic Singularity, 105–40. Fordham University Press, 2022. http://dx.doi.org/10.5422/fordham/9780823299720.003.0005.

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The Roman Catholic and Greek Orthodox churches have a long architectural heritage whose deployment in the design of American cities had preceded their arrival. Placed under a centralized church administration, Italians were subservient to an American Catholicism dominated by the Irish. Architecture became a tool to monopolize living connections with the Italian Renaissance and the Baroque. The Catholic Archdiocese, moreover, orchestrated real estate speculation and urban control through the intentional foundation of national parishes. In contrast, Greek immigrants encountered a fragmented church hierarchy that led to the ad hoc reuse of pre-existing buildings (especially aging Protestant churches). When building churches ex novo, Greek congregations chose the pan-European style of the national Cathedral of Athens, invented by the nation-state in 1842 to replace the medieval Byzantine past. By comparing Italian and Greek architectural stories, we illuminate a pluralism that shifted sameness and otherness across time and space.
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Chatterjee, Ronjaunee. "Introduction." In Feminine Singularity, 1–25. Stanford University Press, 2022. http://dx.doi.org/10.11126/stanford/9781503630802.003.0001.

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The introduction unfolds a theoretical genealogy of the term “singularity” and introduces a constellation of related terms that the book deploys in its chapters: “likeness,” “seriality,” and “minimal difference.” While singularity is often read in continental philosophy—especially the aesthetic tradition after Immanuel Kant—as conceptually errant and unwieldy, the term nevertheless functions as a useful critical optic for untangling normative and prescriptive models of femininity and identity. This introduction opens up a critical conversation between nineteenth-century literature and several vibrant theoretical fields that engage singularity as an alternative to liberal individualism: continental philosophy, psychoanalysis, queer of color theory, and the Black radical tradition.
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Chatterjee, Ronjaunee. "Epilogue." In Feminine Singularity, 156–62. Stanford University Press, 2022. http://dx.doi.org/10.11126/stanford/9781503630802.003.0006.

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In theorizing the long durée of nineteenth-century conceptions of a subject, the concluding section of the book finds that problems of likeness and seriality haunt contemporary posthuman accounts of being as much as they do an earlier liberal humanism. Insofar as contemporary science fiction inherits tropes of doubling and iteration handed down from the Gothic, it remains enmired in basic questions around how difference functions to articulate ontology. The book ends by turning to a contemporary film, Alex Garland’s Ex Machina (2014), to consider the presently popularized AI definition of singularity. This definition is animated by earlier trajectories of literary and philosophical thought. I read the film with Mary Shelley’s novel Frankenstein (1818) to contrast their differing approaches to femininity and subjectivity. The book closes with a short reading of Jean-Luc Nancy’s essay, “Literary Communism.”
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Sainsbury, Mark. "Varieties of Singularity." In Singular Thought and Mental Files, 21–37. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198746881.003.0002.

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What is it for a thought to be singular? The chapter argues that there is no single answer. Singularity in thought is associated with a variety of non-equivalent features. For example, some argue that the object of a singular thought should be something with which we are acquainted, or should involve the exercise of a mental file; or the thought should essentially “involve” its object, or refer to it rigidly. The chapter claims that the main task should be to examine the relations between these various features; there is little interest in trying to determine what a “real” singular thought is.
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Couret, Nilo. "Fictions of the Real." In Mock Classicism. University of California Press, 2018. http://dx.doi.org/10.1525/california/9780520296848.003.0005.

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The Brazilian chanchada, or musical comedy, is a popular genre from the golden age of Brazilian cinema with a substantial Portuguese-language academic literature. Instead of retreading these ontogenetic arguments, this chapter argues the transition from musicarnavalesco to chanchada in light of the Estado Novo implementation of centralized monetary policy and the currency conversion to the Cruzeiro. As money (ex)changes, there is less agreement on evaluative criteria, auguring a crisis of valuation that subtends debates around the value of the genre. Making film a better commodity in an economy of desmedida undergoing a crisis of value presents challenges at levels material (currency restrictions shaped the development of the industry) and aesthetic (money as a form of economic symbolization coincides with the rise of fictionality). Classicism is mocked once more, now discussed in relation to the rise of fictionality rather than the codification of the classical realist text. The chanchada designates a certain intensification of fictionality where we actively feel the tension between the narrativized diegesis, the singularity of the comedic effect, and the present tense of the spectator.
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Mayhew, Henry. "London Omnibus-Drivers and Conductors." In London Labour and the London Poor. Oxford University Press, 2012. http://dx.doi.org/10.1093/owc/9780199697571.003.0025.

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Omnibus Drivers The omnibus drivers have been butchers, farmers, horsebreakers, cheesemongers, old stage-coachmen, broken-down gentlemen, turfmen, gentlemen’s servants, grooms, and a very small sprinkling of mechanics. Nearly all can read and write, the exception being described to me as a singularity; but there are such...
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Lutz, Deborah. "Marginal Scribbling and Defacing." In Victorian Paper Art and Craft, 9–33. Oxford University PressOxford, 2022. http://dx.doi.org/10.1093/oso/9780198858799.003.0002.

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Abstract Chapter 1 considers books from writers’ libraries that they have marked, autographed, and supplemented with matter such as pressed plants, feathers, and fingernail scorings. These haptic texts, thickened with time and adaptation, gained singularity, with meaning developing when samples of the real were left behind. Eliot used some of her books to memorialize—to observe a passing moment, to remember a personal exchange—while in others she wrote comments, indexes on their endpapers, and other glosses of a scholarly nature. Charlotte and Emily Brontë, contrarily, penned diaries in their books, doodled in them, and generally defaced them. This thinking of the published, printed volume as paper with blank spaces inciting script, as a bearer of relationships and memory, as a magical object set in place and time, and as a space that could be inhabited shaped these writers’ own creative acts.
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Jahanbegloo, Ramin. "Indian National Music." In Talking Poetry, 85–86. Oxford University PressOxford, 2022. http://dx.doi.org/10.1093/oso/9780192869180.003.0022.

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Abstract Many musicians like the Carnatic vocalist MS Subbalakshmi became a national and perhaps nationalist icon. Since nothing in India is singular, and the idea of a national music, or a national dance or a national theatre based on singularity, is really not valid. There are and have been two types of Indian classical music, at least eight kinds of classical dance. Plurality is dominant in the classical realm as well. But there was definitely an attempt to assert that we exist as a people and this is our creative wealth. And this was more evident perhaps in music and dance.
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Conference papers on the topic "Real singularity theory"

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Henry, Jean-Pierre, and Adam Parusiński. "Invariants of bi-Lipschitz equivalence of real analytic functions." In Geometric Singularity Theory. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2004. http://dx.doi.org/10.4064/bc65-0-5.

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Koike, Satoshi. "Finiteness theorems on Blow-Nash triviality for real algebraic singularities." In Geometric Singularity Theory. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2004. http://dx.doi.org/10.4064/bc65-0-10.

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Houston, Kevin. "On the classification of real mono-germs of corank one and codimension one." In Geometric Singularity Theory. Warsaw: Institute of Mathematics Polish Academy of Sciences, 2004. http://dx.doi.org/10.4064/bc65-0-6.

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TROTMAN, David. "LECTURES ON REAL STRATIFICATION THEORY." In Proceedings of the 2005 Marseille Singularity School and Conference. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812707499_0004.

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Zhang, Zhen, and Zhigang Suo. "Split Singularities: Applications and Implications." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-41213.

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In the microelectronic system, many materials are integrated together in complex structures, from the level of transistors to the level of motherboard. These materials are of different thermomechanical properties, and usually meet together to form the sharp features, such as trenches, wedges, corners or junctions. These sharp features can concentrate stresses, which in turn fail the devices in the ways of cracking, debonding, or injecting dislocations, etc. The singular stress field is a linear superposition of two modes, usually of unequal exponents, either a pair of complex conjugates, or two unequal real numbers. In the latter case, a stronger and a weaker singularity coexist, known as split singularities. The weaker singularity can readily affect the outcome of failures. A dimensionless parameter, called the mode mixity, is defined to characterize the proportion of the two modes at the length scale where the processes of fracture occur. If the mode mixity is nearly zero, then the singular stress field can be simplified to a single mode, and be characterized by one stress intensity factor, on which the criteria of avoiding the failure initiated from the sharp features can be established. Otherwise, both modes need to be considered. We apply this theory to crack penetration or debond, and dislocation injection into strained silicon.
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Seade, José. "On Milnor's fibration Theorem for real and complex singularities." In Proceedings of the Trieste Singularity Summer School and Workshop. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812706812_0004.

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Abdullah, CheZulkhairi, Mozafar Saadat, and Hamid Rakhodaei. "A Methodology for Workspace Identification of Parallel Robots Using Parametric Sweep Search Method." In ASME 2014 12th Biennial Conference on Engineering Systems Design and Analysis. American Society of Mechanical Engineers, 2014. http://dx.doi.org/10.1115/esda2014-20410.

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In this paper, a methodology for real time identification of various singularities for various workspace types of parallel robots is proposed. Python 3D simulation software has been developed to position the moving platform of the robot’s CAD model through pre-defined rules in order to solve specific problems including singularity identification, obstacle avoidance, and path planning. The system is designed to identify the moving platform’s best possible pose. Boolean logic is used to identify valid path trajectory through parametric sweep search method. Joint constraints are checked to validate the platforms’ positions using the actuators’ stroke length, their angles, and any possible collisions. Solutions for any desired pose, based on line collision and mesh model algorithms, are then found. The path, position and workspace data are verified against a kinematic model of the robot, developed in Solid works and Matlab software tools. The simulation system has been successfully tested using various n-dimensional interpolations based on the given case study.
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Park, Dong Il, Soo Hyun Kim, and Yoon Keun Kwak. "Analysis of the Weighting Matrix for Load Distribution Using Weighted Pseudoinverse in a Redundantly Actuated System." In ASME 7th Biennial Conference on Engineering Systems Design and Analysis. ASMEDC, 2004. http://dx.doi.org/10.1115/esda2004-58404.

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Redundant actuation indicates a situation when there are more actuators than a system’s mobility. A redundant actuated system has many strengths, such as better performance than a non-redundant system, avoiding singularity, reducing impact force using active stiffness control and fault tolerance. However, there are some issues on economic efficiency and minimization of a system, because redundant actuation can use more actuators than non-redundant actuation. Also, in a redundant actuation system, the actuator torque does not have one solution, but rather there are infinite torque sets even though a robot works on the same task. Therefore, it is very important to select a torque distribution method that is suitable for the objectives of the robot. In this paper, we used the weighted pseudoinverse matrix for torque distribution. This method is applied to a five bar link system and the influence of the weighting variables is analyzed. By adjusting the weighting values, we can find the relation between the actuator input and the weighting value and obtain various torque sets in real time. In other words, we find how each actuator torque changes according to the variation of each weighting value and how much the maximum torque reduce for the suggested weighting matrices.
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Gu, Bei, and H. Harry Asada. "Towards a Simulation Knowledge Network With Application to Coupled Physiological Systems." In ASME 2000 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2000. http://dx.doi.org/10.1115/imece2000-2383.

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Abstract A new approach is proposed for the simulation of interacting human physiological subsystems. The new simulation environment will allow users to build, analyze and solve coupled physiological system models based on available distributed subsystem models. The subsystem models as an abstract form of physiological knowledge are shared through the Internet. The simulation knowledge network includes a distributed model database, an information server, and an analysis and solution environment that can be downloaded from the server. To represent the coupled system, we use Differential Algebraic Equations (DAE) as the basic format. There are three common sources of algebraic constraints in models of physiological systems. They are causal conflict, simulation optimization, and multistage processes. The singularly perturbed sliding manifolds method is chosen for solving DAEs. Possible future improvements are discussed. Examples of simulation of coupled circulatory, thermoregulatory, and renal systems are presented to demonstrate the simulation environment.
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10

Freund, Issac. "Optical Vortices in Random Wavefields." In Advances in Optical Imaging and Photon Migration. Washington, D.C.: Optica Publishing Group, 2022. http://dx.doi.org/10.1364/aoipm.1994.wpl.20.

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Vortices (topological phase singularities), which may be either positive or negative in sign, are found in many different types of optical fields. On every zero crossing of the real or imaginary part of the wavefield, adjacent vortices must be of opposite sign. This new "sign principle", which is unaffected by boundaries, leads to the surprising results that for a given set of zero crossings: (i) fixing the sign of any given vortex automatically fixes the signs of all other vortices in the wavefield, (ii) the sign of the first vortex created during the evolution of a wavefield determines the signs of all subsequent vortices, and (iii) the sign of this first vortex places additional strong constraints on the future development of the wavefunction. The sign principle also constrains how contours of equal phase thread through the wavefield from one vortex to another. Amplitude topological (AT) singularities are defined (for the first time) in terms of the gradient of the field amplitude. Such singularities correspond to stationary points of the amplitude and are located at the intersections of the zero crossings of the x- and y-partial derivatives of the amplitude. Amplitude maxima and minima are positive AT singularities and saddle points are negative AT singularities. The sign principle implies that adjacent AT singularities on any given zero crossing must be of opposite sign, that in an unbounded wavefield the total number of maxima and minima must equal the number of saddle points, that in free space stationary points of the amplitude must first appear as positive-negative AT singularity twins, and that there must exist strong correlations between neighboring maxima, minima and saddle points. The numerous, far reaching implications of the sign principle have been verified using a computer simulation that generates a random Gaussian wavefield.
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