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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Fabris, Júlio C., Tales Augusto Oliveira Gomes, and Denis Campos Rodrigues. "Black Hole and Wormhole Solutions in Einstein–Maxwell Scalar Theory." Universe 8, no. 3 (February 27, 2022): 151. http://dx.doi.org/10.3390/universe8030151.
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We classified and studied the charged black hole and wormhole solutions in the Einstein–Maxwell system in the presence of a massless, real scalar field. The possible existence of charged black holes in general scalar–tensor theories was studied in Bronnikov et al., 1999; black holes and wormholes exist for a negative kinetic term for the scalar field. Using a conformal transformation, the static, spherically symmetric possible structures in the minimal coupled system are described. Besides wormholes and naked singularities, only a restricted class of black hole exists, exhibiting a horizon with an infinite surface and a timelike central singularity. The black holes and wormholes defined in the Einstein frame have some specificities with respect to the non-minimal coupling original frame, which are discussed in the text.
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NIÉGAWA, A. "SOFT PHOTON PRODUCTION FROM QUARK–GLUON PLASMA AND CANCELLATION OF MASS SINGULARITY." Modern Physics Letters A 10, no. 05 (February 20, 1995): 379–89. http://dx.doi.org/10.1142/s0217732395000417.
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It has recently been reported that the production rate of soft real photons from a hot quark–gluon plasma exhibits unscreened mass singularities even within the hard-thermal-loop resummation scheme. It is shown that there exist another diagrams that cancel the singular contribution, in accordance with the general theorem of absence of mass singularities in thermal reaction rates, provided one sums over the set of all degenerate initial and final states. An interpretation of the relevant diagrams is given in terms of physical processes taking place in the quark–gluon plasma. The mechanism of canceling mass singularities in this example is similar to the one in vacuum theory.
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Milu Acharya, Pravat Manjari Mohanty,. "Numerical Approximation of Integrals in Presence of Nearby Singularities." Turkish Journal of Computer and Mathematics Education (TURCOMAT) 12, no. 6 (April 5, 2021): 2319–23. http://dx.doi.org/10.17762/turcomat.v12i6.4904.
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The quadrature formulas meant for the numerical approximation of integrals of one-dimensional real variables need to be modified for the sake of accuracy when a singularity is present in the proximity of the path of integration. The required corrective factor has been constructed and some existing quadrature rule has been applied with the corrective factor to obtain better accuracy.
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Bode, Benjamin. "Constructing links of isolated singularities of polynomials ℝ4 → ℝ2." Journal of Knot Theory and Its Ramifications 28, no. 01 (January 2019): 1950009. http://dx.doi.org/10.1142/s0218216519500093.
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We show that if a braid [Formula: see text] can be parametrized in a certain way, then the previous work (B. Bode and M. R. Dennis, Constructing a polynomial whose nodal set is any prescribed knot or link, arXiv:1612.06328 ) can be extended to a construction of a polynomial [Formula: see text] with the closure of [Formula: see text] as the link of an isolated singularity of [Formula: see text], showing that the closure of [Formula: see text] is real algebraic. In particular, we prove that closures of squares of strictly homogeneous braids and certain lemniscate links are real algebraic. We also show that the constructed polynomials satisfy the strong Milnor condition, providing an explicit fibration of the complement of the closure of [Formula: see text] over [Formula: see text].
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Kim, Chan-Gyun. "Existence, multiplicity and non-existence of positive solutions for two-point boundary-value problems with strong singularity." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 140, no. 6 (December 2010): 1187–96. http://dx.doi.org/10.1017/s0308210509000948.
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We study the existence, multiplicity and non-existence of positive solutions for the singular two-point boundary-value problemswhere $\varphi_{p}(s)=|s|^{p-2}s$, $p>1$, λ is a non-negative real parameter and f ∈ C((0, 1) × [0,∞), (0,∞)). Here, f(t, u) may be singular at t = 0 and/or 1. To obtain the main results we use the global continuation theorem and fixed-point index theory.
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LUBBES, NIELS. "ALGORITHMS FOR SINGULARITIES AND REAL STRUCTURES OF WEAK DEL PEZZO SURFACES." Journal of Algebra and Its Applications 13, no. 05 (February 25, 2014): 1350158. http://dx.doi.org/10.1142/s0219498813501582.
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In this paper, we consider the classification of singularities [P. Du Val, On isolated singularities of surfaces which do not affect the conditions of adjunction. I, II, III, Proc. Camb. Philos. Soc.30 (1934) 453–491] and real structures [C. T. C. Wall, Real forms of smooth del Pezzo surfaces, J. Reine Angew. Math.1987(375/376) (1987) 47–66, ISSN 0075-4102] of weak Del Pezzo surfaces from an algorithmic point of view. It is well-known that the singularities of weak Del Pezzo surfaces correspond to root subsystems. We present an algorithm which computes the classification of these root subsystems. We represent equivalence classes of root subsystems by unique labels. These labels allow us to construct examples of weak Del Pezzo surfaces with the corresponding singularity configuration. Equivalence classes of real structures of weak Del Pezzo surfaces are also represented by root subsystems. We present an algorithm which computes the classification of real structures. This leads to an alternative proof of the known classification for Del Pezzo surfaces and extends this classification to singular weak Del Pezzo surfaces. As an application we classify families of real conics on cyclides.
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U¨berall, Herbert, P. P. Delsanto, J. D. Alemar, E. Rosario, and Anton Nagl. "Application of the Singularity Expansion Method to Elastic Wave Scattering." Applied Mechanics Reviews 43, no. 10 (October 1, 1990): 235–49. http://dx.doi.org/10.1115/1.3119152.
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The singularity expansion method (SEM), established originally for electromagnetic-wave scattering by Carl Baum (Proc. IEEE 64, 1976, 1598), has later been applied also to acoustic scattering (H U¨berall, G C Gaunaurd, and J D Murphy, J Acoust Soc Am 72, 1982, 1014). In the present paper, we describe further applications of this method of analysis to the scattering of elastic waves from cavities or inclusions in solids. We first analyze the resonances that appear in the elastic-wave scattering amplitude, when plotted vs frequency, for evacuated or fluid-filled cylindrical and spherical cavities or for solid inclusions. These resonances are interpreted as being due to the phase matching, ie, the formation of standing waves, of surface waves that encircle the obstacle. The resonances are then traced to the existence of poles of the scattering amplitude in the fourth quadrant of the complex frequency plane, thus establishing the relation with the SEM. The usefulness of these concepts lies in their applicability for solving the inverse scattering problem, which is the central problem of NDE. Since for the case of inclusions, or of cavities with fluid fillers, the scattering of elastic waves gives rise to very prominent resonances in the scattering amplitude, it will be of advantage to analyze these with the help of the resonance scattering theory or RST (first formulated by L Flax, L R Dragonette, and H U¨berall, J Acoust Soc Am 63, 1978, 723). These resonances are caused by the proximity of the SEM poles to the real frequency axis, on which the frequencies of physical measurements are located. A brief history of the establishment of the RST is included here immediately following the Introduction.
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Bahia, Carlos A. S., Mateus Broilo, and Emerson G. S. Luna. "Regge Phenomenology at LHC Energies." International Journal of Modern Physics: Conference Series 45 (January 2017): 1760064. http://dx.doi.org/10.1142/s2010194517600643.
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At high energies the Pomeron plays a crucial part in describing the soft interactions. In the light of LHC (Large Hadron Collider) data we perform a detailed analysis of proton-proton ([Formula: see text]) and antiproton-proton ([Formula: see text]) forward scattering data in order to determine the intercept and the slope of the soft Pomeron trajectory. This analysis is performed based on Regge theory using Born-level amplitudes. We investigate the role of the proton-Pomeron vertex form and of the nearest [Formula: see text]-channel singularity. We give predictions for the total cross section and the ratio of the real part to the imaginary part of the elastic amplitude in [Formula: see text] collisions at LHC and cosmic-ray energies.
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Olszok, Charis. "Comparative Literature, Companion Species and the Camel." Comparative Critical Studies 17, no. 1 (February 2020): 47–69. http://dx.doi.org/10.3366/ccs.2020.0343.
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This article brings together theories of both real and literary animals’ readability within Animal Studies and of untranslatability within comparative literature more broadly. Through a focus on Ibrāhīm al-Kūnī’s al-Tibr, in comparison with Mahasweta Devi's ‘Pterodactyl, Puran Sahay and Pirtha’, I read the central human-animal encounters through both their cultural specificity and the wider ‘animal tropes’ to which they point, situating them within local tradition and the flows of world literature. I then shift to an examination of how both texts, through interspecies encounter, theorize the very processes of readability and comparability which they invite. Animals, I suggest, emerge as sites of ‘secrets’, hinting at the dictates of censorship as they shield symbolic import, or at the local which must be preserved from appropriation, and, above all, at a dimension of ‘otherness’ which can never be fully grasped. In al-Tibr, I examine this through a reading of the camel as ‘ āya’ (sign), a central term within Arabic cosmology, and, in ‘Pterodactyl’, through Gayatri Chakravorty Spivak's influential reading of ‘ethical singularity’ in the story.
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BAPTISTELLI, P. H., and M. MANOEL. "The classification of reversible-equivariant steady-state bifurcations on self-dual spaces." Mathematical Proceedings of the Cambridge Philosophical Society 145, no. 2 (September 2008): 379–401. http://dx.doi.org/10.1017/s0305004108001400.
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AbstractIn this paper we apply singularity theory methods to the classification of reversible-equivariant steady-state bifurcations depending on one real parameter. We assume that the group of symmetries and reversing symmetries is a compact Lie group Γ, and the equivalence is defined in order to preserve these symmetries and reversing symmetries in the normal forms and their unfoldings. When the representation of Γ is self-dual, we show that the classification can be reduced to the standard equivariant context. In this case, we establish a one-to-one association between the classification of bifurcations in the reversible-equivariant context and the classification of purely equivariant bifurcations related to them. As an application of the results, we obtain the classification of self-dual representations ofZ2⊕Z2andD4on the plane.
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Hoel, A. S. Aurora. "Technicity and the Virtual." Humanities 11, no. 6 (October 31, 2022): 135. http://dx.doi.org/10.3390/h11060135.
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This article outlines an eco-operational theory of technical mediation that centers on Gilbert Simondon’s notion of technicity. The argument is that technical apparatuses do the work of concepts. However, the eco-operational viewpoint completely alters the status of concepts: what they are, where they are, and what they do. Technicity, as understood here, concerns the efficacious action and operational functioning of a broad range of apparatuses (including living bodies and technical machines), which are conceived as adaptive mediators. The focus on technicity provides a new notion of the virtual, that of the operationally real, which resonates with Gilles Deleuze’s while also marking a new direction. What is more, by approaching mediation in terms of technicity, the eco-operational framework offers a novel understanding of concept or generality that stakes out a middle path between Kantian representational generality and Deleuzian concrete singularity.
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Zhao, Da Xu, En Cang Di, Guo Zhong Shou, and Yu Qi Gu. "Kinematics of a 6-DOF Feeding and Unloading Manipulator." Key Engineering Materials 620 (August 2014): 490–95. http://dx.doi.org/10.4028/www.scientific.net/kem.620.490.
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In order to improve the efficiency of kinematics modeling in analyzing robots, this document used Lie groups and screw theory to describe rigid motion of the robot system, established a kinematic model of operating arm based on Product of Exponentials (POE) formula, and analyzed forward and inverse kinematics of chain topology structure robot, as well as several sub-inverse problem of inverse kinematics. A 6-DOF series-wound configuration loading and unloading manipulator has been used as an example, its kinematics equations are established by POE formula combined with screw theory, the special configuration of end effector under a specific task planning are calculated using Mathematica software. By contrast with D-H parameters method, we can draw a conclusion that POE formula and D-H parameters method are essentially equivalent. However, POE formula and motion screw have more definite geometric and physical meaning, neat expression form, convenient algebraic operation, are able to overcome limitations, such as calculation complexity and singularity in solving process, can meet kinematic analysis and real-time control of robot.
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Meniailava, Darya N., Maksim B. Shundalau, and Yong-Chang Han. "Transport properties of two-component radium – halogen dilute gas media." Journal of the Belarusian State University. Physics, no. 1 (February 8, 2022): 52–64. http://dx.doi.org/10.33581/2520-2243-2022-1-52-64.
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Based on state-of-the-art ab initio potential energy functions and classical kinetic theory, some transport properties (diffusion, viscosity and thermal conductivity coefficients) of two-component dilute gas media of radium and halogen (F, Cl, Br, I) atoms were predicted as functions of the translation temperature up to 3000 K. Calculations were performed by sequential analytical and (or) numerical computations of deflection angle, cross-section and collision integrals. A detailed methodology for the calculation of the transport properties using the Morse potential was developed. Some numerical difficulties arising due to the singularity of the integrands and discontinuous character of the variable of integration are considered. The dependence of transport properties on isotope mass is also shown. Possible errors introduced by using the model Morse potential function instead of the real potential for the interaction between atoms are estimated. These data can be useful for the planning of the experiments on the direct laser cooling of the monohalides of alkaline earth metals.
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Helmzadeh, Amin, and Shahram M. Kouhsari. "Erroneous branch parameters detection and correction in real time simulation of power systems." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 35, no. 5 (September 5, 2016): 1656–71. http://dx.doi.org/10.1108/compel-11-2015-0388.
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Purpose The purpose of this paper is to propose an efficient method for detection and modification of erroneous branch parameters in real time power system simulators. The aim of the proposed method is to minimize the sum of squared errors (SSE) due to mismatches between simulation results and corresponding field measurements. Assuming that the network configuration is known, a limited number of erroneous branch parameters will be detected and corrected in an optimization procedure. Design/methodology/approach Proposing a novel formulation that utilizes network voltages and last modified admittance matrix of the simulation model, suspected branch parameters are identified. These parameters are more likely to be responsible for large values of SSE. Utilizing a Gauss-Newton (GN) optimization method, detected parameters will be modified in order to minimize the value of SSE. Required sensitivities in optimization procedure will be calculated numerically by the real time simulator. In addition, by implementing an efficient orthogonalization method, the more effective parameter will be selected among a set of correlated parameters to avoid singularity problems. Findings Unlike state estimation-based methods, the proposed method does not need the mathematical functions of measurements to simulation model parameters. The method can enhance other parameter estimation methods that are based on state estimation. Simulation results demonstrate the high efficiency of the proposed optimization method. Originality/value Incorrect branch parameter detection and correction procedures are investigated in real time simulators.
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Pratsiovytyi, Mykola, Olha Bondarenko, Sofiia Ratushniak, and Kateryna Franchuk. "Ǭ-representation of Real Numbers as a Generalization of Cantor Numeral Systems." Mohyla Mathematical Journal 5 (December 28, 2022): 9–18. http://dx.doi.org/10.18523/2617-7080520229-18.
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We consider generalization of Cantor numeral system, which is determined by the sequence of bases (sn), 1 < sn ∈ N, and the sequence of alphabets An = {0, 1, ..., sn − 1}:[0; 1] ∋ x = ∞∑ n=1 αn/s1s2...sn, αn ∈ An,the so-called Ǭ-representation. It is defined by an infinite “matrix” ||qik||, where i ∈ Ai, k ∈ N, having the properties0 < qik < 1, mk ∑ i=0 qik = 1, k ∈ N, ∞∏ n=1 max i {qik} = 0,namely[0; 1] ∋ x = ai11 + ∞∑ k=2 [aikk k−1 ∏ j=1 qij (x)j ] ≡ Δi1i2...ik..., where ainn = in−1 ∑ j=0 qjn, in ∈ An, n ∈ N.The applications of this representation of numbers in the metric theory of numbers, the theory of distributions of random variables, the theory of locally complicated functions, and fractal analysis are studied.For the set C[Ǭ; Vn] = {x : x = Δα1...αn..., αn ∈ Vn ⊂ An}, we study its topological and metric structure and derive a formula for calculating its Lebesgue measure:λ(C) = ∞∏ n=1 λ(Fn) / λ(Fn−1) = ∞∏ n=1 (1 − λ(Fn) / λ(Fn−1)),where F0 = [0; 1], Fn is the union of Ǭ-cylinders of rank n, such that there are points of the set C among their interior points of the set C, Fn ≡ Fn−1 \ Fn.A criterion and some sufficient conditions for this set to be a set of zero measure are found. Under additional conditions on the “matrix” ||qik||, the normal property for Ǭ-representation of numbers is found ((i.e., almost all in the sense of Lebesgue measure numbers have this property). The obtained results are used to establish the Lebesgue structure and the type of distribution of a random variable whose digits of Ǭ-representation are independent random variables. It is proved that the digits of the Ǭ-representation of a random variable uniformly distributed on [0; 1] are independent, and their distribution is given.If the cardinalities of the alphabets are finite and the elements of the “matrix” ||qik|| are bounded away from zero, it is proved that to calculate the Hausdorff-Besicovitch fractal dimension of subsets of the segment [0; 1], it is sufficient to cover them with Ǭ-cylinders: Δc1...cm = {x : x = Deltac1...cki1...in..., in ∈ ∈ Ak+n}.For inversor of digits of Ǭ-representation of numbers, that is, the function defined by equality I(x = = Δi1...in...) = Δ[m1−i1]...[mn−in]..., mn ≡ sn − 1 it is proved its continuity, strict monotonicity, and for certain cases, its singularity (the equality of the derivative to zero almost everywhere in the sense of the Lebesgue measure).
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U¨berall, Herbert, Alain Ge´rard, Arde´shir Guran, Jean Duclos, Mohammed El Hocine Khelil, X. L. Bao, and P. K. Raju. "Acoustic Scattering Resonances: Relation to External and Internal Surface Waves." Applied Mechanics Reviews 49, no. 10S (October 1, 1996): S63—S71. http://dx.doi.org/10.1115/1.3101979.
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The resonance scattering theory (RST) and the singularity expansion method (SEM) are both based on the complex-frequency poles of the scattering amplitude in the scattering of acoustic, elastic, or electromagnetic waves from elastic or impenetrable objects, or from cavities. These poles, situated off the real frequency axis at locations with negative imaginary parts, are found to yield, at the real frequencies of the experiments, prominent resonances for acoustic and elastic-wave scattering from elastic objects as discussed in our earlier review (U¨berall et al, Appl Mech Rev43(10), 1990, 235). However, as the authors demonstrated before (U¨berall et al, J Acoust Soc Am61, 1977, 711), the origin of these resonances lies in the phase matching of circumferential or surface waves generated on the target objects during the scattering; hence a study of the resonances will lead to an understanding of, and information on these surface waves. This has been the topic of a large number of studies in recent years, and the results are summarized in the present review for immersed elastic target objects of plane, spherical, and cylindrical geometry, including both elastic-type and fluid-borne surface waves. For multilayered elastic structures, we also describe possible layer-resonance identifications based on acoustic and elastic-wave scattering experiments.
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Leib, S. J. "Nonlinear evolution of subsonic and supersonic disturbances on a compressible free shear layer." Journal of Fluid Mechanics 224 (March 1991): 551–78. http://dx.doi.org/10.1017/s0022112091001878.
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We consider the effects of a nonlinear–non-equilibrium–viscous critical layer on the spatial evolution of subsonic and supersonic instability modes on a compressible free shear layer. It is shown that the instability wave amplitude is governed by an integro-differential equation with cubic-type nonlinearity. Numerical and asymptotic solutions to this equation show that the amplitude either ends in a singularity at a finite downstream distance or reaches an equilibrium value, depending on the Prandtl number, viscosity law, viscous parameter and a real parameter which is determined by the linear in viscid stability theory. A necessary condition for the existence of the equilibrium solution is derived, and whether or not this condition is met is determined numerically for a wide range of physical parameters including both subsonic and supersonic disturbances. It is found that no equilibrium solution exists for the subsonic modes unless the temperature ratio of the low-to high-speed streams exceeds a critical value, while equilibrium solutions for the most rapidly growing supersonic mode exist over most of the parameter range examined.
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ABRAHAM, D. B., and P. J. UPTON. "SUSCEPTIBILITY SINGULARITIES AT FIRST-ORDER PHASE TRANSITIONS." International Journal of Modern Physics C 03, no. 05 (October 1992): 1071–82. http://dx.doi.org/10.1142/s0129183192000701.
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Problems associated with analyticity of thermodynamic functions close to first-order phase transitions are briefly reviewed. The bubble model for correlation functions is then applied to planar Ising-like models at subcritical temperatures (T<Tc) with a bulk magnetic field h. The fluctuation sum is used to calculate the susceptibility χ(h) from the bubble correlation function. We show that χ(h), calculated this way, must contain an essential singularity at h=0 i.e. at the first-order phase boundary. This has important implications to metastability, where we demonstrate that if the ensemble is restricted such that the magnetization stays positive when h goes negative, χ(h) has an infinite number of poles along the negative real axis with a limit-point at h=0. For an unrestricted ensemble, a Yang-Lee circle theorem is derived.
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Lipiński, Kamil. "Obraz przestrzeni dowolnej według Gilles’a Deleuze’a." Przestrzenie Teorii, no. 31 (December 6, 2019): 262–70. http://dx.doi.org/10.14746/pt.2019.31.14.
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The subject matter of the article is Gilles Deleuze’s considerations on the concept of “any-space whatever” and its application in the cinema and the theater. This space is an outcome of the sensorimotor crisis as the development of Henri Bergson’s conception of duration to determine the potential transformations of modern cinema in the post-war period. It is expressed by a potential singularity that finds its locus in pure optical and sound situations. This conception reveals the correlation between the real and virtual connections defined by a genetic sign which relies upon differentiation. As a space characterized by an affection – image is experienced from its inside to define both disjoint and empty spaces. Such affect often emerges in a range of colors to outline the places marked by emptiness. It is strictly associated with “geometrical” orientation actualizing itself via the qualisign. Thus, this article defines the space in terms of the circuit of virtuality and actuality in time-image which crystallizes both in the cinema and TV dramas of potential exhaustion of three languages in theater performances. Namely, the first one is disruptive and enumerative; the second language consists of voices and combinative flows and the third one reunites the previous ones as the language of images, sounds, and coloring which is a movement between words.
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Nguyen, Huong Thu, and Long The Nguyen. "Fingerprints Classification through Image Analysis and Machine Learning Method." Algorithms 12, no. 11 (November 11, 2019): 241. http://dx.doi.org/10.3390/a12110241.
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The system that automatically identifies the anthropometric fingerprint is one of the systems that interact directly with the user, which every day will be provided with a diverse database. This requires the system to be optimized to handle the process to meet the needs of users such as fast processing time, almost absolute accuracy, no errors in the real process. Therefore, in this paper, we propose the application of machine learning methods to develop fingerprint classification algorithms based on the singularity feature. The goal of the paper is to reduce the number of comparisons in automatic fingerprint recognition systems with large databases. The combination of using computer vision algorithms in the image pre-processing stage increases the calculation time, improves the quality of the input images, making the process of feature extraction highly effective and the classification process fast and accurate. The classification results on 3 datasets with the criteria for Precision, Recall, Accuracy evaluation and ROC analysis of algorithms show that the Random Forest (RF) algorithm has the best accuracy (≥96.75%) on all 3 databases, Support Vector Machine (SVM) has the best results (≥95.5%) 2 / 3 databases.
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Znojil, Miloslav. "Quasi-Hermitian Formulation of Quantum Mechanics Using Two Conjugate Schrödinger Equations." Axioms 12, no. 7 (June 28, 2023): 644. http://dx.doi.org/10.3390/axioms12070644.
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To the existing list of alternative formulations of quantum mechanics, a new version of the non-Hermitian interaction picture is added. What is new is that, in contrast to the more conventional non-Hermitian model-building recipes, the primary information about the observable phenomena is provided not only by the Hamiltonian but also by an additional operator with a real spectrum (say, R(t)) representing another observable. In the language of physics, the information carried by R(t)≠R†(t) opens the possibility of reaching the exceptional-point degeneracy of the real eigenvalues, i.e., a specific quantum phase transition. In parallel, the unitarity of the system remains guaranteed, as usual, via a time-dependent inner-product metric Θ(t). From the point of view of mathematics, the control of evolution is provided by a pair of conjugate Schrödiner equations. This opens the possibility od an innovative dyadic representation of pure states, by which the direct use of Θ(t) is made redundant. The implementation of the formalism is illustrated via a schematic cosmological toy model in which the canonical quantization leads to the necessity of working with two conjugate Wheeler-DeWitt equations. From the point of view of physics, the “kinematical input” operator R(t) may represent either the radius of a homogeneous and isotropic expanding empty Universe or, if you wish, its Hubble radius, or the scale factor a(t) emerging in the popular Lemaitre-Friedmann-Robertson-Walker classical solutions, with the exceptional-point singularity of the spectrum of R(t) mimicking the birth of the Universe (“Big Bang”) at t=0.
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Yuan, Mengting, Wenguang Luo, Hongli Lan, and Yongxin Qin. "Research on Multifractal Characteristics of Vehicle Driving Cycles." Machines 11, no. 4 (March 26, 2023): 423. http://dx.doi.org/10.3390/machines11040423.
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Vehicle driving cycles have complex characteristics, but there are few publicly reported methods for their quantitative characterization. This paper innovatively investigates their multifractal characteristics using the fractal theory to characterize their complex properties, laying the foundation for applications such as vehicle driving cycle feature identification, vehicle energy management strategies (EMS), and so on. To explore the scale-invariance of the vehicle driving cycles, the four vehicle driving cycles were analyzed using the Multifractal Detrended Fluctuation Analysis (MF-DFA) method, three of which are standard vehicle test cycles: the New European Driving Cycle (NEDC), the World-wide harmonized Light-duty Test Cycle (WLTC) and the China Light-duty Vehicle Test Cycle for Passenger Car (CLTC-P), and the other is the Urban Road Real Driving Cycle (URRDC), which was obtained by analyzing and processing vehicle driving data collected in actual urban driving conditions. The fluctuation functions, the generalized Hurst exponents, the mass exponent spectra, the multifractal singularity spectra, and the multifractal characteristic parameters were calculated to verify the multifractal characteristics, and to quantify the fluctuation singularities of different driving cycles as the time series. The results show that the fluctuations of all four driving cycles have long-range anticorrelations and exhibit significant multifractal characteristics. The results can provide a basis for the analysis of the complexity of the vehicle driving cycles.
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Munk, Anders Kristian, and Sebastian Abrahamsson. "Empiricist Interventions: Strategy and Tactics on the Ontopolitical Battlefield." Science & Technology Studies 25, no. 1 (January 1, 2012): 52–70. http://dx.doi.org/10.23987/sts.55281.
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Recent papers by prominent scholars in science and technology studies (notably John Law and Bruno Latour) have crystallized a fundamental disagreement about the scope and purpose of intervention in actor-network theory or what we here choose to bracket as empirical philosophy. While the precept of agnostic description is taken as a given, the desired effects of such descriptions are highly debated: Is the goal to interfere with the singularity of the real through the enactment of multiple and possibly conflicting ontologies? Or is it (also) to craft new and comprehensive common worlds supported by notions of due process and parliamentary procedure? In this paper we think about this disagreement as a question of research strategy (a normative discord about the desirable outcome of an intervention) in order to assess its implications for research tactics (a descriptive accord about the practical crafting of an adequate account). A key point here is to challenge the impermeability of such a division and show how the strategic dispute, if to be taken seriously, invariably spills over to swamp the level of tactics. To illustrate this point, we draw upon materials from our recent doctoral research projects and to facilitate the discussion we make two deliberate caricatures: Firstly, we operate with a simplified history of actor-network theory in which a strategy of epistemological critique has been replaced by two contending agendas for ontological intervention. Secondly, we address these two contending agendas as distinct options which map on to the positions of our two main interlocutors. In doing so, it becomes possible to compare their respective tactical implications as we work through two examples of what might constitute an empiricist intervention.
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Seneviratne, Chaturika Priyadarshani, and Ashan Lester Martino. "Budgeting as practice and knowing in action: experimenting with Bourdieu's theory of practice: an empirical evidence from a public university." Asian Journal of Accounting Research 6, no. 3 (February 11, 2021): 309–23. http://dx.doi.org/10.1108/ajar-08-2020-0075.
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PurposeThe present study aims to explore how various doings, strategic actions and power relations stemming from internal agents are instrumental in (re)constituting the different forms and meanings of budgeting in a specific field.Design/methodology/approachThe paper uses a single-case study method based on a Sri Lankan public university. Data are collected using interviews, documentary evidence and observations.FindingsThe empirical evidence suggested that internal agents are crucial, and they are the producers of budgetary practice as they possess practical knowledge and power relations in the field where they operate. The case data demonstrate that organisational agents do have real essence as active and acting to produce effects in budgeting practices, and the significance of exploring the singularity of multiple agents in terms of their viewpoints, trajectories, dispositions and power relations, who may form, sustain or interrupt budgetary practices in a given setting.Research limitations/implicationsAs the research is directed towards the selection of in-depth enquiry of specific setting infused with culture, values, perception and ideology, it might cause to diminish the researcher's analytical objectivity and independence of the research.Practical implicationsAs budgetary practices are product of human interaction, it is important to note that practitioners should be concerned with what agents do in actual practice and their inactions, influences and power relations in budgeting practices, which might not align with the structural forces enlisted in the budgeting. It would be of interest for future empirical research to explore the interplay between the diverse interests of organisational agents and agents beyond the individual organisations.Originality/valueThis study contributes to the literature on management control practices by documenting the importance of understanding the “practice” through relational thinking of all three concepts is emphasised, such interrelated theoretical insights are seldom used to understand accounting practices. This research emphasises the importance of bringing out the microprocessual facets of management control to open up its non-conscious, non-strategic and non-rationalist forms.
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Khudayarov, Bakhtiyar, and Fozilzhon Turaev. "Numerical simulation of a viscoelastic pipeline vibration under pulsating fluid flow." Multidiscipline Modeling in Materials and Structures 18, no. 2 (April 11, 2022): 219–37. http://dx.doi.org/10.1108/mmms-02-2022-0015.
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PurposeThe purpose of this study is to create a mathematical model, a numerical algorithm and a computer program for studying the vibration of composite pipelines based on the theory of beams used in the oil and gas industry, agriculture and water management, housing and communal services and other areas.Design/methodology/approachA mathematical model of vibration of a viscoelastic pipeline based on the theory of beams with a pulsating fluid flowing through it was developed. Using the Bubnov-Galerkin method, based on the polynomial approximation of deflections, the problem is reduced to the study of systems of ordinary integro-differential equations, the solution of which is found by a numerical method. A computational algorithm was developed for solving problems of vibrations of composite pipelines conveying pulsating liquid.FindingsThe stability and amplitude-time characteristics of vibration of composite pipelines with a pulsating fluid flowing in it are studied for wide range of changes in the parameters of deformable systems and fluid flow. The critical velocities of fluid flow at which the viscoelastic pipe loses its rectilinear equilibrium shape are found. The effect of singularity in the kernels of heredity on the vibrations of structures with viscoelastic properties was numerically studied. It is shown that with an increase in the viscosity parameter of the pipeline material, the critical flow velocity decreases. It was determined that an increase in the value of the fluid pulsation frequency and the excitation coefficient leads to a decrease in the critical velocity of the fluid flow. It was established that an increase in the parameters of the Winkler foundation and the rigidity parameter of the continuous layer leads to an increase in the critical flow velocity.Originality/valueThe study of the vibration of pipelines made of composite materials is of great theoretical and applied interest. The solution to this problem is an effective application of the theory of viscoelasticity to real processes. Therefore, the methods and problems of pipeline vibrations attract much attention from researchers. This study is devoted to solving the above problems and therefore its subject is relevant. The paper considers the results of numerical simulation of the processes of vibration of a composite pipeline based on the theory of shells during the flow of a pulsating liquid through it. A mathematical model of vibration of a composite pipeline was developed. A computational algorithm was developed for solving problems of vibrations of composite pipelines conveying pulsating liquid.
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Khudayarov, B. A. "Computational Experiments to Evaluate the Approaches to the Modeling of Viscoelastic Plates Motion Based on Various Theories." Mechanical Engineering and Computer Science, no. 9 (December 2, 2018): 15–33. http://dx.doi.org/10.24108/0918.0001412.
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Mathematical and computer modeling of the flutter of elements and units of the aircraft design is an actual scientific problem; its study is stimulated by the failure of aircraft elements, parts of space and jet engines. In view of the complexity of the flutter phenomenon of aircraft elements, simplifying assumptions are used in many studies. However, these assumptions, as a rule, turn out to be so restrictive that the mathematical model ceases to reflect the real conditions with sufficient accuracy. Therefore, results of theoretical and experimental studies are in bad agreement.At present, the problem of panel flutter is very relevant. Improvement of characteristics of military and civil aircraft inevitably requires reducing their weight, and consequently, the rigidity of paneling, which increases the possibility of a panel flutter. The concept of creating the aircraft with a variable shape, which would inevitably lead to a reduction in paneling thickness are actively discussed. Finally, the use of new materials and, in particular, composites, changes physical properties of the panels and can also lead to a flutter.The above-mentioned scientific problem gives grounds to assert that the development of adequate mathematical models, numerical methods and algorithms for solving nonlinear integral-differential equations of dynamic problems of the hereditary theory of viscoelasticity is actual.In connection with this, the development of mathematical models of individual elements of aircraft made of composite material is becoming very important.Generalized mathematical models of non-linear problems of the flutter of viscoelastic isotropic plates, streamlined by a supersonic gas flow, are constructed in the paper on the basis of integral models. To study oscillation processes in plates, a numerical algorithm is proposed for solving nonlinear integro-differential equations with singular kernels. Based on the developed computational algorithm, a package of applied programs is created. The effect of the singularity parameter in heredity kernels on the vibrations of structures with viscoelastic properties is numerically investigated. In a wide range of changes in plate parameters, critical flutter velocities are determined. Numerical solutions of the problem of viscoelastic plate flutter are compared for different models. It is shown that the most adequate theory for investigating a wide class of problems of the hereditary theory of viscoelasticity is the geometric nonlinear Kirchhoff-Love theory with consideration of elastic waves propagation. It is established that an account of viscoelastic properties of plate material leads to 40-60% decrease in the critical flutter velocity.
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BALADI, V., S. MARMI, and D. SAUZIN. "Natural boundary for the susceptibility function of generic piecewise expanding unimodal maps." Ergodic Theory and Dynamical Systems 34, no. 3 (January 25, 2013): 777–800. http://dx.doi.org/10.1017/etds.2012.161.
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AbstractFor a piecewise expanding unimodal interval map$f$with unique absolutely continuous invariant probability measure$\mu $, a perturbation$X$, and an observable$\varphi $, the susceptibility function is$\Psi _\varphi (z)= \sum _{k=0}^\infty z^k \int X(x) \varphi '( f^k)(x) (f^k)'(x) \, d\mu $. Combining previous results [V. Baladi, On the susceptibility function of piecewise expanding interval maps.Comm. Math. Phys.275(2007), 839–859; V. Baladi and D. Smania, Linear response for piecewise expanding unimodal maps.Nonlinearity21(2008), 677–711] (deduced from spectral properties of Ruelle transfer operators) with recent work of Breuer–Simon [Natural boundaries and spectral theory.Adv. Math.226(2011), 4902–4920] (based on techniques from the spectral theory of Jacobi matrices and a classical paper of Agmon [Sur les séries de Dirichlet.Ann. Sci. Éc. Norm. Supér.(3)66(1949), 263–310]), we show that density of the postcritical orbit (a generic condition) implies that$\Psi _\varphi (z)$has a strong natural boundary on the unit circle. The Breuer–Simon method provides uncountably many candidates for the outer functions of$\Psi _\varphi (z)$, associated with precritical orbits. If the perturbation$X$is horizontal, a generic condition (Birkhoff typicality of the postcritical orbit) implies that the non-tangential limit of$\Psi _\varphi (z)$as$z\to 1$exists and coincides with the derivative of the absolutely continuous invariant probability measure with respect to the map (‘linear response formula’). Applying the Wiener–Wintner theorem, we study the singularity type of non-tangential limits of$\Psi _\varphi (z)$as$z\to e^{i\omega }$for real$\omega $. An additional ‘law of the iterated logarithm’ typicality assumption on the postcritical orbit gives stronger results.
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Barca, Gabriele, Eleonora Giovannetti, and Giovanni Montani. "An Overview on the Nature of the Bounce in LQC and PQM." Universe 7, no. 9 (September 1, 2021): 327. http://dx.doi.org/10.3390/universe7090327.
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We present a review on some of the basic aspects concerning quantum cosmology in the presence of cut-off physics as it has emerged in the literature during the last fifteen years. We first analyze how the Wheeler–DeWitt equation describes the quantum Universe dynamics, when a pure metric approach is concerned, showing how, in general, the primordial singularity is not removed by the quantum effects. We then analyze the main implications of applying the loop quantum gravity prescriptions to the minisuperspace model, i.e., we discuss the basic features of the so-called loop quantum cosmology. For the isotropic Universe dynamics, we compare the original approach, dubbed the μ0 scheme, and the most commonly accepted formulation for which the area gap is taken as physically scaled, i.e., the so-called μ¯ scheme. Furthermore, some fundamental results concerning the Bianchi Universes are discussed, especially with respect to the morphology of the Bianchi IX model. Finally, we consider some relevant criticisms developed over the last ten years about the real link existing between the full theory of loop quantum gravity and its minisuperspace implementation, especially with respect to the preservation of the internal SU(2) symmetry. In the second part of the review, we consider the dynamics of the isotropic Universe and of the Bianchi models in the framework of polymer quantum mechanics. Throughout the paper, we focus on the effective semiclassical dynamics and study the full quantum theory only in some cases, such as the FLRW model and the Bianchi I model in the Ashtekar variables. We first address the polymerization in terms of the Ashtekar–Barbero–Immirzi connection and show how the resulting dynamics is isomorphic to the μ0 scheme of loop quantum cosmology with a critical energy density of the Universe that depends on the initial conditions of the dynamics. The following step is to analyze the polymerization of volume-like variables, both for the isotropic and Bianchi I models, and we see that if the Universe volume (the cubed scale factor) is one of the configurational variables, then the resulting dynamics is isomorphic to that one emerging in loop quantum cosmology for the μ¯ scheme, with the critical energy density value being fixed only by fundamental constants and the Immirzi parameter. Finally, we consider the polymer quantum dynamics of the homogeneous and inhomogeneous Mixmaster model by means of a metric approach. In particular, we compare the results obtained by using the volume variable, which leads to the emergence of a singularity- and chaos-free cosmology, to the use of the standard Misner variable. In the latter case, we deal with the surprising result of a cosmology that is still singular, and its chaotic properties depend on the ratio between the lattice steps for the isotropic and anisotropic variables. We conclude the review with some considerations of the problem of changing variables in the polymer representation of the minisuperspace dynamics. In particular, on a semiclassical level, we consider how the dynamics can be properly mapped in two different sets of variables (at the price of having to deal with a coordinate dependent lattice step), and we infer some possible implications on the equivalence of the μ0 and μ¯ scheme of loop quantum cosmology.
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Jeong, Jae-Tack, and H. K. Moffatt. "Free-surface cusps associated with flow at low Reynolds number." Journal of Fluid Mechanics 241 (August 1992): 1–22. http://dx.doi.org/10.1017/s0022112092001927.
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When two cylinders are counter-rotated at low Reynolds number about parallel horizontal axes below the free surface of a viscous fluid, the rotation being such as to induce convergence of the flow on the free surface, then above a certain critical angular velocity Ωc, the free surface dips downwards and a cusp forms. This paper provides an analysis of the flow in the neighbourhood of the cusp, via an idealized problem which is solved completely: the cylinders are represented by a vortex dipole and the solution is obtained by complex variable techniques. Surface tension effects are included, but gravity is neglected. The solution is analytic for finite capillary number [Cscr ], but the radius of curvature on the line of symmetry on the free surface is proportional to exp (−32π[Cscr ]) and is extremely small for [Cscr ] [gsim ] 0.25, implying (in a real fluid) the formation of a cusp. The equation of the free surface is cubic in (x, y) with coefficients depending on [Cscr ], and with a cusp singularity when [Cscr ] = ∞.The influence of gravity is considered through a stability analysis of the free surface subjected to converging uniform strain, and a necessary condition for the development of a finite-amplitude disturbance of the free surface is obtained.An experiment was carried out using the counter-rotating cylinders as described above, over a range of capillary numbers from zero to 60; the resulting photographs of a cross-section of the free surface are shown in figure 13. For Ω < Ωc, a rounded crest forms in the neighbourhood of the central line of symmetry; for Ω > Ωc, the downward-pointing cusp forms, and its structure shows good agreement with the foregoing theory.
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Ras, Verena, Gerrit Botha, Shaun Aron, Katie Lennard, Imane Allali, Shantelle Claassen-Weitz, Kilaza Samson Mwaikono, et al. "Using a multiple-delivery-mode training approach to develop local capacity and infrastructure for advanced bioinformatics in Africa." PLOS Computational Biology 17, no. 2 (February 25, 2021): e1008640. http://dx.doi.org/10.1371/journal.pcbi.1008640.
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With more microbiome studies being conducted by African-based research groups, there is an increasing demand for knowledge and skills in the design and analysis of microbiome studies and data. However, high-quality bioinformatics courses are often impeded by differences in computational environments, complicated software stacks, numerous dependencies, and versions of bioinformatics tools along with a lack of local computational infrastructure and expertise. To address this, H3ABioNet developed a 16S rRNA Microbiome Intermediate Bioinformatics Training course, extending its remote classroom model. The course was developed alongside experienced microbiome researchers, bioinformaticians, and systems administrators, who identified key topics to address. Development of containerised workflows has previously been undertaken by H3ABioNet, and Singularity containers were used here to enable the deployment of a standard replicable software stack across different hosting sites. The pilot ran successfully in 2019 across 23 sites registered in 11 African countries, with more than 200 participants formally enrolled and 106 volunteer staff for onsite support. The pulling, running, and testing of the containers, software, and analyses on various clusters were performed prior to the start of the course by hosting classrooms. The containers allowed the replication of analyses and results across all participating classrooms running a cluster and remained available posttraining ensuring analyses could be repeated on real data. Participants thus received the opportunity to analyse their own data, while local staff were trained and supported by experienced experts, increasing local capacity for ongoing research support. This provides a model for delivering topic-specific bioinformatics courses across Africa and other remote/low-resourced regions which overcomes barriers such as inadequate infrastructures, geographical distance, and access to expertise and educational materials.
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Akmatov, A., A. Toktorbaev, and N. Zamirbek kyzy. "Applied Problems of Perturbation Theory." Bulletin of Science and Practice, no. 12 (December 15, 2022): 36–42. http://dx.doi.org/10.33619/2414-2948/85/04.
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In this paper, we study solutions to nonlinear singularly perturbed differential equations with initial conditions. Proving the asymptotic closeness of the solutions of the perturbed and unperturbed problems on the real axis is a top-priority task. But it doesn't always work out. For the first time in works in this direction, the concept of bistability of solutions was introduced. The definition of stability to the right and to the left is given. As well as definitions of bistability of solutions. Examples are given. If the solution is bistable, then it is always possible to show the asymptotic closeness of the solutions of the perturbed and unperturbed problems on the real domain.
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Berkowitz, Roger. "The Singularity and the Human Condition." Philosophy Today 62, no. 2 (2018): 337–55. http://dx.doi.org/10.5840/philtoday2018522214.
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Hannah Arendt's The Human Condition is frequently read as offering a “theory” of what it means to be human. But the bite of Arendt’s book is to think through the transformation of the human condition in the modern age. She argues that the rise of a scientific worldview fundamentally alters the earthly and worldly conditions in which human beings live. Since humans are conditioned beings, the change from our pre-modern subjection to fate to our modern human capacity to create a humanly built world threatens a fundamental shift in human being. The transformation Arendt describes is the loss of our human plurality to a technological singularity. She argues, however, that we can choose to hold on to our humanity if we persist in thinking, and thus preserve our human spontaneity and freedom.
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NAKAZATO, HIROMICHI, MIKIO NAMIKI, and SAVERIO PASCAZIO. "TEMPORAL BEHAVIOR OF QUANTUM MECHANICAL SYSTEMS." International Journal of Modern Physics B 10, no. 03 (January 30, 1996): 247–95. http://dx.doi.org/10.1142/s0217979296000118.
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The temporal behavior of quantum mechanical systems is reviewed. We mainly focus our attention on the time development of the so-called “survival” probability of those systems that are initially prepared in eigenstates of the unperturbed Hamiltonian, by assuming that the latter has a continuous spectrum. The exponential decay of the survival probability, familiar, for example, in radioactive decay phenomena, is representative of a purely probabilistic character of the system under consideration and is naturally expected to lead to a master equation. This behavior, however, can be found only at intermediate times, for deviations from it exist both at short and long times and can have significant consequences. After a short introduction to the long history of the research on the temporal behavior of such quantum mechanical systems, the short-time behavior and its controversial consequences when it is combined with von Neumann’s projection postulate in quantum measurement theory are critically overviewed from a dynamical point of view. We also discuss the so-called quantum Zeno effect from this standpoint. The behavior of the survival amplitude is then scrutinized by investigating the analytic properties of its Fourier and Laplace transforms. The analytic property that there is no singularity except a branch cut running along the real energy axis in the first Riemannian sheet is an important reflection of the time-reversal invariance of the dynamics governing the whole process. It is shown that the exponential behavior is due to the presence of a simple pole in the second Riemannian sheet, while the contribution of the branch point yields a power behavior for the amplitude. The exponential decay form is cancelled at short times and dominated at very long times by the branch-point contributions, which give a Gaussian behavior for the former and a power behavior for the latter. In order to realize the exponential law in quantum theory, it is essential to take into account a certain kind of macroscopic nature of the total system, since the exponential behavior is regarded as a manifestation of a complete loss of coherence of the quantum subsystem under consideration. In this respect, a few attempts at extracting the exponential decay form on the basis of quantum theory, aiming at the master equation, are briefly reviewed, including van Hove’s pioneering work and his well-known “λ2T” limit. In the attempt to further clarify the mechanism of the appearance of a purely probabilistic behavior without resort to any approximation, a solvable dynamical model is presented and extensively studied. The model describes an ultrarelativistic particle interacting with N two-level systems (called “spins”) and is shown to exhibit an exponential behavior at all times in the weak-coupling, macroscopic limit. Furthermore, it is shown that the model can even reproduce the short-time Gaussian behavior followed by the exponential law when an appropriate initial state is chosen. The analysis is exact and no approximation is involved. An interpretation for the change of the temporal behavior in quantum systems is drawn from the results obtained. Some implications for the quantum measurement problem are also discussed, in particular in connection with dissipation.
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Peterson, Christopher. "Seuss and the Swerve of Singularity." Comparative Literature 71, no. 3 (September 1, 2019): 298–313. http://dx.doi.org/10.1215/00104124-7546298.
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Abstract This article explores the unstable distinction between “who” and “what” in Seuss’s Horton Hears a Who! The story’s moral that “a person’s a person no matter how small” has often been read as atoning for the racist cartoons that Geisel drew of the Japanese during World War II. Seussian pedagogy teaches us to hear all persons as whos rather than whats or things. Yet this essay argues that all persons are also things. While this thingliness remains unequally distributed thanks to persistent sociopolitical hierarchies, it also calls on us to think about ethics and politics differently. Diverging from the person/who equation, Jacques Derrida conceives the who as an absolute singularity that resists its subjection to the what, and by extension, its reduction to particularity and identity. Expanding beyond Horton’s racial context, the final section of the essay considers how the contemporary “Black Lives Matter” movement reckons with the problem of particularity and identity while also gesturing toward an incalculable singularity—infinitely deferred yet always “present.”
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Gu, Mengqi, and Guo-Ping Jiang. "On the Controllability of Discrete-Time Leader-Follower Multiagent Systems with Two-Time-Scale and Heterogeneous Features." Mathematical Problems in Engineering 2021 (March 20, 2021): 1–13. http://dx.doi.org/10.1155/2021/8893051.
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This paper investigates the controllability of discrete-time leader-follower multiagent systems (MASs) with two-time-scale and heterogeneous features, motivated by the fact that many real systems are operating in discrete-time. In this study, singularly perturbed difference systems are used to model the two-time-scale heterogeneous discrete-time MASs. To avoid the ill-posedness problem caused by the singular perturbation parameter when using the classical control theory to study the model, the singular perturbation method was first applied to decompose the system into two subsystems with slow-time-scale and fast-time-scale feature. Then, from the perspective of algebra and graph theory, several easier-to-use controllability criteria for the related MASs are proposed. Finally, the effectiveness of the main results is verified by simulation.
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Barzilai, Maya. "“One Should Finally Learn How to Read This Breath”: Paul Celan and the Buber-Rosenzweig Bible." Comparative Literature 71, no. 4 (December 1, 2019): 436–54. http://dx.doi.org/10.1215/00104124-7709613.
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Abstract This article examines Paul Celan’s use of the terms cola and breath-unit in his notes for the 1960 “Meridian” address. In the 1920s, Martin Buber and Franz Rosenzweig developed their “colometric translation” of the Bible, using the breath-unit to capture, in German, the spoken qualities of the Hebrew Bible by allowing the human breath to dictate line divisions. Celan repurposed the breath-unit for his post-Shoah poetics: it registered, for him, a further disruption of the Hebrew-German translational link, following the demise of the Jewish community of readers. Celan’s breath-unit became a measure of silence, marking the pauses between poetic lines as sites of interrupted breathing, which entail a painful encounter with deformation and murder. Furthermore, if Buber and Rosenzweig used their breath-inspired cola to bypass the traditional line divisions of biblical verse, Celan’s radicalized breath-unit can be understood as a response to the musicality attributed to his earlier poetry; he drew on the singularity of the breath to forge ever shorter lines and vertical, severed poems that culminate in the lost or buried word.
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Ng, Zhao F. "Mad Love: Surrealism and Soteriological Desire." Literature and Theology 34, no. 3 (July 28, 2020): 363–85. http://dx.doi.org/10.1093/litthe/fraa011.
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Abstract This article proposes that a paradox of love is situated at the heart of the Surrealist project: love is characterised as both a problem and its solution, tied to a series of antinomies (absence/presence, subject/object, chance/necessity, singularity/variance, history/eternity) and the teleological horizon of their reconciliation. The sufferings attributed to love prompt a desire to overcome them that is characterised as an orientation toward salvation. With a specific focus on André Breton’s L’Amour fou (1937), love’s madness is read in relation to a posit of faith. Breton’s appropriation of Hegel is interpreted as a precise reformulation that enables soteriological desire to find a response in (i.) a Surrealist ontology that is both immanent and monist, and (ii.) a theodicy of love.
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Côté, Héloïse, and Denis Simard. "What is the Meaning of the Integration of the Cultural Dimension into Schools, According to the Official Discourse of the Province of Quebec?" Articles 43, no. 3 (April 14, 2009): 327–50. http://dx.doi.org/10.7202/029702ar.
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Abstract Since 1992, Quebec’s Ministry of Education1 and Ministry of Culture and Communications have been creating programs designed to integrate a cultural dimension into schools – a process requiring partnerships between teachers and professionals in the cultural domain. This domain comprises the objects and practices pertaining to the realm of arts and aesthetics and the values which are associated with them, namely expressivity, subjectivity, emotions, sensitivity, singularity, imagination, creativity and feelings (Kerlan, 2004). What does this integration mean, according to Quebec’s official discourse? To answer this question, we relied on sociology of justification theory (Boltanski & Thévenot, 1991; Boltanski & Chiapello, 1999, 2002) and used discourse and content analysis to examine Quebec’s official discourse. Our results suggest that this discourse relies on many definitions of culture and justice. This plurality blurs the meaning of the integration of the cultural dimension and requires that teachers delineate it by themselves.
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Bryan, Jenny. "Philosophy." Greece and Rome 65, no. 2 (September 17, 2018): 269–77. http://dx.doi.org/10.1017/s0017383518000220.
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Three recent volumes indicate a growing appreciation of the significance and complexity of Plato's account of mousikē in the Laws. Anastasia-Erasmia Peponi's edited work, Performance and Culture in Plato's Laws, collects fifteen diverse chapters by prominent scholars in Greek literature, philosophy, and culture to produce an immensely rewarding and original range of perspectives on Plato's treatment of performance and poetics in the Laws. As Peponi notes in her brief introduction, the complexity of the cultural background that Plato manipulates and appropriates in the Laws, as well as the intricacy of the Platonic appropriation itself, combine to present a very real challenge to any scholar seeking to understand them. In addition, it is hard to see that any robust treatment of the Laws’ political theory can avoid getting to grips with the fundamental connections between politics and performance established within the dialogue. Any reader with an interest in either Plato's political philosophy or his poetics will be well rewarded by time spent with this volume. The chapters are divided into four sections, which focus in turn on issues of cultural identity (‘Geopolitics of Performance’), the role of the choruses in Magnesia (‘Conceptualising Chorality’), the Laws’ treatment of genre (‘Redefining Genre’), and the later reception of the Laws’ poetics (‘Poetry and Music in the Afterlife of the Laws’). In the second of the volume's two chapters on cultural identity, Ian Rutherford considers the Laws’ representation of Egypt as a culture that successfully resists political and moral decline via a commitment to stability in mousikē. Setting Plato's account against the external evidence, Rutherford suggests that the Laws offers a partial fiction of stable Egyptian mousikē, useful not least for the implications of its possible critical connection to Dorian culture. In the last of five chapters on the Laws’ interest in the civic apparatus of choral performance, Peponi demonstrates the singularity of choral performance in the work. Whereas the Laws treats most types of performance as producing pleasure in the spectator, in the case of choruses, the emphasis is on the pleasure and experience of the performers. Peponi argues that this shift in focus represents a Platonic attempt to ‘de-aestheticize’ the chorus. In this way, Plato seeks to rehabilitate mousikē by divesting it of the psychological and aesthetic flaws identified in the Republic’s extended critique. However, as Peponi notes in conclusion, the Laws is not altogether comfortable with this sort of performative pleasure. In the first of five chapters on genre, Andrea Nightingale discusses the Laws’ manipulation of generic diversity in service of the unified truth represented by the law code at its heart. Nightingale presents a fascinating and original analysis of the law code as a written text rather different in character from that criticized in the Phaedrus as a pharmakon that destroys our memory of truth. Rather, it serves to encourage the internalization of truths by obliterating the citizens’ memories of previous unwanted cultural norms. In the volume's final chapter, Andrew Barker turns to Aristoxenus for help in making sense of Plato's suggestion that music can be assessed as ‘correct’ or ‘incorrect’, or as ‘good’ or ‘bad’. Contrasting the Platonic focus on mimesis and ethical correctness with Aristoxenus’ assessment of music ‘by the standard of its own intrinsic values’ (413), Barker suggests that, of the two treatments, Plato's is the furthest removed from general Greek opinion. These varied and illuminating chapters are representative of the scope and quality of the volume, which not only serves to open up new directions for research on the Laws but also makes plain that the Laws is at least as important as the Republic for a thorough understanding of Plato's views on art and culture, and their relation to politics.
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Ellis, Susannah. "Messianic Fiction in Antoine Volodine's Nuclear Catastrophe Novel Minor Angels." Paragraph 42, no. 2 (July 2019): 223–37. http://dx.doi.org/10.3366/para.2019.0300.
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In Specters of Marx, Derrida suggests that a non-revolutionary — ‘spectral’ — Marxism could alleviate a contemporary crisis in imagining the future in the late twentieth century. This ‘presentist’ crisis results from the collapse of Communism and the alleged triumph of neoliberal democracy, and leaves a dubious choice between neoliberal consensus and potential totalitarianism. This article outlines Derrida's call to a messianic wait for the singularity of an always-arriving future-to-come, and suggests that it provides an entry into the post-nuclear universe of Antoine Volodine's Minor Angels, where a non-linear plot centres on the ghost of a failed Marxist revolutionary and its return. Outlining how Minor Angels creates a spectral temporality which undercuts both aspirations to a ‘radiant future’ and a stagnant present, this article argues that, read alongside, Derrida and Volodine sketch out a democratic future to come that gestures towards an alternative to presentism.