Journal articles: 'Essential singularities'

1

Gauld, D. B., and G. J. Martin. "Essential singularities of quasimeromorphic mappings." MATHEMATICA SCANDINAVICA 73 (December 1, 1993): 36. http://dx.doi.org/10.7146/math.scand.a-12454.

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2

Cosgrove, Christopher M. "Painlevé Classification Problems Featuring Essential Singularities." Studies in Applied Mathematics 98, no. 4 (May 1997): 355–433. http://dx.doi.org/10.1111/1467-9590.00053.

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3

Dethloff, Gerd-E. "On essential singularities of meromorphic mappings." Mathematische Annalen 283, no. 3 (September 1989): 499–509. http://dx.doi.org/10.1007/bf01442742.

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4

Qadir, Asghar. "Essential singularities of spherically symmetric space‐times." Journal of Mathematical Physics 33, no. 6 (June 1992): 2262–64. http://dx.doi.org/10.1063/1.529597.

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5

Ashley, Michael J. S. L. "The Stability of Abstract Boundary Essential Singularities." General Relativity and Gravitation 34, no. 10 (October 2002): 1625–35. http://dx.doi.org/10.1023/a:1020168106488.

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6

González Pérez, P. D., and F. Hernando. "Quasi-ordinary singularities, essential divisors and Poincaré series." Journal of the London Mathematical Society 79, no. 3 (April 30, 2009): 780–802. http://dx.doi.org/10.1112/jlms/jdp014.

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7

Alameer, Amerah. "Numerically stable conditions on rational and essential singularities." Complex Variables and Elliptic Equations 63, no. 5 (June 28, 2017): 640–51. http://dx.doi.org/10.1080/17476933.2017.1332049.

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8

Sinclair, GB. "Stress singularities in classical elasticity–I: Removal, interpretation, and analysis." Applied Mechanics Reviews 57, no. 4 (July 1, 2004): 251–98. http://dx.doi.org/10.1115/1.1762503.

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This review article has two parts, published in separate issues of this journal, which consider the stress singularities that occur in linear elastostatics. In the present Part I, after a brief review of the singularities that attend concentrated loads, attention is focused on the singularities that occur away from such loading, and primarily on 2D configurations. A number of examples of these singularities are given in the Introduction. For all of these examples, it is absolutely essential that the presence of singularities at least be recognized if the stress fields are to be used in attempts to ensure structural integrity. Given an appreciation of a stress singularity’s occurrence, there are two options open to the stress analyst if the stress analysis is to actually be used. First, to try and improve the modeling so that the singularity is removed and physically sensible stresses result. Second, to try and interpret singularities that persist in a physically meaningful way. Section 2 of the paper reviews avenues available for the removal of stress singularities. At this time, further research is needed to effect the removal of all singularities. Section 3 of the paper reviews possible interpretations of singularities. At this time, interpretations using the singularity coefficient, or stress intensity factor, would appear to be the best available. To implement an approach using stress intensity factors in a general context, two types of companion analysis are usually required: analytical asymptotics to characterize local singular fields; and numerical analysis to capture participation in global configurations. Section 4 of the paper reviews both types of analysis. At this time, methods for both are fairly well developed. Studies in the literature which actually effect asymptotic analyses of specific singular configurations will be considered in Part II of this review article. The present Part I has 182 references.

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Okuyama, Yûsuke, and Pekka Pankka. "Rescaling principle for isolated essential singularities of quasiregular mappings." Proceedings of the American Mathematical Society 143, no. 5 (December 3, 2014): 2043–50. http://dx.doi.org/10.1090/s0002-9939-2014-12378-1.

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10

OLDE DAALHUIS, A. B. "MIXED GEVREY ASYMPTOTICS." Analysis and Applications 06, no. 02 (April 2008): 151–68. http://dx.doi.org/10.1142/s0219530508001109.

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In this paper, we illustrate with two examples that the computation of Stokes multipliers in problems in which the asymptotic expansions are not of Gevrey order one, is much more complicated and that the singularities in the corresponding Borel plane can be essential singularities.

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11

Callies, Martin, and Andriy Haydys. "Local Models of Isolated Singularities for Affine Special Kähler Structures in Dimension Two." International Mathematics Research Notices 2020, no. 17 (July 9, 2018): 5215–35. http://dx.doi.org/10.1093/imrn/rny165.

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Abstract We construct local models of isolated singularities for special Kähler structures in real dimension two assuming that the associated holomorphic cubic form does not have essential singularities. As an application we compute the holonomy of the flat symplectic connection, which is a part of the special Kähler structure.

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12

Hinz, Michael, Seunghyun Kang, and Jun Masamune. "Probabilistic Characterizations of Essential Self-Adjointness and Removability of Singularities." Vestnik Volgogradskogo gosudarstvennogo universiteta. Serija 1. Mathematical Physics and Computer Modeling 20, no. 3 (September 2017): 148–62. http://dx.doi.org/10.15688/mpcm.jvolsu.2017.3.11.

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13

Ioakimidis, N. I. "Location of essential singularities of a class of analytic functions." International Journal of Computer Mathematics 25, no. 2 (January 1988): 129–38. http://dx.doi.org/10.1080/00207168808803666.

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14

SANCHEZ, NORMA G. "CLASSICAL AND QUANTUM STRINGS IN PLANE WAVES, SHOCK WAVES AND SPACE–TIME SINGULARITIES: SYNTHESIS AND NEW RESULTS." International Journal of Modern Physics A 18, no. 26 (October 20, 2003): 4797–809. http://dx.doi.org/10.1142/s0217751x03015787.

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Key issues and essential features of classical and quantum strings in gravitational plane waves, shock waves and space–time singularities are synthetically understood. This includes the string mass and mode number excitations, energy–momentum tensor, scattering amplitudes, vacuum polarization and wave-string polarization effect. The role of the real pole singularities characteristic of the tree level string spectrum (real mass resonances) and that of the space–time singularities is clearly exhibited. This throws light on the issue of singularities in string theory which can be thus classified and fully physically characterized in two different sets: strong singularities (poles of order ≥ 2, and black holes) where the string motion is collective and nonoscillating in time, outgoing states and scattering sector do not appear, the string does not cross the singularities; and weak singularities (poles of order < 2, (Dirac δ belongs to this class) and conic/orbifold singularities) where the whole string motion is oscillatory in time, outgoing and scattering states exist, and the string crosses the singularities. Common features of strings in singular wave backgrounds and in inflationary backgrounds are explicitly exhibited. The string dynamics and the scattering/excitation through the singularities (whatever their kind: strong or weak) is fully physically consistent and meaningful.

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15

Donelan, P. S. "Singularity-theoretic methods in robot kinematics." Robotica 25, no. 6 (November 2007): 641–59. http://dx.doi.org/10.1017/s0263574707003748.

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SUMMARYThe significance of singularities in the design and control of robot manipulators is well known, and there is an extensive literature on the determination and analysis of singularities for a wide variety of serial and parallel manipulators—indeed such an analysis is an essential part of manipulator design. Singularity theory provides methodologies for a deeper analysis with the aim of classifying singularities, providing local models and local and global invariants. This paper surveys applications of singularity-theoretic methods in robot kinematics and presents some new results.

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16

Kent, D. C., and T. A. Richmond. "Ordered compactification of totally ordered spaces." International Journal of Mathematics and Mathematical Sciences 11, no. 4 (1988): 683–94. http://dx.doi.org/10.1155/s0161171288000833.

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17

A. Veliev, O. "Essential spectral singularities and the spectral expansion for the Hill operator." Communications on Pure & Applied Analysis 16, no. 6 (2017): 2227–51. http://dx.doi.org/10.3934/cpaa.2017110.

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18

Alvarez–Parrilla, Alvaro, and Jesús Muciño–Raymundo. "Dynamics of singular complex analytic vector fields with essential singularities I." Conformal Geometry and Dynamics of the American Mathematical Society 21, no. 7 (March 16, 2017): 126–224. http://dx.doi.org/10.1090/ecgd/306.

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19

Domínguez, Patricia. "Residual Julia sets for meromorphic functions with countably many essential singularities." Journal of Difference Equations and Applications 16, no. 5-6 (May 2010): 519–22. http://dx.doi.org/10.1080/10236190903203879.

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20

Song, Hongchuan, Hao Zhan, Lu Xia, and Nan Zhang. "UAV's Precise Trajectory Tracking Control Based on Nonlinear Dynamic Inverse and Quaternions." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 38, no. 4 (August 2020): 705–14. http://dx.doi.org/10.1051/jnwpu/20203840705.

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The precise tracking 3D trajectory that changes dramatically within the boundary of flight performance is the essential capability of the UAV applied to air combat, which requires that flight control law design be adapted to nonlinear characteristics of flight dynamics and solve the singularities problem during the flight. Continuous trajectory control on the basis of nonlinear dynamic inversion (NDI) is studied. The singularities problem is caused by continuous trajectory expressed by flight velocity and flight-path angles. A sudden change of flight-path axis system happens when aircraft flies along a continuous trajectory which results in singularities. A method for amending flight-path axis system is presented to solve the sudden change problem of flight-path axis system. Finally, the combination of the maneuver generator based on quaternions and amending flight-path axis system realize the precise trajectory tracking control without singularities and obtain excellent tracking characteristics.

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21

Kurokawa, Toshiko. "Existence of normal meromorphic functions with a perfect set as the set of essential singularities." Nagoya Mathematical Journal 103 (October 1986): 29–37. http://dx.doi.org/10.1017/s0027763000000568.

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We are interested in whether there is a Cantor set E admitting no exceptionally ramified or normal meromorphic functions with E as the set of essential singularities. As for an exceptionally ramified meromorphic function, we [2] have recently given the following result.

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22

Esparza, Adrián, and Mónica Moreno Rocha. "Families of Baker domains for meromorphic functions with countable many essential singularities." Journal of Difference Equations and Applications 23, no. 11 (September 18, 2017): 1869–83. http://dx.doi.org/10.1080/10236198.2017.1371145.

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23

WATSON, NEIL A. "CALORIC MEASURE FOR ARBITRARY OPEN SETS." Journal of the Australian Mathematical Society 92, no. 3 (June 2012): 391–407. http://dx.doi.org/10.1017/s1446788712000389.

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AbstractWe give a systematic treatment of caloric measure for arbitrary open sets. The caloric measure is defined only on the essential boundary of the set. Our main result gives criteria for the resolutivity of essential boundary functions, and their integral representation in terms of caloric measure. We also characterize the caloric measure null sets in terms of the boundary singularities of nonnegative supertemperatures.

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24

Berry, M. V. "The optical singularities of bianisotropic crystals." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, no. 2059 (June 6, 2005): 2071–98. http://dx.doi.org/10.1098/rspa.2005.1507.

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The electric and magnetic polarization states for plane waves in arbitrary linear crystals, in which each of D and B is coupled to both of E and H , can be characterized by their typical singularities in direction space: degeneracies, where two refractive index eigenvalues coincide; C e and C m points, where the electric or magnetic field is circularly polarized; and L e and L m lines, where either field is linearly polarized. The well-known 4×4 matrix formalism, expressed in terms of the stereographic projection of directions, enables extensive numerical and visual exploration of the singularities in the general case (which involves 65 crystal parameters), incorporating bianisotropy, natural and Faraday optical activity, and absorption, as well as special cases where one or more effect is absent. For crystals whose anisotropy is weak but which are otherwise general, an unusual perturbation theory leads to a powerful 2×2 formalism capturing all the essential singularity phenomena, including the principal feature of the general case, namely the separation between the electric and magnetic singularities.

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25

Campbell, Alain. "Essential spectrum in vibrations of thin shells in membrane approximation: propagation of singularities." Mathematical Methods in the Applied Sciences 28, no. 5 (2005): 505–24. http://dx.doi.org/10.1002/mma.579.

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26

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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27

Paliathanasis, Andronikos, and P. G. L. Leach. "Nonlinear ordinary differential equations: A discussion on symmetries and singularities." International Journal of Geometric Methods in Modern Physics 13, no. 07 (July 25, 2016): 1630009. http://dx.doi.org/10.1142/s0219887816300099.

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Two essential methods, the symmetry analysis and the singularity analysis, for the study of the integrability of nonlinear ordinary differential equations is the purpose of this work. The main similarities and the differences of these two different methods are discussed.

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28

Lejeune-Jalabert, Monique, and Ana J. Reguera. "Exceptional divisors that are not uniruled belong to the image of the Nash map." Journal of the Institute of Mathematics of Jussieu 11, no. 2 (December 13, 2011): 273–87. http://dx.doi.org/10.1017/s1474748011000156.

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AbstractWe prove that, ifXis a variety over an uncountable algebraically closed fieldkof characteristic zero, then any irreducible exceptional divisorEon a resolution of singularities ofXwhich is not uniruled, belongs to the image of the Nash map, i.e. corresponds to an irreducible component of the space of arcs$X_\infty^{\mathrm{Sing}}$onXcentred in SingX. This reduces the Nash problem of arcs to understanding which uniruled essential divisors are in the image of the Nash map, more generally, how to determine the uniruled essential divisors from the space of arcs.

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29

Mello, Débora Falleiros de, Nayara Cristina Pereira Henrique, Letícia Pancieri, Maria de La Ó. Ramallo Veríssimo, Vera Lúcia Pamplona Tonete, and Mary Malone. "Child safety from the perspective of essential needs." Revista Latino-Americana de Enfermagem 22, no. 4 (August 2014): 604–10. http://dx.doi.org/10.1590/0104-1169.3651.2458.

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OBJECTIVE: to characterize the maternal care for children under one year of age with a view to child health promotion at home.METHOD: exploratory study with qualitative data analysis, thematic mode, based on the conceptual framework of the essential needs of children, based on interviews recorded with 16 mothers.RESULTS: the analysis of the maternal narratives showed elements that facilitate the promotion of child safety: presence and involvement of the parents, constant surveillance for physical and emotional protection, experiences to stimulate child development, support networks for childcare at home; and inhibiting elements of child safety: limited perception of characteristics of child development and of children's singularities, overprotection and difficulties to set limits.CONCLUSION: the study enhances the understanding of home care in child health promotion, directing professional actions to guarantee ongoing nurturing relationships, protection, respect for individual differences, experiences appropriate to child development, limit setting and construction of stable and supportive social networks. In addition, the relevance of considering the maternal perspective in child health care is considered, as a strategy to apprehend aspects related to the attendance of the growth and development needs, particularly for child health promotion at home.

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30

Tzoulis, A., and T. F. Eibert. "Review of singular potential integrals for method of moments solutions of surface integral equations." Advances in Radio Science 2 (May 27, 2005): 93–99. http://dx.doi.org/10.5194/ars-2-93-2004.

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Abstract. Accurate evaluation of singular potential integrals is essential for successful method of moments (MoM) solutions of surface integral equations. In mixed potential formulations for metallic and dielectric scatterers, kernels with 1/R and r1/R singularities must be considered. Several techniques for the treatment of these singularities will be reviewed. The most common approach solves the MoM source integrals analytically for specific observation points, thus regularizing the integral. However, in the case of r1/R a logarithmic singularity remains for which numerical evaluation of the testing integral is still difficult. A recently by Yl¨a-Oijala and Taskinen proposed remedy to this issue is discussed and evaluated within a hybrid finite element – boundary integral technique. Convergence results for the MoM coupling integrals are presented where also higher-order singularity extraction is considered.

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31

Merrikh-Bayat, Farshad, and Masoud Karimi-Ghartemani. "On the Essential Instabilities Caused by Fractional-Order Transfer Functions." Mathematical Problems in Engineering 2008 (2008): 1–13. http://dx.doi.org/10.1155/2008/419046.

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The exact stability condition for certain class of fractional-order (multivalued) transfer functions is presented. Unlike the conventional case that the stability is directly studied by investigating the poles of the transfer function, in the systems under consideration, the branch points must also come into account as another kind of singularities. It is shown that a multivalued transfer function can behave unstably because of the numerator term while it has no unstable poles. So, in this case, not only the characteristic equation but the numerator term is of significant importance. In this manner, a family of unstable fractional-order transfer functions is introduced which exhibit essential instabilities, that is, those which cannot be removed by feedback. Two illustrative examples are presented; the transfer function of which has no unstable poles but the instability occurred because of the unstable branch points of the numerator term. The effect of unstable branch points is studied and simulations are presented.

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32

Hu, Jishan. "Reflection coefficient beyond all orders for singular problems. III. Essential singularities on the real axis." Journal of Mathematical Physics 33, no. 1 (January 1992): 37–43. http://dx.doi.org/10.1063/1.529917.

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33

GRÜN, GÜNTHER, and MARTIN RUMPF. "Simulation of singularities and instabilities arising in thin film flow." European Journal of Applied Mathematics 12, no. 3 (June 2001): 293–320. http://dx.doi.org/10.1017/s0956792501004429.

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We present a finite element scheme for nonlinear fourth-order diffusion equations that arise for example in lubrication theory for the time evolution of thin films of viscous fluids. The equations are in general fourth-order degenerate parabolic, but in addition singular terms of second order may occur which model the effects of intermolecular forces or thermocapillarity. Discretizing the arising nonlinearities in a subtle way allows us to establish discrete counterparts of the essential integral estimates found in the continuous setting. As a consequence, the algorithm is efficient, and results on convergence, nonnegativity or even strict positivity of discrete solutions follow in a natural way. Applying this scheme to the numerical simulation of different models shows various interesting qualitative effects, which turn out to be in good agreement with physical experiments.

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34

Murata, Yoshihiro. "The Picard type theorem for essential singularities of solutions of systems of n rational differential equations." Journal of Differential Equations 82, no. 1 (November 1989): 174–90. http://dx.doi.org/10.1016/0022-0396(89)90172-1.

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35

Gnanamuthu, E. Morris Abraham, and P. S. Reddy. "Stability Testing of 2-D Digital Filters Including Those Having Non-essential Singularities of the Second Kind." Journal of Applied Sciences 4, no. 2 (March 15, 2004): 330–34. http://dx.doi.org/10.3923/jas.2004.330.334.

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36

Zhai, Yunyun, and Xianguo Geng. "The coupled Sasa–Satsuma hierarchy: Trigonal curve and finite genus solutions." Analysis and Applications 15, no. 05 (October 19, 2016): 667–97. http://dx.doi.org/10.1142/s0219530516500214.

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Based on the Lenard recursion equations and the stationary zero-curvature equation, we derive the coupled Sasa–Satsuma hierarchy, in which a typical number is the coupled Sasa–Satsuma equation. The properties of the associated trigonal curve and the meromorphic functions are studied, which naturally give the essential singularities and divisors of the meromorphic functions. By comparing the asymptotic expansions for the Baker–Akhiezer function and its Riemann theta function representation, we arrive at the finite genus solutions of the whole coupled Sasa–Satsuma hierarchy in terms of the Riemann theta function.

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37

Mojsilović, Mila. "The dream of wholeness: The poetics of the unpredictable." Arhitektura i urbanizam, no. 52 (2021): 57–64. http://dx.doi.org/10.5937/a-u0-29731.

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By redefining the notion of fragmentarity and existing theoretical conceptions, from romantic fascination with ruins to the contemporary position of variability, the paper places incompleteness as the essential potentiality of form, imagination and contingency in a way that opens new spacetime categories. In the paper, fragmentation is understood as a model for interpreting reality and for examining the capacity of architectural incompleteness. Setting complexity as the context, change as the method and variability as the model for understanding the architectural contemporaries within its reality, spatial and temporal uncertainty become characteristics of the fragmentation and destabilization of relations - their reflection. This way of structuring order out of chaos, or destabilizing order for the purpose of new structures, is the complexity of a higher order. The uncaptured nature of all things, in distracting the new, transports its own limitations, thematized through places of change, separation and path - specific singularities, allowing flexibility through imperfection. The elusive nature of all things, in opening to the new, transcends its own limitations, thematizing itself through places of change, separation and cracking. These are specific singularities that allow flexibility through incompleteness, thus opening up towards new forms of reality, between uncertainty and indeterminacy - in the zone of their overlap, space and time become fragmented. This true spontaneity is the greatest complexity that carries within itself the power of change and essential potentiality - a meaning that is always just emerging. The question of the degree of incompleteness is in the core of the concept of openness, in which the alteration of form and geometry take place.

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MARTÍ-PETE, DAVID. "The escaping set of transcendental self-maps of the punctured plane." Ergodic Theory and Dynamical Systems 38, no. 2 (October 13, 2016): 739–60. http://dx.doi.org/10.1017/etds.2016.36.

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We study the different rates of escape of points under iteration by holomorphic self-maps of $\mathbb{C}^{\ast }=\mathbb{C}\setminus \{0\}$ for which both zero and infinity are essential singularities. Using annular covering lemmas we construct different types of orbits, including fast escaping and arbitrarily slowly escaping orbits to either zero, infinity or both. We also prove several properties about the set of fast escaping points for this class of functions. In particular, we show that there is an uncountable collection of disjoint sets of fast escaping points, each of which has $J(f)$ as its boundary.

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DOTSENKO, Vl S. "THREE-POINT CORRELATION FUNCTIONS OF THE MINIMAL CONFORMAL THEORIES COUPLED TO 2D GRAVITY." Modern Physics Letters A 06, no. 39 (December 21, 1991): 3601–12. http://dx.doi.org/10.1142/s0217732391004152.

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The general three-point correlation functions of the minimal conformal field theories coupled to gravity are calculated using the specific Coulomb gas type quantization technique. The gravity interaction modifies in an essential way the operator algebra of the corresponding minimal model, in particular in canceling the decoupling of a finite number of primary fields, in case of rational theories. This is suggested to be related to the appearance of new physical states, under the BRST analysis of Lian and Zuckerman. Within the analytic technique, this effect is due to the corresponding singularities of the gravity sector operator algebra structure constants.

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40

Daughton, Austin. "A Hecke correspondence theorem for automorphic integrals with infinite log-polynomial sum period functions." International Journal of Number Theory 10, no. 07 (September 9, 2014): 1857–79. http://dx.doi.org/10.1142/s1793042114500596.

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We generalize the correspondence between Dirichlet series with finitely many poles that satisfy a functional equation and automorphic integrals with log-polynomial sum period functions. In particular, we extend the correspondence to hold for Dirichlet series with finitely many essential singularities. We also study Dirichlet series with infinitely many poles in a vertical strip. For Hecke groups with λ ≥ 2 and some weights, we prove a similar correspondence for these Dirichlet series. For this case, we provide a way to estimate automorphic integrals with infinite log-polynomial periods by automorphic integrals with finite log-polynomial periods.

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ELLIS, GEORGE F. R. "THE SPACE OF COSMOLOGICAL SPACE–TIMES." Journal of Hyperbolic Differential Equations 02, no. 02 (June 2005): 331–79. http://dx.doi.org/10.1142/s0219891605000476.

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I first focus on how to best describe the space of cosmological space–times and what its essential properties are and some comments on the dynamical behavior revealed by studies that will be described in more detail by John Wainwright. I will then relate this both to observations and to anthropic issues (i.e. the possible existence of observers). This space includes some viable singularity free solutions which will be briefly described, thus posing the issue of the tension between very special initial conditions and the existence of initial singularities. I will conclude with remarks on the issue of realized infinities in this context and the concept of multiverses.

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42

Stump, David M., and James M. Hill. "On an infinite integral arising in the numerical integration of stochastic differential equations." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, no. 2054 (February 8, 2005): 397–413. http://dx.doi.org/10.1098/rspa.2004.1379.

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We study a stochastic integral that arises during the implementation of the Milstein method for the numerical integration of systems of stochastic differential equations. The distribution of the integral can be written as the inverse Fourier transform of a characteristic function with essential singularities. This leads to a generalized integral that can be expressed as an infinite series involving the derivatives of Meixner polynomials. The generating function of the polynomials in combination with the Mittag–Leffler expansion theorem is used to obtain a novel series representation for the integral and the motivating problem in particular. This new form is rapidly convergent and, therefore, well suited to numerical work.

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43

Kwapiński, Tomasz, and Marcin Kurzyna. "Topological Atomic Chains on 2D Hybrid Structure." Materials 14, no. 12 (June 14, 2021): 3289. http://dx.doi.org/10.3390/ma14123289.

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Mid-gap 1D topological states and their electronic properties on different 2D hybrid structures are investigated using the tight binding Hamiltonian and the Green’s function technique. There are considered straight armchair-edge and zig-zag Su–Schrieffer–Heeger (SSH) chains coupled with real 2D electrodes which density of states (DOS) are characterized by the van Hove singularities. In this work, it is shown that such 2D substrates substantially influence topological states end evoke strong asymmetry in their on-site energetic structures, as well as essential modifications of the spectral density function (local DOS) along the chain. In the presence of the surface singularities the SSH topological state is split, or it is strongly localized and becomes dispersionless (tends to the atomic limit). Additionally, in the vicinity of the surface DOS edges this state is asymmetrical and consists of a wide bulk part together with a sharp localized peak in its local DOS structure. Different zig-zag and armachair-edge configurations of the chain show the spatial asymmetry in the chain local DOS; thus, topological edge states at both chain ends can appear for different energies. These new effects cannot be observed for ideal wide band limit electrodes but they concern 1D topological states coupled with real 2D hybrid structures.

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Kamimoto, Shingo, Takahiro Kawai, and Tatsuya Koike. "On the Singularity Structure of WKB Solution of the Boosted Whittaker Equation: its Relevance to Resurgent Functions with Essential Singularities." Letters in Mathematical Physics 106, no. 12 (October 12, 2016): 1791–815. http://dx.doi.org/10.1007/s11005-016-0887-x.

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45

MARTINEZ, Christine. "LE TERME « ÉCOTOURISME » ET SES QUASISYNONYMES DANS L’ESPACE MÉDIATIQUE FRANÇAIS." FRANCISOLA 1, no. 2 (March 1, 2017): 114. http://dx.doi.org/10.17509/francisola.v1i2.5549.

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RÉSUMÉ. L’évolution du lexème écotourisme dans les quotidiens français (version informatisée) est le but de notre étude. Nous nous référons à Moirand (2007, p. 4) pour voir ce qui se passe « dans et par les médias » et à Charaudeau et Maingueneau (2002, p. 324) pour la mémoire des discours. Non seulement l’usage et les conditions sociales sont importants dans l’appréciation, la compréhension et la manière, dont sont présentées nos collocations, mais surtout le contexte dans lequel elles évoluent. Qu’il soit écologique, officiel (Ministère de l’Ecologie, du Développement durable et de l’Énergie) ou journalistique (slogan de propagande écologique), ces contextes nous paraissent essentiels pour une bonne compréhension. Notre but est l’analyse de ce phénomène. Le concept de écotourisme est riche en traits sémantiques, et malléable suivant les contextes et les visées médiatiques qu’on lui impose. Nous allons essayer d’approfondir ces singularités dans cet article. Mots-clés : collocation, contexte, discours, écotourisme, journaliste, manipulation, trait sémantique, visée discursive. ABSTRACT. The evolution of the lexeme ecotourism in French newspapers (electronic version) is the aim of our study. We refer to Moirand (2007, p. 4) to see what happens "in and through the media" and Patrick Charaudeau et Maingueneau (2002, p. 324) for the memory of the speech. Not only the use and social conditions are important in the appreciation, understanding and speaking, which are presented our collocations, but especially the context in which they operate. It is environmentally friendly, official (Ministry of Ecology, Sustainable Development and Energy) or journalistic (ecological propaganda slogan), these contexts we consider essential for a proper understanding. Our ambition is to analyse this phenomenon. The concept of ecotourism is rich in semantic traits and malleable depending on the context and media referred imposed on it. We will try to deepen these singularities in this article. Keywords: collocation, context, discourse, ecotourism, journalist, manipulation, semantic trait, discursive aim.

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Zhang, Chenguang, and Krishnaswamy Nandakumar. "Approaches to the Numerical Estimates of Grid Convergence of NSE in the Presence of Singularities." International Journal of Nonlinear Sciences and Numerical Simulation 19, no. 3-4 (June 26, 2018): 281–87. http://dx.doi.org/10.1515/ijnsns-2017-0016.

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AbstractEvaluating the order of accuracy (order) is an integral part of the development and application of numerical algorithms. Apart from theoretical functional analysis to place bounds on error estimates, numerical experiments are often essential for nonlinear problems to validate the estimates in a reliable answer. The common workflow is to apply the algorithm using successively finer temporal/spatial grid resolutions ${\delta _i}$, measure the error ${\isin _i}$ in each solution against the exact solution, the order is then obtained as the slope of the line that fits $(\log {\isin _i}, \log {\delta _i})$. We show that if the problem has singularities like divergence to infinity or discontinuous jump, this common workflow underestimates the order if solution at regions around the singularity is used. Several numerical examples with different levels of complexity are explored. A simple one-dimensional theoretical model shows it is impossible to numerically evaluate the order close to singularity on uniform grids.

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Pham, Hai Duong, Wu-Pei Su, Thi Dieu Hien Nguyen, Ngoc Thanh Thuy Tran, and Ming-Fa Lin. "Rich p -type-doping phenomena in boron-substituted silicene systems." Royal Society Open Science 7, no. 12 (December 2020): 200723. http://dx.doi.org/10.1098/rsos.200723.

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The essential properties of monolayer silicene greatly enriched by boron substitutions are thoroughly explored through first-principles calculations. Delicate analyses are conducted on the highly non-uniform Moire superlattices, atom-dominated band structures, charge density distributions and atom- and orbital-decomposed van Hove singularities. The hybridized 2 p z –3 p z and [2s, 2 p x , 2 p y ]–[3s, 3 p x , 3 p y ] bondings, with orthogonal relations, are obtained from the developed theoretical framework. The red-shifted Fermi level and the modified Dirac cones/ π bands/ σ bands are clearly identified under various concentrations and configurations of boron-guest atoms. Our results demonstrate that the charge transfer leads to the non-uniform chemical environment that creates diverse electronic properties.

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Anchouche, Boudjemâa. "On the Asymptotic Behavior of Complete Kähler Metrics of Positive Ricci Curvature." Canadian Journal of Mathematics 62, no. 1 (February 1, 2010): 3–18. http://dx.doi.org/10.4153/cjm-2010-001-0.

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AbstractLet (X, g) be a complete noncompact Kähler manifold, of dimension n ≥ 2, with positive Ricci curvature and of standard type (see the definition below). N. Mok proved that X can be compactified, i.e., X is biholomorphic to a quasi-projective variety. The aim of this paper is to prove that the L2 holomorphic sections of the line bundle K−qXand the volume form of the metric g have no essential singularities near the divisor at infinity. As a consequence we obtain a comparison between the volume forms of the Kähler metric g and of the Fubini-Study metric induced on X. In the case of dimC X = 2, we establish a relation between the number of components of the divisor D and the dimension of the.

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ANDERSON, J. T. "HADRON DEGENERATE MULTIPLET MASS SPECTRUM FROM QUARK-MONOPOLE EQUIVALENCE." Modern Physics Letters A 03, no. 08 (July 1988): 811–17. http://dx.doi.org/10.1142/s0217732388000970.

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Non-observation of quarks or monopoles suggests their equivalence, as has been proposed within string and bag and other models and implied for QCD by the monopole solutions. The possible magnetic nature of quarks is investigated within a non-Abelian field theory with magnetic sources and fermions and color. The sources are shown to eliminate the non-analytic singularities of the field Aμ by a scale-setting mechanism which introduces a degenerate mass. The scale-setting mechanism follows from the requirement of gauge covariance by removal of the non-gauge covariant term which includes essential singulari-ties of [Formula: see text]. The low-lying hadron degenerate mass spectrum is obtained in terms of the degenerate mass and the colored symmetry.

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PHILIPONA, DAVID L., and J. KEVIN O'REGAN. "Color naming, unique hues, and hue cancellation predicted from singularities in reflection properties." Visual Neuroscience 23, no. 3-4 (May 2006): 331–39. http://dx.doi.org/10.1017/s0952523806233182.

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Psychophysical studies suggest that different colors have different perceptual status: red and blue for example are thought of as elementary sensations whereas yellowish green is not. The dominant account for such perceptual asymmetries attributes them to specificities of the neuronal representation of colors. Alternative accounts involve cultural or linguistic arguments. What these accounts have in common is the idea that there are no asymmetries in the physics of light and surfaces that could underlie the perceptual structure of colors, and this is why neuronal or cultural processes must be invoked as the essential underlying mechanisms that structure color perception. Here, we suggest a biological approach for surface reflection properties that takes into account only the information about light that is accessible to an organism given the photopigments it possesses, and we show that now asymmetries appear in the behavior of surfaces with respect to light. These asymmetries provide a classification of surface properties that turns out to be identical to the one observed in linguistic color categorization across numerous cultures, as pinned down by cross cultural studies. Further, we show that data from psychophysical studies about unique hues and hue cancellation are consistent with the viewpoint that stimuli reported by observers as special are those associated with this singularity-based categorization of surfaces under a standard illuminant. The approach predicts that unique blue and unique yellow should be aligned in chromatic space while unique red and unique green should not, a fact usually conjectured to result from nonlinearities in chromatic pathways.

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Journal articles on the topic 'Essential singularities'

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