Статті в журналах: "The Singularity is Near"

1

Marusina, Kate. "Genomic Singularity Is Near." Genetic Engineering & Biotechnology News 34, no. 21 (December 2014): 1, 38–40. http://dx.doi.org/10.1089/gen.34.21.01.

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2

Marusina, Kate. "Genomic Singularity Is Near." Clinical OMICs 1, no. 14 (November 19, 2014): 12–16. http://dx.doi.org/10.1089/clinomi.01.14.06.

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3

Yampolskiy, Roman. "The Singularity May Be Near." Information 9, no. 8 (July 27, 2018): 190. http://dx.doi.org/10.3390/info9080190.

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Toby Walsh in “The Singularity May Never Be Near” gives six arguments to support his point of view that technological singularity may happen, but that it is unlikely. In this paper, we provide analysis of each one of his arguments and arrive at similar conclusions, but with more weight given to the “likely to happen” prediction.

4

Walsh, Toby. "The Singularity May Never Be Near." AI Magazine 38, no. 3 (October 2, 2017): 58–62. http://dx.doi.org/10.1609/aimag.v38i3.2702.

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There is both much optimisim and pessimism around artificial intelligence (AI) today. The optimists are investing millions of dollars, and even in some cases billions of dollars into AI. The pessimists, on the other hand, predict that AI will end many things: jobs, warfare, and even the human race. Both the optimists and the pessimists often appeal to the idea of a technological singularity, a point in time where machine intelligence starts to run away, and a new, more in- telligent “species” starts to inhabit the earth. If the optimists are right, this will be a moment that fundamentally changes our economy and our society. If the pessimists are right, this will be a moment that also fundamentally changes our economy and our society. It is therefore very worthwhile spending some time deciding if either of them might be right.

5

Fleck, M., A. M. Oleś, and L. Hedin. "Magnetism near the Van Hove singularity." Journal of Magnetism and Magnetic Materials 177-181 (January 1998): 599–601. http://dx.doi.org/10.1016/s0304-8853(97)00706-3.

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6

MacLeod, D. I. A., S. Anstis, and E. Shubel. "Singularity of visual dynamics near isoluminance." Journal of Vision 5, no. 12 (December 1, 2005): 27. http://dx.doi.org/10.1167/5.12.27.

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7

Jatkar, Dileep P., and Bas Peeters. "String theory near a conifold singularity." Physics Letters B 362, no. 1-4 (November 1995): 73–77. http://dx.doi.org/10.1016/0370-2693(95)01155-j.

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8

Wei, Haikun, Jun Zhang, Florent Cousseau, Tomoko Ozeki, and Shun-ichi Amari. "Dynamics of Learning Near Singularities in Layered Networks." Neural Computation 20, no. 3 (March 2008): 813–43. http://dx.doi.org/10.1162/neco.2007.12-06-414.

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We explicitly analyze the trajectories of learning near singularities in hierarchical networks, such as multilayer perceptrons and radial basis function networks, which include permutation symmetry of hidden nodes, and show their general properties. Such symmetry induces singularities in their parameter space, where the Fisher information matrix degenerates and odd learning behaviors, especially the existence of plateaus in gradient descent learning, arise due to the geometric structure of singularity. We plot dynamic vector fields to demonstrate the universal trajectories of learning near singularities. The singularity induces two types of plateaus, the on-singularity plateau and the near-singularity plateau, depending on the stability of the singularity and the initial parameters of learning. The results presented in this letter are universally applicable to a wide class of hierarchical models. Detailed stability analysis of the dynamics of learning in radial basis function networks and multilayer perceptrons will be presented in separate work.

9

CAMACHO, CÉSAR, and RUDY ROSAS. "Invariant sets near singularities of holomorphic foliations." Ergodic Theory and Dynamical Systems 36, no. 8 (July 21, 2015): 2408–18. http://dx.doi.org/10.1017/etds.2015.23.

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Consider a complex one-dimensional foliation on a complex surface near a singularity $p$. If ${\mathcal{I}}$ is a closed invariant set containing the singularity $p$, then ${\mathcal{I}}$ contains either a separatrix at $p$ or an invariant real three-dimensional manifold singular at $p$.

10

Li, You Tang, and Huai Qing Li. "Analysis of Stress Singularity near the Tip of Artificial Crack." Key Engineering Materials 525-526 (November 2012): 445–48. http://dx.doi.org/10.4028/www.scientific.net/kem.525-526.445.

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A generalized expression of the stress-singularity function at the tip of artificial crack is proposed, and a formula to calculate the stress intensity factor of artificial crack is obtained in the paper. The solutions of stress singularity of a cracked bi-materials beam under uniform tension and bending were computed. The results show that the degree of stress-singularity is determined by the exponent λ at the tip of artificial crack, and the exponent λ is, not only determined by materials parameter of artificial crack but also by angle. Key words: artificial crack; bi-material; stress singularity; eigen value; stress extrapolation method

11

Krori, K. D., P. Borgohain, and Dipali Das Kar. "Quantum fluctuations near a space–time singularity." Canadian Journal of Physics 67, no. 10 (October 1, 1989): 935–38. http://dx.doi.org/10.1139/p89-161.

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The well-known operator technique in quantum mechanics is used to study quantum fluctuations near the space–time singularity using Kantowski–Sachs and Bianchi type VIo metrics. In both cases the wave function of the universe is found to diverge near the space–time singularity, indicating the divergence of the quantum uncertainty near the initial epoch.

12

Chow, C. L., and T. J. Lu. "On the HRR near-tip singularity fields." Journal of Materials Science Letters 9, no. 8 (August 1990): 879–82. http://dx.doi.org/10.1007/bf00722158.

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13

Joshi, P. S., and S. S. Joshi. "Quantum effects near the black hole singularity." Classical and Quantum Gravity 5, no. 11 (November 1, 1988): L191—L195. http://dx.doi.org/10.1088/0264-9381/5/11/003.

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14

Krori, K. D., P. Borgohain, and Dipali Das (Kar). "Quantum fluctuations near a black-hole singularity." Physics Letters A 146, no. 3 (May 1990): 102–4. http://dx.doi.org/10.1016/0375-9601(90)90644-4.

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15

Chu, C. M. "The stress field singularity near a cusp." Engineering Fracture Mechanics 47, no. 3 (February 1994): 361–65. http://dx.doi.org/10.1016/0013-7944(94)90093-0.

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16

Chen, Dai-heng, and Hironobu Nisitani. "Singular Stress Field Near the Corner of Jointed Dissimilar Materials." Journal of Applied Mechanics 60, no. 3 (September 1, 1993): 607–13. http://dx.doi.org/10.1115/1.2900847.

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In this paper, the characteristics of the stress field near a corner of jointed dissimilar materials are studied as a plane problem. It is found that the order of singularity is dependent not only on the elastic constants of materials and the local geometry of corner, but also on the deformation mode. The dependence of the order of singularity was established for the case of mode I and the case of mode II. An explicit closed-form expression is given for the singular stress field at the close vicinity of the corner, in which the stress field is expressed as a sum of the symmetric state with a stress singularity of 1/r1-λ1 and the skew symmetric state with a stress singularity of 1/r1-λ2. When both λ1 and λ2 are real the singular stress field around the point singularity is defined in terms of two constants K1, λ1, K11, λ2, as in the case of crack problems.

17

KRORI, K. D., P. BORGOHAIN, and DIPALI DAS KAR. "QUANTUM EFFECTS NEAR A CHARGED BLACK HOLE SINGULARITY." Modern Physics Letters A 07, no. 23 (July 30, 1992): 2051–57. http://dx.doi.org/10.1142/s0217732392001786.

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We present in this paper an investigation of the problem of quantum fluctuations near a charged black hole singularity. We show that quantum fluctuations do not vanish near the singularity leading to the conclusion that charged black hole singularities are unlikely to occur in nature. This result may be obvious but we derive it here.

18

JOSHI, PANKAJ S., and SONAL S. JOSHI. "QUANTUM EFFECTS NEAR SPACETIME SINGULARITIES." Modern Physics Letters A 02, no. 12 (December 1987): 913–20. http://dx.doi.org/10.1142/s0217732387001166.

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We incorporate quantum effects into the gravitational dynamics in the vicinity of singularity in the case of three important general relativistic spacetimes, namely the spherically symmetric dust-ball collapse, standard Friedmann models and a general cosmological scenario given by Belinskii et al. The quantum state of the universe is represented by a general wave function where the conformal degree of freedom is quantised. It is seen in each case that the spread around the classical state diverges in the limit of approach to the classically singular epoch. Thus, non-classical, non-singular states can occur with finite probability. Our results show that including quantum effects radically changes the usual singularity scenario.

19

Li, Mu Yang, Jun Lin Li, and Xiu Feng Xie. "Stress Singularities near Interface Crack Tip for Mode II of Orthotropic Bi-Material." Advanced Materials Research 1004-1005 (August 2014): 473–78. http://dx.doi.org/10.4028/www.scientific.net/amr.1004-1005.473.

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Using the method of composite material complex and constructing new stress functions with complex singularity exponents, the problem of singularities near interface crack tip for mode II of orthotropic bi-material is studied. Boundary value problems of generalized bi-harmonic equations can be solved with the help of boundary conditions, then four kinds of stress singularities are deduced, respectively, such as the constant singularity at λ=-1/2, the non-constant singularity at λ=-1/2+ε , the constant oscillation singularity at λ=-1/2+iε, and non-constant oscillation singularity at λ=-1/2+c+iε. For each case, the analytic expressions for stress intensity factors near the central-penetrated interface crack tip for mode II of orthotropic bi-material are obtained.

20

Grandguillaume, Laureen, Sylvain Lavernhe, and Christophe Tournier. "Kinematical Smoothing of Rotary Axis near Singularity Point." Materials Science Forum 836-837 (January 2016): 501–8. http://dx.doi.org/10.4028/www.scientific.net/msf.836-837.501.

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This paper deals with singular configurations of a 5-axis machine tool in high speed milling which may lead to the appearance of large incoherent movements of rotary axes near singularity points. These movements generate slowdowns of the actual feedrate during the execution of the tool path, which affect quality and productivity. Thus, this paper proposes a method to detect these behaviors during machining simulation and correct the tool path. Unlike the literature methods, this correction consists in modifying the tool axis orientation by going through the singularity point while respecting maximum velocity, acceleration and jerk of the rotary axis. For that purpose, the initial articular positions of the rotary axis near the singularity point are fitted with B-spline curves, modified and finally discretized for linear interpolation. Experimental investigations on a test part are carried out to show the efficiency of the method.

21

Guo, Yuhong, Yuhua Guo, Wei Zhang, and Ruiping Wen. "Singularity Analysis of Composite Laminated Piezoelectric Rectangular Plate Structure with 1 : 2 Internal Resonance." Mathematical Problems in Engineering 2021 (August 17, 2021): 1–22. http://dx.doi.org/10.1155/2021/5552304.

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This study investigates the dynamical behavior of the composite laminated piezoelectric rectangular plate with 1 : 2 internal resonance near the singularity using the extended singularity theory method. Based on the previous four-dimensional averaged equations of polar coordinates where the partial derivative terms are not equal to zero, the universal unfolding with codimension 3 of the proposed system is given. The main material parameters that affect the dynamic behavior of the laminated piezoelectric rectangular composite plate near the singularity under transverse excitation are revealed by the transition set of universal unfolding with codimension 3. In addition, the plots of the transition set in three bifurcation parameters space are discussed. These numerical results can show that the stability near the singularity of the proposed system is better when period ratio is less than zero.

22

Grandjean, Vincent, and Daniel Grieser. "The exponential map at a cuspidal singularity." Journal für die reine und angewandte Mathematik (Crelles Journal) 2018, no. 736 (March 1, 2018): 33–67. http://dx.doi.org/10.1515/crelle-2015-0020.

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AbstractWe study spaces with a cuspidal (or horn-like) singularity embedded in a smooth Riemannian manifold and analyze the geodesics in these spaces which start at the singularity. This provides a basis for understanding the intrinsic geometry of such spaces near the singularity. We show that these geodesics combine to naturally define an exponential map based at the singularity, but that the behavior of this map can deviate strongly from the behavior of the exponential map based at a smooth point or at a conical singularity: While it is always surjective near the singularity, it may be discontinuous and non-injective on any neighborhood of the singularity. The precise behavior of the exponential map is determined by a function on the link of the singularity which is an invariant of the induced metric. Our methods are based on the Hamiltonian system of geodesic differential equations and on techniques of singular analysis. The results are proved in the more general natural setting of manifolds with boundary carrying a so-called cuspidal metric.

23

Eichberg, Henning. "”Singularity is near” – en transhumanistisk trosretning spreder sig." Dansk Sociologi 28, no. 1 (February 5, 2017): 87–95. http://dx.doi.org/10.22439/dansoc.v28i1.5598.

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24

Vozmediano, M. A. H., J. González, F. Guinea, J. V. Alvarez, and B. Valenzuela. "Properties of electrons near a Van Hove singularity." Journal of Physics and Chemistry of Solids 63, no. 12 (December 2002): 2295–97. http://dx.doi.org/10.1016/s0022-3697(02)00230-5.

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25

Izabel Camacho, Maria. "The topology of flows near a dicritical singularity." Journal of Differential Equations 193, no. 2 (September 2003): 261–79. http://dx.doi.org/10.1016/s0022-0396(03)00146-3.

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26

Kamath, Sundar M., and Kyung S. Kim. "On Measuring the Near-Tip Plastic Strain Singularity." Journal of Applied Mechanics 57, no. 4 (December 1, 1990): 901–5. http://dx.doi.org/10.1115/1.2897659.

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A recently developed experimental method, stress intensity factor tracer, is extended to measure the strength, J, of the HRR singularity for near-tip plastic deformation. Focal-plane mapping of the HRR field shows that the light intensity, I, collected on a finite area of the focal plane has a simple relationship with J as I = βJ2n/(2n+1). The constant, β, is a product of several experimental parameters and “n” is the hardening parameter of a power-law hardening material. The focal-plane mapping technique is also capable of estimating the shape and size of the HRR-field dominant region for a relatively thin (<10mm) metallic specimen. In addition, a continuous trace of the J variation can be monitored using a single, stationary photodetector. Because the measurement value of this method is independent of crack-tip motion, the transition of HRR singularity from stationary to moving can also be studied. In this paper, the theoretical analysis of the method is presented.

27

Devaney, Robert L., and Folkert Tangerman. "Dynamics of entire functions near the essential singularity." Ergodic Theory and Dynamical Systems 6, no. 4 (December 1986): 489–503. http://dx.doi.org/10.1017/s0143385700003655.

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AbstractWe show that entire functions which are critically finite and which meet certain growth conditions admit ‘Cantor bouquets’ in their Julia sets. These are invariant subsets of the Julia set which are homeomorphic to the product of a Cantor set and the line [0, ∞). All of the curves in the bouquet tend to ∞ in the same direction, and the map behaves like the shift automorphism on the Cantor set. Hence the dynamics near ∞ for these types of maps may be analyzed completely. Among the entire maps to which our methods apply are exp (z), sin (z), and cos (z).

28

González, J., F. Guinea, and M. A. H. Vozmediano. "Kinematics of Electrons near a Van Hove Singularity." Physical Review Letters 84, no. 21 (May 22, 2000): 4930–33. http://dx.doi.org/10.1103/physrevlett.84.4930.

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29

Mead, Walter Russell, and Ray Kurzweil. "The Singularity Is near: When Humans Transcend Biology." Foreign Affairs 85, no. 3 (2006): 160. http://dx.doi.org/10.2307/20031996.

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30

Rump, Siegfried M. "Ill-Conditioned Matrices Are Componentwise Near to Singularity." SIAM Review 41, no. 1 (January 1999): 102–12. http://dx.doi.org/10.1137/s0036144598323216.

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31

CHEN, DaiHeng, and Kuniharu USHIJIMA. "Elastic-Plastic Stress Singularity Near a Bonded Interface." Transactions of the Japan Society of Mechanical Engineers Series A 65, no. 633 (1999): 1067–74. http://dx.doi.org/10.1299/kikaia.65.1067.

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32

Qadir, A., and A. A. Siddiqui. "On quantum effects near a black-hole singularity." Classical and Quantum Gravity 7, no. 3 (March 1, 1990): 511–13. http://dx.doi.org/10.1088/0264-9381/7/3/025.

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33

Hoenselaers, C. "Axisymmetric stationary vacuum solutions near a ring singularity." Classical and Quantum Gravity 7, no. 4 (April 1, 1990): 581–84. http://dx.doi.org/10.1088/0264-9381/7/4/010.

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34

Isaacson, E., and B. Temple. "The Riemann Problem Near a Hyperbolic Singularity II." SIAM Journal on Applied Mathematics 48, no. 6 (December 1988): 1287–301. http://dx.doi.org/10.1137/0148079.

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35

Isaacson, E., and B. Temple. "The Riemann Problem Near a Hyperbolic Singularity III." SIAM Journal on Applied Mathematics 48, no. 6 (December 1988): 1302–18. http://dx.doi.org/10.1137/0148080.

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36

Punsly, Brian. "The Kerr space-time near the ring singularity." General Relativity and Gravitation 22, no. 10 (October 1990): 1169–206. http://dx.doi.org/10.1007/bf00759018.

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37

Krupa, Martin, and Martin Wechselberger. "Local analysis near a folded saddle-node singularity." Journal of Differential Equations 248, no. 12 (June 2010): 2841–88. http://dx.doi.org/10.1016/j.jde.2010.02.006.

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38

Guo, Jun-Qi. "Dynamics near the central singularity in spherical collapse." Journal of Physics Communications 5, no. 7 (July 1, 2021): 075015. http://dx.doi.org/10.1088/2399-6528/ac1505.

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39

Yuanjie, Li. "Boson Bound States Near a Kerr-Newman Naked Singularity." Australian Journal of Physics 45, no. 2 (1992): 127. http://dx.doi.org/10.1071/ph920127.

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We discuss boson bound states near a Kerr-Newman (KN) naked singularity by means of spectroscopic eigenvalue analysis. The results show that in the background of a KN naked singularity, the self-conjugate extension operator of a boson Hamiltonian has and only has discrete eigenvalues. The discrete eigenvalues exist in the interval (-/-�, /-�). Thus, we find that the boson bound states may appear only for /-� i= o. Here /-� is the boson mass.

40

Bridges, Thomas J. "Bifurcation of periodic solutions near a collision of eigenvalues of opposite signature." Mathematical Proceedings of the Cambridge Philosophical Society 108, no. 3 (November 1990): 575–601. http://dx.doi.org/10.1017/s0305004100069462.

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AbstractWhen two purely imaginary eigenvalues of opposite Krein signature coalesce, in a Hamiltonian system, a small perturbation can drive them off of the imaginary axis resulting in a linear instability. The most celebrated example of this instability occurs in the restricted 3-body problem at Routh's critical mass ratio. In this paper the collision of eigenvalues is treated as a singularity. A variational form of the Lyapunov–Schmidt method and distinguished parameter ࡃ2-equivariant singularity theory, with the frequency as distinguished parameter, are used to determine the effect of the degeneracy on the branches of periodic solutions in a neighbourhood. Previous results of Meyer and Schmidt[13], Sokol'skij [16] and van der Meer [12] are recovered in the formulation as a co-dimension 1 singularity. The results are extended to include the effect of an additional degeneracy (a co-dimension 2 singularity). The theory is applied to a spinning double pendulum.

41

Chen, Shao Hua, Guang Xu, and Cong Yan. "Subsonic Interface Crack with Crack Face Contact." Advanced Materials Research 33-37 (March 2008): 307–14. http://dx.doi.org/10.4028/www.scientific.net/amr.33-37.307.

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A steady-state subsonic interface crack propagating between an elastic solid and a rigid substrate with crack face contact is studied. Two cases with respective to the contact length are considered, i.e., semi-infinite and finite crack face contact. Different from a stationary or an open subsonic interface crack, stress singularity at the crack tip in the present paper is found to be non-oscillatory. Furthermore, in the semi-infinite contact case, the singularity of the stress field near the crack tip is less than 1/2. In the finite contact case, no singularity exists near the crack tip, but less than 1/2 singularity does at the end of the contact zone. In both cases, the singularity depends on the linear contact coefficient and the crack speed. Asymptotic solutions near the crack tip are given and analyzed. In order to satisfy the contact conditions, reasonable region of the linear contact coefficient is found. In addition, the solution predicts a non-zero-energy dissipation rate due to crack face contact.

42

Islam, Md Shahidul, Md Golam Kader, M. M. Kamal Uddin, and Mohiuddin Ahmed. "ANALYSIS OF ORDER OF STRESS SINGULARITY AT A VERTEX IN 3D TRANSVERSELY ISOTROPIC PIEZOELECTRIC DISSIMILAR BONDED JOINTS." Journal of Mechanical Engineering 44, no. 1 (July 13, 2014): 1–5. http://dx.doi.org/10.3329/jme.v44i1.19490.

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The order of singularity near the vertex of bonded joints is one of the main factors responsible fordebonding under mechanical or thermal loading. The distribution of stress singularity field near the vertex ofbonded joints is very important to maintain the reliability of intelligent materials. In this paper, order of stresssingularity at vertex in 3D transversely isotropic piezoelectric dissimilar bonded joints is analyzed. Eigenanalysis based on FEM is used for stress singularity field analysis of piezoelectric bonded joints. The eigenequation is used for calculating the order of stress singularity, and the angular function. The numerical resultshows that the angular functions have large value near the interface edge than the inner portion of the joint.Therefore, there is a possibility to debond and delamination may occur at the interface edge of the piezoelectricbonded joints due to the higher stress and electric displacement concentration at the free edge.DOI: http://dx.doi.org/10.3329/jme.v44i1.19490

43

Islam, Md Shahidul, and Hideo Koguchi. "Investigation of Order of Singularity in 3D Transversely Isotropic Piezoelectric Bimaterial Joints by FEM." Journal of Circuits, Systems and Computers 24, no. 02 (November 27, 2014): 1540001. http://dx.doi.org/10.1142/s0218126615400010.

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The order of singularity near the vertex of bonded joints is one of the main factors responsible for debonding of electronic device under mechanical or electrical loading. The distribution of singularity field near the vertex of bonded joints is very important to maintain the reliability of smart electronic structure. Piezoelectric material, due to its characteristic direct-converse piezoelectric effect, has naturally received considerable attentions. Piezoelectric materials have been extensively used as transducers and sensors due to their piezoelectric effects that take place between electric fields and mechanical deformation. The order of singularity at a vertex and at a point on singularity line in 3D transversely isotropic piezoelectric joints is analyzed. Eigen analysis based on FEM is used for stress singularity field analysis of piezoelectric bimaterial joints. The eigen equation is used for calculating the order of stress singularity and the angular function of elastic displacement, electric potential, stress and electric displacement. The numerical result shows that the angular functions have large value near the interface edge than the inner portion of the joint. Therefore, there is a possibility to debond and delamination occurs at interface edge of the piezoelectric bimaterial joints, due to the higher stress and electric displacement concentration at the free edge.

44

Mioc, V., and M. Stavinschi. "The zonal satellite problem - II: Near-escape flow." Serbian Astronomical Journal, no. 158 (1998): 37–41. http://dx.doi.org/10.2298/saj9858037m.

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The study of the zonal satellite problem is continued by tackling the situation r??. New equations of motion (for which the infinite distance is a singularity) and the corresponding first integrals of energy and angular momentum are set up. The infinity singularity is blown up via McGehee-type transformations, and the infinity manifold is pasted on the phase space. The fictitious flow on this manifold is described. Then, resorting to the rotational symmetry of the problem and to the angular momentum integral, the near-escape local flow is depicted. The corresponding phase curves are interpreted as physical motions.

45

Baker, Kyle, Eryn Culton, Joshua Ten Eyck, Zachary Lewis, and Timothy Sands. "Contradictory Postulates of Singularity." Mechanical Engineering Research 9, no. 2 (January 15, 2020): 28. http://dx.doi.org/10.5539/mer.v9n2p28.

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Modification of rigid body angular momentum permits controlled rotational maneuvers, and one common momentum-exchange actuator contains challenging mathematical singularities that occur when the actuator geometrically aligns perpendicularly to the commanded torque direction. Substantial research has arisen toward singularity avoidance, singularity escape (when avoidance fails), and singularity penetration which permits safe flight through regions of singularity. The latter two in particular, singularity escape and penetration require mathematical calculations of singular and near-singular quantities (very large numbers) using constituent numbers that are sometimes very small. This dichotomy leads to interesting peculiarities in some specific geometries. This short communication critically evaluates three often spoke postulates for defining singularity and the axioms that accompany the postulates. Researchers using disparate postulates arrive at contradictory conclusions about singularities, and we examine these peculiarities, leading to a few conclusions. Singular conditions must never be declared in the abstract without consideration for the commanded maneuver (e.g. the claim “the CMG system is singular”). Seeking the true angular momentum capability at near-planar skew angles, this research concludes that performance prediction is difficult installations at low skew angles should be avoided whenever permissible to enhance abilities of mathematical calculations. It will be shown that maximum momentum performance is easily predicted at very high and very low skew angles, and performance will be shown to be lowest at mid-values of skew angle. Meanwhile, maximum singularity-free performance remains elusive at even modestly low skew-angles.

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Dai, Ying, Xing Ji, Lin Ye, and Yiu Wing Mai. "The Reliability of Fragmentation Test." Key Engineering Materials 312 (June 2006): 155–60. http://dx.doi.org/10.4028/www.scientific.net/kem.312.155.

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The single fiber fragmentation test has been continuously used to determine the interfacial shear strength. However, the results of the tests were still suspected by some researchers. To evaluate the reliability of the fragmentation test, the stress singularity near the interface end of fragmentation is investigated. According to the local failure modes near the interface end of a fiber fragment, there are three cases of the interface end conditions to be considered for the fragmentation tests: (A) fiber breaks only, without matrix cracking and de-bonding, (B) fiber breaks and matrix cracks, without interface de-bonding, (C) fiber breaks and interface de-bonds, with or without matrix cracking. After the singularity analysis of stress field near the interface end was depicted, it is obvious, that the interfacial shear strength given by the fragmentation test is not proper, because of that a stress singularity exists near the interface end.

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PIZZI, MARCO, and ARMANDO PAOLINO. "EQUILIBRIUM CONFIGURATIONS IN THE DOUBLE REISSNER-NORDSTROM EXACT SOLUTION." International Journal of Modern Physics A 23, no. 08 (March 30, 2008): 1222–25. http://dx.doi.org/10.1142/s0217751x0804010x.

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The double Reissner-Nordstrom (RN) solution without strings nor struts, recently found by Alekseev and Belinski, shows that classically-forbidden equilibria are allowed for a naked singularity near a black hole. In the following we shows the plots of the electric force lines in three qualitatively different situations: equal-signed charges, opposite charges and the case of a naked singularity near a neutral black hole.

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Dinh, Tien-Cuong, and Hao Wu. "Harmonic currents directed by foliations by Riemann surfaces." Proceedings of the American Mathematical Society 149, no. 8 (May 18, 2021): 3453–61. http://dx.doi.org/10.1090/proc/15470.

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We study local positive d d c dd^{c} -closed currents directed by a foliation by Riemann surfaces near a hyperbolic singularity which have no mass on the separatrices. A theorem of Nguyên says that the Lelong number of such a current at the singular point vanishes. We prove that this property is sharp: one cannot have any better mass estimate for this current near the singularity.

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Yang, Xiaomei, Weiyang Yang, Junlin Li, and Xuexia Zhang. "Oscillatory Singularity Behaviors Near Interface Crack Tip for Mode II of Orthotropic Bimaterial." Journal of Applied Mathematics 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/716768.

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The fracture behaviors near the interface crack tip for mode II of orthotropic bimaterial are discussed. The oscillatory singularity fields are researched. The stress functions are chosen which contain twelve undetermined coefficients and an unknown singularity exponent. Based on the boundary conditions and linear independence, the system of twelve nonhomogeneous linear equations is derived. According to the condition for the system of nonhomogeneous linear equations which has a solution, the singularity exponent is determined. Total coefficients are found by means of successive elimination of the unknowns. The theoretical formulae of stress intensity factors and analytic solutions of stress field near the interface crack tip are obtained. The crack tip field is shown by figures.

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Wang, Xuejun, Xiao Han, and Guangming Pan. "The logarithmic law of sample covariance matrices near singularity." Bernoulli 24, no. 1 (February 2018): 80–114. http://dx.doi.org/10.3150/16-bej867.

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