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Journal articles on the topic 'Index of a singular point'

Author: Grafiati

Published: 4 June 2021

Last updated: 2 February 2022

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1

ENOMOTO, Ryuji, and Masasuke SHIMA. "Singular Point Assignment via the Conley Index Theory." Transactions of the Society of Instrument and Control Engineers 34, no. 6 (1998): 584–92. http://dx.doi.org/10.9746/sicetr1965.34.584.

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2

Iwasokun, Gabriel Babatunde, and Oluwole Charles Akinyokun. "Fingerprint Singular Point Detection Based on Modified Poincare Index Method." International Journal of Signal Processing, Image Processing and Pattern Recognition 7, no. 5 (October 31, 2014): 259–72. http://dx.doi.org/10.14257/ijsip.2014.7.5.23.

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3

BRACCI, FILIPPO, and TATSUO SUWA. "RESIDUES FOR SINGULAR PAIRS AND DYNAMICS OF BIHOLOMORPHIC MAPS OF SINGULAR SURFACES." International Journal of Mathematics 15, no. 05 (July 2004): 443–66. http://dx.doi.org/10.1142/s0129167x04002375.

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We prove the existence of a parabolic curve for a germ of biholomorphic map tangent to the identity at an isolated singular point of a surface under some conditions. For this purpose, we present a Camacho–Sad type index theorem for fixed curves of biholomorphic maps of singular surfaces and develop a local intersection theory of curves in singular surfaces from an analytic approach by means of Grothendieck residues.

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4

Su, Hua, Lishan Liu, and Xinjun Wang. "Solutions forp-Laplacian Dynamic Delay Differential Equations on Time Scales." Journal of Applied Mathematics 2012 (2012): 1–23. http://dx.doi.org/10.1155/2012/652465.

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LetTbe a time scale. We study the existence of positive solutions for the nonlinear four-point singular boundary value problem withp-Laplacian dynamic delay differential equations on time scales, subject to some boundary conditions. By using the fixed-point index theory, the existence of positive solution and many positive solutions for nonlinear four-point singular boundary value problem withp-Laplacian operator is obtained.

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5

Su, Hua, Lishan Liu, and Xinjun Wang. "Higher-Order Dynamic Delay Differential Equations on Time Scales." Journal of Applied Mathematics 2012 (2012): 1–19. http://dx.doi.org/10.1155/2012/939162.

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We study the existence of positive solutions for the nonlinear four-point singular boundary value problem with higher-orderp-Laplacian dynamic delay differential equations on time scales, subject to some boundary conditions. By using the fixed-point index theory, the existence of positive solution and many positive solutions for nonlinear four-point singular boundary value problem withp-Laplacian operator are obtained.

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6

Azamov, Nurulla, and Tom Daniels. "Resonance index and singular μ-invariant." Analysis 40, no. 3 (August 1, 2020): 151–61. http://dx.doi.org/10.1515/anly-2019-0053.

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AbstractGiven a self-adjoint operator and a relatively trace class perturbation, one can associate the singular spectral shift function – an integer-valued function on the real line which measures the flow of singular spectrum, not only at points outside of the essential spectrum, where it coincides with the classical notion of spectral flow, but at points within the essential spectrum too. The singular spectral shift function coincides with both the total resonance index and the singular μ-invariant. In this paper we give a direct proof of the equality of the total resonance index and singular μ-invariant assuming only the limiting absorption principle and no condition of trace class type – a context in which the existence of the singular spectral shift function is an open question. The proof is based on an application of the argument principle to the poles and zeros of the analytic continuation of the scattering matrix considered as a function of the coupling parameter.

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7

Sun, Yan, Lishan Liu, and Yeol Je Cho. "Positive solutions of singular nonlinear Sturm-Liouville boundary value problems." ANZIAM Journal 45, no. 4 (April 2004): 557–71. http://dx.doi.org/10.1017/s1446181100013560.

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AbstractBy using fixed point index theory, we present the existence of positive solutions for a Sturm-Liouville singular boundary value problem with at least one positive solution. Our results significantly extend and improve many known results even for non-singular cases.

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8

Zabreiko, P. P., and A. V. Krivko-Krasko. "Poincaré index of plane polynomial fields of third and fourth degree." Proceedings of the National Academy of Sciences of Belarus. Physics and Mathematics Series 55, no. 1 (March 26, 2019): 22–31. http://dx.doi.org/10.29235/1561-2430-2019-55-1-22-31.

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The conditions of isolation of a zero singular point of plane polynomial fields of third and fourth degree are considered in terms of the coefficients of the components of these fields. The isolation conditions depend on the greatest common divisor of the components of polynomial fields: in some cases only on its degree, and in some cases, additionally, on the presence of nonzero real zeros. The reasoning, which allows one to write out the isolation conditions, is based on the concept of the resultant and subresultants of components of plane polynomial fields. If the zero singular point is isolated, its index is calculated through the values of subresultants and coefficients of components.

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9

Pukhlikov, A. V. "Birationally Rigid Complete Intersections with a Singular Point of High Multiplicity." Proceedings of the Edinburgh Mathematical Society 62, no. 1 (September 26, 2018): 221–39. http://dx.doi.org/10.1017/s0013091518000184.

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AbstractWe prove the birational rigidity of Fano complete intersections of index 1 with a singular point of high multiplicity, which can be close to the degree of the variety. In particular, the groups of birational and biregular automorphisms of these varieties are equal, and they are non-rational. The proof is based on the techniques of the method of maximal singularities, the generalized 4n2-inequality for complete intersection singularities and the technique of hypertangent divisors.

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10

Sakkalis, Takis. "The computation of the index of a Morse function at a critical point." International Journal of Mathematics and Mathematical Sciences 11, no. 4 (1988): 721–26. http://dx.doi.org/10.1155/s0161171288000870.

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A theoretical approach in computing the index of a Morse function at a critical point on a real non-singular hypersurfaceVis given. As a consequence the Euler characteristic ofVis computed. In the case where the hypersurface is polynomial and compact, a procedure is given that finds a linear functionℓ, whose restrictionℓ|V, is a Morse function onV.

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11

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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12

Liu, Bo, and Yansheng Liu. "Positive Solutions of a Two-Point Boundary Value Problem for Singular Fractional Differential Equations in Banach Space." Journal of Function Spaces and Applications 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/585639.

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This paper investigates the existence of positive solutions to a two-point boundary value problem (BVP) for singular fractional differential equations in Banach space and presents a number of new results. First, by constructing a novel cone and using the fixed point index theory, a sufficient condition is established for the existence of at least two positive solutions to the approximate problem of the considered singular BVP. Second, using Ascoli-Arzela theorem, a sufficient condition is obtained for the existence of at least two positive solutions to the considered singular BVP from the convergent subsequence of the approximate problem. Finally, an illustrative example is given to support the obtained new results.

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13

Tian, Yuansheng, and Anping Chen. "The Existence of Positive Solution to Three-Point Singular Boundary Value Problem of Fractional Differential Equation." Abstract and Applied Analysis 2009 (2009): 1–18. http://dx.doi.org/10.1155/2009/314656.

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We investigate the existence of positive solution to nonlinear fractional differential equation three-point singular boundary value problem:Dqu(t)+f(t,u(t))=0,0<t<1,u(0)=0,u(1)=αD(q−1)/2u(t)|t=ξ, where1<q≤2is a real number,ξ∈(0,1/2],α∈(0,+∞)andαΓ(q)ξ(q−1)/2<Γ((q+1)/2),Dqis the standard Riemann-Liouville fractional derivative, andf∈C((0,1]×[0,+∞),[0,+∞)),lim⁡t→+0f(t,⋅)=+∞(i.e.,fis singular att=0). By using the fixed-point index theory, the existence result of positive solutions is obtained.

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14

Kim, Chan-Gyun. "Existence, Nonexistence and Multiplicity of Positive Solutions for Singular Boundary Value Problems Involving φ-Laplacian." Mathematics 7, no. 10 (October 12, 2019): 953. http://dx.doi.org/10.3390/math7100953.

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In this paper, we establish the results on the existence, nonexistence and multiplicity of positive solutions to singular boundary value problems involving φ -Laplacian. Our approach is based on the fixed point index theory. The interesting point is that a result for the existence of three positive solutions is given.

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15

Tudorache, Alexandru, and Rodica Luca. "On a singular Riemann–Liouville fractional boundary value problem with parameters." Nonlinear Analysis: Modelling and Control 26, no. 1 (January 1, 2021): 151–68. http://dx.doi.org/10.15388/namc.2021.26.21414.

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We investigate the existence of positive solutions for a nonlinear Riemann–Liouville fractional differential equation with a positive parameter subject to nonlocal boundary conditions, which contain fractional derivatives and Riemann–Stieltjes integrals. The nonlinearity of the equation is nonnegative, and it may have singularities at its variables. In the proof of the main results, we use the fixed point index theory and the principal characteristic value of an associated linear operator. A related semipositone problem is also studied by using the Guo–Krasnosel’skii fixed point theorem.

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16

KIM, CHAN-GYUN, and YONG-HOON LEE. "EXISTENCE OF MULTIPLE POSITIVE SOLUTIONS FOR p-LAPLACIAN PROBLEMS WITH A GENERAL INDEFINITE WEIGHT." Communications in Contemporary Mathematics 10, no. 03 (June 2008): 337–62. http://dx.doi.org/10.1142/s021919970800279x.

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This paper studies the existence of positive solutions for a class of singular boundary value problems of p-Laplacian. By using Global Continuation Theorem and the fixed point index technique, criteria of the existence, multiplicity and nonexistence of positive solutions are established.

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17

Zhang, Xinguang, Lixin Yu, Jiqiang Jiang, Yonghong Wu, and Yujun Cui. "Solutions for a Singular Hadamard-Type Fractional Differential Equation by the Spectral Construct Analysis." Journal of Function Spaces 2020 (September 29, 2020): 1–12. http://dx.doi.org/10.1155/2020/8392397.

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In this paper, we consider the existence of positive solutions for a Hadamard-type fractional differential equation with singular nonlinearity. By using the spectral construct analysis for the corresponding linear operator and calculating the fixed point index of the nonlinear operator, the criteria of the existence of positive solutions for equation considered are established. The interesting point is that the nonlinear term possesses singularity at the time and space variables.

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18

Yang, Xiao-Song. "Index sums of isolated singular points of positive vector fields." Discrete & Continuous Dynamical Systems - A 25, no. 3 (2009): 1033–39. http://dx.doi.org/10.3934/dcds.2009.25.1033.

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19

Agarwal, Ravi P., and Rodica Luca. "Positive Solutions for a Semipositone Singular Riemann–Liouville Fractional Differential Problem." International Journal of Nonlinear Sciences and Numerical Simulation 20, no. 7-8 (November 18, 2019): 823–31. http://dx.doi.org/10.1515/ijnsns-2018-0376.

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AbstractWe study the existence of multiple positive solutions for a nonlinear singular Riemann–Liouville fractional differential equation with sign-changing nonlinearity, subject to Riemann–Stieltjes boundary conditions which contain fractional derivatives. In the proof of our main theorem, we use various height functions of the nonlinearity of equation defined on special bounded sets, and two theorems from the fixed point index theory.

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20

Zhao, Yulin, Guobing Ye, and Haibo Chen. "Multiple Positive Solutions of a Singular Semipositone Integral Boundary Value Problem for Fractionalq-Derivatives Equation." Abstract and Applied Analysis 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/643571.

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By using the fixed point index theorem, this paper investigates a class of singular semipositone integral boundary value problem for fractionalq-derivatives equations and obtains sufficient conditions for the existence of at least two and at least three positive solutions. Further, an example is given to illustrate the applications of our main results.

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21

Duduchava, R., and F. O. Speck. "Singular Integral Equations in Special Weighted Spaces." Georgian Mathematical Journal 7, no. 4 (December 2000): 633–42. http://dx.doi.org/10.1515/gmj.2000.633.

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Abstract We prove the boundedness of the Cauchy singular integral operator in special weighted Sobolev and Hölder-Zygmund spaces for large values of the smoothness parameter, which is an integer m ≥ 0, when the underlying contour is piecewise-smooth with angular points and even with cusps. We obtain Fredholm criteria and an index formula for singular integral equations with piecewise-continuous coefficients and complex conjugation in the spaces and provided that the underlying contour has only angular points but no cusps. The Fredholm property and the index turn out to be independent of the smoothness parameter m.

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22

Gerovska, Daniela, Marcos J. Araúzo-Bravo, Petar Stavrev, and Kathryn Whaler. "MaGSoundDST — 3D automatic inversion of magnetic and gravity data based on the differential similarity transform." GEOPHYSICS 75, no. 1 (January 2010): L25—L38. http://dx.doi.org/10.1190/1.3298619.

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We present an automatic procedure — Magnetic And Gravity SOUNDing Differential Similarity Transform (MaGSoundDST) — for inversion of regular or irregular magnetic- and gravity-grid data measured on even or uneven surfaces. It solves for horizontal position, depth, and structural index of simple sources and is independent of a linear background. In addition, it estimates the shape of sources consisting of several singular points and lines. The method uses the property of the differential similarity transform (DST) of a magnetic or a gravity anomaly to become zero or linear at all observation points when the central point of similarity of the transform, which we refer to as the probing point, coincides with a source’s singular point. It uses a measured anomalous field and its calculated or measured (gradiometry) first-order derivatives. The method is independent of the magnetization-vector direction in the magnetic data case and does notrequire reduction-to-the-pole transformed data as input. With MaGSoundDST, we provide an important alternative interpretation technique to the Euler deconvolution procedures, combining a moving-window method, whereby the solutions are linked to singular points of causative bodies, with an approach in which the solutions are linked to the real sources. The procedure involves calculating a 3D function that evaluates the linearity of the DST for different integer or noninteger structural indices, using a moving window. We sound the subsurface along a vertical line under each window center. Then we combine the 3D results for different structural indices and present them in three easy-to-interpret maps, avoiding the need for clustering techniques. We deduce only one solution for location and type of simple sources, which is a major advantage over Euler deconvolution. Application to different cases of synthetic and real data shows the method’s applicability to various types of magnetic and gravity field investigations.

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23

Luca, Rodica. "Existence and multiplicity of positive solutions for a singular Riemann-Liouville fractional differential problem." Filomat 34, no. 12 (2020): 3931–42. http://dx.doi.org/10.2298/fil2012931l.

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We investigate the existence and multiplicity of positive solutions for a nonlinear Riemann-Liouville fractional differential equation with a nonnegative singular nonlinearity, subject to Riemann-Stieltjes boundary conditions which contain fractional derivatives. In the proofs of our main results, we use an application of the Krein-Rutman theorem and some theorems from the fixed point index theory.

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24

Li, Yongxiang, and Xiaoyu Jiang. "Positive Periodic Solutions for Second-Order Ordinary Differential Equations with Derivative Terms and Singularity in Nonlinearities." Journal of Function Spaces and Applications 2012 (2012): 1–15. http://dx.doi.org/10.1155/2012/945467.

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The existence results of positiveω-periodic solutions are obtained for the second-order ordinary differential equationu′′(t)=f(t,u(t),u'(t)),t∈ℝwhere,f:ℝ×(0,∞)×ℝ→ℝis a continuous function, which isω-periodic intandf(t,u,v)may be singular atu=0. The discussion is based on the fixed point index theory in cones.

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25

Lu, Xinmiao, Hong Zhao, Haijun Lin, and Qiong Wu. "Multifractal Analysis for Soft Fault Feature Extraction of Nonlinear Analog Circuits." Mathematical Problems in Engineering 2016 (2016): 1–7. http://dx.doi.org/10.1155/2016/7305702.

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Aiming at the nonstationarity and nonlinearity of soft fault signals of nonlinear analog circuits, the use of multifractal detrended fluctuation analysis can effectively reveal the dynamic behavior hidden in multiscale nonstationary signals. This paper adopts a new method that uses multifractal detrended fluctuation analysis to calculate the multifractal singularity spectrum of soft fault signals of nonlinear analog circuits. Moreover, this method endows the parameters of the spectrum with definite physical meanings including width, maximum singular index, minimum singular index, and corresponding singularity index of the extreme point. Therefore, this method can be applied to characterize the internal dynamic mechanism of the soft fault signals of nonlinear analog circuits, making it suitable for the feature extraction of fault circuits. All multifractal feature parameters can be organized into a feature set, which will be then input to a support vector machine, and fault detection for the nonlinear analog circuit can be conducted via the support vector machine.

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26

Dick, Alexander, Othmar Koch, Roswitha März, and Ewa Weinmüller. "Convergence of collocation schemes for boundary value problems in nonlinear index 1 DAEs with a singular point." Mathematics of Computation 82, no. 282 (September 10, 2012): 893–918. http://dx.doi.org/10.1090/s0025-5718-2012-02637-8.

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27

Jin, Peng. "On weak solutions of SDEs with singular time-dependent drift and driven by stable processes." Stochastics and Dynamics 18, no. 02 (December 11, 2017): 1850013. http://dx.doi.org/10.1142/s0219493718500132.

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Let [Formula: see text]. In this paper, we study weak solutions for the following type of stochastic differential equations: [Formula: see text], where [Formula: see text] is the starting point, [Formula: see text] is measurable, and [Formula: see text] is a [Formula: see text]-dimensional centered [Formula: see text]-stable process with index [Formula: see text]. We show that if the centered [Formula: see text]-stable process [Formula: see text] is non-degenerate and [Formula: see text] for some [Formula: see text] with [Formula: see text], then the above SDE has a unique weak solution for every starting point [Formula: see text].

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28

Liu, Jian, Hanying Feng, and Xingfang Feng. "Multiplicity of Positive Solutions for a Singular Second-Order Three-Point Boundary Value Problem with a Parameter." Journal of Applied Mathematics 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/603203.

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This paper is concerned with the following second-order three-point boundary value problemu″t+β2ut+λqtft,ut=0,t∈0 , 1,u0=0,u(1)=δu(η), whereβ∈(0,π/2),δ>0,η∈(0,1), andλis a positive parameter. First, Green’s function for the associated linear boundary value problem is constructed, and then some useful properties of Green’s function are obtained. Finally, existence, multiplicity, and nonexistence results for positive solutions are derived in terms of different values ofλby means of the fixed point index theory.

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29

Zhao, Daliang, and Yansheng Liu. "Eigenvalues of a Class of Singular Boundary Value Problems of Impulsive Differential Equations in Banach Spaces." Journal of Function Spaces 2014 (2014): 1–12. http://dx.doi.org/10.1155/2014/720494.

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This paper is devoted to investigating the eigenvalue problems of a class of nonlinear impulsive singular boundary value problem in Banach spaces:μx′′+f(t,x)=0,t∈(0,1),t≠ti;Δx|t=ti=αix(ti-0),i=1,2,…,k;ax(0)-bx′(0)=θ;cx(1)+dx′(1)=θ,whereθdenotes the zero element of Banach space,Δx|t=ti=x(ti+0)-x(ti-0),αi>-1,a,b,c,d∈R+,γ=ac+ad+bc>0,μis a parameter, andf(t,x)may be singular att=0,1andx=θ. The arguments are mainly based upon the theory of fixed point index, measure of noncompactness, and the special cone, which is constructed to overcome the singularity.

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30

Antyushina, I. V., and N. M. Bliznyakov. "Newton diagrams, odd points, and the index of singular points of planar vector fields." Mathematical Notes 89, no. 5-6 (June 2011): 757–60. http://dx.doi.org/10.1134/s0001434611050178.

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31

Suárez, Antonio. "Nonnegative solutions for a heterogeneous degenerate competition model." ANZIAM Journal 46, no. 2 (October 2004): 273–97. http://dx.doi.org/10.1017/s1446181100013845.

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AbstractThis paper deals with the existence, uniqueness and qualitative properties of nonnegative and nontrivial solutions of a spatially heterogeneous Lotka-Volterra competition model with nonlinear diffusion. We give conditions in terms of the coefficients involved in the setting of the problem which assure the existence of nonnegative solutions as well as the uniqueness of a positive solution. In order to obtain these results we employ monotonicity methods, singular spectral theory and a fixed point index.

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32

Sun, Ling Tao, Dong Ping Shi, Chao Zhong Guo, Xu Yang Xiao, and Jing Bai. "A Molecular Dynamics Study on the Physical Properties of (CuPd)₁₄₇ Alloy Nanoparticles." Applied Mechanics and Materials 723 (January 2015): 497–501. http://dx.doi.org/10.4028/www.scientific.net/amm.723.497.

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The melting of CuPd bimetallic clusters was studied by using molecular dynamics with the embedded-atom method. The results show that the same number of Cu atoms with Pd clusters, their temperature curve of clusters and the melting point value can be induced by the process of Cu atomic segregation to appear big differences. According to the analysis of HA index and clusters snapshot image, the singular phenomenon is caused by hierarchical differences between Cu atomic distances from the inner surface segregation. It is concluded that the difference of the melting point of Cu-Pd bimetallic clusters provides an effective method of controllable preparation.

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33

Tudorache, Alexandru, and Rodica Luca. "Positive Solutions of a Fractional Boundary Value Problem with Sequential Derivatives." Symmetry 13, no. 8 (August 13, 2021): 1489. http://dx.doi.org/10.3390/sym13081489.

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We investigate the existence of positive solutions of a Riemann-Liouville fractional differential equation with sequential derivatives, a positive parameter and a nonnegative singular nonlinearity, supplemented with integral-multipoint boundary conditions which contain fractional derivatives of various orders and Riemann-Stieltjes integrals. Our general boundary conditions cover some symmetry cases for the unknown function. In the proof of our main existence result, we use an application of the Krein-Rutman theorem and two theorems from the fixed point index theory.

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34

Attili, Basem S. "Continuation method for computing certain singular points for index-1 differential algebraic equations." Applied Mathematics and Computation 175, no. 2 (April 2006): 1026–38. http://dx.doi.org/10.1016/j.amc.2005.08.016.

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35

Jeong, Jeongmi, and Chan-Gyun Kim. "Existence of Positive Solutions to Singular φ-Laplacian Nonlocal Boundary Value Problems when φ is a Sup-multiplicative-like Function." Mathematics 8, no. 3 (March 14, 2020): 420. http://dx.doi.org/10.3390/math8030420.

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In this paper, using a fixed point index theorem on a cone, we present some existence results for one or multiple positive solutions to φ -Laplacian nonlocal boundary value problems when φ is a sup-multiplicative-like function and the nonlinearity may not satisfy the L 1 -Carath e ´ odory condition.

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36

Shiga, S. "Rubber Processability Index Using Electrical Resistivity." Rubber Chemistry and Technology 65, no. 3 (July 1, 1992): 660–72. http://dx.doi.org/10.5254/1.3538632.

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Abstract It may not be realistic to expect a single processability index to be useful for every feature of rubber mixing due to the complexity of its mechanisms. Many processability indices have been proposed. One can find properties available to define the indices in Table I. The indices can be conceptually classified into two categories. One is founded on the singularity of some properties at the minimum mixing time. The compound mixed over this time is Theologically homogeneous in contrast to that mixed insufficiently. Therefore, this time is a phase-transition point. Not all, but most of the properties indicate the sudden change in the time-derivatives characteristic to singular points. After the time, the change becomes smaller. The other is founded on the properties of final compounds, which could be assumed as existing in a pseudoequilibrium state. Electrical volume resisitivity (resisitivity, hereafter) is chosen for this purpose. It looks simple and suitable for practice, i.e., in rubber factories. Actually, as reported by Boonstra, the measurement requires skill in addition to special equipment and is not a popular method. Nevertheless, we have used it to express the processability and, more generally, to clarify the mixing mechanism. There are three reasons for this methodology: first, we find that EPR, the object of our study, apparently shows constant minimum mixing time; second, the pseudoequilibrium-like resistivity is parallel to other processability indices, namely, the larger the resistivity, the worse the processability as described in Reference 1; third, the resistivity directly corresponds to the percolation theory. Of course, other processability indices have their own theoretical origins. However, properties other than resistivity can not be quantitatively supported by theory because of the complexity of mixing. The exceptions are microscopic methods as exemplified by the counting of large agglomerates and their size distribution, but these are more tedious and require more skill.

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37

Kučerová, Ivana. "Moderately growing solutions of third-order differential equations with a singular nonlinearity and regularly varying coefficients." Journal of Applied Mathematics, Statistics and Informatics 11, no. 1 (May 1, 2015): 33–61. http://dx.doi.org/10.1515/jamsi-2015-0003.

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AbstractThis paper is concerned with asymptotic analysis of moderately growing solutions of the third-order differential equation with singular nonlinerity((((x′)α₁*)′)α₂*)′ +q(t)x-β= 0;(A) where α1, α2and β are positive constants and σ : [α;∞)→(0;∞) is a continuous regularly varying function of index σ, α > 0 and uγ*= |u|γsgnu. An application of the theory of regular variation allows us to establish necessary and sufficient conditions for the existence of regularly varying solutions of (A) which are moderately growing and to acquire precise information about the asymptotic behavior at infinity of these solutions. The Schauder-Tychonoff fixed point technique is used.

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38

Zhao, Yulin. "Positive Solutions for (k,n−k) Conjugate Multipoint Boundary Value Problems in Banach Spaces." International Journal of Mathematics and Mathematical Sciences 2012 (2012): 1–18. http://dx.doi.org/10.1155/2012/727468.

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By means of the fixed point index theory of strict-set contraction operator, we study the existence of positive solutions for the multipoint singular boundary value problem(-1)n-kun(t)=f(t,ut),0<t<1,n≥2,1≤k≤n-1,u(0)=∑i=1m-2‍aiu(ξi),u(i)(0)=u(j)(1)=θ,1≤i≤k−1,0≤j≤n−k−1in a real Banach spaceE, whereθis the zero element ofE,0<ξ1<ξ2<⋯<ξm-2<1,ai∈[0,+∞),i=1,2,…,m-2.As an application, we give two examples to demonstrate our results.

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Zeiaee, Amin, Rana Soltani-Zarrin, Reza Langari, and Reza Tafreshi. "Kinematic Design Optimization of an Eight Degree-of-Freedom Upper-Limb Exoskeleton." Robotica 37, no. 12 (June 25, 2019): 2073–86. http://dx.doi.org/10.1017/s0263574719001085.

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SummaryThis paper studies the problem of optimizing the kinematic structure of an eight degree-of-freedom upper-limb rehabilitation exoskeleton. The objective of optimization is achieving minimum volume and maximum dexterity in the workspace of daily activities specified by a set of upper-arm configurations. To formulate the problem, a new index is proposed for effective characterization of kinematic dexterity for wearable robots. Additionally, a set of constraints are defined to ensure that the optimal design can cover the desired workspace of the exoskeleton, while singular configurations and physical interferences are avoided. The formulated multi-objective optimization problem is solved using an evolutionary algorithm (Non-dominated Sorting Genetic Algorithm II) and the weighted sum approach. Among the resulted optimal points, the point with least sensitivity with respect to the variations of design variables is chosen as the final design.

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Shabalin, Pavel, and Rafael Faizov. "Hilbert boundary value problem for generalized analytic functions with a singular line." E3S Web of Conferences 274 (2021): 11003. http://dx.doi.org/10.1051/e3sconf/202127411003.

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In this paper, we study an inhomogeneous Hilbert boundary value problem with a finite index and a boundary condition on a circle for a generalized Cauchy-Riemann equation with a singular coefficient. To solve this problem, we conducted a complete study of the solvability of the Hilbert boundary value problem of the theory of analytic functions with an infinite index due to a finite number of points of a special type of vorticity. Based on these results, we have derived a formula for the general solution and studied the existence and number of solutions to the boundary value problem of the theory of generalized analytic functions.

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Tan, Xian. "Financial Index Prediction Based on Wavelet Analysis and SVM." Applied Mechanics and Materials 303-306 (February 2013): 1114–18. http://dx.doi.org/10.4028/www.scientific.net/amm.303-306.1114.

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The analysis of the time sequence can be two ways in the time domain and frequency domain. But many financial time series exhibit strong non-stationary and long memory, which makes many traditional individually focused on the research and analysis of the time domain or frequency domain method is no longer applicable. In this paper, wavelet analysis and support vector machines for use in the time domain and frequency domain have the ability to characterize the local signal characteristics, location and mutation of the singular points and irregular mutation analysis, these mutations detected the degree of significance.

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Chistyakov, V. F., and E. V. Chistyakova. "Evaluation of the Index and Singular Points of Linear Differential-Algebraic Equations of Higher Order." Journal of Mathematical Sciences 231, no. 6 (May 19, 2018): 827–45. http://dx.doi.org/10.1007/s10958-018-3852-7.

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Jeon, Youngmok. "A quadrature method for constant-coefficient Cauchy singular integral equations on an interval." ANZIAM Journal 42, no. 2 (October 2000): 287–311. http://dx.doi.org/10.1017/s1446181100011937.

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AbstractWe consider a mesh grading quadrature method for real constant-coefficient Cauchy singular integral equations of index 0. The quadrature method is based on the trapezoidal rule. A complete stability and convergence analysis is given by the use of the noncompact perturbation analysis as in Jeon [10] and Elschner and Stephan [7]. The order of convergence can be arbitrarily high if the order of mesh grading is high enough. We also provide an efficient way of evaluating asymptotics of the solution at the end points. Experimentally, we observe that the method also works well for Cauchy singular integral equations with variable coefficients.

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TIAN, YUAN, GAOYUAN CUI, and HARRY MORRIS. "DIGITAL IMAGING BASED ON FRACTAL THEORY AND ITS SPATIAL DIMENSIONALITY." Fractals 28, no. 08 (June 13, 2020): 2040014. http://dx.doi.org/10.1142/s0218348x20400149.

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Due to the complexity of digital imaging targets and imaging conditions, fractal theory techniques in existing digital imaging systems still have various shortcomings. In this paper, a digital imaging processing method based on fractal theory is proposed for the first time. For X-ray images, the rapid calculation method of H-parameters is derived based on the fractional Brownian random field model. The H-parameters of X-ray images are calculated point by point. After that, all the singular points are connected, which is the edge of the defect in the image. We apply this method to analyze and process the X-ray images with defects such as missing joints, skins and hollows. Secondly, by means of fractal geometry, the contour slice measurement of the digital imaging space of this fractal is studied. The approximate index value is the digital imaging section profile dimension (D1 dimension) and the section shadow dimension (D2 dimension), so that the dimension determines the complexity of the form and detail of digital imaging. Finally, it can be seen from the experimental results that this method is effective and explores a new way for the development of digital imaging technology. At the same time, it is of great significance to the automatic pattern recognition of the application.

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Stavrev, Petar, and Alan Reid. "Degrees of homogeneity of potential fields and structural indices of Euler deconvolution." GEOPHYSICS 72, no. 1 (January 2007): L1—L12. http://dx.doi.org/10.1190/1.2400010.

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Homogeneity is a well-known property of the potential fields of simple point sources used in field inversion. We find that the analytical expressions of potential fields created by sources of complicated shape and constant or variable density or magnetization also show this property. This is true if all variables of length dimension are involved in the test of homogeneity. The coordinates of observation points and the source coordinates and sizes form an extended set of variables, in relation to which the field expression is homogeneous. In this case, the principal definition of homogeneity applied to a potential field can be treated as an operator of a space transform of similarity. The ratio between the transformed and original fields determines the value and sign of the degree of homogeneity [Formula: see text]. The latter may take on positive, zero, or negative values. The degree of homogeneity depends on the type of field and on the assumed physical parameter of the field source, and can be nonunique for a given field element. We analyze the potential field of one singular point as the simplest case of homogeneity. Thus, we deduce results for the structural index, [Formula: see text], in Euler deconvolution. The structural index can also be positive, zero, or negative, but it has a unique value. Analytical considerations, as well as numerical tests on the gravity contact model, confirm the proposed physical interpretation of [Formula: see text], and lead to an extended version of Euler’s differential equation for potential fields.

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Kikuchi, Hiroaki, and Juncheng Wei. "A bifurcation diagram of solutions to an elliptic equation with exponential nonlinearity in higher dimensions." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 148, no. 1 (October 17, 2017): 101–22. http://dx.doi.org/10.1017/s0308210517000154.

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We consider the following semilinear elliptic equation:where B1 is the unit ball in ℝd, d ≥ 3, λ > 0 and p > 0. Firstly, following Merle and Peletier, we show that there exists an eigenvalue λp,∞ such that (*) has a solution (λp,∞,Wp) satisfying lim|x|→0Wp(x) = ∞. Secondly, we study a bifurcation diagram of regular solutions to (*). It follows from the result of Dancer that (*) has an unbounded bifurcation branch of regular solutions that emanates from (λ, u) = (0, 0). Here, using the singular solution, we show that the bifurcation branch has infinitely many turning points around λp,∞ when 3 ≤ d ≤ 9. We also investigate the Morse index of the singular solution in the d ≥ 11 case.

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YU, XIA, KE-QIU CHEN, and YAN ZHANG. "PERFECT OPTICAL TRANSPORT AND OPTICAL BAND GAP IN QUASIPERIODIC SUPERLATTICES." Modern Physics Letters B 26, no. 17 (June 3, 2012): 1250110. http://dx.doi.org/10.1142/s0217984912501102.

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A three-component quasiperiodic superlattice structures composing of both positive and negative refractive index materials are shown to display resonant transport behavior and optical band gaps. When the structure is composed of nondispersive refractive index material, the number of the resonant transmission peaks increases and the optical band gap becomes broad with the increasing of the medium generation. The band gap covers all the wavelength except for some singular wavelength points when the structure is composed of negative refractive index materials. Moreover, it is found that the spectrum shifts to low frequency for oblique incidence. And with the increasing of the optical thickness, the band gap splits and new perfect transport channels emerge. For a more realistic dispersive negative refractive index material, the transmission coefficients are characterized by a rich transmission profile without symmetry, more wide band gaps and abundance transmissive channels appear.

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Lamb, Kevin, and Patrick Weed. "A distance for circular Heegaard splittings." Journal of Knot Theory and Its Ramifications 28, no. 09 (August 2019): 1950059. http://dx.doi.org/10.1142/s0218216519500597.

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For a knot [Formula: see text], its exterior [Formula: see text] has a singular foliation by Seifert surfaces of [Formula: see text] derived from a circle-valued Morse function [Formula: see text]. When [Formula: see text] is self-indexing and has no critical points of index 0 or 3, the regular levels that separate the index-1 and index-2 critical points decompose [Formula: see text] into a pair of compression bodies. We call such a decomposition a circular Heegaard splitting of [Formula: see text]. We define the notion of circular distance (similar to Hempel distance) for this class of Heegaard splitting and show that it can be bounded under certain circumstances. Specifically, if the circular distance of a circular Heegaard splitting is too large: (1) [Formula: see text] cannot contain low-genus incompressible surfaces, and (2) a minimal-genus Seifert surface for [Formula: see text] is unique up to isotopy.

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Gerovska, Daniela, Marcos J. Araúzo-Bravo, Kathryn Whaler, Petar Stavrev, and Alan Reid. "Three-dimensional interpretation of magnetic and gravity anomalies using the finite-difference similarity transform." GEOPHYSICS 75, no. 4 (July 2010): L79—L90. http://dx.doi.org/10.1190/1.3453765.

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We present an automatic procedure for interpretation of magnetic or gravity gridded anomalies based on the finite-difference similarity transform (FDST). It is called MaGSoundFDST (magnetic and gravity sounding based on the finite-difference similarity transform) and uses a “focusing” principle in contrast to deriving multiple clusters of many solutions as in the widely used Euler deconvolution method. The source parameters are characterized by isolated solutions, and the interpreter obtains parallel images showing the horizontal position, depth, and structural index [Formula: see text] value. The underlying principle is that the FDST of a potential field anomaly becomes zero or linear at all observation points when the central point of similarity (CPS) of the transform coincides with a source field’s singular point and a correct [Formula: see text] value is used. The procedure involves calculating a 3D function that evaluates the linearity of the FDST for a series of [Formula: see text] values, using a moving window and sounding the subsurface along a verticalline under each window center. We then combine the 3D results for different [Formula: see text] values into a single map whose minima determine the horizontal position of the sources. The [Formula: see text] value and the CPS depth associated with each minimum determine the [Formula: see text] value and depth of the corresponding source. Only one estimate characterizes a simple source, which is a major advantage over other window-based procedures. MaGSoundFDST uses only the measured anomalous field and its upward continuation, thus avoiding the direct use of field derivatives. It is independent of the magnetization-vector direction in the magnetic data case. The procedure accounts for a linear background of local gravity or magnetic anomalies and has been applied effectively to several cases of synthetic and real data. MaGSoundFDST shares common features with the magnetic and gravity sounding based on the differential similarity transform (MaGSoundDST) but is more stable in estimating depth and structural index in the presence of random noise.

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Maisto, Maria Antonia, Mehdi Masoodi, Giovanni Leone, Raffaele Solimene, and Rocco Pierri. "Scattered Far-Field Sampling in Multi-Static Multi-Frequency Configuration." Sensors 21, no. 14 (July 10, 2021): 4724. http://dx.doi.org/10.3390/s21144724.

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This paper deals with an inverse scattering problem under a linearized scattering model for a multi-static/multi-frequency configuration. The focus is on the determination of a sampling strategy that allows the reduction of the number of measurement points and frequencies and at the same time keeping the same achievable performance in the reconstructions as for full data acquisition. For the sake of simplicity, a 2D scalar geometry is addressed, and the scattered far-field data are collected. The relevant scattering operator exhibits a singular value spectrum that abruptly decays (i.e., a step-like behavior) beyond a certain index, which identifies the so-called number of degrees of freedom (NDF) of the problem. Accordingly, the sampling strategy is derived by looking for a discrete finite set of data points for which the arising semi-discrete scattering operator approximation can reproduce the most significant part of the singular spectrum, i.e., the singular values preceding the abrupt decay. To this end, the observation variables are suitably transformed so that Fourier-based arguments can be used. The arising sampling grid returns several data that is close to the NDF. Unfortunately, the resulting data points (in the angle-frequency domain) leading to a complicated measurement configuration which requires collecting the data at different spatial positions for each different frequency. To simplify the measurement configuration, a suboptimal sampling strategy is then proposed which, by an iterative procedure, enforces the sampling points to belong to a rectangular grid in the angle-frequency domain. As a result of this procedure, the overall data points (i.e., the couples angle-frequency) actually increase but the number of different angles and frequencies reduce and lead to a measurement configuration that is more practical to implement. A few numerical examples are included to check the proposed sampling scheme.

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