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Journal articles on the topic 'Asymptotic Analysis'

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Published: 4 June 2021
Last updated: 31 August 2024

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1

Delcroix, A., and D. scarpalezos. "Asymptotic scales-asymptotic algebras." Integral Transforms and Special Functions 6, no. 1-4 (March 1998): 181–90. http://dx.doi.org/10.1080/10652469808819162.

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2

Cai, Chun-Hao, Jun-Qi Hu, and Ying-Li Wang. "Asymptotics of Karhunen–Loève Eigenvalues for Sub-Fractional Brownian Motion and Its Application." Fractal and Fractional 5, no. 4 (November 17, 2021): 226. http://dx.doi.org/10.3390/fractalfract5040226.

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In the present paper, the Karhunen–Loève eigenvalues for a sub-fractional Brownian motion are considered. Rigorous large n asymptotics for those eigenvalues are shown, based on the functional analysis method. By virtue of these asymptotics, along with some standard large deviations results, asymptotical estimates for the small L2-ball probabilities for a sub-fractional Brownian motion are derived. Asymptotic analysis on the Karhunen–Loève eigenvalues for the corresponding “derivative” process is also established.
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3

Bunoiu, Renata, Giuseppe Cardone, and Sergey A. Nazarov. "Scalar problems in junctions of rods and a plate." ESAIM: Mathematical Modelling and Numerical Analysis 52, no. 2 (March 2018): 481–508. http://dx.doi.org/10.1051/m2an/2017047.

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In this work we deal with a scalar spectral mixed boundary value problem in a spacial junction of thin rods and a plate. Constructing asymptotics of the eigenvalues, we employ two equipollent asymptotic models posed on the skeleton of the junction, that is, a hybrid domain. We, first, use the technique of self-adjoint extensions and, second, we impose algebraic conditions at the junction points in order to compile a problem in a function space with detached asymptotics. The latter problem is involved into a symmetric generalized Green formula and, therefore, admits the variational formulation. In comparison with a primordial asymptotic procedure, these two models provide much better proximity of the spectra of the problems in the spacial junction and in its skeleton. However, they exhibit the negative spectrum of finite multiplicity and for these “parasitic” eigenvalues we derive asymptotic formulas to demonstrate that they do not belong to the service area of the developed asymptotic models.
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4

Yi, Taishan, Yuming Chen, and Jianhong Wu. "Asymptotic propagations of asymptotical monostable type equations with shifting habitats." Journal of Differential Equations 269, no. 7 (September 2020): 5900–5930. http://dx.doi.org/10.1016/j.jde.2020.04.025.

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5

Chicone, Carmen, and Weishi Liu. "Asymptotic phase revisited." Journal of Differential Equations 204, no. 1 (September 2004): 227–46. http://dx.doi.org/10.1016/j.jde.2004.03.011.

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6

Artstein-Avidan, Shiri, Hermann König, and Alexander Koldobsky. "Asymptotic Geometric Analysis." Oberwolfach Reports 13, no. 1 (2016): 507–65. http://dx.doi.org/10.4171/owr/2016/11.

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7

Wu, Xiao-Bo, Yu Lin, Shuai-Xia Xu, and Yu-Qiu Zhao. "Uniform asymptotics for discrete orthogonal polynomials on infinite nodes with an accumulation point." Analysis and Applications 14, no. 05 (July 27, 2016): 705–37. http://dx.doi.org/10.1142/s0219530515500177.

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In this paper, we develop the Riemann–Hilbert method to study the asymptotics of discrete orthogonal polynomials on infinite nodes with an accumulation point. To illustrate our method, we consider the Tricomi–Carlitz polynomials [Formula: see text] where [Formula: see text] is a positive parameter. Uniform Plancherel–Rotach type asymptotic formulas are obtained in the entire complex plane including a neighborhood of the origin, and our results agree with the ones obtained earlier in [W. M. Y. Goh and J. Wimp, On the asymptotics of the Tricomi–Carlitz polynomials and their zero distribution. I, SIAM J. Math. Anal. 25 (1994) 420–428] and in [K. F. Lee and R. Wong, Uniform asymptotic expansions of the Tricomi–Carlitz polynomials, Proc. Amer. Math. Soc. 138 (2010) 2513–2519].
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8

Lee, K., C. A. Morales, and H. Villavicencio. "Asymptotic expansivity." Journal of Mathematical Analysis and Applications 507, no. 1 (March 2022): 125729. http://dx.doi.org/10.1016/j.jmaa.2021.125729.

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9

Nemes, Gergő. "The resurgence properties of the large-order asymptotics of the Hankel and Bessel functions." Analysis and Applications 12, no. 04 (June 17, 2014): 403–62. http://dx.doi.org/10.1142/s021953051450033x.

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The aim of this paper is to derive new representations for the Hankel and Bessel functions, exploiting the reformulation of the method of steepest descents by Berry and Howls [Hyperasymptotics for integrals with saddles, Proc. R. Soc. Lond. A 434 (1991) 657–675]. Using these representations, we obtain a number of properties of the large-order asymptotic expansions of the Hankel and Bessel functions due to Debye, including explicit and numerically computable error bounds, asymptotics for the late coefficients, exponentially improved asymptotic expansions, and the smooth transition of the Stokes discontinuities.
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10

Storozhuk, K. V. "Asymptotic Rank Theorems." Algebra and Logic 58, no. 4 (September 2019): 337–44. http://dx.doi.org/10.1007/s10469-019-09555-x.

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11

Plociniczak, Lukasz. "ON ASYMPTOTICS OF SOME FRACTIONAL DIFFERENTIAL EQUATIONS." Mathematical Modelling and Analysis 18, no. 3 (June 1, 2013): 358–73. http://dx.doi.org/10.3846/13926292.2013.804888.

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In this paper we study the large-argument asymptotic behaviour of certain fractional differential equations with Caputo derivatives. We obtain exponential and algebraic asymptotic solutions. The latter, decaying asymptotics differ significantly from the integer-order derivative equations. We verify our theorems numerically and find that our formulas are accurate even for small values of the argument. We analyze the zeros of fractional oscillations and find the approximate formulas for their distribution. Our methods can be used in studying many other fractional equations.
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12

YARMUKHAMEDOV, R., and M. K. UBAYDULLAEVA. "ON ASYMPTOTICS OF THREE-BODY BOUND STATE RADIAL WAVE FUNCTIONS OF HALO NUCLEI NEAR THE HYPERANGLE φ~0 AND φ~π/2 IN THE CONFIGURATION SPACE AND THREE-BODY ASYMPTOTIC NORMALIZATION FACTORS FOR 6He NUCLEUS IN THE (n+n+α)-CHANNEL." International Journal of Modern Physics E 18, no. 07 (August 2009): 1561–85. http://dx.doi.org/10.1142/s0218301309013701.

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Asymptotic expressions for the bound state radial partial wave functions of three-body (nnc) halo nuclei with two loosely bound valence neutrons (n) are obtained in explicit form, when the relative distance between two neutrons (r) tends to infinity and the relative distance between the center of mass of core (c) and two neutrons (ρ) is too small or vice versa. These asymptotic expressions contain a factor that can strongly influence the asymptotic values of the three-body radial wave function in the vicinity of the hyperangle of φ~0 except 0 (r→∞ and ρ is too small except 0) or φ~π/2 except π/2 (ρ→∞ and r is too small except 0) in the configuration space. The derived asymptotic forms are applied to the analysis of the asymptotic behavior of the three-body (nnα) wave function for 6He nucleus obtained by other authors on the basis of multicluster stochastic variational method using the two forms of the αN-potential. The ranges of r (or ρ) from the asymptotical regions are determined for which the agreement between the calculated wave function and the asymptotics formulae is reached. Information about the values of the three-body asymptotic normalization factors is extracted.
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13

Ferreira, Chelo, José L. López, and Ester Pérez Sinusía. "Convergent and asymptotic expansions of solutions of second-order differential equations with a large parameter." Analysis and Applications 12, no. 05 (August 28, 2014): 523–36. http://dx.doi.org/10.1142/s0219530514500328.

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We consider the second-order linear differential equation [Formula: see text] where x ∈ [0, X], X > 0, α ∈ (-∞, 2), Λ is a large complex parameter and g is a continuous function. The asymptotic method designed by Olver [Asymptotics and Special Functions (Academic Press, New York, 1974)] gives the Poincaré-type asymptotic expansion of two independent solutions of the equation in inverse powers of Λ. We add initial conditions to the differential equation and consider the corresponding initial value problem. By using the Green's function of an auxiliary problem, we transform the initial value problem into a Volterra integral equation of the second kind. Then using a fixed point theorem, we construct a sequence of functions that converges to the unique solution of the problem. This sequence has also the property of being an asymptotic expansion for large Λ (not of Poincaré-type) of the solution of the problem. Moreover, we show that the idea may be applied also to nonlinear differential equations with a large parameter.
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14

Smarzewski, Ryszard. "Asymptotic Chebyshev centers." Journal of Approximation Theory 59, no. 3 (December 1989): 286–95. http://dx.doi.org/10.1016/0021-9045(89)90093-2.

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15

Kurina, Galina, and Margarita Kalashnikova. "Justification of Direct Scheme for Asymptotic Solving Three-Tempo Linear-Quadratic Control Problems under Weak Nonlinear Perturbations." Axioms 11, no. 11 (November 16, 2022): 647. http://dx.doi.org/10.3390/axioms11110647.

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The paper deals with an application of the direct scheme method, consisting of immediately substituting a postulated asymptotic solution into a problem condition and determining a series of control problems for finding asymptotics terms, for asymptotics construction of a solution of a weakly nonlinearly perturbed linear-quadratic optimal control problem with three-tempo state variables. For the first time, explicit formulas for linear-quadratic optimal control problems, from which all terms of the asymptotic expansion are found, are justified, and the estimates of the proximity between the asymptotic and exact solutions are proved for the control, state trajectory, and minimized functional. Non-increasing of the minimized functional, if a next approximation to the optimal control is used, following from the proposed algorithm of the asymptotics construction, is also established.
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16

Alber, H. D., and A. G. Ramm. "Inverse scattering: asymptotic analysis." Inverse Problems 2, no. 4 (November 1, 1986): L43—L46. http://dx.doi.org/10.1088/0266-5611/2/4/001.

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17

Krichagina, E. V. "Asymptotic analysis of queueingnetworks." Stochastics and Stochastic Reports 40, no. 1-2 (August 1992): 43–76. http://dx.doi.org/10.1080/17442509208833781.

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18

Džurina, Jozef, and Vincent Šoltés. "Asymptotic analysis of ODEs." Journal of Computational and Applied Mathematics 67, no. 2 (March 1996): 301–7. http://dx.doi.org/10.1016/0377-0427(94)00130-8.

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19

Kirk, W. A., and Hong-Kun Xu. "Asymptotic pointwise contractions." Nonlinear Analysis: Theory, Methods & Applications 69, no. 12 (December 2008): 4706–12. http://dx.doi.org/10.1016/j.na.2007.11.023.

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20

Durán, A. L., R. Estrada, and R. P. Kanwal. "Pre-asymptotic Expansions." Journal of Mathematical Analysis and Applications 202, no. 2 (September 1996): 470–84. http://dx.doi.org/10.1006/jmaa.1996.0328.

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21

Hovhannisyan, Gro. "Asymptotic stability and asymptotic solutions of second-order differential equations." Journal of Mathematical Analysis and Applications 327, no. 1 (March 2007): 47–62. http://dx.doi.org/10.1016/j.jmaa.2006.03.076.

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22

Jones, D. S. "Asymptotic Remainders." SIAM Journal on Mathematical Analysis 25, no. 2 (March 1994): 474–90. http://dx.doi.org/10.1137/s0036141092228684.

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23

Cook, Nicholas John. "Reliability of Extreme Wind Speeds Predicted by Extreme-Value Analysis." Meteorology 2, no. 3 (July 31, 2023): 344–67. http://dx.doi.org/10.3390/meteorology2030021.

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The reliability of extreme wind speed predictions at large mean recurrence intervals (MRI) is assessed by bootstrapping samples from representative known distributions. The classical asymptotic generalized extreme value distribution (GEV) and the generalized Pareto (GPD) distribution are compared with a contemporary sub-asymptotic Gumbel distribution that accounts for incomplete convergence to the correct asymptote. The sub-asymptotic model is implemented through a modified Gringorten method for epoch maxima and through the XIMIS method for peak-over-threshold values. The mean bias error is shown to be minimal in all cases, so that the variability expressed by the standard error becomes the principal reliability metric. Peak-over-threshold (POT) methods are shown to always be more reliable than epoch methods due to the additional sub-epoch data. The generalized asymptotic methods are shown to always be less reliable than the sub-asymptotic methods by a factor that increases with MRI. This study reinforces the previously published theory-based arguments that GEV and GPD are unsuitable models for extreme wind speeds by showing that they also provide the least reliable predictions in practice. A new two-step Weibull-XIMIS hybrid method is shown to have superior reliability.
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24

Booton, Barry, and Yoram Sagher. "Asymptotic behavior of Hardy operators." Journal of Mathematical Inequalities, no. 3 (2011): 383–400. http://dx.doi.org/10.7153/jmi-05-34.

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25

Motta, M., and F. Rampazzo. "Asymptotic controllability and optimal control." Journal of Differential Equations 254, no. 7 (April 2013): 2744–63. http://dx.doi.org/10.1016/j.jde.2013.01.006.

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26

Picard, Rainer, and Stefan Seidler. "On asymptotic equipartition of energy." Journal of Differential Equations 68, no. 2 (June 1987): 198–209. http://dx.doi.org/10.1016/0022-0396(87)90191-4.

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27

Thomsen, Klaus. "Asymptotic Homomorphisms and EquivariantKK-Theory." Journal of Functional Analysis 163, no. 2 (April 1999): 324–43. http://dx.doi.org/10.1006/jfan.1998.3377.

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28

Simon, Barry. "Ratio asymptotics and weak asymptotic measures for orthogonal polynomials on the real line." Journal of Approximation Theory 126, no. 2 (February 2004): 198–217. http://dx.doi.org/10.1016/j.jat.2003.12.002.

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29

Bostan, Mihai. "Strongly anisotropic diffusion problems; asymptotic analysis." Journal of Differential Equations 256, no. 3 (February 2014): 1043–92. http://dx.doi.org/10.1016/j.jde.2013.10.008.

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30

Nemes, Gergő. "Error bounds and exponential improvement for Hermite's asymptotic expansion for the Gamma function." Applicable Analysis and Discrete Mathematics 7, no. 1 (2013): 161–79. http://dx.doi.org/10.2298/aadm130124002n.

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In this paper we reconsider the asymptotic expansion of the Gamma function with shifted argument, which is the generalization of the well-known Stirling series. To our knowledge, no explicit error bounds exist in the literature for this expansion. Therefore, the first aim of this paper is to extend the known error estimates of Stirling?s series to this general case. The second aim is to give exponentially-improved asymptotics for this asymptotic series.
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31

Hwang, Hsien-Kuei, Alois Panholzer, Nicolas Rolin, Tsung-Hsi Tsai, and Wei-Mei Chen. "Probabilistic Analysis of the (1+1)-Evolutionary Algorithm." Evolutionary Computation 26, no. 2 (June 2018): 299–345. http://dx.doi.org/10.1162/evco_a_00212.

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We give a detailed analysis of the optimization time of the [Formula: see text]-Evolutionary Algorithm under two simple fitness functions (OneMax and LeadingOnes). The problem has been approached in the evolutionary algorithm literature in various ways and with different degrees of rigor. Our asymptotic approximations for the mean and the variance represent the strongest of their kind. The approach we develop is based on an asymptotic resolution of the underlying recurrences and can also be extended to characterize the corresponding limiting distributions. While most of our approximations can be derived by simple heuristic calculations based on the idea of matched asymptotics, the rigorous justifications are challenging and require a delicate error analysis.
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32

Zhang, Xing, Zhitao Li, and Lixin Gao. "Stability analysis of a SAIR epidemic model on scale-free community networks." Mathematical Biosciences and Engineering 21, no. 3 (2024): 4648–68. http://dx.doi.org/10.3934/mbe.2024204.

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<abstract><p>The presence of asymptomatic carriers, often unrecognized as infectious disease vectors, complicates epidemic management, particularly when inter-community migrations are involved. We introduced a SAIR (susceptible-asymptomatic-infected-recovered) infectious disease model within a network framework to explore the dynamics of disease transmission amid asymptomatic carriers. This model facilitated an in-depth analysis of outbreak control strategies in scenarios with active community migrations. Key contributions included determining the basic reproduction number, $ R_0 $, and analyzing two equilibrium states. Local asymptotic stability of the disease-free equilibrium is confirmed through characteristic equation analysis, while its global asymptotic stability is investigated using the decomposition theorem. Additionally, the global stability of the endemic equilibrium is established using the Lyapunov functional theory.</p></abstract>
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33

Lyashko, S. I., V. H. Samoilenko, Yu I. Samoilenko, and N. I. Lyashko. "Asymptotic analysis of the Korteweg-de Vries equation by the nonlinear WKB technique." Mathematical Modeling and Computing 8, no. 3 (2021): 368–78. http://dx.doi.org/10.23939/mmc2021.03.368.

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The paper deals with the Korteweg-de Vries equation with variable coefficients and a small parameter at the highest derivative. The non-linear WKB technique has been used to construct the asymptotic step-like solution to the equation. Such a solution contains regular and singular parts of the asymptotics. The regular part of the solution describes the background of the wave process, while its singular part reflects specific features associated with soliton properties. The singular part of the searched asymp\-totic solution has the main term that, like the soliton solution, is the quickly decreasing function of the phase variable $\tau$. In contrast, other terms do not possess this property. An algorithm of constructing asymptotic step-like solutions to the singularly perturbed Korteweg--de Vries equation with variable coefficients is presented. In some sense, the constructed asymptotic solution is similar to the soliton solution to the Korteweg-de Vries equation $u_t+uu_x+u_{xxx}=0$. Statement on the accuracy of the main term of the asymptotic solution is proven.
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34

Chowdhury, Indranil, and Prosenjit Roy. "On the asymptotic analysis of problems involving fractional Laplacian in cylindrical domains tending to infinity." Communications in Contemporary Mathematics 19, no. 05 (May 13, 2016): 1650035. http://dx.doi.org/10.1142/s0219199716500358.

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The paper is an attempt to investigate the issues of asymptotic analysis for problems involving fractional Laplacian where the domains tend to become unbounded in one-direction. Motivated from the pioneering work on second-order elliptic problems by Chipot and Rougirel in [On the asymptotic behaviour of the solution of elliptic problems in cylindrical domains becoming unbounded, Commun. Contemp. Math. 4(1) (2002) 15–44], where the force functions are considered on the cross-section of domains, we prove the non-local counterpart of their result.Recently in [Asymptotic behavior of elliptic nonlocal equations set in cylinders, Asymptot. Anal. 89(1–2) (2014) 21–35] Yeressian established a weighted estimate for solutions of non-local Dirichlet problems which exhibit the asymptotic behavior. The case when [Formula: see text] was also treated as an example to show how the weighted estimate might be used to achieve the asymptotic behavior. In this paper, we extend this result to each order between [Formula: see text] and [Formula: see text].
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35

Berthon, Christophe, and Rodolphe Turpault. "Asymptotic preserving HLL schemes." Numerical Methods for Partial Differential Equations 27, no. 6 (August 4, 2010): 1396–422. http://dx.doi.org/10.1002/num.20586.

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36

Gromak, Elena V., and Anatoly A. Kilbas. "Asymptotic expansions of 𝒴ηtransform." Integral Transforms and Special Functions 16, no. 5-6 (July 2005): 407–14. http://dx.doi.org/10.1080/10652460412331320386.

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37

Jung, Soon-Mo. "Asymptotic properties of isometries." Journal of Mathematical Analysis and Applications 276, no. 2 (December 2002): 642–53. http://dx.doi.org/10.1016/s0022-247x(02)00399-2.

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38

Fakhari, Abbas, C. A. Morales, and Khosro Tajbakhsh. "Asymptotic measure expansive diffeomorphisms." Journal of Mathematical Analysis and Applications 435, no. 2 (March 2016): 1682–87. http://dx.doi.org/10.1016/j.jmaa.2015.11.042.

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39

Jachymski, Jacek, and Izabela Jóźwik. "On Kirk's asymptotic contractions." Journal of Mathematical Analysis and Applications 300, no. 1 (December 2004): 147–59. http://dx.doi.org/10.1016/j.jmaa.2004.06.037.

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40

Estrada, R., and R. P. Kanwal. "Asymptotic Separation of Variables." Journal of Mathematical Analysis and Applications 178, no. 1 (September 1993): 130–42. http://dx.doi.org/10.1006/jmaa.1993.1296.

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41

Hinton, D. B., M. Klaus, and J. K. Shaw. "Asymptotic phase, asymptotic modulus, and Titchmarsh-Weyl coefficient for a Dirac system." Journal of Mathematical Analysis and Applications 142, no. 1 (August 1989): 108–29. http://dx.doi.org/10.1016/0022-247x(89)90169-8.

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42

Chen, Chao-Ping, and H. M. Srivastava. "Complete asymptotic expansions related to the probability density function of the χ2-distribution." Applicable Analysis and Discrete Mathematics, no. 00 (2022): 15. http://dx.doi.org/10.2298/aadm210720015c.

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In this paper, we consider the function fp(t) = ? 2p?2(?2pt + p;p), where ?2(x;n) defined by ?2(x;p) = 2?p/2/?(p/2) e?x/2xp/2?1, is the density function of a ?2-distribution with n degrees of freedom. The asymptotic expansion of fp(t) for p ? ?, where p is not necessarily an integer, is obtained by an application of the standard asymptotics of ln ?(x). Two different methods of obtaining the coefficients in the asymptotic expansion are presented, which involve the use of the Bell polynomials.
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43

Saavedra, Mariana. "Asymptotic expansion of the period function." Journal of Differential Equations 193, no. 2 (September 2003): 359–73. http://dx.doi.org/10.1016/s0022-0396(03)00091-3.

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44

Murdock, James, and David Malonza. "An improved theory of asymptotic unfoldings." Journal of Differential Equations 247, no. 3 (August 2009): 685–709. http://dx.doi.org/10.1016/j.jde.2009.04.014.

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45

Arrieta, José M., Rosa Pardo, and Aníbal Rodríguez-Bernal. "Asymptotic behavior of degenerate logistic equations." Journal of Differential Equations 259, no. 11 (December 2015): 6368–98. http://dx.doi.org/10.1016/j.jde.2015.07.028.

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46

Mosco, U. "Composite Media and Asymptotic Dirichlet Forms." Journal of Functional Analysis 123, no. 2 (August 1994): 368–421. http://dx.doi.org/10.1006/jfan.1994.1093.

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47

Beltita, Daniel, and Mihai Sabac. "An Asymptotic Formula for the Commutators." Journal of Functional Analysis 153, no. 2 (March 1998): 262–75. http://dx.doi.org/10.1006/jfan.1997.3212.

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48

Clarke, F. H., Yu S. Ledyaev, and R. J. Stern. "Asymptotic Stability and Smooth Lyapunov Functions." Journal of Differential Equations 149, no. 1 (October 1998): 69–114. http://dx.doi.org/10.1006/jdeq.1998.3476.

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49

Lin, Xin, and Chang in Deng. "Asymptotic expansion for generalized Mathieu series." Journal of Mathematical Inequalities, no. 3 (2023): 1113–27. http://dx.doi.org/10.7153/jmi-2023-17-72.

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50

Esham, Jr., Benjamin F. "Asymptotics and an Asymptotic Galerkin Method for Hyperbolic-Parabolic Singular Perturbation Problems." SIAM Journal on Mathematical Analysis 18, no. 3 (May 1987): 762–76. http://dx.doi.org/10.1137/0518058.

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