Journal articles: 'Spectrum stability'

1

Upsal, Jeremy, and Bernard Deconinck. "Real Lax spectrum implies spectral stability." Studies in Applied Mathematics 145, no. 4 (September 3, 2020): 765–90. http://dx.doi.org/10.1111/sapm.12335.

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2

Bermúdez, Teresa, Manuel González, and Antonio Martinón. "Stability of the local spectrum." Proceedings of the American Mathematical Society 125, no. 2 (1997): 417–25. http://dx.doi.org/10.1090/s0002-9939-97-03477-1.

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3

Grossberg, Rami, and Olivier Lessmann. "Shelah's stability spectrum and homogeneity spectrum in finite diagrams." Archive for Mathematical Logic 41, no. 1 (January 1, 2002): 1–31. http://dx.doi.org/10.1007/s001530200000.

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4

Hu, Yuan, Mei-ling Yu, and Lian-shou Liu. "Levy Stability Index from Multifractal Spectrum." Chinese Physics Letters 16, no. 8 (August 1, 1999): 553–54. http://dx.doi.org/10.1088/0256-307x/16/8/003.

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5

Hou, Ting, Weihai Zhang, and Hongji Ma. "Spectral Perspective on the Stability of Discrete-Time Markov Jump Systems with Multiplicative Noise." Mathematical Problems in Engineering 2014 (2014): 1–6. http://dx.doi.org/10.1155/2014/769302.

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We apply the spectrum analysis approach to address the stability of discrete-time Markov jump systems with state-multiplicative noise. In terms of the spectral distribution of a generalized Lyapunov operator, spectral criteria are presented to testify three different kinds of stochastic stabilities: asymptotic mean square stability, critical stability, and essential instability.

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Nicholls, David P. "Spectral Stability of Traveling Water Waves: Analytic Dependence of the Spectrum." Journal of Nonlinear Science 17, no. 4 (June 11, 2007): 369–97. http://dx.doi.org/10.1007/s00332-006-0808-8.

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7

Koch, Wolfram. "Structure, stability, and vibrational spectrum of HCNKrF+." Journal of the Chemical Society, Chemical Communications, no. 4 (1989): 215. http://dx.doi.org/10.1039/c39890000215.

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Andersen, Odd Jan, and Jørgen Løvseth. "Stability modifications of the Frøya wind spectrum." Journal of Wind Engineering and Industrial Aerodynamics 98, no. 4-5 (April 2010): 236–42. http://dx.doi.org/10.1016/j.jweia.2009.10.019.

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9

Kuzmany, H., W. Plank, J. Winter, O. Dubay, N. Tagmatarchis, and K. Prassides. "Raman spectrum and stability of(C59N)2." Physical Review B 60, no. 2 (July 1, 1999): 1005–12. http://dx.doi.org/10.1103/physrevb.60.1005.

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Banshchikova, I. N. "Local assignability of Lyapunov exponents of linear discrete-time system." Izvestiya Instituta Matematiki i Informatiki Udmurtskogo Gosudarstvennogo Universiteta 57 (May 2021): 3–76. http://dx.doi.org/10.35634/2226-3594-2021-57-01.

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We consider sufficient and necessary conditions for the proportional local assignability of the Lyapunov spectrum of the system $$x(m+1)=\left(A(m)+B(m)U(m)\right)x(m), \quad m\in\mathbb Z,\quad x\in\mathbb R^n.$$ The properties of stability of the Lyapunov spectrum and integral separation of linear discrete-time systems are studied, description of the spectral set of a linear system in the case of the full spectrum stability is obtained, the property of uniform complete controllability of a linear system with discrete time is studied, and the properties of the Bebutov shell of a linear discrete-time control system are investigated.

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11

Charalampidis, Efstathios G., Ross Parker, Panayotis G. Kevrekidis, and Stéphane Lafortune. "The stability of the b-family of peakon equations." Nonlinearity 36, no. 2 (January 10, 2023): 1192–217. http://dx.doi.org/10.1088/1361-6544/acac5b.

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Abstract In the present work we revisit the b-family model of peakon equations, containing as special cases the b = 2 (Camassa–Holm) and b = 3 (Degasperis–Procesi) integrable examples. We establish information about the point spectrum of the peakon solutions and notably find that for suitably smooth perturbations there exists point spectrum in the right half plane rendering the peakons unstable for b < 1. We explore numerically these ideas in the realm of fixed-point iterations, spectral stability analysis and time-stepping of the model for the different parameter regimes. In particular, we identify exact, stationary (spectrally stable) lefton solutions for b < − 1 , and for − 1 < b < 1 , we dynamically identify ramp-cliff solutions as dominant states in this regime. We complement our analysis by examining the breakup of smooth initial data into stable peakons for b > 1. While many of the above dynamical features had been explored in earlier studies, in the present work, we supplement them, wherever possible, with spectral stability computations.

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12

BOGENSCHÜTZ, THOMAS. "Stochastic stability of invariant subspaces." Ergodic Theory and Dynamical Systems 20, no. 3 (June 2000): 663–80. http://dx.doi.org/10.1017/s0143385700000353.

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We prove that a relevant part of the Lyapunov spectrum and the corresponding Oseledets spaces of a quasi-compact linear cocycle are stable under a certain type of random perturbation. The basic approach is a graph-transform argument. The result applies to the spectrum of (not necessarily i.i.d.) randomly perturbed expanding maps and yields generalizations of results recently obtained by Baladi, Kondah and Schmitt [5] with different methods.

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Ammar, Aymen, Mohammed Dhahri, and Aref Jeribi. "Stability of essential approximate point spectrum and essential defect spectrum of linear operator." Filomat 29, no. 9 (2015): 1983–94. http://dx.doi.org/10.2298/fil1509983a.

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In the present paper, we use the notion of measure of noncompactness to give some results on Fredholm operators and we establish a fine description of the essential approximate point spectrum and the essential defect spectrum of a closed densely defined linear operator.

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14

Li, Jing, Wenjiang Tan, Jinhai Si, Zhen Kang, and Xun Hou. "Generation of Ultrabroad and Intense Supercontinuum in Mixed Multiple Thin Plates." Photonics 8, no. 8 (August 3, 2021): 311. http://dx.doi.org/10.3390/photonics8080311.

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Supercontinuum (SC) generation using multiple thin plates is demonstrated with a femtosecond laser pulse. We propose an improved technique to obtain larger spectrum broadening and higher spectral intensity by employing mixed multiple thin plates with different thicknesses and materials. Furthermore, the spectrum has good stability, which is superior to that of the spectrum induced by the traditional single filament in bulk material. Our approach offers a route towards simple and stable SC generation for potential applications.

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15

Koverda, V., and V. Skokov. "Stability of Random Processes with 1/fa Spectrum." Доклады академии наук 483, no. 1 (November 2018): 29–32. http://dx.doi.org/10.31857/s086956520003405-8.

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16

Molloy, Cynthia A., Kim N. Dietrich, and Amit Bhattacharya. "Postural Stability in Children with Autism Spectrum Disorder." Journal of Autism and Developmental Disorders 33, no. 6 (December 2003): 643–52. http://dx.doi.org/10.1023/b:jadd.0000006001.00667.4c.

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17

Smith, S. P., and S. C. Jardin. "Ideal magnetohydrodynamics stability spectrum with a resistive wall." Physics of Plasmas 15, no. 8 (August 2008): 080701. http://dx.doi.org/10.1063/1.2965499.

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18

Matson, Johnny L., and Max Horovitz. "Stability of Autism Spectrum Disorders Symptoms over Time." Journal of Developmental and Physical Disabilities 22, no. 4 (February 20, 2010): 331–42. http://dx.doi.org/10.1007/s10882-010-9188-y.

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19

Yoo, Jong-Kwang, and Hyuk Han. "ON THE STABILITY OF THE LOCALIZABLE SPECTRUM II." Far East Journal of Mathematical Sciences (FJMS) 98, no. 3 (September 4, 2015): 267–80. http://dx.doi.org/10.17654/fjmsoct2015_267_280.

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20

BALDWIN, JOHN T., and SAHARON SHELAH. "THE STABILITY SPECTRUM FOR CLASSES OF ATOMIC MODELS." Journal of Mathematical Logic 12, no. 01 (June 2012): 1250001. http://dx.doi.org/10.1142/s0219061312500018.

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We prove two results on the stability spectrum for Lω1,ω. Here [Formula: see text] denotes an appropriate notion (at or mod) of Stone space of m-types over M. (1) Theorem for unstable case: Suppose that for some positive integer m and for every α < δ(T), there is an M ∈ K with [Formula: see text]. Then for every λ ≥ |T|, there is an M with [Formula: see text]. (2) Theorem for strictly stable case: Suppose that for every α < δ (T), there is Mα ∈ K such that λα = |Mα| ≥ ℶα and [Formula: see text]. Then for any μ with μℵ0 > μ, K is not i-stable in μ. These results provide a new kind of sufficient condition for the unstable case and shed some light on the spectrum of strictly stable theories in this context. The methods avoid the use of compactness in the theory under study. In this paper, we expound the construction of tree indiscernibles for sentences of Lω1,ω. Further we provide some context for a number of variants on the Ehrenfeucht–Mostowski construction.

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21

Guirgis, G. A., T. S. Little, H. M. Badawi, and J. R. Durig. "Microwave spectrum and conformational stability of isopropyl carboxaldehyde." Journal of Molecular Structure 142 (March 1986): 93–96. http://dx.doi.org/10.1016/0022-2860(86)85071-2.

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22

Lifschitz, A. "Essential spectrum and local stability condition in hydrodynamics." Physics Letters A 152, no. 3-4 (January 1991): 199–204. http://dx.doi.org/10.1016/0375-9601(91)91092-r.

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23

Anbo, Yuki, and Koichiro Ikeda. "A note on stability spectrum of generic structures." Mathematical Logic Quarterly 56, no. 3 (May 19, 2010): 257–61. http://dx.doi.org/10.1002/malq.200810051.

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24

Moonsuwan, Sawitree, Gul Rahmat, Atta Ullah, Muhammad Yasin Khan, Kamran, and Kamal Shah. "Hyers–Ulam Stability, Exponential Stability, and Relative Controllability of Non-Singular Delay Difference Equations." Complexity 2022 (October 18, 2022): 1–19. http://dx.doi.org/10.1155/2022/8911621.

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In this paper, we study the uniqueness and existence of the solutions of four types of non-singular delay difference equations by using the Banach contraction principles, fixed point theory, and Gronwall’s inequality. Furthermore, we discussed the Hyers–Ulam stability of all the given systems over bounded and unbounded discrete intervals. The exponential stability and controllability of some of the given systems are also characterized in terms of spectrum of a matrix concerning the system. The spectrum of a matrix can be easily obtained and can help us to characterize different types of stabilities of the given systems. At the end, few examples are provided to illustrate the theoretical results.

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25

Li, Gang, and Ming Chen. "The Stability and Stabilization of Stochastic Delay-Time Systems." Mathematical Problems in Engineering 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/272745.

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The aim of this paper is to investigate the stability and the stabilizability of stochastic time-delay deference system. To do this, we use mainly two methods to give a list of the necessary and sufficient conditions for the stability and stabilizability of the stochastic time-delay deference system. One way is in term of the operator spectrum andH-representation; the other is by Lyapunov equation approach. In addition, we introduce the notion of unremovable spectrum of stochastic time-delay deference system, describe the PBH criterion of the unremovable spectrum of time-delay system, and investigate the relation between the unremovable spectrum and the stabilizability of stochastic time-delay deference system.

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26

Jean Marc, Bomisso G., Tour\'{e} K. Augustin, and Yoro Gozo. "Stabilization of Variable Coefficients Euler-Bernoulli Beam with Viscous Damping under a Force Control in Rotation and Velocity Rotation." Journal of Mathematics Research 9, no. 6 (October 2, 2017): 1. http://dx.doi.org/10.5539/jmr.v9n6p1.

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This paper investigates the problem of exponential stability for a damped Euler-Bernoulli beam with variable coefficients clamped at one end and subjected to a force control in rotation and velocity rotation. We adopt the Riesz basis approach for show that the closed-loop system is a Riesz spectral system. Therefore, the exponential stability and the spectrum-determined growth condition are obtained.

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27

Sandstede, B., and A. Scheel. "Spectral stability of modulated travelling waves bifurcating near essential instabilities." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 130, no. 2 (April 2000): 419–48. http://dx.doi.org/10.1017/s0308210500000238.

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Localized travelling waves to reaction-diffusion systems on the real line are investigated. The issue addressed in this work is the transition to instability which arises when the essential spectrum crosses the imaginary-axis. In the first part of this work, it has been shown that large modulated pulses bifurcate near the onset of instability; they are a superposition of the primary pulse with spatially periodic Turing patterns of small amplitude. The bifurcating modulated pulses can be parametrized by the wavelength of the Turing patterns. Furthermore, they are time periodic in a moving frame. In the second part, spectral stability of the bifurcating modulated pulses is addressed. It is shown that the modulated pulses are spectrally stable if and only if the small Turing patterns are spectrally stable, that is, if their continuous spectrum only touches the imaginary-axis at zero. This requires an investigation of the period map associated with the time-periodic modulated pulses.

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28

Bronski, Jared C., Vera Mikyoung Hur, and Samuel Lee Wester. "Superharmonic instability for regularized long-wave models*." Nonlinearity 36, no. 1 (November 25, 2022): 133–70. http://dx.doi.org/10.1088/1361-6544/ac81ae.

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Abstract We examine the spectral stability and instability of periodic traveling waves for regularized long-wave models. Examples include the regularized Boussinesq, Benney–Luke, and Benjamin–Bona–Mahony equations. Of particular interest is a striking new instability phenomenon—spectrum off the imaginary axis extending into infinity. The spectrum of the linearized operator of the generalized Korteweg–de Vries equation, for instance, lies along the imaginary axis outside a bounded set. The spectrum for a regularized long-wave model, by contrast, can vary markedly with the parameters of the periodic traveling waves. We perform rigorous spectral asymptotics for short wavelength perturbations to establish conditions under which the spectrum tends to infinity along the imaginary axis or some curve whose real part is nonzero. We conduct numerical experiments which corroborate our analytical findings.

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Engelborghs, Koen, Dirk Roose, and Tatyana Luzyanina. "Bifurcation Analysis of Periodic Solutions of Neural Functional Differential Equations: A Case Study." International Journal of Bifurcation and Chaos 08, no. 10 (October 1998): 1889–905. http://dx.doi.org/10.1142/s0218127498001595.

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This paper deals with the numerical bifurction analysis of periodic solutions of a system of neutral functional differential equations (NFDEs). Compared with retarded functional differential equations, the solution operator of a system of NFDEs does not smooth the initial data as time increases and it is no longer a compact operator. The stability of a periodic solution is determined both by the point spectrum and by the essential spectrum of the Poincaré operator. We show that a periodic solution can change its stability not only by means of a "normal" bifurcation but also when the essential spectrum crosses the unit circle. In order to monitor the essential spectrum during continuation, we derive an upper bound on its spectral radius. The upper bound remains valid even at points where the radius of the essetial spectrum is noncontinuous. This can occur when the delay and the period are rationally dependent. Our numerical results present these new dynamical phenomena and we state a number of open questions. Although we restrict our discussion to a specific example, we strongly believe that the issues we discuss are representative for a general class of NFDEs.

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VILA, J., R. MACIÀ, R. SLEEMAN, and A. M. CORREIG. "ON THE STABILITY OF THE EARTH'S FLUCTUATIONS SPECTRAL PEAKS AT THEIR LOWEST AMPLITUDE LEVEL." Fluctuation and Noise Letters 08, no. 03n04 (December 2008): L237—L248. http://dx.doi.org/10.1142/s021947750800501x.

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We studied Earth's fluctuations at its lowest level of excitation, in an attempt to gain insight into the underlying features of such activity. We used a set of 42 worldwide broadband seismic stations that were individually analyzed for at least one year in successive 30-minute windows. The power spectrum of each window was computed and, for each station, the series of spectra were sequentially compared and the frequency bin of lowest amplitude was selected. This resulting "pseudo" spectrum contains the minimum contribution of signal that is present in all 30-minute windows (minimum amplitude for each frequency component). We refer to this "pseudo" spectrum as the Base Level Noise Seismic Spectrum. By comparing the minimum spectra at different stations, we find that for continental stations all spectra coalesce to a common shape and amplitude. This feature is notable for the northern hemisphere stations. Continental stations in the southern hemisphere share the same shape and predominant peaks as those of the northern hemisphere, but with higher amplitude. Stations at oceanic or continental margin sites differ slightly from continental stations, presenting strong fluctuations but sharing the same spectral peaks. These results confirms our previous findings that microseism activity at its lowest level can be interpreted as the resonant response of the Earth.

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31

Khan, Arham Amin, Tony Liang, Armani Batista, and Joseph Kuehl. "On Energy Redistribution for the Nonlinear Parabolized Stability Equations Method." Fluids 7, no. 8 (August 3, 2022): 264. http://dx.doi.org/10.3390/fluids7080264.

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We identify and quantify a seemingly overlook mechanism for energy transfer between adjacent frequency disturbances in the Nonlinear Parabolized Stability Equations method. Physically, this energy transfer results from the finite-bandwidth nature of actual disturbance spectrums versus the common numerical assumption of a discrete spectrum representation. Both quiet wind tunnel and flight conditions are considered and it is found that, for Mack’s second-mode instability, the mechanism is most significant in the 0.1–1% disturbance amplitude range (based on normalized pressure) and is responsible for a 15–30% increase in predicted disturbance amplitude.

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32

NIJBOER, R. J., A. E. LIFSCHITZ, and J. P. GOEDBLOED. "Spectrum and stability of a rigidly rotating compressible plasma." Journal of Plasma Physics 58, no. 1 (July 1997): 101–21. http://dx.doi.org/10.1017/s0022377897005862.

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We consider the spectrum and stability of a compressible, rigidly rotating plasma column with constant magnetic pitch. It is found that when the pressure on axis is zero, a continuous spectrum arises, which may become unstable. When the pressure on axis is finite or a conducting core is included, the spectrum is discrete, but may still be unstable. The instability is due to the poloidal magnetic field and/or the rotation of the cylinder in combination with the density profile. It is found numerically that the pressure stabilizes both types of instabilities.

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Guo, Jun Ying, Rong Ji Li, and Xu Zhen Zhang. "Analysis on Influence of Earthquake Motion to Loess Slope Stability." Advanced Materials Research 243-249 (May 2011): 5157–60. http://dx.doi.org/10.4028/www.scientific.net/amr.243-249.5157.

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Selected the typical loess landslide to analyze and calculate, adoption of elastic-plastic dynamic FEM and Drucker-Prager yield criterion, using Earthquake motion time-histories as the seismic input will be based on the fitting of , class standard response spectrum curve in the current seismic resistance design code. From the analysis of loess slope deformation and breach at different peak acceleration, spectral and duration, it shows the dynamic response and change rule of soil under earthquake effect.

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34

Beneddine, Samir, Denis Sipp, Anthony Arnault, Julien Dandois, and Lutz Lesshafft. "Conditions for validity of mean flow stability analysis." Journal of Fluid Mechanics 798 (June 6, 2016): 485–504. http://dx.doi.org/10.1017/jfm.2016.331.

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This article provides theoretical conditions for the use and meaning of a stability analysis around a mean flow. As such, it may be considered as an extension of the works by McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382) to non-parallel flows and by Turton et al. (Phys. Rev. E, vol. 91 (4), 2015, 043009) to broadband flows. Considering a Reynolds decomposition of the flow field, the spectral (or temporal Fourier) mode of the fluctuation field is found to be equal to the action on a turbulent forcing term by the resolvent operator arising from linearisation about the mean flow. The main result of the article states that if, at a particular frequency, the dominant singular value of the resolvent is much larger than all others and if the turbulent forcing at this frequency does not display any preferential direction toward one of the suboptimal forcings, then the spectral mode is directly proportional to the dominant optimal response mode of the resolvent at this frequency. Such conditions are generally met in the case of weakly non-parallel open flows exhibiting a convectively unstable mean flow. The spatial structure of the singular mode may in these cases be approximated by a local spatial stability analysis based on parabolised stability equations (PSE). We have also shown that the frequency spectrum of the flow field at any arbitrary location of the domain may be predicted from the frequency evolution of the dominant optimal response mode and the knowledge of the frequency spectrum at one or more points. Results are illustrated in the case of a high Reynolds number turbulent backward facing step flow.

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35

Fox, Jeremy T., and Patrick Bajari. "Measuring the Efficiency of an FCC Spectrum Auction." American Economic Journal: Microeconomics 5, no. 1 (February 1, 2013): 100–146. http://dx.doi.org/10.1257/mic.5.1.100.

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We propose a method to structurally estimate the deterministic component of bidder valuations in FCC spectrum auctions, and apply it to the 1995–1996 C block auction. We base estimation on a pairwise stability condition: two bidders cannot exchange two licenses in a way that increases the sum of their valuations. Pairwise stability holds in some theoretical models of simultaneous ascending auctions under intimidatory collusion and demand reduction. Pairwise stability results in a matching game approach to estimation. We find that a system of four large regional licenses would raise the allocative efficiency of the C block outcome by 48 percent. (JEL D44, D45, H82, L82)

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Wang, Yitu, Wei Wang, Vincent K. N. Lau, Lin Chen, and Zhaoyang Zhang. "Heterogeneous Spectrum Aggregation: Coexistence From a Queue Stability Perspective." IEEE Transactions on Wireless Communications 17, no. 4 (April 2018): 2471–85. http://dx.doi.org/10.1109/twc.2018.2796576.

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37

Godunov, S. K. "Spectrum dichotomy and a stability criterion for sectorial operators." Siberian Mathematical Journal 36, no. 6 (November 1995): 1152–58. http://dx.doi.org/10.1007/bf02106837.

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38

Poirel, Laurent, Nicolas Kieffer, and Patrice Nordmann. "Stability of cefiderocol against clinically significant broad-spectrum oxacillinases." International Journal of Antimicrobial Agents 52, no. 6 (December 2018): 866–67. http://dx.doi.org/10.1016/j.ijantimicag.2018.11.005.

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39

Sadeghi, R., S. Gh Etemad, E. Keshavarzi, and M. Haghshenasfard. "Investigation of alumina nanofluid stability by UV–vis spectrum." Microfluidics and Nanofluidics 18, no. 5-6 (September 30, 2014): 1023–30. http://dx.doi.org/10.1007/s10404-014-1491-y.

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40

Tho Nguyen, Minh. "Structure, stability and vibrational spectrum of the fluoroformate anion." Journal of Molecular Structure: THEOCHEM 133 (November 1985): 269–76. http://dx.doi.org/10.1016/0166-1280(85)85024-7.

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41

Liu, Hai Ming, Xiaxin Tao, and Li Yuan Wang. "The Stability of Ground Motions Randomly Synthesized for an Engineering Site." Applied Mechanics and Materials 477-478 (December 2013): 1069–74. http://dx.doi.org/10.4028/www.scientific.net/amm.477-478.1069.

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The ground motions at two rock stations where motions were recorded during the great Wenchuan earthquae are randomly synthsized for 10 times. The mean response spectrum and mean PGA of each synthesis and the general mean spectrum and PGA after each synthesis are calculated. The result shows the fact that the general mean spectrum after 10 syntheses, and the general mean PGA could be improved just a little. It means that it is not necessary to synthsize ground motion many times for an engineering site in practice, if the mean spectrum and PG are taken from the syntheses by 30 source models.

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42

Tan, Chao, Li Fang, and Xue Bai. "CS Optical Pumping Magnetic Sensor Spectrum Lamp Drive Circuit Design Based on PI Feedback Controller." Applied Mechanics and Materials 568-570 (June 2014): 473–77. http://dx.doi.org/10.4028/www.scientific.net/amm.568-570.473.

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The optical source is one of the key components for the optical pump magnetic field sensor, its spectral width, stability and emission intensity directly related to the sensitivity of the sensor. The CS Spectral Lamp drive signal source was produced by crystal oscillator and amplified by the power controllable RF power amplifier. For achieving the aim of luminous intensity controllable and more stability, the reference controllable analog PI negative feedback control measures were used in the drive circuit. Contrast experimental result show that: the emission intensity of CS spectrum lamp is more stable and less affected by temperature if using the drive circuit which discussed in this paper.

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CHIBA, HAYATO. "A proof of the Kuramoto conjecture for a bifurcation structure of the infinite-dimensional Kuramoto model." Ergodic Theory and Dynamical Systems 35, no. 3 (October 11, 2013): 762–834. http://dx.doi.org/10.1017/etds.2013.68.

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AbstractThe Kuramoto model is a system of ordinary differential equations for describing synchronization phenomena defined as coupled phase oscillators. In this paper, a bifurcation structure of the infinite-dimensional Kuramoto model is investigated. A purpose here is to prove the bifurcation diagram of the model conjectured by Kuramoto in 1984; if the coupling strength $K$ between oscillators, which is a parameter of the system, is smaller than some threshold ${K}_{c} $, the de-synchronous state (trivial steady state) is asymptotically stable, while if $K$ exceeds ${K}_{c} $, a non-trivial stable solution, which corresponds to the synchronization, bifurcates from the de-synchronous state. One of the difficulties in proving the conjecture is that a certain non-selfadjoint linear operator, which defines a linear part of the Kuramoto model, has the continuous spectrum on the imaginary axis. Hence, the standard spectral theory is not applicable to prove a bifurcation as well as the asymptotic stability of the steady state. In this paper, the spectral theory on a space of generalized functions is developed with the aid of a rigged Hilbert space to avoid the continuous spectrum on the imaginary axis. Although the linear operator has an unbounded continuous spectrum on a Hilbert space, it is shown that it admits a spectral decomposition consisting of a countable number of eigenfunctions on a space of generalized functions. The semigroup generated by the linear operator will be estimated with the aid of the spectral theory on a rigged Hilbert space to prove the linear stability of the steady state of the system. The center manifold theory is also developed on a space of generalized functions. It is proved that there exists a finite-dimensional center manifold on a space of generalized functions, while a center manifold on a Hilbert space is of infinite dimension because of the continuous spectrum on the imaginary axis. These results are applied to the stability and bifurcation theory of the Kuramoto model to obtain a bifurcation diagram conjectured by Kuramoto.

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44

Barreira, Luis, and Claudia Valls. "Stability of delay equations." Electronic Journal of Qualitative Theory of Differential Equations, no. 45 (2022): 1–24. http://dx.doi.org/10.14232/ejqtde.2022.1.45.

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For a large class of nonautonomous linear delay equations with distributed delay, we obtain the equivalence of hyperbolicity, with the existence of an exponential dichotomy, and Ulam–Hyers stability. In particular, for linear equations with constant or periodic coefficients and with a simple spectrum these two properties are equivalent. We also show that any linear delay equation with an exponential dichotomy and its sufficiently small Lipschitz perturbations are Ulam–Hyers stable.

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Xu, Houbao, Weihua Guo, Jingyuan Yu, and Guangtian Zhu. "Asymptotic stability of a repairable system with imperfect switching mechanism." International Journal of Mathematics and Mathematical Sciences 2005, no. 4 (2005): 631–43. http://dx.doi.org/10.1155/ijmms.2005.631.

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This paper studies the asymptotic stability of a repairable system with repair time of failed system that follows arbitrary distribution. We show that the system operator generates a positiveC0-semigroup of contraction in a Banach space, therefore there exists a unique, nonnegative, and time-dependant solution. By analyzing the spectrum of system operator, we deduce that all spectra lie in the left half-plane and0is the unique spectral point on imaginary axis. As a result, the time-dependant solution converges to the eigenvector of system operator corresponding to eigenvalue0.

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Belytschko, T., B. Moran, and M. Kulkarni. "Stability and Imperfections in Quasistatic Viscoplastic Solutions." Applied Mechanics Reviews 43, no. 5S (May 1, 1990): S251—S255. http://dx.doi.org/10.1115/1.3120819.

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The effect of imperfections on the structure of shear bands in strain-softening viscoplasticity is studied via a closed form solution. The stability of various solutions is then examined by varying the data through imperfections. It is shown that a step-function imperfection, such as commonly used in finite element solutions, leads to a step-function shear strain field, which is an unstable solution. Arbitrary C0 and C1 imperfections lead to C0 and C1 strain fields, respectively. Fourier analyses show that the imperfection scales the response of the viscoplastic material: the Fourier spectrum of the strain field is strongly influenced by the Fourier spectrum of the imperfection.

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Kuball, M., F. Demangeot, J. Frandon, M. A. Renucci, N. Grandjean, and O. Briot. "Thermal Stability of GaN Investigated by Raman Scattering." MRS Internet Journal of Nitride Semiconductor Research 4, S1 (1999): 653–58. http://dx.doi.org/10.1557/s1092578300003203.

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We have investigated the thermal stability of GaN using Raman scattering. Noninvasive optical monitoring of the degradation of GaN during high-temperature processing has been demonstrated. GaN samples grown by molecular-beam epitaxy (MBE) and metalorganic vapor phase epitaxy (MOCVD) were studied. Characteristic features in the Raman spectrum identify three thermal stability regimes: (1) annealing below 900°C does not affect the GaN Raman spectrum; (2) annealing between 900°C and 1000°C results in the appearance of disorder-induced Raman scattering between the E2 and A1(LO) phonon; (3) annealing at temperatures higher than 1000°C gives rise to distinct Raman modes at 630 cm−1, 656 cm−1 and 770 cm−1. The evolution of the Raman spectrum of GaN with increasing annealing temperature is discussed in terms of disorder-induced Raman scattering. We find clear indications for an interfacial reaction between GaN and sapphire for annealing temperatures higher than 1000°C.

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Kaky, Kawa M., G. Lakshminarayana, S. O. Baki, Mohamed Kamari Halimah, and M. A. Mahdi. "Structural, Thermal and Optical Studies of Bismuth Doped Multicomponent Tellurite Glass." Solid State Phenomena 268 (October 2017): 165–71. http://dx.doi.org/10.4028/www.scientific.net/ssp.268.165.

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In this communication, structural, thermal and optical absorption properties of bismuth doped multicomponent tellurite glass (69TeO2-10ZnO-10WO3-5Na2O-5TiO2-1.0Bi2O3 (mol %)) synthesized using melt quench method is reported. The X-ray diffraction confirms the amorphous structure of the synthesized glass. IR spectrum of bismuth doped glass show band at 601 cm-1. Raman analysis observed mainly in four spectral regions which are R1 (65-150) cm-1, R2 (280-550) cm-1, R3 (880-950) cm-1 and R4 (916-926) cm-1 and identified bands are assigned to respective molecular groups. Thermogravimetric analysis profile show stability regarding to weight loss. Differential scanning calorimetry indicates good thermal stability of the synthesized glass for its applications in optical fibers. The absorption spectrum identified the cutoff wavelength at 430 nm.

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Bachmann, Christian J., Bettina Gerste, and Falk Hoffmann. "Diagnoses of autism spectrum disorders in Germany: Time trends in administrative prevalence and diagnostic stability." Autism 22, no. 3 (December 20, 2016): 283–90. http://dx.doi.org/10.1177/1362361316673977.

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For Germany, no data on trends in autism spectrum disorder diagnoses are available. The primary aim of this study was to establish the time trends in the administrative prevalence of autism spectrum disorder diagnoses. The second aim was to assess the stability of autism spectrum disorder diagnoses over time. We analysed administrative outpatient data (2006–2012) from a nationwide health insurance fund and calculated the prevalence of autism spectrum disorder diagnoses for each year, stratified by age and sex. Additionally, we studied a cohort with a first-time diagnosis of autism spectrum disorder in 2007 through 2012, investigating the percentage of retained autism spectrum disorder diagnoses. From 2006 to 2012, the prevalence of autism spectrum disorder diagnoses in 0- to 24-year-olds increased from 0.22% to 0.38%. In insurees with a first-time autism spectrum disorder diagnosis in 2007, this diagnosis was carried on in all years through 2012 in 33.0% (The International Classification of Diseases, Tenth Revision diagnoses: F84.0/F84.1/F84.5) and 11.2% (F84.8/F84.9), respectively. In Germany, like in other countries, there has been an increase in the administrative prevalence of autism spectrum disorder diagnoses. Yet, prevalences are still lower than in some other Western countries. The marked percentage of autism spectrum disorder diagnoses which were not retained could indicate a significant portion of autism spectrum disorder misdiagnoses, which might contribute to rising autism spectrum disorder prevalences.

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Belko, Nikita V., Michael P. Samtsov, and Dzmitry S. Tarasau. "Spectrophotometrical purity and stability testing of a photosensitizer based on an indotricarbocyanine dye." Journal of the Belarusian State University. Physics, no. 3 (October 7, 2020): 17–23. http://dx.doi.org/10.33581/2520-2243-2020-3-17-23.

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The express method for testing purity and stability of an indotricarbocyanine dye based photosensitizer for photodynamic therapy was developed. Storage of the hydrophilic photosensitizer under unfavorable conditions resulted in contamination with a hydrophobic dye. The absorption spectrum of the hydrophobic dye was characterized by a new band at 514 nm that was absent in the absorption spectrum of the photosensitizer. There was no spectral overlap between this absorption band and the absorbance of the photosensitizer. Therefore, presence of the band at 514 nm allowed us to detect contamination of the photosensitizer substance with the hydrophobic dye. It was established that the optimal photosensitizer concentration for purity testing is ca. 0.8 mmol/L, when as little as 0.6 wt. % of the impurity can be detected. The developed method is not time consuming and requires accessible equipment only. Data obtained with this method was verified with the aid of liquid chromatography-mass spectrometry.

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Journal articles on the topic 'Spectrum stability'

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