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Artykuły w czasopismach na temat „Spectral mechanics”

Autor: Grafiati

Data publikacji: 2 czerwca 2025

Data aktualizacji: 31 lipca 2025

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1

BERA, P. K., S. BHATTACHARYYA, and B. TALUKDAR. "SPECTRAL INVERSE PROBLEM IN SUPERSYMMETRIC QUANTUM MECHANICS." International Journal of Modern Physics A 08, no. 23 (1993): 4123–29. http://dx.doi.org/10.1142/s0217751x93001697.

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The supersymmetric WKB quantization condition is used to study the so-called spectral inverse problem. Wavefunctions for the harmonic oscillator and hydrogen atom are obtained from the knowledge of their bound-state energy spectra. The analysis presented is based essentially on a repackaging of the conventional theory of integral equations.

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2

Shariff, M. H. B. M. "Spectral Derivatives in Continuum Mechanics." Quarterly Journal of Mechanics and Applied Mathematics 70, no. 4 (2017): 479–96. http://dx.doi.org/10.1093/qjmam/hbx014.

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3

Zúñiga Zamalloa, Carlo, Henry Chi-Hin Ng, Pinaki Chakraborty, and Gustavo Gioia. "Spectral analogues of the law of the wall, the defect law and the log law." Journal of Fluid Mechanics 757 (September 19, 2014): 498–513. http://dx.doi.org/10.1017/jfm.2014.497.

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AbstractUnlike the classical scaling relations for the mean-velocity profiles of wall-bounded uniform turbulent flows (the law of the wall, the defect law and the log law), which are predicated solely on dimensional analysis and similarity assumptions, scaling relations for the turbulent-energy spectra have been informed by specific models of wall turbulence, notably the attached-eddy hypothesis. In this paper, we use dimensional analysis and similarity assumptions to derive three scaling relations for the turbulent-energy spectra, namely the spectral analogues of the law of the wall, the defe

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4

Mammadova, Leyla I., and Ibrahim M. Nabiev. "Uniqueness of recovery of the Sturm-Liouville operator with a spectral parameter quadratically entering the boundary condition." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 79 (2022): 14–24. http://dx.doi.org/10.17223/19988621/79/2.

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The work is devoted to the study of the inverse problem for the Sturm-Liouville operator with a real square-integrable potential. The boundary conditions are non-separated. One of these boundary conditions includes a quadratic function of the spectral parameter. A uniqueness theorem is proved and an algorithm for solving the inverse problem is constructed. As spectral data, we use the spectrum of the considered boundary value problem, the constant term of the quadratic function of the spectral parameter included in the boundary condition, and some special sequence of signs. From these spectral

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5

Al-Yousef, Ibraheem F., Moayad Ekhwan, H. Bahlouli, and A. D. Alhaidari. "Spectral Problem of the Hamiltonian in Quantum Mechanics without Reference to a Potential Function." Axioms 12, no. 4 (2023): 334. http://dx.doi.org/10.3390/axioms12040334.

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Following the celebrated postulates of quantum mechanics, we write the quantum mechanical wavefunction as a convergent series of suitably selected complete square-integrable basis functions in configuration space. The expansion coefficients of the series are energy orthogonal polynomials that contain all spectral information about the system. We exploit the properties of these polynomials to introduce physical systems with rich and highly nontrivial energy spectra. In this approach, no reference is made at all to the usual potential energy function. We consider, in this new approach, a few rep

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6

Liu, Zhao, and Liu Wang-Yun. "Higher Toda Mechanics and Spectral Curves." Communications in Theoretical Physics 42, no. 1 (2004): 9–18. http://dx.doi.org/10.1088/0253-6102/42/1/9.

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7

Meyer, H., J.-C. Anglès d'Auriac, and H. Bruus. "Spectral properties of statistical mechanics models." Journal of Physics A: Mathematical and General 29, no. 18 (1996): L483—L488. http://dx.doi.org/10.1088/0305-4470/29/18/006.

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8

Maraner, P., E. Onofri, and G. P. Tecchioli. "Spectral methods in computational quantum mechanics." Journal of Computational and Applied Mathematics 37, no. 1-3 (1991): 209–19. http://dx.doi.org/10.1016/0377-0427(91)90119-5.

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9

Collas, Peter. "Quantum mechanics versus spectral differential geometry." Physics Letters A 149, no. 4 (1990): 179–83. http://dx.doi.org/10.1016/0375-9601(90)90322-f.

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10

Noce, Canio, and Alfonso Romano. "Undecidability and Quantum Mechanics." Encyclopedia 2, no. 3 (2022): 1517–27. http://dx.doi.org/10.3390/encyclopedia2030103.

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Recently, great attention has been devoted to the problem of the undecidability of specific questions in quantum mechanics. In this context, it has been shown that the problem of the existence of a spectral gap, i.e., energy difference between the ground state and the first excited state, is algorithmically undecidable. Using this result herein proves that the existence of a quantum phase transition, as inferred from specific microscopic approaches, is an undecidable problem, too. Indeed, some methods, usually adopted to study quantum phase transitions, rely on the existence of a spectral gap.

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11

Colbrook, Matthew J. "Computing Spectral Measures and Spectral Types." Communications in Mathematical Physics 384, no. 1 (2021): 433–501. http://dx.doi.org/10.1007/s00220-021-04072-4.

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AbstractSpectral measures arise in numerous applications such as quantum mechanics, signal processing, resonance phenomena, and fluid stability analysis. Similarly, spectral decompositions (into pure point, absolutely continuous and singular continuous parts) often characterise relevant physical properties such as the long-time dynamics of quantum systems. Despite new results on computing spectra, there remains no general method able to compute spectral measures or spectral decompositions of infinite-dimensional normal operators. Previous efforts have focused on specific examples where analyti

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12

Rugescu, Radu Dan, Daniele Mortari, Stefan Staicu, and Sorin Aldea. "Orthonormality and Spectral Analysis for Robotics and Astrodynamics." Solid State Phenomena 164 (June 2010): 392–404. http://dx.doi.org/10.4028/www.scientific.net/ssp.164.392.

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A rigid transform of the E3 space into itself stands as the basis of a complete description of mechanical motions of solid bodies, where the orthogonal and normalized character (orthonormality) of the transform matrix are used as a postulate. However, the orthonormality is in fact a consequence of the condition of rigidity. The demonstration is outlined through the spectral analysis for application in the engineering of robots and astrodynamics. The problem posed is to directly find, in a general and confident manner, the elements of the rotation matrix when the direction and magnitude of the

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13

Deloff, A. "Semi-spectral Chebyshev method in quantum mechanics." Annals of Physics 322, no. 6 (2007): 1373–419. http://dx.doi.org/10.1016/j.aop.2006.07.004.

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14

BOLTE, JENS. "SOME STUDIES ON ARITHMETICAL CHAOS IN CLASSICAL AND QUANTUM MECHANICS." International Journal of Modern Physics B 07, no. 27 (1993): 4451–553. http://dx.doi.org/10.1142/s0217979293003759.

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Several aspects of classical and quantum mechanics applied to a class of strongly chaotic systems are studied. The latter consists of single particles moving without external forces on surfaces of constant negative Gaussian curvature whose corresponding fundamental groups are supplied with an arithmetic structure. It is shown that the arithmetical features of the considered systems lead to exceptional properties of the corresponding spectra of lengths of closed geodesics (periodic orbits). The most significant one is an exponential growth of degeneracies in these geodesic length spectra. Furth

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15

Li, Jun, Zahra Sharif Khodaei, and M. H. Aliabadi. "Spectral BEM for the Analysis of Wave Propagation and Fracture Mechanics." Journal of Multiscale Modelling 08, no. 03n04 (2017): 1740007. http://dx.doi.org/10.1142/s1756973717400078.

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This paper presents a spectral boundary element formulation for analysis of structures subjected to dynamic loading. Two types of spectral elements based on Lobatto polynomials and Legendre polynomials are used. Two-dimensional analyses of elastic wave propagation in solids with and without cracks are carried out in the Laplace frequency domain with both conventional BEM and the spectral BEM. By imposing the requirement of the same level of accuracy, it was found that the use of spectral elements, compared with conventional quadratic elements, reduced the total number of nodes required for mod

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16

Zhezhera, T., P. Gluchowski, M. Nowicki, et al. "Efficient near-infrared quantum cutting by cooperative energy transfer in Bi3TeBO9:Nd3+ phosphors." Journal of Materials Science 57, no. 1 (2022): 185–203. http://dx.doi.org/10.1007/s10853-021-06642-2.

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Abstract An efficient near-infrared quantum cutting process by cooperative down-conversion of active Bi3+ and Nd3+ ions was demonstrated in Bi3TeBO9:Nd3+ phosphors. In particular, the near-infrared emission of Nd3+ ions enhanced by Bi3+ ions of a series of novel Bi3TeBO9:Nd3+ microcrystalline powders doped with Nd3+ ions in various concentrations was investigated. In order to investigate the luminescent properties of BTBO:Nd3+ powders, the excitation and emission spectra and the fluorescence decay time were measured and analyzed. In particular, the emission of Bi3TeBO9:Nd3+ at 890 and 1064 nm

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17

Fassois, S. D. "A Fast Rational Model Approach to Parametric Spectral Estimation—Part II: Properties and Performance Evaluation." Journal of Vibration and Acoustics 112, no. 3 (1990): 328–36. http://dx.doi.org/10.1115/1.2930512.

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In the first part of this paper (Fassois, 1990), the basic form of a novel, fast rational model approach to parametric spectral estimation was introduced. In this second part the consistency property of the approach is proven, and two modified versions, characterized by mathematically guaranteed stability, developed. Unlike most alternative techniques, the proposed approach is then capable of effectively estimating all types of spectra, including those characterized by sharp valleys. Its performance is finally evaluated via numerical simulations and comparisons with the Blackman-Tukey and the

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18

Yang, Yan, and Jian-Zhou Zhu. "Turbulence compressibility reduction with helicity." Physics of Fluids 34, no. 4 (2022): 045113. http://dx.doi.org/10.1063/5.0089333.

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A numerical test of isotropic turbulence compressibility reduction with helicity in a cyclic box is performed. The ratios of compressibility-relevant-mode spectra over those of kinetic energy present power laws at large wavenumbers in the dissipation range, indicating a common difference of 11/15 in the exponents of the algebraic prefactor of the nonhelical power spectra over those of helical ones. Our results being not derived from the shapes of the spectra themselves, the implied information about the helicity effect on the complex singularities of the discretized dynamical system can be of

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19

Karpov, Eduard G., Larry A. Danso, and John T. Klein. "Anomalous strain energy transformation pathways in mechanical metamaterials." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 475, no. 2226 (2019): 20190041. http://dx.doi.org/10.1098/rspa.2019.0041.

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This discussion starts with a mechanics version of Parseval's energy theorem applicable to any discrete lattice material with periodic internal structure: a microtruss, grid, frame, origami or tessellation. It provides a simple relationship between the strain energy volumetric/usual and spectral distributions in the reciprocal space. The spectral energy distribution leads directly to a spectral entropy of lattice deformation (Shannon's type), whose variance with a material coordinate represents the decrease of information about surface loads in the material interior. Spectral entropy is also a

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20

Cassidy, David C. "Oppenheimer's first paper: Molecular band spectra and a professional style." Historical Studies in the Physical and Biological Sciences 37, no. 2 (2007): 247–70. http://dx.doi.org/10.1525/hsps.2007.37.2.247.

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Beginning early in the 20th century spectroscopists attributed the infrared band spectra emitted by diatomic molecules to quantum vibration and rotation modes of the molecules. Because of these relatively simple motions, band spectra offered a convenient .rst phenomenon to which to apply formulations of the new quan-tum mechanics in 1926. In his .rst paper, completed in Cambridge in May 1926, Oppenheimer presented a derivation of the frequencies and relative intensities of the observed spectral lines on the basis of Paul Dirac's new quantum commutator algebra. At the same time Lucy Mensing pub

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21

Scholtz, F. G., and B. Chakraborty. "Spectral triplets, statistical mechanics and emergent geometry in non-commutative quantum mechanics." Journal of Physics A: Mathematical and Theoretical 46, no. 8 (2013): 085204. http://dx.doi.org/10.1088/1751-8113/46/8/085204.

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22

Theocaris, P. S., and D. P. Sokolis. "Spectral decomposition of anisotropic elasticity." Acta Mechanica 150, no. 3-4 (2001): 237–61. http://dx.doi.org/10.1007/bf01181814.

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23

Annenkov, Sergei Y., and Victor I. Shrira. "Spectral evolution of weakly nonlinear random waves: kinetic description versus direct numerical simulations." Journal of Fluid Mechanics 844 (April 12, 2018): 766–95. http://dx.doi.org/10.1017/jfm.2018.185.

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Kinetic equations are widely used in many branches of science to describe the evolution of random wave spectra. To examine the validity of these equations, we study numerically the long-term evolution of water wave spectra without wind input using three different models. The first model is the classical kinetic (Hasselmann) equation (KE). The second model is the generalised kinetic equation (gKE), derived employing the same statistical closure as the KE but without the assumption of quasistationarity. The third model, which we refer to as the DNS-ZE, is a direct numerical simulation algorithm

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24

Evans, Mogoi N., and Wafula A. M. "Spectral Conditions for Norm-Attainment in Bounded Operators on Hilbert Spaces." Asian Research Journal of Mathematics 21, no. 4 (2025): 160–69. https://doi.org/10.9734/arjom/2025/v21i4918.

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On this note, we have investigated the conditions for norm-attainment in bounded operators on Hilbert spaces, focusing on key criteria such as spectral gaps, isolated norms, and nonzero spectral projections. Concrete examples, such as diagonal and weighted shift operators, are used to demonstrate norm-attainment under specific conditions. The impact of compact operator perturbations, essential spectra, and unitary equivalence is also explored. The methodology combines analytical techniques and numerical simulations, and the study concludes by suggesting future research directions, including th

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25

Ford, J. E., and J. A. Walker. "Dynamic spectral power equalization using micro-opto-mechanics." IEEE Photonics Technology Letters 10, no. 10 (1998): 1440–42. http://dx.doi.org/10.1109/68.720287.

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26

Hlystunov, Mikhail S., Valery I. Prokopiev, and Zhanna G. Mogilyuk. "The Numerical Models Spectral Phantoms in Solid Mechanics." Procedia Engineering 111 (2015): 297–301. http://dx.doi.org/10.1016/j.proeng.2015.07.092.

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27

Zeinstra, Rein. "On a spectral identity of Quantum Statistical Mechanics." Indagationes Mathematicae 20, no. 3 (2009): 477–82. http://dx.doi.org/10.1016/s0019-3577(09)80020-7.

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28

Martinez, Diane, and Jody Trout. "Asymptotic Spectral Measures, Quantum Mechanics, and E -Theory." Communications in Mathematical Physics 226, no. 1 (2002): 41–60. http://dx.doi.org/10.1007/s002200200595.

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29

Andrianov, A. A., and F. Cannata. "Nonlinear supersymmetry for spectral design in quantum mechanics." Journal of Physics A: Mathematical and General 37, no. 43 (2004): 10297–321. http://dx.doi.org/10.1088/0305-4470/37/43/019.

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30

Williams, Kurt C., and Snezhana I. Abarzhi. "Fluctuations spectra of specific kinetic energy, density, and mass flux in Rayleigh–Taylor mixing." Physics of Fluids 34, no. 12 (2022): 122118. http://dx.doi.org/10.1063/5.0120521.

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Rayleigh–Taylor (RT) interfacial mixing is critically important in a broad range of processes in nature and technology. To understand self-similar RT dynamics, a bias free interpretation of data is in need. This work yields the physics properties and the anomalous scaling of Rayleigh–Taylor mixing based on the analysis of experimental data. Fluctuations spectra are analyzed of the specific kinetic energy of the velocity component in the acceleration direction, the density, and the mass flux. Theoretical foundations and statistical method are developed, under group theory guidance, to investiga

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31

Jin, Hu, Bo Gao, and Yusheng Shen. "Model Analysis of Sandstone Tunnel Cracking Based on Fracture Mechanics Theory and Sensor Testing Technology Research." Journal of Sensors 2022 (February 14, 2022): 1–13. http://dx.doi.org/10.1155/2022/2482638.

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In this paper, we survey sandstone tunnels using sensor testing technology and conduct an in-depth analysis and research on the model of sandstone tunnel cracking based on the theory of fracture mechanics. This paper systematically investigates the static mechanical properties, energy evolution and distribution law, acoustic emission monitoring, and digital image correlation methods of intact and jointed rock chamber enclosures (including parallel jointed rock chamber enclosures and cross jointed rock chamber enclosures) under static loads, based on physical simulation test methods and combine

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32

STIASSNIE, M., A. REGEV, and Y. AGNON. "Recurrent solutions of Alber's equation for random water-wave fields." Journal of Fluid Mechanics 598 (February 25, 2008): 245–66. http://dx.doi.org/10.1017/s0022112007009998.

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The study addresses the linear instability of narrow spectra homogeneous seas and its subsequent evolution in time, subject to inhomogeneous disturbances. Specifically, we study unidirectional spectra, where according to the kinetic equation no spectral evolution is expected. In the region of instability, recurrent evolution is discovered. This recurrence is the stochastic counterpart of the Fermi–Pasta–Ulam recurrence obtained for the cubic Schrödinger equation.

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33

Hayitova, Hilola Gʻafurovna, and Sevarabonu To'xtasinovna Ibodova. "ABOUT EXPLORING THE SPECIFIC VALUES OF THE FRIDRIXS MODEL WITH MATHEMATICAL PACKAGES." EURASIAN JOURNAL OF ACADEMIC RESEARCH 1, no. 3 (2021): 421–27. https://doi.org/10.5281/zenodo.4976585.

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<em>In some important problems of mathematical physics, hydrodynamics, solid state physics, quantum field theory, statistical physics and nonrealistic quantum mechanics, it is important to study the spectral properties of the Friedrich operator in several dynamic problems. in statistical physics, the lattice gas represents the binding state, and in quantum mechanics, the specific values represent the binding states of the energies. Furthermore, the three- and multi-particle systems that emerge in nonreiltivistic quantum mechanics are inextricably linked with the spectral properties of Hamilton

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34

Sun, Jun, Xia Ming Jin, Ze Gao Dai, Mei Xia Zhang, Xin Chen Shen, and Wen Xia Lv. "Discrimination of the Lettuce Leaf Nitrogen Level Based on the BP Neural Network and the Spectral Information." Advanced Materials Research 756-759 (September 2013): 1993–97. http://dx.doi.org/10.4028/www.scientific.net/amr.756-759.1993.

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According to the problem that the intelligence is not high of the soccer robot, using the mechanical theory as a guide, making some mechanical analyses and calculations on the pressure and transmutation states of chip kick mechanics, and conducting optimal design too, then making the structure of chip kick mechanics more and more rationalization. Experiments show that the new soccer robot controller features a quick response and high servo rigidity, and provide a kind of method for improving and perfecting the soccer robot control system, at the same time, filling the needs of producing.

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35

Kirby, Robert M., and Spencer J. Sherwin. "Stabilisation of spectral/hp element methods through spectral vanishing viscosity: Application to fluid mechanics modelling." Computer Methods in Applied Mechanics and Engineering 195, no. 23-24 (2006): 3128–44. http://dx.doi.org/10.1016/j.cma.2004.09.019.

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Hebb, J. P., E. G. Cravalho, and M. I. Flik. "Thermal Radiation Absorption in Doped Semiconductors Due to Direct Intersubband Transitions." Journal of Heat Transfer 117, no. 4 (1995): 948–54. http://dx.doi.org/10.1115/1.2836315.

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This work proposes an engineering model for thermal radiation absorption due to direct intersubband transitions in doped semiconductors, which are excitations of bound electrons in the infrared spectral region. An existing quantum-mechanical approach is to model these transitions as a continuum of damped harmonic oscillators. This study modifies this approach to yield a more effective method for determining the optical constants of doped semiconductors. The room-temperature absorptance spectra of p-type GaAs samples with dopant concentrations from 8 × 1017 to 1 × 1020 cm-3 are measured using a

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37

Chung, Hyun Soo, and Seung Jun Chang. "Some Applications of the Spectral Theory for the Integral Transform Involving the Spectral Representation." Journal of Function Spaces and Applications 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/573602.

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In many previous papers, an integral transformℱγ,βwas just considered as a transform on appropriate function spaces. In this paper we deal with the integral transform as an operator on a function space. We then apply various operator theories toℱγ,β. Finally we give an application for the spectral representation of a self-adjoint operator which plays a key role in quantum mechanics.

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38

Vanel, Florence O., and Oktay Baysal. "Investigation of Dispersion-Relation-Preserving Scheme and Spectral Analysis Methods for Acoustic Waves." Journal of Vibration and Acoustics 119, no. 2 (1997): 250–57. http://dx.doi.org/10.1115/1.2889711.

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Important characteristics of acoustic wave propagation are encoded in their dispersion relations. Hence, a computational algorithm, which attempts to preserve these relations, was investigated. Considering the linearized, 2-D Euler equations, simulations were performed to validate this scheme and its boundary conditions. The results were found to agree favorably with the exact solutions. The boundary conditions were transparent to the outgoing waves, except when the disturbance source was close to a corner boundary. The time-domain data generated by such computations were often intractable unt

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39

Alotta, Gioacchino, Mario Di Paola, and Francesco Paolo Pinnola. "Cross-correlation and cross-power spectral density representation by complex spectral moments." International Journal of Non-Linear Mechanics 94 (September 2017): 20–27. http://dx.doi.org/10.1016/j.ijnonlinmec.2017.02.001.

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Vijay, Amrendra, and Robert E. Wyatt. "Spectral filters in quantum mechanics: A measurement theory perspective." Physical Review E 62, no. 3 (2000): 4351–64. http://dx.doi.org/10.1103/physreve.62.4351.

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41

Fernández C, David J., and Barnana Roy. "Confluent second-order supersymmetric quantum mechanics and spectral design." Physica Scripta 95, no. 5 (2020): 055210. http://dx.doi.org/10.1088/1402-4896/ab4be2.

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42

Hall, Richard L. "Spectral geometry of power-law potentials in quantum mechanics." Physical Review A 39, no. 11 (1989): 5500–5507. http://dx.doi.org/10.1103/physreva.39.5500.

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43

Vladimirov, Vasilii S., I. V. Volovich, and E. I. Zelenov. "SPECTRAL THEORY INp-ADIC QUANTUM MECHANICS, AND REPRESENTATION THEORY." Mathematics of the USSR-Izvestiya 36, no. 2 (1991): 281–309. http://dx.doi.org/10.1070/im1991v036n02abeh002022.

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44

Zakirova, G. A. "Inverse Spectral Problems and Mathematical Models of Continuum Mechanics." Bulletin of the South Ural State University. Series "Mathematical Modelling, Programming and Computer Software" 12, no. 2 (2019): 5–24. http://dx.doi.org/10.14529/mmp190201.

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45

Giovanis, Dimitris G., and Vissarion Papadopoulos. "Spectral representation-based neural network assisted stochastic structural mechanics." Engineering Structures 84 (February 2015): 382–94. http://dx.doi.org/10.1016/j.engstruct.2014.11.044.

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46

Molchanova, Evgeniya A. "Variational simulation of the spectral problem." Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, no. 75 (2022): 33–37. http://dx.doi.org/10.17223/19988621/75/3.

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The ordinary fourth-order differential equation which is the zero approximation of the eigenvalue boundary problem is solved by the variational method to produce approximate formulas for eigenvalues. To obtain an explicit formula for eigenvalues, a transition is made from the differential problem to the variational problem in the Galerkin form. Calculating integrals in it gives a general formula for eigenvalues. The selection of functions satisfying certain boundary conditions yields approximate formulas suitable for the analysis of multiparameter dependencies. In particular, it is shown how t

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Rath, Biswanath. "Can The Spectra Of Hermitian Operator Be Invariant Under x â‡€ â†½ p ? :Case Study :1D General." JOURNAL OF ADVANCES IN PHYSICS 14, no. 1 (2018): 5326–30. http://dx.doi.org/10.24297/jap.v14i1.7278.

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We address an intriguing question on spectral invariance in quantum mechanics onexchange of co-ordinate and momentum x â‡€ â†½ p considering general oscillator as anexample.Key words:exchange of co-ordinate and momentum , spectral invariance , generaloscillator .

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Peng, Er Bao, Hong Ge Zhang, and Hong Ying Wang. "Mechanics and Pretreatment Research of Vibration Signals for the Numerical Control Machine." Advanced Materials Research 676 (March 2013): 162–65. http://dx.doi.org/10.4028/www.scientific.net/amr.676.162.

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To study vibration signals processing mechanics and the analysis method of the numerical control machine. vibration signals analysis method include time and frequent domain analysis: the time domain analysis mainly has the statistical analysis and the correlation function analysis. frequency domain analysis include spectral analysis, cepstrum analysis, data envelopment analysis. vibration signals pretreatment is the most commonly used and effective method on the mechanical device condition monitor and the failure diagnosis.

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Heinrichs, Wilhelm. "Algebraic spectral multigrid methods." Computer Methods in Applied Mechanics and Engineering 80, no. 1-3 (1990): 281–86. http://dx.doi.org/10.1016/0045-7825(90)90031-g.

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Kozánek, Jan, and Ladislav Půst. "Spectral properties and identification of aerostatic bearings." Acta Mechanica Sinica 27, no. 1 (2011): 63–67. http://dx.doi.org/10.1007/s10409-011-0407-2.

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