Academic literature on the topic 'Differential-spectral description'

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Journal articles on the topic "Differential-spectral description"

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Mogilevskii, V. I. "Description of spectral functions of differential operators with arbitrary deficiency indices." Mathematical Notes 81, no. 3-4 (2007): 553–59. http://dx.doi.org/10.1134/s0001434607030339.

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Kalitov, M. A., and N. P. Kornyshev. "Mathematical description of the processes of synthesis of digital multispectral images." Journal of Physics: Conference Series 2052, no. 1 (2021): 012018. http://dx.doi.org/10.1088/1742-6596/2052/1/012018.

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Abstract The article discusses the features of the formation of digital multispectral images corresponding to narrow registration zones. The processes of signal transformations are analyzed during the synthesis of such images from the original multispectral images with overlapping spectral flux registration zones. Questions of the mathematical description of the differential and multiplicative method for the synthesis of spectrozonal images are discussed. Analytical expressions are given that correspond to signal transformations of the original digital multispectral images in their differentia
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BRAIN, SIMON, and GIOVANNI LANDI. "THE 3D SPIN GEOMETRY OF THE QUANTUM TWO-SPHERE." Reviews in Mathematical Physics 22, no. 08 (2010): 963–93. http://dx.doi.org/10.1142/s0129055x10004119.

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We study a three-dimensional differential calculus [Formula: see text] on the standard Podleś quantum two-sphere [Formula: see text], coming from the Woronowicz 4D+ differential calculus on the quantum group SU q(2). We use a frame bundle approach to give an explicit description of [Formula: see text] and its associated spin geometry in terms of a natural spectral triple over [Formula: see text]. We equip this spectral triple with a real structure for which the commutant property and the first order condition are satisfied up to infinitesimals of arbitrary order.
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Taimanov, I. A. "Floquet–Bloch Functions on Non-simply Connected Manifolds, the Aharonov–Bohm Fluxes, and Conformal Invariants of Immersed Surfaces." Proceedings of the Steklov Institute of Mathematics 325, no. 1 (2024): 280–91. http://dx.doi.org/10.1134/s0081543824020160.

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Abstract We define spectral (Bloch) varieties of multidimensional differential operators on non-simply connected manifolds. In their terms we give a description of the analytic dependence of the spectra of magnetic Laplacians on non-simply connected manifolds on the values of the Aharonov–Bohm fluxes, construct analogs of spectral curves for two-dimensional Dirac operators on Riemann surfaces, and thereby find new conformal invariants of immersions of surfaces into three- and four-dimensional Euclidean spaces.
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Rybakov, K. A. "Spectral method of analysis and optimal estimation in linear stochastic systems." International Journal of Modeling, Simulation, and Scientific Computing 11, no. 03 (2020): 2050022. http://dx.doi.org/10.1142/s1793962320500221.

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It is proposed to use the spectral form of mathematical description of control systems for modeling continuous-time Markov random processes described by linear stochastic differential equations with additive or multiplicative noise. The obtained results are applied to solve the output process analysis problem and the optimal estimation problem.
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Rybakov, Konstantin. "Spectral representation of stochastic integration operators." MATEC Web of Conferences 362 (2022): 01027. http://dx.doi.org/10.1051/matecconf/202236201027.

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The spectral representation for stochastic integration operators with respect to the Wiener process is proposed in the form of a composition of spectral characteristics used in the spectral form of mathematical description for control systems. This spectral representation can be defined relative to the various orthonormal bases. For given deterministic square-integrable kernels, the spectral characteristic of a stochastic integration operator is determined as an infinite random matrix. The main applications of such a representation suppose solving linear stochastic differential equations and m
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Childs, Andrew M., Jin-Peng Liu, and Aaron Ostrander. "High-precision quantum algorithms for partial differential equations." Quantum 5 (November 10, 2021): 574. http://dx.doi.org/10.22331/q-2021-11-10-574.

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Quantum computers can produce a quantum encoding of the solution of a system of differential equations exponentially faster than a classical algorithm can produce an explicit description. However, while high-precision quantum algorithms for linear ordinary differential equations are well established, the best previous quantum algorithms for linear partial differential equations (PDEs) have complexity poly(1/ϵ), where ϵ is the error tolerance. By developing quantum algorithms based on adaptive-order finite difference methods and spectral methods, we improve the complexity of quantum algorithms
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Rybakov, K. A. "Algorithms of Numerical-spectral Methods for Modeling Stochastic Dynamical Systems." Моделирование и анализ данных 13, no. 3 (2023): 79–95. http://dx.doi.org/10.17759/mda.2023130306.

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<p>Representations of iterated Stratonovich and Ito stochastic integrals are obtained on the basis of the spectral form of mathematical description, they have both theoretical and practical significance. The latter is due to the possibility of constructing quite simple algorithms for the approximate modeling iterated stochastic integrals, which are necessary for the implementation of numerical methods for solving stochastic differential equations. The use of spectral representations of iterated stochastic integrals in numerical methods forms the numerical-spectral methods. Algorithms for
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Rustemova, K., G. Takibaeva, A. Sabalakhova, and B. Tursynbek. "SPECTRAL PROPERTIES OF SOME DIFFERENTIATION OPERATOR WITH DEVIATED ARGUMENT." Scientific heritage, no. 90 (June 6, 2022): 108–16. https://doi.org/10.5281/zenodo.6616192.

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Differential equations with a deviating argument appeared in the literature as early as the 18th century in connection with the solution of the Euler problem of finding the general form of a line similar to its evolute. However, until 1950, the main theorems of the general theory of differential equations with a deviating argument were not formulated; there was not even a clear statement of the initial problem in the literature. This was first done in the dissertation of Myshkis A.D. [one]. The period of rapid development of the theory of differential equations with deviating argument coincide
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Akhatov, Semyat, Narzankul Makhmetova, and Vladimir Solonenko. "SOLUTION OF DIFFERENTIAL EQUATIONS OF WAGON OVERSPREAD MASSES OSCILLATION." International Journal of Advanced Logistics, Transport and Engineering 2, no. 2 (2022): 8–13. http://dx.doi.org/10.52167/2790-5829-2022-2-2-8-13.

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The paper gives the methodology of differential equations solution for description of bouncing, galloping and side swaying oscillations of railcar with asymmetrically located cargoes of different masses which were carried out on computer. Continuous ­vertical irregularities in the rail track and level difference (track skewness) of two rail tracks in the vertical transverse plane were taken as disturbances­, spectral density of which is shown, respectively. To obtain the spectral densities depending on the speed, the abscissa of the spectral densities plots were multiplied by the speed, and th
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Dissertations / Theses on the topic "Differential-spectral description"

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Zang, Xiaoyun 1971. "Spectral description of low frequency oceanic variability." Thesis, Massachusetts Institute of Technology, 2000. http://hdl.handle.net/1721.1/59094.

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Thesis (Ph.D.)--Joint Program in Physical Oceanography (Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences and the Woods Hole Oceanographic Institution), 2000.<br>Includes bibliographical references (p. 179-187).<br>A simple dynamic model is used with various observations to provide an approximate spectral description of low frequency oceanic variability. Such a spectrum has wide application in oceanography, including the optimal design of observational strategy for the deployment of floats, the study of Lagrangian statistics and the estimate of uncertai
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Пархоменко, Максим Вікторович, Максим Викторович Пархоменко та Maksim Viktorovych Parkhomenko. "Метод кодування для підвищення бітової швидкості динамічного відеоресурсу в інформаційних системах". Thesis, Національний авіаційний університет, 2021. https://er.nau.edu.ua/handle/NAU/48933.

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У дисертаційній роботі вирішена актуальна науково-прикладна задача щодо підвищення бітової швидкості динамічного відеоресурсу в інформаційно-телекомунікаційних системах в процесі управління об’єктами критичної інфраструктури. Виявлено проблемні недоліки існуючих концепцій побудови стандартизованих ІТОДВ. Проведено обґрунтування того, що для удосконалення ІТОДВ пропонується використовувати технологічний підхід, який базується на обробці послідовності кадрів ДВІР з використанням структурнокомбінаторного підходу, який враховує наявність значної кількості відповідної міжкадрової надмірності. Нада
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Books on the topic "Differential-spectral description"

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Zang, Xiaoyun. Spectral description of low frequency oceanic variability. Massachusetts Institute of Technology, 2000.

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Book chapters on the topic "Differential-spectral description"

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Robert Owen Bussey III, Dr. "Advantages of Ion Mobility Coupled with HPLC/UPLC." In Analytical Liquid Chromatography - New Perspectives [Working Title]. IntechOpen, 2022. http://dx.doi.org/10.5772/intechopen.102380.

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Ion mobility is a new separation technique that can be coupled with high performance liquid chromatography (HPLC) or ultra-performance liquid chromatography (UPLC). Variances in cross-sectional ionic areas of different molecules create differential speeds through a gas allowing for millisecond separations. Combining ion mobility with both liquid chromatography and mass spectrometry with fragmentation, separations can be achieved on the second (HPLC), millisecond (ion mobility), and microsecond (mass spectrometry) timescales. This orthogonal separation greatly cleans up mass spectral data of co
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Field, Timothy R. "Dynamics of K-Scattering." In Electromagnetic Scattering from Random Media. Oxford University PressOxford, 2008. http://dx.doi.org/10.1093/oso/9780198570776.003.0010.

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Abstract We derive the stochastic dynamics of the complex-valued amplitude resulting from coherent scattering from a random population of scatterers when this becomes asymptotically large. Considerations of a random walk model, introduced by Jakeman, are used to derive stochastic differential equations (SDEs) for the amplitude and corresponding intensity and phase stochastic processes. An analysis of the correlation structure in the fluctuations is provided and interpreted geometrically in terms of the gauge invariant properties of the field and the Markov property. A Fokker–Planck description
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Bortsov, Alexander. "Laser Opto-Electronic Oscillator and the Modulation of a Laser Emission." In Fiber Optics - Technology and Applications. IntechOpen, 2021. http://dx.doi.org/10.5772/intechopen.98924.

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The autonomous optoelectronic generator (OEO) is considered in the chapter as a source of low-noise oscillations. Differential equations are considered and methods with OEO modulation with direct and external modulation are analyzed. The complexity of both approaches is related to the non-standard way of description of the nonlinear method modulation for the internal (direct) structure and the utilization of the specific Mach-Zehnder modulator for the first stage on external modulation. The purpose of the presentation is to consider the main features of OEO as a low-noise generator. This inclu
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Conference papers on the topic "Differential-spectral description"

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Osborne, Alfred R. "Theory of Nonlinear Fourier Analysis: The Construction of Quasiperiodic Fourier Series for Nonlinear Wave Motion." In ASME 2020 39th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/omae2020-18850.

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Abstract I give a description of nonlinear water wave dynamics using a recently discovered tool of mathematical physics I call nonlinear Fourier analysis (NLFA). This method is based upon and is an application of a theorem due to Baker [1897, 1907] and Mumford [1984] in the field of algebraic geometry and from additional sources by the author [Osborne, 2010, 2018, 2019]. The theory begins with the Kadomtsev-Petviashvili (KP) equation, a two dimensional generalization of the Korteweg-deVries (KdV) equation: Here the NLFA method is derived from the complete integrability of the equation by finit
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Gravel, Jean-François, Martin Allard, François Babin, François Chateauneuf, and Eric Bergeron. "Oil Pipeline Standoff Leak Detection: A Novel Approach for Airborne Remote Detection of Small Leaks." In 2016 11th International Pipeline Conference. American Society of Mechanical Engineers, 2016. http://dx.doi.org/10.1115/ipc2016-64704.

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While natural gas pipelines already benefit from airborne, remote detection of leaks [1, 2], oil pipeline leak detection has been for a long time reliant on SCADA systems limited in their capability to detect very small leaks, and/or visual inspection of the right of way (line flyers, pipeline employees or members of the public). This paper presents a novel and complementary way of detecting small leaks (i.e. sensitivity of 0.1 L/minute, 1 barrel/day) of oil (crude or refined products) using an optical detection system mounted on an airborne platform (UAV, plane or helicopter). The scope of th
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Monir, Solmaz Seyed, Juhua Hu, Ben Tribelhorn, and Heather E. Dillon. "Enhanced Chaotic Transition Prediction Using Hierarchical Clustering for the Lorenz System." In ASME 2023 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2023. http://dx.doi.org/10.1115/imece2023-112433.

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Abstract In this research, we propose a novel way using unsupervised machine learning to improve the accuracy of predicting chaotic transitions in natural convection systems. Previous work has focused on the application of machine learning methods to natural convection systems for understanding turbulent convection transitions. We build on the prior work using the Lorenz system to investigate the potential of unsupervised machine learning models without expert inputs. The Lorenz system was selected due to its relatively simple equations and well-documented chaotic behavior. The Lorenz equation
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