In 1901 P. V.Voronets generalised Chaplygin's work to the cases of noncyclic holonomic coordinates and of nonstationary constraints.
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This article provides an error analysis of time discretization applied to spatially discrete approximation of the stationary and nonstationary Navier- Stokes equations. The nonlinearity of the convection term is the main problem in solving a stationary or nonstationary Navier-Stokes equation or Euler equation problems. Stoke incorporated ‘the method of artificial compressibility’ to solve these problems.
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In 2012, The Journal of Econometrics dedicated two FestschriftsVolume 169, Issues 1 and 2 to Phillips under the title Recent Advances in Nonstationary Time Series: A Festschrift in honor of Peter C.B. Phillips.
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Efficient generation of fractional Brownian surfaces poses significant challenges. Since the Brownian surface represents a Gaussian process with a nonstationary covariance function, one can use the Cholesky decomposition method. A more efficient method is Stein's method, which generates an auxiliary stationary Gaussian process using the circulant embedding approach and then adjusts this auxiliary process to obtain the desired nonstationary Gaussian process. The figure below shows three typical realizations of fractional Brownian surfaces for different values of the roughness or Hurst parameter.
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Without leaving the time domain, EMD is adaptive and highly efficient. Since the decomposition is based on the local characteristic time scale of the data, it can be applied to nonlinear and nonstationary processes.
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7, pp. 1076-1086, July 2012. Finally, a different rationale towards addressing the problem of modeling nonstationary data by means of hidden Markov models was suggested in 2012. It consists in employing a small recurrent neural network (RNN), specifically a reservoir network,M.
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NACA Report No. 736 - Nonstationary Flow about a Wing-aileron-tab Combination Including Aerodynamic Balance was issued by the United States National Advisory Committee for Aeronautics in 1942. It analyzes the oscillating air forces on an airfoil that is equipped with various control or lift-augmenting devices.
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Patrick Flandrin is a specialist of signal processing. Since his PhD in 1982, he has conducted research activities in three main directions. He first contributed to fundamental advances in time-frequency analysis, with the development of comprehensive approaches aimed at analyzing, decomposing, and processing nonstationary signalsW. Martin, P. Flandrin, « Wigner-Ville spectral analysis of non-stationary processes », IEEE Trans.
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Since the signal is decomposed in time domain and the length of the IMFs is the same as the original signal, HHT preserves the characteristics of the varying frequency. This is an important advantage of HHT since real-world signal usually has multiple causes happening in different time intervals. The HHT provides a new method of analyzing nonstationary and nonlinear time series data.
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In numerical linear algebra, the Chebyshev iteration is an iterative method for determining the solutions of a system of linear equations. The method is named after Russian mathematician Pafnuty Chebyshev. Chebyshev iteration avoids the computation of inner products as is necessary for the other nonstationary methods. For some distributed-memory architectures these inner products are a bottleneck with respect to efficiency.
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In the case of an incompressible flow the velocity potential satisfies Laplace's equation, and potential theory is applicable. However, potential flows also have been used to describe compressible flows. The potential flow approach occurs in the modeling of both stationary as well as nonstationary flows. Applications of potential flow are for instance: the outer flow field for aerofoils, water waves, electroosmotic flow, and groundwater flow.
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The latter is excited by the acoustic source terms, which are determined from the turbulent fluctuations. Since the aeroacoustics are described by the equations of classical acoustics, the methods are called aeroacoustic analogies. The Lighthill analogy considers a free flow, as for example with an engine jet. The nonstationary fluctuations of the stream are represented by a distribution of quadrupole sources in the same volume.
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If (P,≤) is not a stationary set preserving notion of forcing, i.e., there is a stationary subset of ω1, which becomes nonstationary when forcing with (P,≤), then there is a collection D of \aleph_1 dense subsets of (P,≤), such that there is no D-generic filter. This is why MM is called the maximal extension of Martin's axiom. The existence of a supercompact cardinal implies the consistency of Martin's maximum.
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Lewis received a BS degree in mathematics and a BA degree in political science at Eckerd College, graduating in 1992. He proceeded to earn an MS degree in theoretical statistics from Florida State University in 1995 and a PhD degree in industrial and systems engineering from Georgia Tech in 1998. Lewis' PhD thesis Bias Optimality in a Two-Class Nonstationary Queueing System at Georgia Tech was advised by Robert E. Foley.
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The Hilbert–Huang transform (HHT) is a way to decompose a signal into so- called intrinsic mode functions (IMF) along with a trend, and obtain instantaneous frequency data. It is designed to work well for data that is nonstationary and nonlinear. In contrast to other common transforms like the Fourier transform, the HHT is more like an algorithm (an empirical approach) that can be applied to a data set, rather than a theoretical tool.
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A trojan wave packet is a wave packet that is nonstationary and nonspreading. It is part of an artificially created system that consists of a nucleus and one or more electron wave packets, and that is highly excited under a continuous electromagnetic field. The strong, polarized electromagnetic field, holds or "traps" each electron wave packet in an intentionally selected orbit (energy shell). They derive their names from the trojan asteroids in the Sun–Jupiter system.
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Kaashoeks research interests are in the field of 'the "analysis and Operator Theory, and various connections between Operator Theory, Matrix Theory and Mathematical Systems Theory. In particular, Wiener–Hopf integral equations and Toeplitz operators, their nonstationary variants, and other structured operators, such as continuous operator analogs of Bezout and resultant matrices. State space methods for problems in analysis. Also metric constrained interpolation problems and completion problems for partially given operators, including relaxed commutant lifting problems."M.
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The Heisenberg picture is closest to classical Hamiltonian mechanics (for example, the commutators appearing in the above equations directly correspond to classical Poisson brackets). The Schrödinger picture, the preferred formulation in introductory texts, is easy to visualize in terms of Hilbert space rotations of state vectors, although it lacks natural generalization to Lorentz invariant systems. The Dirac picture is most useful in nonstationary and covariant perturbation theory, so it is suited to quantum field theory and many-body physics.
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The algorithm convergence does not depend on the initial conditions and it will converge for any arbitrarily initial value, hence, it provides good performance in nonstationary images. Disadvantages: The exact values of the expectations of the TDLMS adaptive filter will not converges to a fixed value, if we need to maintain its tracking ability. Therefore, the design choice of μ depends on the particular application and it involves a tradeoff between the convergence speed, tracking ability, and steady-state MSE.
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Olhede earned a master's degree from Imperial College London in 2000, and completed her doctorate there in 2003. Her dissertation, Analysis via Time, Frequency and Scale of Nonstationary Signals, was supervised by Andrew T. Walden. She began her academic career as a lecturer in statistics at Imperial in 2002, and moved to University College London as a professor in 2007. At University College London, she was also an honorary professor of computer science and an honorary senior research associate in mathematics.
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Another recent extension is the triplet Markov model, in which an auxiliary underlying process is added to model some data specificities. Many variants of this model have been proposed. One should also mention the interesting link that has been established between the theory of evidence and the triplet Markov models and which allows to fuse data in Markovian contextBoudaren et al., M. Y. Boudaren, E. Monfrini, W. Pieczynski, and A. Aissani, Dempster-Shafer fusion of multisensor signals in nonstationary Markovian context, EURASIP Journal on Advances in Signal Processing, No. 134, 2012.
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Lukosevicius, H. Jaeger (2009) Reservoir computing approaches to recurrent neural network training, Computer Science Review 3: 127–149. to capture the evolution of the temporal dynamics in the observed data. This information, encoded in the form of a high-dimensional vector, is used as a conditioning variable of the HMM state transition probabilities. Under such a setup, we eventually obtain a nonstationary HMM the transition probabilities of which evolve over time in a manner that is inferred from the data itself, as opposed to some unrealistic ad-hoc model of temporal evolution.
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Analytical and experimental studies have shown that a judicious tradeoff between performance and state complexity leads to practical schemes with considerable performance gains. Thus, reduced- state approaches are promising for increasing linear density. Depending on the surface roughness and particle size, particulate media might exhibit nonstationary data-dependent transition or medium noise rather than colored stationary medium noise. Improvements o\in the quality of the readback head as well as the incorporation of low-noise preamplifiers may render the data- dependent medium noise a significant component of the total noise affecting performance.
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Jech (2003) p.684 The proof uses Shelah's theories of semiproper forcing and iteration with revised countable supports. MM implies that the value of the continuum is \aleph_2Jech (2003) p.685 and that the ideal of nonstationary sets on ω1 is \aleph_2-saturated.Jech (2003) p.687 It further implies stationary reflection, i.e., if S is a stationary subset of some regular cardinal κ≥ω2 and every element of S has countable cofinality, then there is an ordinal α<κ such that S∩α is stationary in α. In fact, S contains a closed subset of order type ω1.
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In mathematics, particularly in set theory, Fodor's lemma states the following: If \kappa is a regular, uncountable cardinal, S is a stationary subset of \kappa, and f:S\rightarrow\kappa is regressive (that is, f(\alpha)<\alpha for any \alpha\in S, \alpha eq 0) then there is some \gamma and some stationary S_0\subseteq S such that f(\alpha)=\gamma for any \alpha\in S_0. In modern parlance, the nonstationary ideal is normal. The lemma was first proved by the Hungarian set theorist, Géza Fodor in 1956. It is sometimes also called "The Pressing Down Lemma".
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Song Yoo-geun (born November 27, 1997) is a South Korean person who gained recognition as a child prodigy in South Korea since 2004. After graduating college in 2009, he was involved in a number of controversies during his ultimately unsuccessful doctorate program at Korean University of Science and Technology (UST), including one involving his paper in October 2015 written with his advisor, Park Seok-jae. The paper, entitled "Axisymmetric, Nonstationary Black Hole Magnetospheres: Revisited" appeared in the Astrophysical Journal (ApJ). However, the paper was soon retracted due to conerns that it plagiarized a 2002 book chapter.
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Agros2D is an open-source code for numerical solutions of 2D coupled problems in technical disciplines. Its principal part is a user interface serving for complete preprocessing and postprocessing of the tasks (it contains sophisticated tools for building geometrical models and input of data, generators of meshes, tables of weak forms for the partial differential equations and tools for evaluating results and drawing graphs and maps). The processor is based on the library Hermes containing the most advanced numerical algorithms for monolithic and fully adaptive solution of systems of generally nonlinear and nonstationary partial differential equations (PDEs) based on hp-FEM (adaptive finite element method of higher order of accuracy). Both parts of the code are written in C++.
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Being in charge of the investigations Minin took part in the works on adaptation of the developed algorithms and creation of the brand new parallel ones for numerical simulation, implemented on the basis of upgraded 128-processor machine PS-2000 as all-in-one decision field. Together with the display stations “Gamma” type it is incorporated in general simulation complex. This system which had no analogues in the USSR made it possible to simulate various significant nonstationary processes of the mechanics of continua. By 1990-91 all the TV centres of the USSR were equipped with video-computer graphic stations GAMMA-T. By means of the developed software-hardware complex the problems of meteoroid protection for spaceship “Vega” (in “Vega-Galley” project) were solved.
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Information processing and inference across wirelessly connected low-power and low-cost sensors, have well documented merits in application domains such as environmental sensing for habitat surveillance, intelligent agriculture, and health monitoring using body area networks. Such wireless sensor networks (WSNs) with or without a central computing unit (fusion center) face major challenges due to their limited bandwidth, stringent power to prolong sensor lifetime, the need to cope with nonstationary and spatiotemporally correlated data, synchronization, access, and resource allocation, to carry out the desired distributed inference tasks. Giannakis and his team pioneered energy-efficient sensor scheduling, power- efficient modulations, and bandwidth-constrained estimators, along with relevant fundamental performance bounds, by investigating inference jointly with compression, quantization, and censoring. Surprisingly, even with a few (1-3) bits per sensor sample, the fusion center could attain 90% of the estimation and tracking performance possible with unquantized observations even with a Kalman tracker utilizing just the sign of innovations.
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