Applications of adjoint data assimilation, which is designed to bring an ocean circulation model into consistency with ocean observations, are computationally demanding. To improve the convergence rate of an optimization, reduced-order optimization methods that reduce the size of the control vector by projecting it onto a limited number of basis functions were suggested. In this paper, we show ...

The purpose of the research is to determine area setting argument τ and its discretizationintervals when constructing an algorithm for adaptive nonlinearoptimal smoothing multi-parameter data trajectory measurements, which makes it possible tojointly implement spatial temporal redundancy obtained. wascarried out by a Λ-orthogonal basis function in order obtain independent estimatesfor coefficie...

This work demonstrates the use of Latin Hypercube Sampling and Proper Orthogonal Decomposition in combination with a Radial Basis Function model to perform on vehicle prediction coupled fluid–thermal–structure. We regarded Mach number, flight altitude angle attack as input parameters established rapid model. The basic process numerical simulation hypersonic fluid–thermal–structure was studied o...

We prove that there is an orthonormal basis for square-integrable (waveform) cuspforms on SL2(Z)\H. First, we reconsider the well-known fact that the Hilbert space L(T) on the circle T = R/2πZ has an orthogonal Hilbert-space basis of exponentials e with n ∈ Z, using ideas relevant to situations lacking analogues of Dirichlet or Fejer kernels. These exponentials are eigenfunctions for the Laplac...

In the past of two decades, wavelet methods have been adopted enthusiastically in many engineering applications such as signal and image processing. However, like most of the classic orthogonal expansions, wavelet expansions also exhibit Gibbs phenomenon around discontinuities of the original signals. Therefore, the recovered signals using wavelet expansions could be corrupted by the overshoot ...

Sets of neuronal tuning curves, which describe the responses of neurons as functions of a stimulus, can serve as a basis for approximating other functions of stimulus parameters. In a function-approximating network, synaptic weights determined by a correlation-based Hebbian rule are closely related to the coefficients that result when a function is expanded in an orthogonal basis. Although neur...

We prove universality of local eigenvalue statistics in the bulk of the spectrum for orthogonal invariant matrix models with real analytic potentials with one interval limiting spectrum. Our starting point is the Tracy-Widom formula for the matrix reproducing kernel. The key idea of the proof is to represent the differentiation operator matrix written in the basis of orthogonal polynomials as a...

This study describes a method of calculating the mean squared error (MSE) incurred when estimating the spherical harmonic coefficients of a climatological field that is sampled at a small network of points. The method can also be applied to the coefficients of any other set of orthonormal basis functions that are defined on the sphere. It, therefore, provides a formalism that can be applied in ...

Connected chaotic systems can, under some circumstances, synchronize their states with an exchange of matter and energy between the systems. This is the case for toy models like the Lorenz 63, and more complex models. In this study we perform synchronization experiments with two connected quasi-geostrophic (QG) models of the atmosphere with 1449 degrees of freedom. The purpose is to determine w...

In several areas of computational mathematics, wavelet-based algorithms are becoming popular for modelling and analyzing data, providing efficient means for hierarchical data decomposition, reconstruction, editing and compression. Such algorithms are typically based on the decomposition of function spaces into mutually orthogonal wavelet spaces, each of which is endowed with a basis. The basis ...