On the Exact Evaluation of Integrals of Wavelets by Enza Pellegrino, Chiara Sorgentone, Francesca Pitolli

“…For this reason, they find applications in a variety of fields, from signal processing to approximation theory. Wavelets are usually derived from refinable functions, which are the solution of a recursive functional equation called the refinement equation. …”
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Data Based Construction of Kernels for Semi-Supervised Learning With Less Labels by Hrushikesh Mhaskar, Sergei V. Pereverzyev, Vasyl Yu. Semenov, Evgeniya V. Semenova

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Effects of Turbulence on the Vortex Modes Carried by Quasi-Diffracting Free Finite Energy Beam in Ocean by Qiyong Liang, Yixin Zhang, Dongyu Yang

“…By developing new wave structure function of a beam waves, we derive the transmitting probability of signal vortex modes in oceanic turbulence based on Rytov approximation theory. Applying this transmitting probability of signal vortex modes, we study the influence of oceanic turbulence on the transmittance of the vortex modes carried by Mathieu-Gaussian beam. …”
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Hierarchically Local Tasks and Deep Convolutional Networks by Deza, Arturo, Liao, Qianli, Banburski, Andrzej, Poggio, Tomaso

“…Recent results in approximation theory have shown that there is an exponential advantage of deep convolutional-like networks in approximating functions with hierarchical locality in their compositional structure. …”
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Heat transfer in the flow of a cold, axisymmetric vertical liquid jet against a hot, horizontal plate by Shu, Jian Jun, Wilks, Graham

“…In a parallel approximation theory, an advanced polynomial approximation for the velocity and temperature distribution is employed and results are in good agreement with those obtained using a simple Pohlhausen polynomial and the numerical solutions.…”
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Design and development of autonomous biomimetic blacktip shark by Wong, Wei Loong

“…The kinematic model and kinetic model approach has been utilized to develop the theoretical model by trajectory approximation theory and beam theory for estimating the robotic fish swimming performance. …”
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Optimized Self-Similar Borel Summation by Simon Gluzman, Vyacheslav I. Yukalov

“…The method is based on the combination of optimized perturbation theory, self-similar approximation theory, and Borel-type transformations. General Borel Fractional transformation of the original series is employed. …”
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Singularity-Free Fixed-Time Adaptive Control with Dynamic Surface for Strict-Feedback Nonlinear Systems with Input Hysteresis by Xuxiang Feng, Jun Chen, Tongyao Niu

“…Based on the universal approximation theory, the radial basis function neural networks are employed to approximate the unknown functions in the nonlinear dynamics. …”
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Numerical investigation of cilia beating modulated flow of magnetized viscous fluid in a curved channel with variable thermal conductivity by Zaheer Abbas, M. Shakib Arslan, M. Yousuf Rafiq

“…The constitutive equations are simplified by the hypothesis of lubrication approximation theory and then solved numerically using the implicit finite difference method (FDM). …”
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On the sharpness of a superconvergence estimate in connection with one-dimensional Galerkin methods by Goebbels StJ

“…<p/> <p>The present paper studies some aspects of approximation theory in the context of one-dimensional Galerkin methods. …”
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The homology groups $H_{n+1} \left( \mathbb{C}\Omega_n \right)$ by A.M. Pasko

“…The spaces $\mathbb{C}\Omega_n$ consist of complex-valued functions and are the analogue of the spaces $\Omega_n$, widely known in the approximation theory. The spaces $\mathbb{C}\Omega_n$ have been introduced in 2015 by A.M. …”
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Application of Bernstein polynomials to suppress the Gibbs effect (literature review) by I.V. Boykov, G.Yu. Salimov

“…Materials and methods. Methods of approximation theory were used in the construction of computational schemes. …”

Approximation Properties of an Extended Family of the Szász–Mirakjan Beta-Type Operators by Hari Mohan Srivastava, Gürhan İçöz, Bayram Çekim

“…Motivated essentially by this aspect of approximation theory, our present study systematically investigates the approximation and other associated properties of a class of the Sz&#225;sz-Mirakjan-type operators, which are introduced here by using an extension of the familiar Beta function. …”
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Reducing computational requirement of stability analysis of milling by partial averaging by Godwin Ozoegwu Chigbogu, Sam Omenyi

“…PA is applied on the Second Order Least Squares Approximated Full-discretization method of [18] to illustrate its usefulness for reducing the cumbersome analysis and CT of the full-discretization method when analysis gets more complicated by higher order interpolation/approximation theory.…”
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Enhancing interest in research activities in mathematics students in teacher training universities by Vlasenko Kateryna, Rovenska Olha, Lovianova Iryna, Kondratyeva Oksana, Achkan Vitaliy

“…The study is dedicated to the feasibility of involving the 5E Instructional Model to the organization of students’ scientific research during the workshop on the Approximation Theory and Fourier Series. The research considers the results of the survey among students who helped to evaluate their emotional state during the workshop. …”
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Approximation of signals (functions) belonging to certain Lipschitz classes by almost Riesz means of its Fourier series by Deepmala, Laurian-Ioan Piscoran

“…The approximation properties of the periodic signals in L r ( r ≥ 1 ) $L^{r}\ (r \geq1)$ -spaces, Lipschitz classes Lipα, Lip ( α , r ) $\operatorname{Lip}(\alpha, r)$ , Lip ( ξ ( t ) , r ) $\operatorname{Lip}(\xi(t), r)$ , and a weighted Lipschitz class W ( L r , ξ ( t ) ) $W(L^{r}, \xi( t))$ through a Fourier series, known as the Fourier approximation in the approximation theory, have wide applications in digital filters and signal analysis. …”
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Error bounds of a function related to generalized Lipschitz class via the pseudo-Chebyshev wavelet and its applications in the approximation of functions by S. Lal, S. Kumar, S.K. Mishra, A.K. Awasthi

“…In this paper, a new computation method derived to solve the problems of approximation theory. This method is based upon pseudo-Chebyshev wavelet approximations. …”
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Study on Numerical Simulation and Electromagnetic Scattering of Time-Invariant Freak Waves by Lichen Han, Gengkun Wu, Bin Liu

“…In this paper, the Kirchhoff approximation theory is used to study the electromagnetic scattering (EM scattering) properties of freak waves on the large scale. …”
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Axisymmetric free vibration of layered conical shells using chebyshev polynomial with collocation method by Viswanathan, K. K., Aziz, Z. A., Lee, J. H., Nurul Izyan, M. D.

“…The formulation of the problem is based on an extension of Love’s first approximation theory. The governing partial differential equations of motion are obtained in terms of the reference surface displacements. …”

Free vibration of layered truncated conical shells filled with quiescent fluid using spline method by Izyan, M. D. N., Viswanathan, K. K., Aziz, Z. A., Lee, J. H., Prabakar, K.

“…Free vibration of layered truncated conical shells filled with quiescent fluid using spline method is studied. Love's first approximation theory is used to formulate the equations of motion of truncated conical shells. …”