Entropy numbers of embeddings of function spaces with Muckenhoupt weights, III. Some limiting cases by Dorothee D. Haroske, Leszek Skrzypczak

“…Essential tools are a discretisation in terms of wavelet bases, as well as a refined study of associated embeddings in sequence spaces and interpolation arguments in endpoint situations.…”
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Projected Adaptive Cubic Regularization Algorithm with Derivative-Free Filter Technique for Box Constrained Optimization by Lingyun He, Peng Wang, Detong Zhu

“…The affine scaling interior-point cubic model is based on the quadratic probabilistic interpolation approach on the objective function. The new iterations are obtained by the solutions of the projected adaptive cubic regularization algorithm with filter technique. …”
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Unified Framework of Approximating and Interpolatory Subdivision Schemes for Construction of Class of Binary Subdivision Schemes by Pakeeza Ashraf, Ghulam Mustafa, Abdul Ghaffar, Rida Zahra, Kottakkaran Sooppy Nisar, Emad E. Mahmoud, Wedad R. Alharbi

“…The proposed algorithm is based on three-point approximating binary and four-point interpolating binary subdivision schemes. It contains a parameter which classifies members of the new class of subdivision schemes. …”
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On constraints of the (β-deformed) partition functions with W-representations by Yu-Sen Zhu, Ren Cuo Ji, Min-Li Li, Rui Wang

“…We investigate the constraints of the (β-deformed) partition functions with W-representations in the literature, which can be realized by the interpolating two-matrix models (two β-ensembles). For the non-deformed partition functions, we construct their Virasoro and higher order constraints using the total derivative operators. …”
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Intelligent prediction and understanding of self-shrinkage in ultra-high performance concrete based on machine learning by Ji Hao, Wenbin Jiao, Xinpo Xie, Dula Man, Shengwei Huang

“…Initially, missing data were interpolated using the modified Akima interpolation method, with visualized results provided for discussion. …”
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Environmental Covariates for Sampling Optimization and Pest Prediction in Soybean Crops by Cenneya Lopes Martins, Maiara Pusch, Wesley Augusto Conde Godoy, Lucas Rios do Amaral

“…The data showed no spatial dependence, making using geostatistical interpolators inappropriate. However, a multi-objective optimized sampling design, tailored to refine configurations for identifying and estimating variograms and spatial trends essential for spatial interpolation, produced the most accurate predictions. …”
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Multivariate p-Adic Fermionic q-Integral on ℤp and Related Multiple Zeta-Type Functions by Min-Soo Kim, Taekyun Kim, Jin-Woo Son

“…They also raised the following problem: “are there analytic multiple twisted Carlitz's type q-zeta functions which interpolate multiple twisted Carlitz's type q-Euler (Bernoulli) polynomials?” …”
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Numerical Integration of a Class of Singularly Perturbed Delay Differential Equations with Small Shift by Gemechis File, Y. N. Reddy

“…Then, Simpson’s rule and linear interpolation are employed to get the three-term recurrence relation which is solved easily by discrete invariant imbedding algorithm. …”
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First Characterization of a New Method for Numerically Solving the Dirichlet Problem of the Two-Dimensional Electrical Impedance Equation by Marco Pedro Ramirez-Tachiquin, Cesar Marco Antonio Robles Gonzalez, Rogelio Adrian Hernandez-Becerril, Ariana Guadalupe Bucio Ramirez

“…The analysis is performed by introducing interpolating piecewise separable-variables conductivity functions in the unit circle. …”
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Classical Theory of Linear Multistep Methods for Volterra Functional Differential Equations by Yunfei Li, Shoufu Li

“…Based on the linear multistep methods for ordinary differential equations (ODEs) and the canonical interpolation theory that was presented by Shoufu Li who is exactly the second author of this paper, we propose the linear multistep methods for general Volterra functional differential equations (VFDEs) and build the classical stability, consistency, and convergence theories of the methods. …”
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Displacement Field Approximations for Force-Based Elements in Large Displacement Analyses by M. Vahidi, V. Jafari, M. H. Abyaneh, SH. Vahdani

“…The three fields, introduced in this review, are: curvature-based displacement interpolation (CBDI) used in matrix-based flexibility formulations, linear displacement approximation applied in state space, and higher-order displacement approximation utilized again in state space. …”
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On the Bivariate Spectral Homotopy Analysis Method Approach for Solving Nonlinear Evolution Partial Differential Equations by S. S. Motsa

“…The new approach, termed bivariate spectral homotopy analysis method (BISHAM), is based on the use of bivariate Lagrange interpolation in the so-called rule of solution expression of the HAM algorithm. …”
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Implicit One-Step Block Hybrid Third-Derivative Method for the Direct Solution of Initial Value Problems of Second-Order Ordinary Differential Equations by Mohammad Alkasassbeh, Zurni Omar

“…In deriving this method, a power series approximate function is interpolated at {xn,xn+r} while its second and third derivatives are collocated at all points {xn,xn+r,xn+s,xn+t,xn+1} in the given interval. …”
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An Implicit Collocation Method for Direct Solution of Fourth Order Ordinary Differential Equations by B. Alechenu, D.O. Oyewola

“… This paper presented a linear multistep method for solving fourth order initial value problems of ordinary differential equations. Collocation and interpolation methods are adopted in the derivation of the new numerical scheme which is further applied to finding direct solution of fourth order ordinary differentiation equations. …”
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On Generalized Arakawa–Kaneko Zeta Functions with Parameters a,b,c by Nestor G. Acala, Edward Rowe M. Aleluya

“…In this paper, an interpolation formula between these generalized zeta functions and the poly-Bernoulli polynomials with a,b,c parameters is obtained. …”
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An Implicit Collocation Method for Direct Solution of Fourth Order Ordinary Differential Equations by B. Alechenu, D.O. Oyewola

“… This paper presented a linear multistep method for solving fourth order initial value problems of ordinary differential equations. Collocation and interpolation methods are adopted in the derivation of the new numerical scheme which is further applied to finding direct solution of fourth order ordinary differentiation equations. …”
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Calculation of Correction Factors for Vickers’ Hardness Measurements on a Non-Planar Surface by S. G. Sandomirski, A. L. Val’ko, S. P. Rudenko

“…The K values for d/D ratios not given in the tables are determined by interpolation from the closest to the measured tabulated d/D values. …”
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Repairbads: An automatic and adaptive method to repair bad channels and segments for OPM-MEG by Fulong Wang, Yujie Ma, Tianyu Gao, Yue Tao, Ruonan Wang, Ruochen Zhao, Fuzhi Cao, Yang Gao, Xiaolin Ning

“…Most common methods directly reject or interpolate to repair these bad channels and segments. …”
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Numerical Prediction of Fatigue Life for Landing Gear Considering the Shock Absorber Travel by Haihong Tang, Panglun Liu, Jianbin Ding, Jinsong Cheng, Yiyao Jiang, Bingyan Jiang

“…In this way, the fatigue stress of the MLG with any actual SAT can be obtained by interpolating the stress components of the seven FEMs. …”
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Approximate Solutions of Fisher's Type Equations with Variable Coefficients by A. H. Bhrawy, M. A. Alghamdi

“…The spatial derivatives are collocated at a Legendre-Gauss-Lobatto interpolation nodes. The proposed method has the advantage of reducing the problem to a system of ordinary differential equations in time. …”
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