An Improved Unscented Kalman Filter for Discrete Nonlinear Systems with Random Parameters by Yue Wang, Zhijian Qiu, Xiaomei Qu

“…The theoretical analysis reveals that the approximated mean and covariance via the improved unscented transformation match the true values correctly up to the third order of Taylor series expansion. Based on the improved unscented transformation, an improved UKF method is proposed to expand the application of the UKF for nonlinear systems with random parameters. …”
Get full text

Using Chebyshev’s polynomials for solving Fredholm integral equations of the second kind by José Antonio Ezquerro, Miguel Ángel Hernández-Verón

“…Thus, when we want to apply the Newton method directly to solve an integral equation, the existence of the inverse of the first derivative is guaranteed, when the kernel is sufficiently differentiable into any of its two components, through its approximation by Taylor’s polynomial. In this paper, we study the case in which the kernel is not differentiable in any of its two components. …”
Get full text

Orthogonally Additive and Orthogonality Preserving Holomorphic Mappings between C*-Algebras by Jorge J. Garcés, Antonio M. Peralta, Daniele Puglisi, María Isabel Ramírez

“…We study holomorphic maps between C*-algebras A and B, when f:BA(0,ϱ)→B is a holomorphic mapping whose Taylor series at zero is uniformly converging in some open unit ball U=BA(0,δ). …”
Get full text

HV&I Reviewer Highlight by Ronald Ellis, Adam Weiss

Get full text

Approximation algorithm to symmetric alpha stable distribution with bi-region curve model by Kang WANG, Zhi-jiang XU, Li-min MENG

“…The symmetric alpha stable (S S) was used to model a non-Gaussian,heavy tail and impulsive noise of com-α munication channels.However,explicit expressions for the probability density functions (PDF) in terms of elementary functions are still unknown except for some special cases,which limits the application of the SαS distribution in practice,which the bi-region separated by the triple divergence was proposed Specially,within the triple divergence,a simple exponential function with two special parameters was constructed,the two parameters were determined by using Taylor serial expansion.Compared with conventional algorithms using the series expansion,the proposed algorithm avoids the selecting the number of the series items and the risk of series expansion divergence.Moreover,numerical results verify that the proposed approximation is closer to the actual SαS PDF than the conventional Cauchy-Gaussian mixture approximation.…”
Get full text

Some Novel Sixth-Order Iteration Schemes for Computing Zeros of Nonlinear Scalar Equations and Their Applications in Engineering by M. A. Rehman, Amir Naseem, Thabet Abdeljawad

“…We develop these iteration schemes with the help of Taylor’s series expansion, generalized Newton-Raphson’s method, and interpolation technique. …”
Get full text

Public Land Management Agencies’ and Nonindustrial Private Forest Landowners’ Perceptions towards Ecosystem Services by Taylor Stein, Namyun Kil, Alexis Frank, Alison E. Adams, Damian C. Adams, Francisco J. Escobedo

“…This 5-page fact sheet was written by Taylor Stein, Namyun Kil, Alexis Frank, Alison E. …”
Get full text

NON-PROBABILISTIC RELIABILITY SENSITIVITY ANALYSIS BASED ON CONVEX MODEL by QIAO XinZhou, SU QuanWei, LI Long, Ge HongYu

“…Through-two different choices of the linearization point, the approximate functions of non-linear limit state functions can be then obtained by using the first-order Taylor expansion, then the approximate analytical equations of non-probabilistic reliability sensitivity were given. …”
Get full text

Planar Two-Dimensional Vibration Isolator Based on Compliant Mechanisms by Ruizhe Zhu, Jinpeng Hu, Long Huang, Leiyu Zhang, Guangan Ren

“…The dynamic model is established by using the third-order Taylor expansion and the harmonic balance method. …”
Get full text

Protrusion of the Rod Electrode in the Electrospinning Process by Jan Valtera, Lucie Vysloužilová, Jiří Komárek, Josef Skřivánek, Petr Žabka, Jaroslav Beran, David Lukáš

“…The principal study and experiments with basic apparatus were carried out and presented by Taylor in 1966. This study is focused on the arrangement closely related to the design of the real electrospinning device with respect to the safety and technological aspects. …”
Get full text

Advancing numerical solutions for a system of singularly perturbed delay differential equations at linear rate by Dany Joy, Dinesh Kumar S, Fathalla A Rihan

“…The innovation of this approach stems from its unique integration of three key elements: the Numerov method, known for its accuracy in solving second-order ODEs; a fitting factor, which improves handling of the singular perturbation parameter essential for accurately modeling SPDDEs; and the Taylor series expansion, which approximates first-order derivative terms, facilitating the application of the Numerov method to the system. …”
Get full text

Celtic Stone Dynamics Revisited Using Dry Friction and Rolling Resistance by J. Awrejcewicz, G. Kudra

“…In the numerical experiments the simulation results of the Celtic stone with the friction forces modelled by the use of approximants of different complexity (from no coupling between friction force and torque to the second order Padé approximation) are compared to results obtained from model with friction approximated in the form of piecewise polynomial functions (based on the Taylor series with hertzian stress distribution). …”
Get full text

Composite trapezoidal quadrature for computing hypersingular integrals on interval by Xiaoping Zhang, Jin Li

“…In this paper, composite trapezoidal quadrature for numerical evaluation of hypersingular integrals was first introduced. By Taylor expansion at the singular point $ y $, error functional was obtained. …”
Get full text

Halál és halhatatlanság a Phaidónban by Máté Héthelyi

“…Az érvet több szerző is hibásnak tekinti a Platón-szakirodalomban – például Taylor, Bostock –, ugyanis abból, hogy valami halhatatlan, nem feltétlenül következik, hogy egyben elpusztíthatatlan is. …”
Get full text

Semidefinite Optimization Providing Guaranteed Bounds on Linear Functionals of Solutions of Linear Integral Equations with Smooth Kernels by Guangming Zhou, Chao Deng, Kun Wu

“…Firstly, the primal problem with smooth kernel is converted to a series of approximative problems with Taylor polynomials obtained by expanding the smooth kernel. …”
Get full text

Icebreakers for Adults by Megan Stein, Taylor Nash

“…Written by Megan Stein and Taylor Nash. …”
Get full text

Religions as a source of (dis)order by J. Urbaniak

“…Building upon insights of Charles Taylor and Hans Küng, I show in what sense the world religions can be considered the source of order as well as disorder and how the plurality of religiouslybased “orders” can be accepted and embraced with trust rather than suspicion. …”
Get full text

Asymptotic solution for turbulent variances: application to convergence of averages and particle dispersion by Gervásio Annes Degrazia, Michel Stefanello, Felipe Denardin Costa, Luís Gustavo Nogueira Martins, Otávio Costa Acevedo

“… An alternative solution to the asymptotic Taylor statistical diffusion theorem (variance of particle dispersion) and the asymptotic variance quantifying convergence of averages is presented. …”
Get full text

Icebreakers for Adults by Megan Stein, Taylor Nash

“…Written by Megan Stein and Taylor Nash. …”
Get full text