Christophe Pere, PhD’s Post

In the paper published in Foundations of Computational Mathematics, Hu Jun research group from #PKU School of Mathematical Sciences proposes a construction of C^r conforming finite element spaces with arbitrary r in any dimension. https://lnkd.in/gSnANyAc #PKUResearch #Mathematics

https://lnkd.in/g289C7Ve Beautifully written, the book contains practical applications as well as conceptual developments in finite mathematics and combinatorics. #mathematics #algorithms #finitemathematics #combination #computerscience

So I was trying to find why conformal transformations are at most quadratic for more dimensions higher than 2. Textbooks often gloss over this argument by making a small jump in reasoning. I wrote a small note on why conformal transformations are quadratic where I filled in the gap in the logic of the usual argument and then gave an alternative reason why this happens. The note is too short (and not so important) for putting on arxiv so I have put it on my website and you can read it there if you want (link below). #physics #scicomm #research #academia

Our latest research on "Fourth-Order Trapezoid Algorithm with Four Iterative Schemes for Nonlinear Integral Equations" has just been published with @SpringerNature in @Lobachevskii Journal of Mathematics. Read here: https://rdcu.be/dpI0o

Happy to share that our work on the Nullstellensatz and Graph Coloring is finally published on SIAM Discrete Math! https://lnkd.in/dmWQQNsV

🚀#mdpisymmetry #featurepaper Excited to share a Feature Paper with you. "On Independent Secondary Dominating Sets in Generalized Graph Products" 🔸https://lnkd.in/gXb3y834 🔹Authors: Adrian Michalski and Paweł Bednarz Rzeszow University of Technology 🔸Abstract: In 2008, Hedetniemi et al. introduced (1,𝑘)-domination in graphs. The research on this concept was extended to the problem of existence of independent (1,𝑘)-dominating sets, which is an 𝒩𝒫-complete problem. In this paper, we consider independent (1,1)- and (1,2)-dominating sets, which we name as (1,1)-kernels and (1,2)-kernels, respectively... #graphtheory Mathematics Section of Symmetry

A new research paper has been accepted to publish with the following title Comparative Analysis on Bilinear Time Series Models with Time-Varying and Symmetric GARCH Coefficients: Estimation and Simulation, Journal: Symmetry MDPI. Section: Mathematics. Special Issue: Advance in Functional Equations, Second Edition. Authored by Ma’mon Abu Hammad, Rami Alkhateeb, Nabil LAICHE, Adel Ouannas, Shameseddin Alshorm. Abstract The paper aims to work on a sample of bilinear time series models that are famous in the statistical literature. The coefficients of the sample models take a varied situation one time. The GARCH (1,1) model is defined as the white noise of the coefficients for sample models that are satisfied by time-varying coefficients. These, necessary conditions of stationarity for the models are presented. To estimate the coefficients, the least squares method is used. The impact of estimators and their approximations according to the sample size is illustrated by applying the fundamental theorem of Klimko and Nilsen. This also demonstrates the clarification of the GARCH white noise trace in estimating the model’s coefficients. The results are determined as related between the model and the nature of white noise. Keywords: Bilinear time series models; GARCH models; least squares approach.

Check out our latest paper titled: New High-Order Numerical Methods for Hyperbolic Systems of Nonlinear PDEs with Uncertainties published in Communications on Applied Mathematics and Computation https://lnkd.in/eNt4FCAF