2022

Another Proof of Zagier's Matrix Conjecture

Yawen Ma, Lee-Peng Teo

Journal of Integer Sequences

Describing Amoebas

Mounir Nisse, Frank Sottile 

Pacific Journal of Mathematics

Forecasting Heterogeneous Municipal Solid Waste Generation via Bayesian-optimised Neural Network with Ensemble Learning for Improve Generalisation 

Zheng Xuan Hoy, Kok Sin Woon, Wen Cheong Chin, Haslenda Hashim, Yee Van Fan

Computers & Chemical Engineering

Theta Function and Adiabatic Curvature on an Elliptic Curve

Ching Hao Chang, JH Cheng, IH Tsai 

The Journal of Geometric Analysis

Simpon's Second-Type Inequalities for Co-Ordinated Convex Functions and Applications for Cubature Formulas
Sabah Iftikhar, Samet Erden, Muhammad Aamir Ali, Jamel Baili and Hijaz Ahmad

Fractal and Fractional

2021

Infinitesimal homogeneity and bundles

Arash Bazdar, Andrei Teleman

Annals of Global Analysis and Geometry

Stagnation point bionanofluid slip flow model: Sensitivity analysis

Sze Qi Chan, Fazlina Aman, Syahira Mansur

Alexandria Engineering Journal

Summary: summary_chan_szeqi_2021.pdf 

Restrictions on the Existence of a Canonical System Flow Hierarchy

Injo Hur, Darren C. Ong

Integral Equations and Operator Theory

Simon’s OPUC Hausdorff dimension conjecture

David Damanik, Shuzheng Guo, Darren C. Ong 

Mathematische Annalen

Summary: summary_darren_ong_2021.pdf

Thermodynamic analysis of CaS production from various Ca-based precursors: A prequel to SO2 reduction mediated by CaS/CaSO4 redox agents 

Kim Hoong Ng, Siaw Ching Liew, and Shaoliang Zhang 

Process Safety and Environmental Protection

The zero-temperature limit of grand canonical ensembles via tropical geometry 

Mounir Nisse and Yen-Kheng Lim

Analysis and Mathematical Physics

Summary: summary_nisse_yklim_tropical_2021.pdf

A Natural Topological Manifold Structure of Phase Tropical Hypersurfaces

Young Rock Kim, Mounir Nisse 

Journal of Korean Mathematics Society

Light-ring pairs from A-discriminantal varieties

Yen-Kheng Lim, Mounir Nisse

Physical Review D

Summary: summary_yklim_nisse_light_2021.pdf 

Donaldson–Thomas invariants of abelian threefolds and Bridgeland stability conditions 

Georg Oberdieck, Dulip Piyaratne, Yukinobu Toda

Journal of Algebraic Geometry

Summary

Resolvent trace formula and determinants of n Laplacians on orbifold Riemann surfaces

Lee-Peng Teo

SIGMA

Aperiodic Quantum Walk Models Exhibiting Exotic Spectral Behaviour Connected to Quantum Computing

Darren Ong Chung Lee (funded by FRGS)

Asymptotic Behavior of Arithmetic Functions 

Teo Lee Peng (funded by XMUMRF)

In analytic number theory, estimating the asymptotic behavior of arithmetic functions is an important topic. Despite being classical, the research in improving the estimates in the error terms of the prime number theorem and the Siegel-Walfisztheorem has never stopped. Usually, some auxiliary functions and parameters are used. We plan to employ some optimization method to choose the auxiliary function and parameters.   

Adaptive Mesh-Free Wavelet-Based Collocation Method for the Coupled Analysis of Thermal-Magneto-Electro-Elastic Plates

Liew Siaw Ching, Liu MeiFeng (funded by XMUMRF)

In this research, an adaptive meshless simulation for the coupled analysis of Thermo-magneto-electro-elastic (TMEE) plate based on wavelet multiscale resolution and radial basis (RBF) collocation will be presented. Nonlinear governing equations for the thermo-magneto-electro-elastic (TMEE) plate subjected to coupling applied load will be derived under the consideration of finite strain deformation, and then meshless method will be adopted to take over the tasks for static behaviour or dynamical response of the invented mathematical model. The adaptive element-free wavelet method (AEFWM) will be developed in this research project by using two-scale Daubechies wavelets in accordance with the radical basis collocation function. Node adaption will be implemented according to the tendency of wavelet coefficients, additional nodes will be added on the neighbourhood of active node point, the adaptive criterion and node refinement scheme for the AEFWM will be discussed in detail. The proposed numerical method can be used to find out the solution for the partial differential equations aroused in the coupled TMEE plate due to crack, shock wave, moving boundary conditions or nonlinear applied load etc.