Xuezhi Zhao
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View article: Comparison of Teaching Content on Inequalities between China and Indonesia
Comparison of Teaching Content on Inequalities between China and Indonesia Open
In this study, we select inequality content from a set of Indonesian instructional materials and compare it with the corresponding inequality content in the People’s Education Press (PEP) textbooks. The comparison is significant because th…
View article: Word Length Formulae and Normal Forms of Conjugacy Classes in Surface Groups
Word Length Formulae and Normal Forms of Conjugacy Classes in Surface Groups Open
In this paper, we primarily investigate the following symmetric presentation of the surface group $π_1(Σ_g)=\left\langle c_1,\dots, c_{2g}\mid c_1\cdots c_{2g}c_1^{-1}\cdots c_{2g}^{-1}\right\rangle$. For every nontrivial element $x\in π_1…
View article: Multi-dimensional Empowerment System for General Education Curriculum Reform from Cross-cultural Perspectives
Multi-dimensional Empowerment System for General Education Curriculum Reform from Cross-cultural Perspectives Open
View article: Radiological Levels and Assessment of the Environment and Wastewater in Shale Gas Areas
Radiological Levels and Assessment of the Environment and Wastewater in Shale Gas Areas Open
View article: An Onsager-type Theorem for General 2D Active Scalar Equations
An Onsager-type Theorem for General 2D Active Scalar Equations Open
This paper concerns the Onsager-type problem for general 2-dimensional active scalar equations of the form: $\partial_t θ+u\cdot\nabla θ= 0$, with $u=T[θ]$ being a divergence-free velocity field and $T$ being a Fourier multiplier operator …
View article: Elevating student engagement and academic performance: A quantitative analysis of Python programming integration in the Merdeka Belajar curriculum
Elevating student engagement and academic performance: A quantitative analysis of Python programming integration in the Merdeka Belajar curriculum Open
Python programming is widely employed in educational institutions worldwide. Within the Merdeka Belajar curriculum context, this programming is recognized as a suitable vehicle for mathematics instruction, significantly influencing student…
View article: A Novel Relocalization Method-Based Dynamic Steel Billet Flaw Detection and Marking System
A Novel Relocalization Method-Based Dynamic Steel Billet Flaw Detection and Marking System Open
In the current steel production process, occasional flaws within the billet are somewhat inevitable. Overlooking these flaws can compromise the quality of the resulting steel products. To address and mark these flaws for further handling, …
View article: On the Whitney disks in Heegaard Floer homology theory
On the Whitney disks in Heegaard Floer homology theory Open
The Whitney disks play a central role in defining Heegaard Floer homology of a $3$-dimensional manifold. We use Nielsen theory to a simple criterion to the existence of Whitney disks, connecting two given intersections.
View article: Persistence of sub-chain groups
Persistence of sub-chain groups Open
In this work, we present a generalization of extended persistent homology to filtrations of graded sub-groups by defining relative homology in this setting. Our work provides a more comprehensive and flexible approach to get an algebraic i…
View article: Human Cognitive: Learning Mathematics through Python Programming to Support Students’ Problem-Solving Skills
Human Cognitive: Learning Mathematics through Python Programming to Support Students’ Problem-Solving Skills Open
Programming languages have been used and developed in the field of education.Python programming was employed in this study.The goal of this study is to see whether there is an effect of using Pydroid in mathematics learning on students' pr…
View article: Periodic points of self-maps of a space with π1X = Zps
Periodic points of self-maps of a space with π1X = Zps Open
The crucial homotopy invariants in Nielsen periodic point theory are the numbers: NPn(f), which is a lower bounds of the number of periodic points of length equal n, and NFn(f) a lower bounds of the number of periodic…
View article: On the Kernel of the Borel’s Characteristic Map of Lie Groups
On the Kernel of the Borel’s Characteristic Map of Lie Groups Open
For compact and connected Lie group $G$ with a maximal torus $T$ the quotient space $G/T$ is canonically a smooth projective manifold, known as the complete flag manifold of the group $G.$ The cohomology ring map $c^∗: H^∗ (B_T) → H^∗ (G/T…
View article: Fixed point indices and fixed words at infinity of selfmaps of graphs II
Fixed point indices and fixed words at infinity of selfmaps of graphs II Open
The index $\mathrm{ind}(\mathbf{F})$ of a fixed point class $\mathbf{F}$ is a classical invariant in the Nielsen fixed point theory. In the recent paper \cite{ZZ}, the authors introduced a new invariant $\mathrm{ichr}(\mathbf{F})$ called t…
View article: Olfactory dysfunction after COVID‐19: metanalysis reveals persistence in one-third of patients 6 months after initial infection
Olfactory dysfunction after COVID‐19: metanalysis reveals persistence in one-third of patients 6 months after initial infection Open
View article: CD11c+ B Cells Participate in the Pathogenesis of Graves’ Disease by Secreting Thyroid Autoantibodies and Cytokines
CD11c+ B Cells Participate in the Pathogenesis of Graves’ Disease by Secreting Thyroid Autoantibodies and Cytokines Open
Graves’ disease (GD) is a common autoimmune disorder with an elevation in pathogenic autoantibodies, specifically anti-thyrotropin receptor antibodies (TRAbs), which are secreted by autoreactive B cells. To date, there has been little rese…
View article: Cytokines in the Immune Microenvironment Change the Glycosylation of IgG by Regulating Intracellular Glycosyltransferases
Cytokines in the Immune Microenvironment Change the Glycosylation of IgG by Regulating Intracellular Glycosyltransferases Open
Background Changes in IgG glycosylation, as a novel pathological feature, are observed in various autoimmune diseases (AIDs). The glycosylation patterns of IgG play a critical role in regulating the biological function and stability of IgG…
View article: Schubert calculus and intersection theory of flag manifolds
Schubert calculus and intersection theory of flag manifolds Open
Hilbert's 15th problem called for a rigorous foundation of Schubert calculus, of which a long-standing and challenging part is the Schubert problem of characteristics. In the course of securing a foundation for algebraic geometry, Van der …
View article: Исчисление Шуберта и теория пересечений многообразий флагов
Исчисление Шуберта и теория пересечений многообразий флагов Open
В 15-й проблеме Гильберта была поставлена задача строгого обоснования исчисления Шуберта; сложной частью такого обоснования является давняя проблема характеристик Шуберта. В ходе создания основ алгебраической геометрии Ван дер Варден и А. …
View article: Make Schubert's Calculus Calculable
Make Schubert's Calculus Calculable Open
Hilbert's 15th problem asked for a rigorous foundation of Schubert's enumerative calculus, in which a long standing and challenging part is Schubert's problem of characteristics. In the course to secure the foundation of intersection theor…
View article: Cope with the COVID-19 pandemic: Dynamic bed allocation and patient subsidization in a public healthcare system
Cope with the COVID-19 pandemic: Dynamic bed allocation and patient subsidization in a public healthcare system Open
View article: A stronger version of Borsuk-Ulam theorem
A stronger version of Borsuk-Ulam theorem Open
The classical Borsuk-Ulam theorem states that for any continuous map $f: S^m\rightarrow \mathbb{R}^m$, there is a pair of antipodal points having the same image. In this paper, we shall prove that there is also another pair of non-antipoda…
View article: The multiple points of maps from sphere to Euclidean space
The multiple points of maps from sphere to Euclidean space Open
In this paper, we obtain some sufficient conditions to guarantee the existence of multiple points of maps from $S^m$ to $\mathbb{R}^d$. Our main tool is the ideal-valued index of $G$-space defined by E. Fadell and S. Husseini. We obtain mo…
View article: Fixed point indices and fixed words at infinity of selfmaps of graphs
Fixed point indices and fixed words at infinity of selfmaps of graphs Open
View article: The Impact of the SARS-COV-2 Pandemic on the Mental Health and Employment Decisions of Medical Students in North China
The Impact of the SARS-COV-2 Pandemic on the Mental Health and Employment Decisions of Medical Students in North China Open
Background: The outbreak of severe respiratory syndrome coronavirus 2 (SARS-COV-2) has led to long periods of social isolation for individuals across the world. Although medical students generally have a high prevalence of mental health pr…
View article: The Immune Microenvironment of Hashimoto’s Thyroiditis Regulates the Glycosylation Modification of IgG
The Immune Microenvironment of Hashimoto’s Thyroiditis Regulates the Glycosylation Modification of IgG Open
Objectives: Elevation of anti-thyroglobulin antibodies that are primarily IgG isotype is a hallmark of Hashimoto’s thyroiditis (HT). As for IgG,it bears two conserved repertoire of N-linked glycans attached to its crystallizable fragment (…
View article: Spatial and temporal variation characteristics of atmospheric NO2 and SO2 in the Beijing-Tianjin-Hebei region before and after the COVID-19 outbreak
Spatial and temporal variation characteristics of atmospheric NO2 and SO2 in the Beijing-Tianjin-Hebei region before and after the COVID-19 outbreak Open
View article: Simple Smale flows and their templates on S3
Simple Smale flows and their templates on S3 Open
View article: Cope with the COVID-19 Pandemic: Dynamic Bed Allocation and Patient Subsidization in a Public Healthcare System
Cope with the COVID-19 Pandemic: Dynamic Bed Allocation and Patient Subsidization in a Public Healthcare System Open
View article: Recommendation from Peking Union Medical College Hospital for urgent hemodialysis during the COVID-19 pandemic
Recommendation from Peking Union Medical College Hospital for urgent hemodialysis during the COVID-19 pandemic Open
View article: The clinical characteristics and outcomes of patients with diabetes and secondary hyperglycaemia with coronavirus disease 2019: A single‐centre, retrospective, observational study in Wuhan
The clinical characteristics and outcomes of patients with diabetes and secondary hyperglycaemia with coronavirus disease 2019: A single‐centre, retrospective, observational study in Wuhan Open
Aim To explore whether coronavirus disease 2019 (COVID‐19) patients with diabetes and secondary hyperglycaemia have different clinical characteristics and prognoses than those without significantly abnormal glucose metabolism. Materials an…