Hao Pan

ORCID: 0000-0003-2709-1494
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About
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Research Areas
  • Analytic Number Theory Research
  • History and Theory of Mathematics
  • Limits and Structures in Graph Theory
  • COVID-19 Pandemic Impacts
  • COVID-19 epidemiological studies
  • Advanced Mathematical Identities
  • Advanced Mathematical Theories
  • Functional Equations Stability Results
  • Graph Labeling and Dimension Problems
  • Algebraic Geometry and Number Theory
  • Graph theory and applications
  • Ideological and Political Education
  • Advanced Algebra and Geometry
  • Mathematics and Applications
  • Viral Infectious Diseases and Gene Expression in Insects
  • Analytic and geometric function theory
  • Higher Education Learning Practices
  • Benford’s Law and Fraud Detection
  • Advanced Combinatorial Mathematics
  • Cryptography and Residue Arithmetic
  • Education and Work Dynamics
  • Air Quality Monitoring and Forecasting
  • Mathematical Approximation and Integration
  • Heavy Metal Exposure and Toxicity
  • Kruppel-like factors research

Anhui Normal University
2023-2025

Union Hospital
2022-2024

Shuguang Hospital
2024

Shanghai University of Traditional Chinese Medicine
2024

Huazhong University of Science and Technology
2024

Shanghai Children's Medical Center
2023

Shanghai Jiao Tong University
2023

Institute of Applied Physics and Computational Mathematics
2020-2022

China Southern Power Grid (China)
2022

Nanjing University of Finance and Economics
2022

Developmental language disorder (DLD) is a condition that significantly affects children's achievement but has been understudied. We aim to estimate the prevalence of DLD in Shanghai, compare co-occurrence difficulties between children with and those typical development (TD), investigate early risk factors for DLD.We estimated using data from population-based survey cluster random sampling design China. A subsample (aged 5-6 years) received an onsite evaluation, each child was categorized as...

10.1016/j.lanwpc.2023.100713 article EN cc-by-nc-nd The Lancet Regional Health - Western Pacific 2023-02-17

Based on SEIR (susceptible–exposed–infectious–removed) epidemic model, we propose a modified mathematical model to describe the spread of coronavirus disease 2019 (COVID-19) in Wuhan, China. Using public data, uncertainty parameters proposed for COVID-19 Wuhan were calibrated. The control basic reproduction number was studied with posterior probability density function parameters. used inverse deduce earliest start date infection consideration lack information initial conditions model....

10.3390/biology11081157 article EN cc-by Biology 2022-08-02

Excessive screen time has been associated with a higher risk for mental health problems, but whether the associations differ by content types is unclear.

10.1001/jamapediatrics.2023.5220 article EN JAMA Pediatrics 2023-12-04

Abstract Let $\mathbb{N}$ be the set of all non-negative integers. For any integer r and m , let $r+m\mathbb{N}=\{r+mk: k\in\mathbb{N}\}$ . $S\subseteq \mathbb{N}$ $n\in $R_{S}(n)$ denote number solutions equation $n=s+s'$ with $s, s'\in S$ $s \lt s'$ $r_{1}, r_{2}, m$ integers $0 r_{1} r_{2} $2\mid r_{1}$ In this paper, we prove that there exist two sets C D $C\cup D=\mathbb{N}$ $C\cap D=(r_{1}+m\mathbb{N})\cup (r_{2}+m\mathbb{N})$ such $R_{C}(n)=R_{D}(n)$ for $n\in\mathbb{N}$ if only...

10.1017/s0013091524000907 article EN Proceedings of the Edinburgh Mathematical Society 2025-02-03

Cadmium(Cd) is a heavy metal that harmful to human health. Early studies have shown cadmium can damage testicular structure, affecting testosterone synthesis and spermatogenesis. However, the effect of paternal Cd exposure on reproductive system offspring remains unclear. In this study, male 8-week C57BL/6 J mice were used as research objects, was injected intraperitoneally every other day at dose 1 mg/kg for 5 weeks, after which studied. Our results showed body weight increased faster, with...

10.1016/j.ecoenv.2022.113947 article EN cc-by-nc-nd Ecotoxicology and Environmental Safety 2022-08-08

Efficient manufacturing of recombinant adenovirus-associated virus (AAV) vectors is critical to the successful development genomic medicines. We attempted optimize AAV vector production in a producer cell line platform. In this system, helper functions required for replication and are provided via infection with replication-competent wild-type Adenovirus. To evaluate strategies reduction packaging adenovirus understand interplay during production, was compared mutant (Ad5ts149) containing...

10.1016/j.omtm.2024.101370 article EN cc-by-nc-nd Molecular Therapy — Methods & Clinical Development 2024-11-04

Objective: Depression and osteoporosis are usually concurrent health problems. This study aimed to explore the development of in depressive mice model investigate beneficial effects classical herbal formula Chaihu-Shugan-San (CHSG) on brain bone. Methods: CHSG powder was prepared by spray-drying following extraction with water. The fingerprint analyzed using liquid chromatography. depressive-like established chronic unpredictable mild stress (CUMS) female mice. behaviors trabecular bone...

10.2147/dddt.s480077 article EN cc-by-nc Drug Design Development and Therapy 2024-12-01

SPRY4 is a protein encoding gene that belongs to the Spry family. It inhibits mitogen-activated kinase (MAPK) signaling pathway and plays role in various biological functions under normal pathological conditions. The has specific structure interacts with other molecules regulate cellular behavior. serves as negative feedback inhibitor of receptor tyrosine kinases (RTK) interferes cell proliferation migration. also influences inflammation, oxidative stress, apoptosis. In different types...

10.3389/fonc.2024.1376873 article EN cc-by Frontiers in Oncology 2024-04-15

10.1007/s41980-023-00786-4 article EN Bulletin of the Iranian Mathematical Society 2023-05-04

Abstract Background Barthel Index (BI) is one of the most widely utilized tools for assessing functional independence in activities daily living. Most existing BI studies used populations with specific diseases (e.g., Alzheimer’s and stroke) to test prognostic factors scores; however, generalization these findings was limited when target varied. Objectives The aim present study utilize electronic health records (EHRs) data mining techniques develop a generic procedure identifying that...

10.1186/s12877-021-02422-4 article EN cc-by BMC Geriatrics 2021-09-06

We give an elementary proof of the well-known congruence $$ \binom{\frac{p-1}{2}}{\frac{p-1}{4}} \equiv \frac{2^{p-1}+1}{2} \bigg(2a-\frac{p}{2a}\bigg) \pmod{p^2}, where $p 1 \pmod{4}$ is prime and = a^2 + b^2$ with $a \pmod{4}$.

10.11650/twjm/1500406847 article EN other-oa Taiwanese Journal of Mathematics 2012-11-01

We prove that, for any $c_1,c_2,c_3\in(1,41/35)$, every sufficiently large odd number $N$ can be represented as the sum of three primes $N = p_1 + p_2 +p_3$ such that $p_i \lfloor n_{i}^{c_i}\rfloor$ some $n_i \in{\mathbb N}$ each $1 \leq i 3$. Our arguments are based on a variant Green's transference principle due to Matom\"aki, Maynard and Shao. necessary restriction estimate using Bourgain's strategy employ Harman's sieve method optimize our upper bound $c_i$.

10.48550/arxiv.1912.12572 preprint EN other-oa arXiv (Cornell University) 2019-01-01

For an odd integer $n \ge 3$ and $a\in \mathbb {Z}$ with $(a,n)=1$, let $$ \mathcal {U}_{a,n}=\biggl \{1\le x\le \frac {n-1}{2}: \{ax\}_n\ge {n+1}{2}\bigg \}, $$\mathcal {I}_{a,n}=\biggl \{(i,j): 1\le i \lt j\le {n-1}{2}\text { }\|ai\|_

10.4064/cm8738-7-2022 article EN Colloquium Mathematicum 2022-09-05

We prove several extensions of the Erdos-Fuchs theorem.

10.48550/arxiv.1608.08433 preprint EN other-oa arXiv (Cornell University) 2016-01-01

We prove a Lucas-type congruence for q-Delannoy numbers.

10.48550/arxiv.1508.02046 preprint EN other-oa arXiv (Cornell University) 2015-01-01

We prove that |{1<=y<=x: y is odd and not of the form p+2^a+2^b}|>>x^{1-ε} for any ε>0, where implied constant only depends on ε.

10.48550/arxiv.0905.3809 preprint EN other-oa arXiv (Cornell University) 2009-01-01

We prove that $$ \sum_{n \leq x} \varphi([x/n])\leq\bigg(\frac{1380}{4009}+\frac{2629}{4009}\cdot\frac1{\zeta(2)}+o(1)\bigg)x\log x as $x\to\infty$, where $\varphi$ denotes the Euler totient function and $[x]$ integer part of $x$.

10.48550/arxiv.1809.10381 preprint EN other-oa arXiv (Cornell University) 2018-01-01

We obtain reasonably tight upper and lower bounds on the sum $\sum_{n \leqslant x} \varphi \left( \left\lfloor{x/n}\right\rfloor\right)$, involving Euler functions $\varphi$ integer parts $\left\lfloor{x/n}\right\rfloor$ of reciprocals integers.

10.48550/arxiv.1808.00188 preprint EN other-oa arXiv (Cornell University) 2018-01-01

Let $p_n$ denote the $n$-th prime. For any $m\geq 1$, there exist infinitely many $n$ such that $p_{n}-p_{n-m}\leq C_m$ for some large constant $C_m>0$, and $$p_{n+1}-p_n\geq \frac{c_m\log n\log\log n\log\log\log\log n}{\log\log\log n}, $$ small $c_m>0$. Furthermore, we also obtain a related result concerning least primes in arithmetic progressions.

10.48550/arxiv.1802.02470 preprint EN other-oa arXiv (Cornell University) 2018-01-01

Objective To explore the impact of kanban network platform on quality teaching medical interns. Methods The experimental control method was used in this research. Starting from 2018, Totally two hundred and eight undergraduate senior trainees 2013 to 2014 five-year clinical medicine majors Wenzhou Medical University who entered orthopedics department first affiliated hospitals batches March 2018 2019. Each batch students orthopaedic trainee were randomly assigned group (n=102) (n=106)...

10.3760/cma.j.issn.1673-677x.2019.11.013 article EN Chinese Journal of Medical Education 2019-11-01
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