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Ruihua Wang

Publications and source records attributed to Ruihua Wang.

6 recordsLinked to original sources
arXiv2026

Obstructions to coloring arithmetic graphs

The arithmetic graph $B_n$ joins distinct $a,b\in\N$ when $\max(a,b)/\gcd(a,b)\le n$. We prove $χ(B_{205})=206$, disproving the conjecture that $χ(B_n)=n$ for every $n$, equivalently the Rainbow Cascades Conjecture. The proof reduces an arbitrary tiling by the arithmetic exponent tile to a periodic tiling, then to two families of finite quotients, which are excluded using exact computations. We also construct a $208$-coloring using $\Z_{104}\times\Z_2$ and prove $212\leχ(B_{211})\le213$. The lower bound at $211$ follows from prime-cardinality tiling rigidity and the published nonexistence of a cyclic logarithm of length $211$; we give a direct proof of the required rigidity statement. Finally, we record the equivalence with the List Cascade Coloring Conjecture and the conjecture on ironic decorations, and deduce finite graph counterexamples to both. The least $n$ with $χ(B_n)>n$ is either $195$ or $205$; determining which remains open.

math.CO↗
arXiv2026

Large zeta sums and zeros of the Riemann zeta function

For real $t$ and $x\ge 1$, set \[ S(x,t)=\sum_{n\le x} n^{\ii t}. \] We prove an unconditional inverse theorem relating large values of $S(x,t)$, with $|t|$ large, to zeros of the Riemann zeta function near height $t$. More precisely, if $T\le |t|\le 2T$, $\exp(\sqrt{\log T})\le x\le \sqrt T$, and $|S(x,t)|=x/N$ with $N\le (\log x)^{1/100}$, then for every $cN^6\le L\le (\log x)/2$ a disk centered at $1+\iiϕ$, where $|ϕ-t|\ll N$, contains at least $L/360$ zeros of $ζ(s)$. As a consequence, a quantitative restriction on zeros in a short family of arbitrarily thin fixed windows to the left of the line $\Ree s=1$ yields $S(x,t)\ll x/(\log x)^{1/100}$ in polynomial ranges of $x$. The proof adapts the zero-forcing mechanism of Granville and Soundararajan for large character sums. In the zeta setting the spectral height is shifted by $t$, and an additional residue from the pole of $ζ(s)$ appears in the Gaussian transform; in the range considered here that residue is exponentially small.

math.NT↗
arXiv2026

Large values of quadratic character sums

In this paper, we investigate large values of quadratic Dirichlet character sums. We prove new Omega results for both short and long quadratic character sums under the assumption of the Generalized Riemann Hypothesis (GRH), which improve the previous results.

math.NT↗
arXiv2025

Note on large quadratic character sums

In this article, we investigate the conditional large values of quadratic Dirichlet character sums. We prove an Omega result for quadratic character sums under the assumption of the generalized Riemann hypothesis.

math.NT↗
arXiv2025

Design of a Noval Wearable ECG Monitoring Device

The aim of this project is to develop a new wireless powered wearable ECG monitoring device. The main goal of the project is to provide a wireless, small-sized ECG monitoring device that can be worn for a long period of time by the monitored person. Electrocardiogram ECG reflects physiological and pathological information about heart activity and is commonly used to diagnose heart disease. Existing wearable smart ECG solutions suffer from high power consumption in both ECG diagnosis and transmission for high accuracy. Monitoring of ECG devices is mainly done by data extraction and acquisition, pre-processing, feature extraction, processing and analysis, visualisation and auxiliary procedures. During the pre-processing of the information, different kinds of noise generated during the signal collection need to be taken into account. The quality of the signal-to-noise ratio can usually be improved by optimising algorithms and reducing the noise power. The choice of electrodes usually has a direct impact on the signal-to-noise ratio and the user experience, and conventional Ag/AgCl gel electrodes are not suitable for long-term and dynamic monitoring as they are prone to skin irritation, inflammation and allergic reactions. Therefore, a completely new way of combining electrodes and wires will be used in the report. The electrodes and wires are cut in one piece from a silver-plated fabric. The wire portion is cut into a curved structure close to an S shape to ensure that it has good ductility for comfort and signal integrity during daily movement of the garment.

eess.SP↗