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Lifeng Xi

Publications and source records attributed to Lifeng Xi.

9 recordsLinked to original sources
arXiv2025

Universal Battery Degradation Forecasting Driven by Foundation Model Across Diverse Chemistries and Conditions

Accurate forecasting of battery capacity fade is essential for the safety, reliability, and long-term efficiency of energy storage systems. However, the strong heterogeneity across cell chemistries, form factors, and operating conditions makes it difficult to build a single model that generalizes beyond its training domain. This work proposes a unified capacity forecasting framework that maintains robust performance across diverse chemistries and usage scenarios. We curate 20 public aging datasets into a large-scale corpus covering 1,704 cells and 3,961,195 charge-discharge cycle segments, spanning temperatures from $-5\,^{\circ}\mathrm{C}$ to $45\,^{\circ}\mathrm{C}$, multiple C-rates, and application-oriented profiles such as fast charging and partial cycling. On this corpus, we adopt a Time-Series Foundation Model (TSFM) backbone and apply parameter-efficient Low-Rank Adaptation (LoRA) together with physics-guided contrastive representation learning to capture shared degradation patterns. Experiments on both seen and deliberately held-out unseen datasets show that a single unified model achieves competitive or superior accuracy compared with strong per-dataset baselines, while retaining stable performance on chemistries, capacity scales, and operating conditions excluded from training. These results demonstrate the potential of TSFM-based architectures as a scalable and transferable solution for capacity degradation forecasting in real battery management systems.

cs.LG↗
arXiv2019

Multiplication on uniform $λ$-Cantor sets

Let $C$ be the middle-third Cantor set. Define $C*C=\{x*y:x,y\in C\}$, where $*=+,-,\cdot,÷$ (when $*=÷$, we assume $y\neq0$). Steinhaus \cite{HS} proved in 1917 that \[ C-C=[-1,1], C+C=[0,2]. \] In 2019, Athreya, Reznick and Tyson \cite{Tyson} proved that \[ C÷C=\bigcup_{n=-\infty}^{\infty}\left[ 3^{-n}\dfrac{2}{3},3^{-n}\dfrac {3}{2}\right] . \] In this paper, we give a description of the topological structure and Lebesgue measure of $C\cdot C$. We indeed obtain corresponding results on the uniform $λ$-Cantor sets.

math.DS↗
arXiv2019

Multiple codings for self-similar sets with overlaps

In this paper we consider a general class $\mathcal E$ of self-similar sets with complete overlaps. Given a self-similar iterated function system $Φ=(E, \{f_i\}_{i=1}^m)\in\mathcal E$ on the real line, for each point $x\in E$ we can find a sequence $(i_k)=i_1i_2\ldots\in\{1,\ldots,m\}^\mathbb N$, called a coding of $x$, such that $$ x=\lim_{n\to\infty}f_{i_1}\circ f_{i_{2}}\circ\cdots\circ f_{i_n}(0). $$ For $k=1,2,\ldots, \aleph_0$ or $2^{\aleph_0}$ we investigate the subset $\mathcal U_k(Φ)$ which consists of all $x\in E$ having precisely $k$ different codings. Among several equivalent characterizations we show that $\mathcal U_1(Φ)$ is closed if and only if $\mathcal U_{\aleph_0}(Φ)$ is an empty set. Furthermore, we give explicit formulae for the Hausdorff dimension of $\mathcal U_k(Φ)$, and show that the corresponding Hausdorff measure of $\mathcal U_k(Φ)$ is always infinite for any $k\ge 2$. Finally, we explicitly calculate the local dimension of the self-similar measure at each point in $\mathcal U_k(Φ)$ and ${U_{\aleph_0}(Φ)}$.

math.DS↗
arXiv2019

On arithmetic progressions in self-similar sets

Given a sequence $\{b_{i}\}_{i=1}^{n}$ and a ratio $λ\in (0,1),$ let $E=\cup_{i=1}^n(λE+b_i)$ be a homogeneous self-similar set. In this paper, we study the existence and maximal length of arithmetic progressions in $E$. Our main idea is from the multiple $β$-expansions.

math.NT↗
arXiv2018

Interiors of continuous images of the middle-third Cantor set

Let $C$ be the middle-third Cantor set, and $f$ a continuous function defined on an open set $U\subset \mathbb{R}^{2}$. Denote the image \begin{equation*} f_{U}(C,C)=\{f(x,y):(x,y)\in (C\times C)\cap U\}. \end{equation*} If $\partial _{x}f$, $\partial _{y}f$ are continuous on $U,$ and there is a point $(x_{0},y_{0})\in (C\times C)\cap U$ such that \begin{equation*} 1<\left\vert \frac{\partial _{x}f|_{(x_{0},y_{0})}}{\partial _{y}f|_{(x_{0},y_{0})}}\right\vert <3\text{ or }1<\left\vert \frac{\partial _{y}f|_{(x_{0},y_{0})}}{\partial _{x}f|_{(x_{0},y_{0})}}\right\vert <3, \end{equation*} then $f_{U}(C,C)$ has a non-empty interior. As a consequence, if \begin{equation*} f(x,y)=x^{α}y^{β}(αβ\neq 0),\text{ }x^{α}\pm y^{α}(α\neq 0)\text{ or }\sin (x)\cos (y), \end{equation*} then $f_{U}(C,C)$ contains a non-empty interior.

math.DS↗
arXiv2018

Arithmetic representations of real numbers in terms of self-similar sets

Suppose $n\geq 2$ and $\mathcal{A}_{i}\subset \{0,1,\cdots ,(n-1)\}$ for $ i=1,\cdots ,l,$ let $K_{i}=\bigcup\nolimits_{a\in \mathcal{A}_{i}}n^{-1}(K_{i}+a)$ be self-similar sets contained in $[0,1].$ Given $ m_{1},\cdots ,m_{l}\in \mathbb{Z}$ with $\prod\nolimits_{i}m_{i}\neq 0,$ we let \begin{equation*} S_{x}=\left\{ \mathbf{(}y_{1},\cdots ,y_{l}\mathbf{)}:m_{1}y_{1}+\cdots +m_{l}y_{l}=x\text{ with }y_{i}\in K_{i}\text{ }\forall i\right\} . \end{equation*} In this paper, we analyze the Hausdorff dimension and Hausdorff measure of the following set \begin{equation*} U_{r}=\{x:\mathbf{Card}(S_{x})=r\}, \end{equation*} where $\mathbf{Card}(S_{x})$ denotes the cardinality of $S_{x}$, and $r\in \mathbb{N}^{+}$. We prove under the so-called covering condition that the Hausdorff dimension of $U_{1}$ can be calculated in terms of some matrix. Moreover, if $r\geq 2$, we also give some sufficient conditions such that the Hausdorff dimension of $U_{r}$ takes only finite values, and these values can be calculated explicitly. Furthermore, we come up with some sufficient conditions such that the dimensional Hausdorff measure of $U_{r}$ is infinity. Various examples are provided. Our results can be viewed as the exceptional results for the classical slicing problem in geometric measure theory.

math.DS↗
arXiv2018

Lipschitz equivalence of self-similar sets with exact overlaps

In this paper, we study a class $\mathcal{A}(λ,n,m)$ of self-similar sets with $m$ exact overlaps generated by $n$ similitudes of the same ratio $ λ$. We obtain a necessary condition for a self-similar set in $\mathcal{A}(λ,n,m)$ to be Lipschitz equivalent to a self-similar set satisfying the strong separation condition, i.e., there exists an integer $ k\geq 2$ such that $x^{2k}-mx^{k}+n$ is reducible, in particular, $m$ belongs to $\{a^{i}:a\in \mathbb{N}$ with $i\geq 2\}.$

math.DS↗
arXiv2018

Multiplication on self-similar sets with overlaps

Let $A,B\subset\mathbb{R}$. Define $$A\cdot B=\{x\cdot y:x\in A, y\in B\}.$$ In this paper, we consider the following class of self-similar sets with overlaps. Let $K$ be the attractor of the IFS $\{f_1(x)=λx, f_2(x)=λx+c-λ,f_3(x)=λx+1-λ\}$, where $f_1(I)\cap f_2(I)\neq \emptyset, (f_1(I)\cup f_2(I))\cap f_3(I)=\emptyset,$ and $I=[0,1]$ is the convex hull of $K$. The main result of this paper is $K\cdot K=[0,1]$ if and only if $(1-λ)^2\leq c$. Equivalently, we give a necessary and sufficient condition such that for any $u\in[0,1]$, $u=x\cdot y$, where $x,y\in K$.

math.DS↗