arXiv subjects

Liping Li

Publications and source records attributed to Liping Li.

At least 37 records · Page 2Linked to original sources

arXiv2025

On domination for (non-symmetric) Dirichlet forms

The primary aim of this article is to investigate the domination relationship between two $L^2$-semigroups using probabilistic methods. According to Ouhabaz's domination criterion, the domination of semigroups can be transformed into relationships involving the corresponding Dirichlet forms. Our principal result establishes the equivalence between the domination of Dirichlet forms and the killing transformation of the associated Markov processes, which generalizes and completes the results in \cite{Y962} and \cite{Y96}. Based on this equivalence, we provide a representation of the dominated Dirichlet form using the bivariate Revuz measure associated with the killing transformation and further characterize the sandwiched Dirichlet form within the broader Dirichlet form framework. In particular, our findings apply to the characterization of operators sandwiched between the Dirichlet Laplacian and the Neumann Laplacian. For the local boundary case, we eliminate all technical conditions identified in the literature \cite{AW03} and deliver a complete representation of all sandwiched operators governed by a Robin boundary condition determined by a specific quasi-admissible measure. Additionally, our results offer a comprehensive characterization of related operators in the non-local Robin boundary case, specifically resolving an open problem posed in the literature \cite{OA21}.

math.PR↗

arXiv2025

SN 2024aecx: A double-peaked rapidly evolving Type IIb supernova at 11 Mpc

We present the results of low-resolution spectroscopic and densely sampled multi-band photometric follow-up of supernova (SN) 2024aecx. The SN was discovered in the spiral galaxy NGC 3521 (distance $\sim$11 Mpc) within a day after the explosion. The early spectra of SN 2024aecx show a weak signature of hydrogen lines, which disappeared in $\sim$30 days after the explosion. Light curves in all bands show a distinct feature of two peaks, and the first peak is likely due to the shock cooling emission. The early phase light curve evolution of SN 2024aecx has similarity with the typical Type IIb events, but the decay rate in different bands (e.g., $\rm Δm_{15}$ = 1.60 $\pm$ 0.05 mag, $g$-band) is significantly faster in the post-peak phase. It attained the secondary maximum in $\sim$19 days ($g$-band) with a peak absolute magnitude of M$_{g}$ = -17.94 $\pm$ 0.10 mag. SN 2024aecx colors trend redder in early epochs ($<$8 days), followed by a duration in which it grows bluer, then later gets redder again $>$20 days after explosion. The analytical model fitting to the light curves reveals an envelope mass and progenitor radii in the range of $\sim$0.03 - 0.24 $M_\odot$ and $\sim$169 - 200 $R_\odot$, respectively. Modeling of the pseudo-bolometric light curve suggests that synthesized $^{56}$Ni in the explosion was $\sim$0.15 M$_{\odot}$ with ejecta mass and kinetic energy of $\sim$0.7 M$_{\odot}$ and $\sim$0.16 $\times$ 10$^{51}$ erg, respectively. The observational properties and modeling indicate that the SN~2024aecx progenitor belongs to the extended progenitor category.

astro-ph.HE↗

arXiv2025

SN 2024gy: Multi-epoch Spectroscopic Features Suggestive of Delayed Detonation in a Type Ia Supernova

We present photometric and spectroscopic observations of SN 2024gy, a Type Ia supernova (SN Ia) exhibiting high-velocity features (HVFs) in its early-time spectra. This SN reaches a peak $B$-band magnitude of $-19.25 \pm 0.29$ mag and subsequently declines by $Δm_{15}(B) \approx 1.12$ mag, consistent with the luminosity-width relation characteristic of normal SNe Ia. Based on the peak thermal luminosity of $(1.2 \pm 0.3) \times 10^{43}$ erg s$^{-1}$, we estimate that $0.57 \pm 0.14~\rm M_{\odot}$ of $^{56}$Ni was synthesized during the explosion. Our dense early spectral monitoring revealed significant velocity disparities within the ejecta. Notably, absorption features from the Ca II near-infrared triplet were observed at velocities exceeding 25,000 km s$^{-1}$, while the Si II $λ$6355 line velocity at the same epoch was significantly lower at $\sim$ 16,000 km s$^{-1}$. This velocity disparity likely reflects distinct ionization states of intermediate-mass elements in the outermost layers. The prominent Ca II HVFs may originate from ionization suppression within the highest-velocity ejecta, potentially indicative of minimal hydrogen mixing in a delayed-detonation explosion scenario. Additionally, the Ni/Fe ratio derived from the nebular spectrum of SN 2024gy provides further support for this model.

astro-ph.HE↗

arXiv2025

SN 2024iss: A Double-peaked Type IIb Supernova with Evidence of Circumstellar Interaction

We present optical, ultraviolet, and X-ray observations of supernova (SN) 2024iss, a Type IIb SN that shows a prominent double-peaked light curve. We modeled the first peak with a semianalytical shock-cooling model and the X-ray emission with a free-free model. We compare the envelope radius and mass-loss rate with other Type IIb SNe to explore the relationships between the progenitor envelope and the circumstellar material (CSM). The shock-cooling peak in the $V$-band light curve reached $M_V = -17.33\pm 0.26$mag, while the $^{56}$Ni-powered second peak attained $M_V = -17.43\pm 0.26$mag. Early spectra show an photospheric velocity of $\sim19,400\,km\,s^{-1}$ at 3.82days from the H$α$ P~Cygni profile. The Balmer lines persist at least +87 days after the explosion, characterizing hydrogen-rich ejecta. Modeling the first light-curve peak suggests an extended envelope with a mass of $0.11\pm0.04\,M_{\odot}$ and a radius of $244\pm43~R_{\odot}$. Fitting the second light-curve peak with an Arnett-like model indicates a typical $^{56}$Ni mass of $ 0.117\pm0.013~M_{\odot}$ and a relatively low ejecta mass of $1.272\pm0.343\,M_{\odot}$. X-ray observations reveal bright thermal bremsstrahlung emission and indicate a mass-loss rate of $1.6\times10^{-5}\ M_{\odot} \ \rm{yr}^{-1}$. SN 2024iss occupies a transitional position between the two subclasses of extended (eIIb) and compact (cIIb) Type IIb SNe. Its envelope radius and pre-explosion mass-loss rate appear to be correlated as theoretically predicted. The observational properties of SN 2024iss are compatible with a binary interaction scenario being the dominant mechanism for envelope stripping. Furthermore, the low column density of neutral hydrogen suggests a compact CSM with an outer radius of $\lesssim1.3\times10^{14}$ cm, indicating that the progenitor star experienced eruptive mass loss within $\sim4\,yr$ of its terminal explosion.

astro-ph.HE↗

arXiv2025

On representations of permutation groups and orbit categories

Given an infinite set $Ω$ and a ring $R$ as well as a group $G$ acting on them, we show that $G$ and a subgroup $H$ share the same canonical relational structure on $Ω$ if and only if the restriction functor gives an equivalence from the category of discrete representations of $G$ to that of $H$. Moreover, the age of this relational structure satisfies the strong amalgamation property if and only if there is a canonical isomorphism from the category of finite substructures of $Ω$ and embeddings to the opposite category of the orbit category of $G$. As an application, we prove that finitely generated discrete representations of highly homogeneous groups over the polynomial ring $k[Ω]$ are Noetherian.

math.RT↗

arXiv2025

Noetherianity of polynomial rings up to group actions

Let $k$ be a commutative Noetherian ring, and $k[S]$ the polynomial ring whose indeterminates are parameterized by elements in a set $S$. We show that $k[S]$ is Noetherian up to highly homogenous actions of groups. In particular, there is a special linear order $\leqslant$ on infinite $S$ such that $k[S]$ is Noetherian up to actions of $\mathrm{Aut}(S, \leqslant)$, and the existence of such a linear order for every infinite set is equivalent to the axiom of choice. These Noetherian results are proved via a sheaf theoretic approach based on Artin's theorem, the work of Nagel-Römer, and a classification of highly homogenous groups by Cameron.

math.RT↗

arXiv2025

A torsion theoretic interpretation for sheaves of modules and Grothendieck topologies on directed categories

We prove that every Grothendieck topology induces a hereditary torsion pair in the category of presheaves of modules on a ringed site, and obtain a homological characterization of sheaves of modules: a presheaf of modules is a sheaf of modules if and only if it is saturated with respect to torsion presheaves, or equivalently, it is right perpendicular to torsion presheaves in the sense of Geigle and Lenzing. We also study Grothendieck topologies on directed categories $\mathscr{C}$ satisfying certain finiteness condition, and show that every Grothendieck topology on $\mathscr{C}$ is a subcategory topology if and only if $\mathscr{C}$ is an artinian EI category. Consequently, in this case every sheaf category is equivalent to the presheaf category over a full subcategory of $\mathscr{C}$. Finally, we classify all Grothendieck topologies on a special type of noetherian EI categories, and extend the locally self-injective property of representations of $\mathrm{F}$ and $\mathrm{VI}$ to representations of their infinite full subcategories. Some potential applications in group representation theory are given at the end of this paper.

math.RT↗

arXiv2025

Birth-death processes are time-changed Feller's Brownian motions

A Feller's Brownian motion is a diffusion process on the half-line with general boundary behavior at the origin, described by four parameters. A birth-death process, on the other hand, is a continuous-time Markov chain on the nonnegative integers, characterized by three parameters reflecting its behavior at infinity. This paper aims to build a connection between the two: we show that any Feller's Brownian motion can be transformed into a birth-death process via a specific time change, and vice versa. The transformation identifies a precise correspondence between their parameters. Our approach is based on a pathwise representation of the Feller process and offers a constructive framework for birth-death processes, filling a gap in the existing literature.

math.PR↗

arXiv2025

Representations over diagrams of abelian categories II: Abelian model structures

This is the second paper in a series on representations over diagrams of abelian categories. We show that, under certain conditions, a compatible family of abelian model categories indexed by a skeletal small category can be amalgamated into an abelian model structure on the category of representations. Our approach focuses on classes of morphisms rather than cotorsion pairs of objects. Additionally, we provide an explicit description of cofibrant objects in the resulting abelian model category. As applications, we construct Gorenstein injective and Gorenstein flat model structures on the category of presheaves of modules over a special class of index category and characterize Gorenstein homological objects within this framework.

math.CT↗

arXiv2025

Sheaves of modules on atomic sites and discrete representations of topological groups

The main goal of this paper is to establish close relations among sheaves of modules on atomic sites, representations of categories, and discrete representations of topological groups. We characterize sheaves of modules on atomic sites as saturated representations, which are precisely representations right perpendicular to torsion representations in the sense of Geigle and Lenzing. Consequently, the category of sheaves is equivalent to the Serre quotient of the category of presheaves by the category of torsion presheaves. We also interpret the sheaf cohomology functors as derived functors of the torsion functor and for some special cases as the local cohomology functors. These results as well as a classical theorem of Artin provides us a new approach to study discrete representations of topological groups. In particular, by importing established facts in representation stability theory, we explicitly classify simple or indecomposable injective discrete representations of some topological groups such as the infinite symmetric group, the infinite general or special linear group over a finite field, and the automorphism group of the linearly ordered set $\mathbb{Q}$. We also show that discrete representations $V$ of these topological groups satisfy a certain stability property.

math.RT↗

arXiv2025

Optical and Near-infrared Observations of SN 2023ixf for over 600 days after the Explosion

Context.We present a comprehensive photometric and spectroscopic study of the nearby Type II supernova (SN) 2023ixf, with our extensive observations spanning the phases from ~3 to over 600 days after the first light.\\ Aims.The aim of this study is to obtain key information on the explosion properties of SN\,2023ixf and the nature of its progenitor.\\ Methods.The observational properties of SN\,2023ixf are compared with those of a sample of Type IIP/L SNe to investigate commonalities and diversities. We conduct a detailed analysis of temporal evolution of major spectral features observed throughout different phases of the SN\,2023ixf explosion. Several interpretations are addressed through a comparison between the data and the model spectra for progenitor stars within a range of zero-age main sequence (ZAMS) masses.\\ Results.Our observations indicate that SN\,2023ixf is a transitional SN that bridges the gap between Type IIP and IIL subclasses of H-rich SNe, characterized by a relatively short plateau ($\lesssim 70$\,d) in the light curve. It shows a rather prompt spectroscopic evolution toward the nebular phase; emission lines of Na, O, H, and Ca in nebular spectra all exhibit multipeak profiles, which might be attributed to bipolar distribution of the ejecta. In particular, the H$α$ profile can be separated into two central peaked components (with a velocity of about 1500\,km\,s$^{-1}$) that is likely due to nickel-powered ejecta and two outer peak/box components (with a velocity extending up to ~8000 km\,s$^{-1}$) that can arise from interaction of the outermost ejecta with a circumstellar shell at a distance of $\sim6.2\times10^{15}$cm. The nebular-phase spectra of SN\,2023ixf show good agreement with those predicted by model spectra for progenitor stars with a ZAMS mass ranging from 15 to 19\,M${_\odot}$. A distance $D = 6.35^{+0.31}_{-0.39}$\,Mpc is estimated for M101.

astro-ph.HE↗

arXiv2024

Representations of $\mathbb{N}^{\infty}$-type combinatorial categories

In this paper we consider representations of certain combinatorial categories, including the poset $\D$ of positive integers and division, the Young lattice $\mathscr{Y}$ of partitions of finite sets, the opposite category of the orbit category $\mathscr{Z}$ of $(\mathbb{Z}, +)$ with respect to nontrivial subgroups, and the category $\mathscr{CI}$ of finite cyclic groups and injective homomorphisms. We describe explicit upper bounds for homological degrees of their representations, and deduce that finitely presented representations (resp., representations presented in finite degrees) over a field form abelian subcategories of the representation categories. We also give an explicit description for the category of sheaves over the ringed atomic site $(\mathscr{Z}, \, J_{at}, \, \underline{\mathbb{C}})$, and show that irreducible sheaves are parameterized by primitive roots of the unit.

math.RT↗

arXiv2024

SN 2014C: a metamorphic supernova exploded in the intricate and hydrogen-rich surroundings

We present photometric and spectroscopic observations of supernova (SN) 2014C, primarily emphasizing the initial month after the explosion at approximately daily intervals. During this time, it was classified as a Type Ib SN exhibiting a notably higher peak luminosity ($L_{\rm peak}\approx4.3\times10^{42}\rm erg\,s^{-1}$), a faster rise to brightness ($t_{\rm rise} \approx 11.6$ d), and a more gradual dimming ($Δm_{15}^{V} \approx 0.48$ mag) compared to typical SNe Ib. Analysis of the velocity evolution over the first $\sim$ 20 days after the explosion supports the view that the absorption near 6200Åis due to high-velocity H$α$ in the outer layers of the ejecta, indicating the presence of a small amount of hydrogen in the envelope of progenitor before the explosion. Assuming the peak luminosity is entirely attributed to radioactive decay, we estimate that 0.14 ${\rm M}_{\odot}$ of $^{56}$Ni was synthesized in the explosion. However, this amount of nickel could no longer maintain observed brightness approximately ten days after peak luminosity, suggesting additional energy sources beyond radioactive decay. This supplementary energy likely originates from interaction with the circumstellar medium (CSM). Consequently, the timing of the SN-CSM interaction in SN 2014C may occur much earlier than the emergence of IIn-like features during the nebular phase.

astro-ph.HE↗

arXiv2024

Addressing Imbalance Risk with Reserves and Flexibility Options: An ERCOT-like Case Study

As the role of variable renewables in electricity markets expands, new market products help system operators manage imbalances caused by uncertainty and variability. Whereas work in the last decade has focused on constructing demand curves for central procurement of those products, little attention has been paid to designing their settlement scheme and understanding the connections between the economic value of these products, the schedule of variable resources, and the cost of flexibility. In this article, we compare a new product called Flexibility Options, which addresses these gaps, with a traditional reserve product using a case study similar to the 2019 Texas (ERCOT) system. Our findings suggest that both products are equally effective in managing imbalances, but Flexibility Options have superior risk management properties and keep the system operator revenue adequate.

eess.SY↗

arXiv2024

Compatible weak factorization systems and model structures

In this paper the concept of compatible weak factorization systems in general categories is introduced as a counterpart of compatible complete cotorsion pairs in abelian categories. We describe a method to construct model structures on general categories via two compatible weak factorization systems satisfying certain conditions, and hence generalize a very useful result by Gillespie for abelian model structures. As particular examples, we show that weak factorizations systems associated to some classical model structures (for example, the Kan-Quillen model structure on $\mathsf{sSet}$) satisfy these conditions.

math.CT↗

arXiv2024

Robust DOA Estimation Based on Dual Lawson Norm for RIS-Aided Wireless Communication Systems

Reconfigurable intelligent surfaces (RIS) can actively perform beamforming and have become a crucial enabler for wireless systems in the future. The direction-of-arrival (DOA) estimates of RIS received signals can help design the reflection control matrix and improve communication quality. In this paper, we design a RIS-assisted system and propose a robust Lawson norm-based multiple-signal-classification (LN-MUSIC) DOA estimation algorithm for impulsive noise, which is divided into two parts. The first one, the non-convex Lawson norm is used as the error criterion along with a regularization constraint to formulate the optimization problem. Then, a Bregman distance based alternating direction method of multipliers is used to solve the problem and recover the desired signal. The second part is to use the multiple signal classification (MUSIC) to find out the DOAs of targets based on their sparsity in the spatial domain. In addition, we also propose a RIS control matrix optimization strategy that requires no channel state information, which effectively enhances the desired signals and improves the performance of the LN-MUSIC algorithm. A Cramer-Rao-lower-bound (CRLB) of the proposed DOA estimation algorithm is presented and verifies its feasibility. Simulated results show that the proposed robust DOA estimation algorithm based on the Lawson norm can effectively suppress the impact of large outliers caused by impulsive noise on the estimation results, outperforming existing methods.

cs.IT↗

arXiv2024

Approximation of birth-death processes

The birth-death process is a special type of continuous-time Markov chain with index set $\mathbb{N}$. Its resolvent matrix can be fully characterized by a set of parameters $(γ, β, ν)$, where $γ$ and $β$ are non-negative constants, and $ν$ is a positive measure on $\mathbb{N}$. By employing the Ray-Knight compactification, the birth-death process can be realized as a càdlàg process with strong Markov property on the one-point compactification space $\overline{\mathbb{N}}_{\partial}$, which includes an additional cemetery point $\partial$. In a certain sense, the three parameters that determine the birth-death process correspond to its killing, reflecting, and jumping behaviors at $\infty$ used for the one-point compactification, respectively. In general, providing a clear description of the trajectories of a birth-death process, especially in the pathological case where $|ν|=\infty$, is challenging. This paper aims to address this issue by studying the birth-death process using approximation methods. Specifically, we will approximate the birth-death process with simpler birth-death processes that are easier to comprehend. For two typical approximation methods, our main results establish the weak convergence of a sequence of probability measures, which are induced by the approximating processes, on the space of all càdlàg functions. This type of convergence is significantly stronger than the convergence of transition matrices typically considered in the theory of continuous-time Markov chains.

math.PR↗

arXiv2024

Ray-Knight compactification of birth and death processes

A birth and death process is a continuous-time Markov chain with the minimal state space $\mathbb N$, whose transition matrix is standard and whose density matrix is the given birth-death matrix. Birth and death process is unique if and only if $\infty$ is an entrance or natural. When $\infty$ is neither an entrance nor natural, there are two ways in the literature to obtain all birth and death processes. The first one is an analytic treatment proposed by Feller in 1959, and the second one is a probabilistic construction completed by Wang in 1958. In this paper we will give another way to study birth and death processes using the Ray-Knight compactification. This way has the advantage of both the analytic and probabilistic treatments above. By applying the Ray-Knight compactification, every birth and death process can be modified into a càdlàg Ray process on $\mathbb N\cup \{\infty\}\cup\{\partial\}$, which is either a Doob processes or a Feller $Q$-process. Every birth and death process in the second class has a modification that is a Feller process on $\mathbb N\cup\{\infty\}\cup \{\partial\}$. We will derive the expression of its infinitesimal generator, which explains its boundary behaviours at $\infty$. Furthermore, by utilizing transformations of killing and Ikeda-Nagasawa-Watanabe's piecing out, we will also provide a probabilistic construction for birth and death processes. This construction relies on a triple determining the resolvent matrix introduced by Wang and Yang in their work (1992')}.

math.PR↗