arXiv subjects

Wei Qi

Publications and source records attributed to Wei Qi.

69 records · Page 4Linked to original sources

arXiv2022

Characterizing $S$-projective modules and $S$-semisimple rings by uniformity

Let $R$ be a ring and $S$ a multiplicative subset of $R$. An $R$-module $P$ is called uniformly $S$-projective provided that the induced sequence $0\rightarrow \mathrm{Hom}_R(P,A)\rightarrow \mathrm{Hom}_R(P,B)\rightarrow \mathrm{Hom}_R(P,C)\rightarrow 0$ is $u$-$S$-exact for any $u$-$S$-short exact sequence $0\rightarrow A\rightarrow B\rightarrow C\rightarrow 0$. Some characterizations and properties of $u$-$S$-projective modules are obtained. The notion of $u$-$S$-semisimple modules is also introduced. A ring $R$ is called a $u$-$S$-semisimple ring provided that any free $R$-module is $u$-$S$-semisimple. Several characterizations of $u$-$S$-semisimple rings are provided in terms of $u$-$S$-semisimple modules, $u$-$S$-projective modules, $u$-$S$-injective modules and $u$-$S$-split $u$-$S$-exact sequences.

math.AC↗

arXiv2022

Realization of Qi-Wu-Zhang model in spin-orbit-coupled ultracold fermions

Based on the optical Raman lattice technique, we experimentally realize the Qi-Wu-Zhang model for quantum anomalous Hall phase in ultracold fermions with two-dimensional (2D) spin-orbit (SO) coupling. We develop a novel protocol of pump-probe quench measurement to probe, with minimal heating, the resonant spin flipping on particular quasi-momentum subspace called band-inversion surfaces. With this protocol we demonstrate the first Dirac-type 2D SO coupling in a fermionic system, and detect non-trivial band topology by observing the change of band-inversion surfaces as the two-photon detuning varies. The non-trivial band topology is also observed by slowly loading the atoms into optical Raman lattices and measuring the spin textures. Our results show solid evidence for the realization of the minimal SO-coupled quantum anomalous Hall model, which can provide a feasible platform to investigate novel topological physics including the correlation effects with SO-coupled ultracold fermions.

cond-mat.quant-gas↗

arXiv2022

On two versions of Cohen's theorem for modules

Parkash and Kour obtained a new version of Cohen's theorem for Noetherian modules, which states that a finitely generated $R$-module $M$ is Noetherian if and only if for every prime ideal $\mathfrak{p}$ of $R$ with Ann$(M)\subseteq \mathfrak{p}$, there exists a finitely generated submodule $N^\mathfrak{p}$ of $M$ such that $\mathfrak{p} M\subseteq N^\mathfrak{p}\subseteq M(\mathfrak{p})$, where $M(\mathfrak{p})=\{x\in M\mid sx\in \mathfrak{p} M $ for some $s\in R \setminus \mathfrak{p} \}$. In this paper, we generalize the Parkash and Kour version of Cohen's theorem for Noetherian modules to those for $S$-Noetherian modules and $w$-Noetherian modules.

math.AC↗

arXiv2022

On Cohen's theorem for Artinian modules

In this paper, we prove that a finitely embedded $R$-module $M$ is Artinian if and only if for every prime ideal $\mathfrak{p}$ of $R$ with $(0:_RM)\subseteq \mathfrak{p}$, there exists a submodule $N^\mathfrak{p}$ of $M$ such that $M/N^\mathfrak{p}$ is finitely embedded and $M[\mathfrak{p}]\subseteq N^\mathfrak{p}\subseteq (0:_M\mathfrak{p})$.

math.AC↗

arXiv2022

Uniformly $S$-Noetherian rings

Let $R$ be a ring and $S$ a multiplicative subset of $R$. Then $R$ is called a uniformly $S$-Noetherian ($u$-$S$-Noetherian for abbreviation) ring provided there exists an element $s\in S$ such that for any ideal $I$ of $R$, $sI \subseteq K$ for some finitely generated sub-ideal $K$ of $I$. We give the Eakin-Nagata-Formanek Theorem for $u$-$S$-Noetherian rings. Besides, the $u$-$S$-Noetherian properties on several ring constructions are given. The notion of $u$-$S$-injective modules is also introduced and studied. Finally, we obtain the Cartan-Eilenberg-Bass Theorem for uniformly $S$-Noetherian rings.

math.AC↗

arXiv2021

New Characterizations of $S$-coherent rings

In this paper, we introduce and study the class $S$-$\mathcal{F}$-ML of $S$-Mittag-Leffler modules with respect to all flat modules. We show that a ring $R$ is $S$-coherent if and only if $S$-$\mathcal{F}$-ML is closed under submodules. As an application, we obtain the $S$-version of Chase Theorem: a ring $R$ is $S$-coherent if and only if any direct product of $R$ is $S$-flat if and only if any direct product of flat $R$-modules is $S$-flat. Consequently, we provide an answer to the open question proposed by D. Bennis and M. El Hajoui [3].

math.AC↗

arXiv2021

Semi-regular flat modules over strong Prüfer rings

We first introduce and study the notion of semi-regular flat modules, and then show that a ring $R$ is a strong \Prufer\ ring if and only if every submodule of a semi-regular flat $R$-module is semi-regular flat, if and only if every ideal of $R$ is semi-regular flat, if and only if every $R$-module has a surjective semi-regular flat (pre)envelope.

math.AC↗

arXiv2021

The $S$-global dimensions of commutative rings

Let $R$ be a commutative ring with identity and $S$ a multiplicative subset of $R$. First, we introduce and study the $S$-projective dimensions and $S$-injective dimensions of $R$-modules, and then explore the $S$-global dimension $S$-gl.dim$(R)$ of a commutative ring $R$ which is defined to be the supremum of $S$-projective dimensions of all $R$-modules. Finally, we investigated the $S$-global dimension of factor rings and polynomial rings.

math.AC↗

arXiv2021

Some remarks on nonnil-coherent rings and $ϕ$-IF rings

Let $R$ be a commutative ring. If the nilpotent radical $Nil(R)$ of $R$ is a divided prime ideal, then $R$ is called a $ϕ$-ring. In this paper, we first distinguish the classes of nonnil-coherent rings and $ϕ$-coherent rings introduced by Bacem and Ali [10], and then characterize nonnil-coherent rings in terms of $ϕ$-flat modules and nonnil-FP-injective modules. A $ϕ$-ring $R$ is called a $ϕ$-IF ring if any nonnil-injective module is $ϕ$-flat. We obtain some module-theoretic characterizations of $ϕ$-IF rings. Two examples are given to distinguish $ϕ$-IF rings and IF $ϕ$-rings.

math.AC↗

arXiv2020

Multimode silicon photonics using on-chip geometrical-optics

On-chip optical interconnect has been widely accepted as a promising technology to realize future large-scale multiprocessors. Mode-division multiplexing (MDM) provides a new degree of freedom for optical interconnects to dramatically increase the link capacity. Present on-chip multimode devices are based on traditional wave-optics. Although large amount of computation and optimization are adopted to support more modes, mode-independent manipulation is still hard to be achieved due to severe mode dispersion. Here, we propose a universal solution to standardize the design of fundamental multimode building blocks, by introducing a geometrical-optics-like concept adopting waveguide width larger than the working wavelength. The proposed solution can tackle a group of modes at the same time with very simple processes, avoiding demultiplexing procedure and ensuring compact footprint. Compare to conventional schemes, it is scalable to larger mode channels without increasing the complexity and whole footprint. As a proof of concept, we demonstrate a set of multimode building blocks including crossing, bend, coupler and switches. Low losses of multimode waveguide crossing and bend are achieved, as well as ultra-low power consumption of the multimode switch is realized since it enables reconfigurable routing for a group of modes simultaneously. Our work promotes the multimode photonics research and makes the MDM technique more practical.

physics.optics↗

arXiv2020

Anomalous stopping of laser-accelerated intense proton beam in dense ionized matter

Ultrahigh-intensity lasers (10$^{18}$-10$^{22}$W/cm$^{2}$) have opened up new perspectives in many fields of research and application [1-5]. By irradiating a thin foil, an ultrahigh accelerating field (10$^{12}$ V/m) can be formed and multi-MeV ions with unprecedentedly high intensity (10$^{10}$A/cm$^2$) in short time scale ($\sim$ps) are produced [6-14]. Such beams provide new options in radiography [15], high-yield neutron sources [16], high-energy-density-matter generation [17], and ion fast ignition [18,19]. An accurate understanding of the nonlinear behavior of beam transport in matter is crucial for all these applications. We report here the first experimental evidence of anomalous stopping of a laser-generated high-current proton beam in well-characterized dense ionized matter. The observed stopping power is one order of magnitude higher than single-particle slowing-down theory predictions. We attribute this phenomenon to collective effects where the intense beam drives an decelerating electric field approaching 1GV/m in the dense ionized matter. This finding will have considerable impact on the future path to inertial fusion energy.

physics.plasm-ph↗

arXiv2017

A Second Order Cone Programming Model for Planning PEV Fast-Charging Stations

This paper studies siting and sizing of plug-in electric vehicle (PEV) fast-charging stations on coupled transportation and power networks. We develop a closed-form service rate model of highway PEV charging stations' service abilities, which considers heterogeneous PEV driving ranges and charging demands.We utilize a modified capacitated flow refueling location model (CFRLM) to explicitly capture time-varying PEV charging demands on the transportation network under driving range constraints. We explore extra constraints of the CFRLM to enhance model accuracy and computational efficiency.We then propose a stochastic mixed-integer second order cone programming (SOCP) model for PEV fast-charging station planning. The model considers the transportation network constraints of CFRLM and the power network constraints with AC power flow. Numerical experiments are conducted to illustrate the effectiveness of the proposed method.

math.OC↗

arXiv2017

Joint Planning of PEV Fast-Charging Network and Distributed PV Generation Using the Accelerated Generalized Benders Decomposition

Integration of plug-in electric vehicles (PEVs) with distributed renewable resources will decrease PEVs' well-to-wheels greenhouse gas emissions, promote renewable power adoption and defer power system investments. This paper proposes a multidisciplinary approach to jointly planning PEV fast-charging stations and distributed photovoltaic (PV) power plants on coupled transportation and power networks. First, we develop models of 1) PEV fast-charging stations; 2) highway transportation networks under PEV driving range constraints; 3) PV power plants with reactive power control. Then, we formulate a two-stage stochastic mixed integer second order cone program (MISOCP) to determine the sites and sizes of 1) PEV fast-charging stations; 2) PV power plants. To address the uncertainty of future scenarios, a significant number of future typical load, traffic flow and PV generation curves are adopted. This makes the problem large scale. We design a Generalized Benders Decomposition Algorithm to efficiently solve it. To the authors' knowledge, this work is the first that jointly plans both PEV fast-charging stations and PV plants with consideration for PEV driving range limits and reactive PV power control. We conduct numerical experiments to illustrate the effectiveness of the proposed method, and validate the benefits of the joint planning and adopting advanced PV reactive power control.

math.OC↗

arXiv2014

An embryo of protocell membrane: The capsule of graphene oxide

Many signs indicate that the graphene could widely occur on the early Earth. Here, we report a new theory that graphene might be an embryo of protocell membrane, and found several evidences. Firstly, the graphene oxide and phospholipid-graphene oxide composite would curl into capsules in strongly acidic saturated solution of Pb(NO3)2 at low temperature, providing a protective space for biochemical reactions. Secondly, L-animi acids exhibit higher reactivity than D-animi acids for graphene oxides in favor of the formation of left-handed proteins. Thirdly, monolayer graphene with nanopores prepared by unfocused 84Kr25+ has high selectivity for permeation of the monovalent metal ions (Rb+ > K+ > Cs+ > Na+ > Li+), but does not allow Cl- through, which could be attributed to the ion exchange of oxygen-containing groups on the rim of nanopores. It is similar to K+ channels, which would cause efflux of some ions from capsule of graphene oxides with the decrease of pH in the primitive ocean, creating a suitable inner condition for the origin of life. Consequently, the strongly acidic, high salinity and strong radiation as well as temperature changes in the early Earth, regarded as negative factors, would be indispensable for the origin of protocell. In short, graphene bred life, but digested gradually by the evolution.

q-bio.PE↗

arXiv2006

FDCSUSYDecay: A MSSM Decay package

FDCSUSYDecay is a FORTRAN program package generated by FDC (Feynman Diagram Calculation) system fully automatically. It is dedicated to calculate at tree-level all the possible 2-body decays of SUSY and Higgs particles in the Minimal Supersymmetric extension of the Standard Model (MSSM). The format of its output files complies with SUSY Les Houches Accord and can be easily imported by other packages.

hep-ph↗