In this paper, we mainly investigate some properties of strongly n-Gorenstein projective, injective and flat modules under the extension of rings, which mainly including excellent extensions, morita equivalences, poly...In this paper, we mainly investigate some properties of strongly n-Gorenstein projective, injective and flat modules under the extension of rings, which mainly including excellent extensions, morita equivalences, polynomial extensions and localizations.展开更多
In the Gorenstein homological theory, Gorenstein projective and Gorenstein injective dimensions play an important and fundamental role. In this paper, we aim at studying the closely related strongly Gorenstein flat an...In the Gorenstein homological theory, Gorenstein projective and Gorenstein injective dimensions play an important and fundamental role. In this paper, we aim at studying the closely related strongly Gorenstein flat and Gorenstein FP-injective dimensions, and show that some characterizations similar to Gorenstein homological dimensions hold for these two dimensions.展开更多
This paper is a study of strongly Ding projective modules with respect to a semidualizing module. The class of strongly Ding flat modules with respect to a semidualizing module is also investigated, and the relationsh...This paper is a study of strongly Ding projective modules with respect to a semidualizing module. The class of strongly Ding flat modules with respect to a semidualizing module is also investigated, and the relationship between strongly Ding projective modules and strongly Ding flat modules with respect to a semidualizing module is characterized.Some well-known results on strongly Ding projective modules, n-strongly Ding projective modules and strongly D_C-projective modules are generalized and unified.展开更多
Let R be an associative ring with identity.In this paper,we consider generalizations of Gorenstein FP-injective R-modules and FP-injective complexes,give the definitions and characterizations of strongly Gorenstein FP...Let R be an associative ring with identity.In this paper,we consider generalizations of Gorenstein FP-injective R-modules and FP-injective complexes,give the definitions and characterizations of strongly Gorenstein FPinjective R-modules and strongly FP-injective complexes,which are induced by strongly FP-injective modules.Then we investigate the strongly FP-injective dimension of complexes.展开更多
The notion of strongly W-Gorenstein complexes is introduced for a self-orthogonal class W of modules. We obtain a characterization of such complexes and apply to strongly Gorenstein injective complexes.
Let R be a commutative ring with 1, and M is a (left) R-module. We introduce the concept of coprimarily packed submodules as a proper submodule N of an R-module M which is said to be Coprimarily Packed Submodule. If w...Let R be a commutative ring with 1, and M is a (left) R-module. We introduce the concept of coprimarily packed submodules as a proper submodule N of an R-module M which is said to be Coprimarily Packed Submodule. If where Na is a primary submodule of M for each , then for some . When there exists such that;N is called Strongly Coprimarily Packed submodule. In this paper, we list some basic properties of this concept. We end this paper by explaining the relations between p-compactly packed and coprimarily packed submodules, and also the relations between strongly p-compactly packed and strongly coprimarily packed submodules.展开更多
We consider the conditions under which the class of （m, d）-injective R-modules is （pre）covering. It is shown that every left R-module over a left （m, d）-coherent ring has an （rn, d）-injective cover. Moreover, ...We consider the conditions under which the class of （m, d）-injective R-modules is （pre）covering. It is shown that every left R-module over a left （m, d）-coherent ring has an （rn, d）-injective cover. Moreover, the classes of Gorenstein （m, d）-flat modules and Gorenstein （m, d）-injecitve modules are introduced and studied. For a right （m, d）-coherent ring R, we prove that a left R-module M is Gorenstein （m, d）-flat if and only if M＋ is Gorenstein （m, d）- injective as a right R-module. Some results on Gorenstein flat modules and Gorenstein n-flat modules are generalized.展开更多
Fe-based catalysts are widely used for CO_(2)hydrogenation to light olefins(C_(2–4)=);however,precise regulation of active phases and the balance between intermediate reactions remain significant challenges.Herein,we...Fe-based catalysts are widely used for CO_(2)hydrogenation to light olefins(C_(2–4)=);however,precise regulation of active phases and the balance between intermediate reactions remain significant challenges.Herein,we find that the addition of moderate amounts of Ti forms a strong interaction with Fe compositions,modulating the Fe_(3)O_(4)and Fe_(5)C_(2)contents.Enhanced interaction leads to an increased Fe_(5)C_(2)/Fe_(3)O_(4)ratio,which in turn enhances the adsorption of reactants and intermediates,promoting CO hydrogenation to unsaturated alkyl groups and facilitating C–C coupling.Furthermore,the strong Fe-Ti interaction induces the preferential growth of Fe_(5)C_(2)into prismatic structures that expose the(020),(–112),and(311)facets,forming compact active interfacial sites with Fe_(3)O_(4)nanoparticles.These facet and interfacial effects significantly promote the synergistic coupling of the reverse water gas shift and Fischer-Tropsch reactions.The optimized 3K/FeTi catalyst with the highest Fe_(5)C_(2)/Fe_(3)O_(4)ratio of 3.6 achieves a 52.2%CO_(2)conversion rate,with 44.5%selectivity for C2–4=and 9.5%for CO,and the highest space-time yield of 412.0 mg gcat^(–1)h^(–1)for C_(2–4)=.展开更多
Atomically thin semiconductors exhibit tunable exciton resonances that can be harnessed for dynamic manipulation of visible light in ultra-compact metadevices.However,the rapid nonradiative decay and dephasing of exci...Atomically thin semiconductors exhibit tunable exciton resonances that can be harnessed for dynamic manipulation of visible light in ultra-compact metadevices.However,the rapid nonradiative decay and dephasing of excitons at room temperature limit current active excitonic metasurfaces to a few-percent efficiencies.Here,we leverage the combined merits of pristine 2D heterostructures and non-local dielectric metasurfaces to enhance the excitonic lightmatter interaction,achieving strong and electrically tunable exciton-photon coupling at ambient conditions in a hybrid-2D excitonic metasurface.Using this,we realize a free-space optical modulator and experimentally demonstrate 9.9 dB of reflectance modulation.The electro-optic response,characterized by a continuous transition from strong to weak coupling,is mediated by gating-induced variations in the free carrier concentration,altering the exciton’s nonradiative decay rate.These results highlight how hybrid-2D excitonic metasurfaces offer novel opportunities to realize nanophotonic devices for active wavefront manipulation and optical communication.展开更多
Let R be a graded ring. We define and study strongly Gorenstein gr-projective, gr-injective, and gr-flat modules. Some connections among these modules are discussed. We also explore the relations between the graded an...Let R be a graded ring. We define and study strongly Gorenstein gr-projective, gr-injective, and gr-flat modules. Some connections among these modules are discussed. We also explore the relations between the graded and the ungraded strongly Gorenstein modules.展开更多
There is a variety of nice results about strongly Gorenstein flat modules over coherent rings. These results are done by Ding, Lie and Mao. The aim of this paper is to generalize some of these results, and to give hom...There is a variety of nice results about strongly Gorenstein flat modules over coherent rings. These results are done by Ding, Lie and Mao. The aim of this paper is to generalize some of these results, and to give homological descriptions of the strongly Gorenstein flat dimension (of modules and rings) over arbitrary associative rings.展开更多
Strong optical feedback in a birefringent dual frequency He-Ne laser with a high reflectivity feedback mirror has been investigated for the first time. The output characteristics of two orthogonally polarized modes ar...Strong optical feedback in a birefringent dual frequency He-Ne laser with a high reflectivity feedback mirror has been investigated for the first time. The output characteristics of two orthogonally polarized modes are demonstrated in two different optical feedback cases： one is for both modes being fed back and the other is for only one of the modes being fed back. Strong mode competition can be observed between the two modes with strong optical feedback, And when one mode＇s intensity is near its maximum, the other mode is nearly extinguished. When both modes are fed back into the laser cavity, the mode competition is stronger than when only one mode is fed back, The difference in initial intensity between the two orthogonally polarized modes plays an important role in the mode competition, which has been experimentally and theoretically demonstrated.展开更多
Strongly irreducible submodules of modules are defined as follows： A submodule N of an Rmodule M is said to be strongly irreducible if for submodules L and K of M, the inclusion L ∩ K ∈ N implies that either L ∈ N...Strongly irreducible submodules of modules are defined as follows： A submodule N of an Rmodule M is said to be strongly irreducible if for submodules L and K of M, the inclusion L ∩ K ∈ N implies that either L ∈ N or K ∈ N. The relationship among the families of irreducible, strongly irreducible, prime and primary submodules of an R-module M is considered, and a characterization of Noetherian modules which contain a non-prime strongly irreducible submodule is given.展开更多
When R satisfies (strong unit) 1-stable range and M is a R-R-bimodule, the authors calculate that K_1(R(?) M)≌U(R(?) M)/L(R(?) M). As applications, the authors also calculate some Whitehead groups for exchange rings ...When R satisfies (strong unit) 1-stable range and M is a R-R-bimodule, the authors calculate that K_1(R(?) M)≌U(R(?) M)/L(R(?) M). As applications, the authors also calculate some Whitehead groups for exchange rings with artinian primitive factors.展开更多
The concepts of strongly lifting modules and strongly dual Rickart modules are introduced and their properties are studied and relations between them are given in this paper. It is shown that a strongly lifting module...The concepts of strongly lifting modules and strongly dual Rickart modules are introduced and their properties are studied and relations between them are given in this paper. It is shown that a strongly lifting module has the strongly summand sum property and the generalized Hopfian property, and a ring R is a strongly regular ring if and only if RR is a strongly dual Rickart module, if and only if aR is a fully invariant direct summand of RR for every a∈R.展开更多
Hierarchical porous carbon co-doped with heterogeneous atoms has attracted much attention thanks to sizable internal void space accommodating electrolyte,high-density microporous structure physically con-fining polysu...Hierarchical porous carbon co-doped with heterogeneous atoms has attracted much attention thanks to sizable internal void space accommodating electrolyte,high-density microporous structure physically con-fining polysulfides(LPS),and heterogeneous atoms serving as active sites to capture LPS.However,solely relying on carbon material defects to capture LPS proves ineffective.Hence,metal compounds must be introduced to chemisorb LPS.Herein,cobalt ions are in-situ grown on the polydopamine layer coated on the surface of biomass-derived S,N,P co-doped hierarchical porous carbon(SNP-PC).Then a layer of nitrogen-doped porous carbon(MPC)dotted with CoSe nanoparticles is acquired by selenizing.Thus,a strong-polar/weak-polar composite material of SNP-PC studded with CoSe nanoparticles is obtained(SNP-PC@MPC@CoSe).Button cells assembled with SNP-PC@MPC@CoSe-modified separator enable superb long-cycle stability and satisfactory rate performance.An excellent rate capacity of 796 mAh g^(−1)at a high current rate of 4 C with an ultra-low capacity fading of 0.06%over 700 cycles can be acquired.More impressively,even in a harsh test condition of 5.65 mg cm^(−2)sulfur loading and 4μL mg^(−1)ratio of electrolyte to active materials,the battery can still display a specific capacity of 980 mAh g^(−1)(area capacity of∼5.54 mAh cm^(−2))at 0.1 C.This work provides a promising route toward high-performance Li-S batteries.展开更多
Cavity electro-optic(EO)modulation plays a pivotal role in optical pulse and frequency comb synthesis,supporting a wide range of applications including communication,computing,ranging,and quantum information.The ever-...Cavity electro-optic(EO)modulation plays a pivotal role in optical pulse and frequency comb synthesis,supporting a wide range of applications including communication,computing,ranging,and quantum information.The ever-growing demand for these applications has driven efforts in enhancing modulation coupling strength and bandwidth towards advanced pulse-comb synthesis.However,the effects of strong-coupling and high-bandwidth cavity EO modulation remain underexplored,due to the lack of a general,unified model that captures this extreme condition.In this work,we present a universal framework for pulse-comb synthesis under cavity EO modulation,where coupling strength and modulation bandwidth far exceed the cavity’s free spectral range(FSR).We show that,under such intense and ultrafast driving conditions,EO-driven frequency combs and pulses exhibit rich higher-order nonlinear dynamics,including temporal pulse compression and comb generation with arbitrary pump detuning.Leveraging this framework,we reveal a direct link between the higher-order dynamics of EO pulse-comb generation and the band structure of synthetic dimension.Furthermore,we demonstrate arbitrary comb shaping via machine-learning-based inverse microwave drive design,achieving a tenfold enhancement in cavity EO comb flatness by exploring the synergistic effects of high-bandwidth driving and detuning-induced frequency boundaries.Our findings push cavity EO modulation into a new frontier,unlocking significant potential for universal and machine-learning-programmable EO frequency combs,topological photonics,as well as photonic quantum computing in the strong-coupling and high-bandwidth regimes.展开更多
基金Supported by the NNSF of China(10901129)Supported by the SRFDP(20096203120001)
文摘In this paper, we mainly investigate some properties of strongly n-Gorenstein projective, injective and flat modules under the extension of rings, which mainly including excellent extensions, morita equivalences, polynomial extensions and localizations.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1120137711261050)+1 种基金China Postdoctoral Science Foundation(Grant No.2013M541509)Program of Science and Technique of Gansu Province(Grant No.1208RJZA145)
文摘In the Gorenstein homological theory, Gorenstein projective and Gorenstein injective dimensions play an important and fundamental role. In this paper, we aim at studying the closely related strongly Gorenstein flat and Gorenstein FP-injective dimensions, and show that some characterizations similar to Gorenstein homological dimensions hold for these two dimensions.
基金Supported by the Postdoctoral Science Foundation of China（2017M611851）, the Jiangsu Planned Projects for Postdoctoral Research Funds（1601151C） and the Provincial Natural Science Foundation of Anhui Province（KJ2017A040）
文摘This paper is a study of strongly Ding projective modules with respect to a semidualizing module. The class of strongly Ding flat modules with respect to a semidualizing module is also investigated, and the relationship between strongly Ding projective modules and strongly Ding flat modules with respect to a semidualizing module is characterized.Some well-known results on strongly Ding projective modules, n-strongly Ding projective modules and strongly D_C-projective modules are generalized and unified.
基金supported by the Gansu Natural Science Foundation Project(No.25JRRK002).
文摘Let R be an associative ring with identity.In this paper,we consider generalizations of Gorenstein FP-injective R-modules and FP-injective complexes,give the definitions and characterizations of strongly Gorenstein FPinjective R-modules and strongly FP-injective complexes,which are induced by strongly FP-injective modules.Then we investigate the strongly FP-injective dimension of complexes.
基金Supported by the National Natural Science Foundation of China(Grant No.11501451)The Fund for Talent Introduction of Northwest Minzu University(Grant No.xbmuyjrc201406)
文摘The notion of strongly W-Gorenstein complexes is introduced for a self-orthogonal class W of modules. We obtain a characterization of such complexes and apply to strongly Gorenstein injective complexes.
基金Supported by the National Natural Science Foundation of China（11161006, 11171142） Supported by the Natural Science Foundation of Guangxi Province（2011GXNSFA018144, 018139, 2010GXNSFB 013048, 0991102）+2 种基金 Supported by the Guangxi New Century 1000 Talents Project Supported by the Guangxi Graduate Student Education Innovation Project（2011106030701M06） Supported by the SRF of Guangxi Education Committee
文摘In this paper we investigate strongly regular rings. In terms of W-ideals of rings some characterizations of strongly regular rings are given.
文摘Let R be a commutative ring with 1, and M is a (left) R-module. We introduce the concept of coprimarily packed submodules as a proper submodule N of an R-module M which is said to be Coprimarily Packed Submodule. If where Na is a primary submodule of M for each , then for some . When there exists such that;N is called Strongly Coprimarily Packed submodule. In this paper, we list some basic properties of this concept. We end this paper by explaining the relations between p-compactly packed and coprimarily packed submodules, and also the relations between strongly p-compactly packed and strongly coprimarily packed submodules.
基金Supported by the Provincial Natural Science Research Program of Higher Education Institution of Anhui Province(Grant No.KJ2012Z028)
文摘We consider the conditions under which the class of （m, d）-injective R-modules is （pre）covering. It is shown that every left R-module over a left （m, d）-coherent ring has an （rn, d）-injective cover. Moreover, the classes of Gorenstein （m, d）-flat modules and Gorenstein （m, d）-injecitve modules are introduced and studied. For a right （m, d）-coherent ring R, we prove that a left R-module M is Gorenstein （m, d）-flat if and only if M＋ is Gorenstein （m, d）- injective as a right R-module. Some results on Gorenstein flat modules and Gorenstein n-flat modules are generalized.
文摘Fe-based catalysts are widely used for CO_(2)hydrogenation to light olefins(C_(2–4)=);however,precise regulation of active phases and the balance between intermediate reactions remain significant challenges.Herein,we find that the addition of moderate amounts of Ti forms a strong interaction with Fe compositions,modulating the Fe_(3)O_(4)and Fe_(5)C_(2)contents.Enhanced interaction leads to an increased Fe_(5)C_(2)/Fe_(3)O_(4)ratio,which in turn enhances the adsorption of reactants and intermediates,promoting CO hydrogenation to unsaturated alkyl groups and facilitating C–C coupling.Furthermore,the strong Fe-Ti interaction induces the preferential growth of Fe_(5)C_(2)into prismatic structures that expose the(020),(–112),and(311)facets,forming compact active interfacial sites with Fe_(3)O_(4)nanoparticles.These facet and interfacial effects significantly promote the synergistic coupling of the reverse water gas shift and Fischer-Tropsch reactions.The optimized 3K/FeTi catalyst with the highest Fe_(5)C_(2)/Fe_(3)O_(4)ratio of 3.6 achieves a 52.2%CO_(2)conversion rate,with 44.5%selectivity for C2–4=and 9.5%for CO,and the highest space-time yield of 412.0 mg gcat^(–1)h^(–1)for C_(2–4)=.
基金funded by a Vidi grant(VI.Vidi.203.027)from the Dutch National Science Foundation(NWO).
文摘Atomically thin semiconductors exhibit tunable exciton resonances that can be harnessed for dynamic manipulation of visible light in ultra-compact metadevices.However,the rapid nonradiative decay and dephasing of excitons at room temperature limit current active excitonic metasurfaces to a few-percent efficiencies.Here,we leverage the combined merits of pristine 2D heterostructures and non-local dielectric metasurfaces to enhance the excitonic lightmatter interaction,achieving strong and electrically tunable exciton-photon coupling at ambient conditions in a hybrid-2D excitonic metasurface.Using this,we realize a free-space optical modulator and experimentally demonstrate 9.9 dB of reflectance modulation.The electro-optic response,characterized by a continuous transition from strong to weak coupling,is mediated by gating-induced variations in the free carrier concentration,altering the exciton’s nonradiative decay rate.These results highlight how hybrid-2D excitonic metasurfaces offer novel opportunities to realize nanophotonic devices for active wavefront manipulation and optical communication.
基金Acknowledgements This work was Foundation of China （Grant No. 11371187） Province of China （Grant No. BK20160771） supported by the National Natural Science and the Natural Science Foundation of Jiangsu
文摘Let R be a graded ring. We define and study strongly Gorenstein gr-projective, gr-injective, and gr-flat modules. Some connections among these modules are discussed. We also explore the relations between the graded and the ungraded strongly Gorenstein modules.
文摘There is a variety of nice results about strongly Gorenstein flat modules over coherent rings. These results are done by Ding, Lie and Mao. The aim of this paper is to generalize some of these results, and to give homological descriptions of the strongly Gorenstein flat dimension (of modules and rings) over arbitrary associative rings.
基金Project supported by the Major Program of National Natural Science Foundation of China （Grant No 60438010）.
文摘Strong optical feedback in a birefringent dual frequency He-Ne laser with a high reflectivity feedback mirror has been investigated for the first time. The output characteristics of two orthogonally polarized modes are demonstrated in two different optical feedback cases： one is for both modes being fed back and the other is for only one of the modes being fed back. Strong mode competition can be observed between the two modes with strong optical feedback, And when one mode＇s intensity is near its maximum, the other mode is nearly extinguished. When both modes are fed back into the laser cavity, the mode competition is stronger than when only one mode is fed back, The difference in initial intensity between the two orthogonally polarized modes plays an important role in the mode competition, which has been experimentally and theoretically demonstrated.
文摘Strongly irreducible submodules of modules are defined as follows： A submodule N of an Rmodule M is said to be strongly irreducible if for submodules L and K of M, the inclusion L ∩ K ∈ N implies that either L ∈ N or K ∈ N. The relationship among the families of irreducible, strongly irreducible, prime and primary submodules of an R-module M is considered, and a characterization of Noetherian modules which contain a non-prime strongly irreducible submodule is given.
基金This research is supported by the National Natural Science Foundation of China (19801012)the Ministry of Education of China([2000]65)
文摘When R satisfies (strong unit) 1-stable range and M is a R-R-bimodule, the authors calculate that K_1(R(?) M)≌U(R(?) M)/L(R(?) M). As applications, the authors also calculate some Whitehead groups for exchange rings with artinian primitive factors.
基金Acknowledgements This work was supported by the Natural Science Foundation of Gansu Province （No. 1310RJZA029） and the Fundamental Research F~nds for the Universities in Gansu Province.
文摘The concepts of strongly lifting modules and strongly dual Rickart modules are introduced and their properties are studied and relations between them are given in this paper. It is shown that a strongly lifting module has the strongly summand sum property and the generalized Hopfian property, and a ring R is a strongly regular ring if and only if RR is a strongly dual Rickart module, if and only if aR is a fully invariant direct summand of RR for every a∈R.
基金supported by the National Natural Science Foundation of China(No.52003110)the Natural Science Foundation of Jiangxi Province(Nos.20202ACB202002,20202ACB214002).
文摘Hierarchical porous carbon co-doped with heterogeneous atoms has attracted much attention thanks to sizable internal void space accommodating electrolyte,high-density microporous structure physically con-fining polysulfides(LPS),and heterogeneous atoms serving as active sites to capture LPS.However,solely relying on carbon material defects to capture LPS proves ineffective.Hence,metal compounds must be introduced to chemisorb LPS.Herein,cobalt ions are in-situ grown on the polydopamine layer coated on the surface of biomass-derived S,N,P co-doped hierarchical porous carbon(SNP-PC).Then a layer of nitrogen-doped porous carbon(MPC)dotted with CoSe nanoparticles is acquired by selenizing.Thus,a strong-polar/weak-polar composite material of SNP-PC studded with CoSe nanoparticles is obtained(SNP-PC@MPC@CoSe).Button cells assembled with SNP-PC@MPC@CoSe-modified separator enable superb long-cycle stability and satisfactory rate performance.An excellent rate capacity of 796 mAh g^(−1)at a high current rate of 4 C with an ultra-low capacity fading of 0.06%over 700 cycles can be acquired.More impressively,even in a harsh test condition of 5.65 mg cm^(−2)sulfur loading and 4μL mg^(−1)ratio of electrolyte to active materials,the battery can still display a specific capacity of 980 mAh g^(−1)(area capacity of∼5.54 mAh cm^(−2))at 0.1 C.This work provides a promising route toward high-performance Li-S batteries.
基金National Research Foundation funded by the Korea government(NRF-2022M3K4A1094782).
文摘Cavity electro-optic(EO)modulation plays a pivotal role in optical pulse and frequency comb synthesis,supporting a wide range of applications including communication,computing,ranging,and quantum information.The ever-growing demand for these applications has driven efforts in enhancing modulation coupling strength and bandwidth towards advanced pulse-comb synthesis.However,the effects of strong-coupling and high-bandwidth cavity EO modulation remain underexplored,due to the lack of a general,unified model that captures this extreme condition.In this work,we present a universal framework for pulse-comb synthesis under cavity EO modulation,where coupling strength and modulation bandwidth far exceed the cavity’s free spectral range(FSR).We show that,under such intense and ultrafast driving conditions,EO-driven frequency combs and pulses exhibit rich higher-order nonlinear dynamics,including temporal pulse compression and comb generation with arbitrary pump detuning.Leveraging this framework,we reveal a direct link between the higher-order dynamics of EO pulse-comb generation and the band structure of synthetic dimension.Furthermore,we demonstrate arbitrary comb shaping via machine-learning-based inverse microwave drive design,achieving a tenfold enhancement in cavity EO comb flatness by exploring the synergistic effects of high-bandwidth driving and detuning-induced frequency boundaries.Our findings push cavity EO modulation into a new frontier,unlocking significant potential for universal and machine-learning-programmable EO frequency combs,topological photonics,as well as photonic quantum computing in the strong-coupling and high-bandwidth regimes.
