The results of invertibility and spectrum for some different classes of infinite-dimensional Hayniltonian operators, after a brief classification by domains. are given. By the above results, the associated infinite-di...The results of invertibility and spectrum for some different classes of infinite-dimensional Hayniltonian operators, after a brief classification by domains. are given. By the above results, the associated infinite-dimensional Hamiltonian operator with simple supported rectangular plate is proved to be invertible. Furthermore, by a certain compactness, we find that the spectrum of this operator consists only of isolated eigenvalues with finite geometric multiplicity, which will play a significant role in finding the analytical and numerical solution based on Hamiltonian system for a class of plate bending equations.展开更多
To implement restoration in a single motion blurred image,the PSF(Point Spread Function)is difficult to estimate and the image deconvolution is ill-posed as a result that a good recovery effect cannot be obtained.Cons...To implement restoration in a single motion blurred image,the PSF(Point Spread Function)is difficult to estimate and the image deconvolution is ill-posed as a result that a good recovery effect cannot be obtained.Considering that several different PSFs can get joint invertibility to make restoration wellposed,we proposed a motion-blurred image restoration method based on joint invertibility of PSFs by means of computational photography.Firstly,we designed a set of observation device which composed by multiple cameras with the same parameters to shoot the moving target in the same field of view continuously to obtain the target images with the same background.The target images have the same brightness,but different exposure time and different motion blur length.It is easy to estimate the blur PSFs of the target images make use of the sequence frames obtained by one camera.According to the motion blur superposition feature of the target and its background,the complete blurred target images can be extracted from the observed images respectively.Finally,for the same target images with different PSFs,the iterative restoration is solved by joint solution of multiple images in spatial domain.The experiments showed that the moving target observation device designed by this method had lower requirements on hardware conditions,and the observed images are more convenient to use joint-PSF solution for image restoration,and the restoration results maintained details well and had lower signal noise ratio(SNR).展开更多
From the point of mathematical mapping, this paper discusses the invertibility of nonlinear systems, and presents definition, equivalence theorem, sufficient and necessary conditions of strong invertibility for single...From the point of mathematical mapping, this paper discusses the invertibility of nonlinear systems, and presents definition, equivalence theorem, sufficient and necessary conditions of strong invertibility for single input single output systems. Then it analyzes the feasibility of inverse system control method, and yields some conclusions on feasibility.展开更多
In this paper, we consider functional operators with shift in weighted H?lder spaces. We present the main idea and the scheme of proof of the conditions of invertibility for these operators. As an application, we prop...In this paper, we consider functional operators with shift in weighted H?lder spaces. We present the main idea and the scheme of proof of the conditions of invertibility for these operators. As an application, we propose to use these results for solution of equations with shift which arise in the study of cyclic models for natural systems with renewable resources.展开更多
Let 3V denote the set of all possible transfer function matrices of weakly invertible linear finite automata over a given finite field F. A classification and an enumeration on the infinite set are given.
We survey some recent results on linear maps on operator algebras that preserve invertibility. We also consider related problems such as the problem of the characterization of linear maps preserving spectrum, various ...We survey some recent results on linear maps on operator algebras that preserve invertibility. We also consider related problems such as the problem of the characterization of linear maps preserving spectrum, various parts of spectrum, spectral radius, quasinilpotents, etc. We present some results on elementary operators and additive operators preserving invertibility or related properties. In particular, we give a negative answer to a problem posed by Gao and Hou on characterizing spectrum-preserving elementary operators. Several open problems are also mentioned.展开更多
In this paper,the so-called invertibility is introduced for rational univariate representations,and a characterization of the invertibility is given.It is shown that the rational univariate representations,obtained by...In this paper,the so-called invertibility is introduced for rational univariate representations,and a characterization of the invertibility is given.It is shown that the rational univariate representations,obtained by both Rouillier’s approach and Wu’s method,are invertible.Moreover,the ideal created by a given rational univariate representation is defined.Some results on invertible rational univariate representations and created ideals are established.Based on these results,a new approach is presented for decomposing the radical of a zero-dimensional polynomial ideal into an intersection of maximal ideals.展开更多
Ra, Rb transformations were successfully applied to establish invertibility theory for linear and quasi-linear finite automata over finite fields. In aprevious paper, the authors generalized R., Rb transformations to ...Ra, Rb transformations were successfully applied to establish invertibility theory for linear and quasi-linear finite automata over finite fields. In aprevious paper, the authors generalized R., Rb transformations to deal with nonlinear memory finite automata, and gave sufficient conditions for weak inverse andfor weakly invertible memory finite automata and inversion processes concerned;methods by transformation to generate a kind of nonlinear memory finite automatasatisfying one of these sufficient conditions were also given. This paper extends theconcepts, methods and results to general finite automata, in which states consist offinite input history, finite output history and finite 'inner state' history.展开更多
We characterize the additive singularity preserving almost surjective maps on Mn （F）, the algebra of all n×n matrices over a field F with char F=0. We also describe additive invertibility preserving surjective ...We characterize the additive singularity preserving almost surjective maps on Mn （F）, the algebra of all n×n matrices over a field F with char F=0. We also describe additive invertibility preserving surjective maps on Mn （F） and give examples showing that all the assunlptions in these two theorems are indispensable.展开更多
The weak invertibility problem of finite automata (FAs) has received continuous considerations. The weak invertibility theory has applications in cryptography, both conventional cryptosystems and public key cryptosyst...The weak invertibility problem of finite automata (FAs) has received continuous considerations. The weak invertibility theory has applications in cryptography, both conventional cryptosystems and public key cryptosystems. Given a finite commutative ring (?) with identity, it is known, that the weak invertibility of a linear finite automaton(LFA) over (?) depends only on its transfer function matrix. Let H be the set of all possible transfer function matrices which weakly invertible LFAs over (?) can have. Our展开更多
We investigate some probabilistic properties of a new class of nonlinear time series models.A sufficient condition for the existence of a unique causal,strictly and weakly stationary solution is derived.To understand ...We investigate some probabilistic properties of a new class of nonlinear time series models.A sufficient condition for the existence of a unique causal,strictly and weakly stationary solution is derived.To understand the proposed models better,we further discuss the moment structure and obtain some Yule-Walker difference equations for the second and third order cumulants,which can also be used for identification purpose.A sufficient condition for invertibility is also provided.展开更多
In this note an alternative proof of the equivalence of Drazin invertibility of operators AB and BA is given. As an application, we will prove that σD(AB) = σD(BA) and σD(A) = σD(A), where σD(M) and ■ denote the...In this note an alternative proof of the equivalence of Drazin invertibility of operators AB and BA is given. As an application, we will prove that σD(AB) = σD(BA) and σD(A) = σD(A), where σD(M) and ■ denote the Drazin spectrum and the Aluthge transform of an operator M ∈ B(H), respectively.展开更多
This article investigates the robust current tracking control problem of three-phase grid-connected inverters with LCL filter under external disturbance by a dynamic state feedback control method.First,this paper cons...This article investigates the robust current tracking control problem of three-phase grid-connected inverters with LCL filter under external disturbance by a dynamic state feedback control method.First,this paper constructs an internal model to learn the information of the states and input of the grid-connected inverter under steady state.Second,by utilizing the internal model principle,the paper turns the tracking control problem into the robust stabilization control problem based on some appropriate coordinate transformations.Then,The paper designs a dynamics state feedback control law to deal with this robust stabilization problem,and thus the solution of the robust current tracking control problem of three-phase grid-connected inverters can be obtained.This control method can ensure the asymptotic stability of the closedloop system.Finally,the paper illustrates the effectiveness of the proposed control approach through several groups of simulations,and compares it with the feedforward control method to verify the robustness of the proposed control method to uncertain parameters.展开更多
This paper gives a necessary condition for a kind of weakly invertible, invertible, weak inverse or inverse finite automata by linear RaRb transformation sequence. For such finite automata the existence of terminating...This paper gives a necessary condition for a kind of weakly invertible, invertible, weak inverse or inverse finite automata by linear RaRb transformation sequence. For such finite automata the existence of terminating RaRb transformation sequence is also established.展开更多
Let p be an analytic polynomial on the unit disk.We obtain a necessary and sufficient condition for Toeplitz operators with the symbol z+p to be invertible on the Bergman space when all coefficients of p are real numb...Let p be an analytic polynomial on the unit disk.We obtain a necessary and sufficient condition for Toeplitz operators with the symbol z+p to be invertible on the Bergman space when all coefficients of p are real numbers.Furthermore,we establish several necessary and sufficient,easy-to-check conditions for Toeplitz operators with the symbol z+p to be invertible on the Bergman space when some coefficients of p are complex numbers.展开更多
With the increasing integration of renewable energy,microgrids are increasingly facing stability challenges,primarily due to the lack of inherent inertia in inverter-dominated systems,which is traditionally provided b...With the increasing integration of renewable energy,microgrids are increasingly facing stability challenges,primarily due to the lack of inherent inertia in inverter-dominated systems,which is traditionally provided by synchronous generators.To address this critical issue,Virtual Synchronous Generator(VSG)technology has emerged as a highly promising solution by emulating the inertia and damping characteristics of conventional synchronous generators.To enhance the operational efficiency of virtual synchronous generators(VSGs),this study employs smallsignal modeling analysis,root locus methods,and synchronous generator power-angle characteristic analysis to comprehensively evaluate how virtual inertia and damping coefficients affect frequency stability and power output during transient processes.Based on these analyses,an adaptive control strategy is proposed:increasing the virtual inertia when the rotor angular velocity undergoes rapid changes,while strengthening the damping coefficient when the speed deviation exceeds a certain threshold to suppress angular velocity oscillations.To validate the effectiveness of the proposed method,a grid-connected VSG simulation platform was developed inMATLAB/Simulink.Comparative simulations demonstrate that the proposed adaptive control strategy outperforms conventional VSGmethods by significantly reducing grid frequency deviations and shortening active power response time during active power command changes and load disturbances.This approach enhances microgrid stability and dynamic performance,confirming its viability for renewable-dominant power systems.Future work should focus on experimental validation and real-world parameter optimization,while further exploring the strategy’s effectiveness in improvingVSG low-voltage ride-through(LVRT)capability and power-sharing applications in multi-parallel configurations.展开更多
Molecular tailoring of self-assembled hole-transporting monolayers(SAMs)has been proven as an efficient approach for improving the device performance of inverted perovskite solar cells.Herein,a novel SAM with extended...Molecular tailoring of self-assembled hole-transporting monolayers(SAMs)has been proven as an efficient approach for improving the device performance of inverted perovskite solar cells.Herein,a novel SAM with extended conjugation is designed and synthesized,named NaPh-4PACz.Compared to Ph-4PACz,NaPh-4PACz exhibits a larger adsorption energy with the ITO substrate,enabling the formation of a more uniform and dense film,thereby preventing direct contact between the perovskite and ITO.Additionally,NaPh-4PACz also has a stronger interaction with the perovskite,which can reduce buried interface defects and suppress non-radiative recombination.Consequently,NaPh-4PACz-based devices achieved a power conversion efficiency of 25.48%due to their interfacial“adhesive”ability.Importantly,the stability of the NaPh-4PACz-based devices was significantly improved.展开更多
β-Ga_(2)O_(3) MOS inverter should play a crucial role in β-Ga_(2)O_(3) electronic circuits. Enhancement-mode(E-mode) MOSFET was fabricated based on β-Ga_(2)O_(3) film grown by atomic layer deposition technology, an...β-Ga_(2)O_(3) MOS inverter should play a crucial role in β-Ga_(2)O_(3) electronic circuits. Enhancement-mode(E-mode) MOSFET was fabricated based on β-Ga_(2)O_(3) film grown by atomic layer deposition technology, and the β-Ga_(2)O_(3) inverter was further monolithically integrated on this basis. The β-Ga_(2)O_(3) n MOSFET exhibits excellent electrical characteristics with an on/off current ratio reaching 10^(5). The logic inverter shows outstanding voltage inversion characteristics under low-frequency from 1 to 400 Hz operation. As the frequency continues to increase to 10 K, the reverse characteristic becomes worse due to parasitic capacitance induced by processes, and the difference between the highest and lowest values of VOUT has an exponential decay relationship with the frequency. This paper provides the practice for the development of β-Ga_(2)O_(3)-based circuits.展开更多
Recent progress in inverted perovskite solar cells(i PSCs)highlights the critical role of interface engineering between the charge transport layer and perovskite.Self-assembled monolayers(SAM)on transparent conductive...Recent progress in inverted perovskite solar cells(i PSCs)highlights the critical role of interface engineering between the charge transport layer and perovskite.Self-assembled monolayers(SAM)on transparent conductive oxide electrodes serve effectively as hole transport layers,though challenges such as energy mismatches and surface inhomogeneities remain.Here,a blended self-assembled monolayer of(2-(9H-carbazol-9-yl)ethyl)phosphonic acid(2PACz)and(4-(3,6-Dimethyl-9H-carbazol-9-yl)butyl)phosphonic acid(Me-4PACz)is developed,offering improved surface potential uniformity and interfacial energy alignment compared to individual SAMs.Interactions between the SAMs and ionic species are investigated with simulation analysis conducted,revealing the elimination of interfacial energy barriers through precise energy-level tuning.This strategy enables wide-bandgap(1.67 e V)perovskite solar cells with inverted structures with over 24%efficiency,an open-circuit voltage(V_(oc))of 1.268 V,and a certified fill factor(FF)of 86.8%,leading to a certified efficiency of 23.42%.The approach also enables high-efficiency semi-transparent devices and a mechanically stacked four-terminal perovskite/silicon tandem solar cell reaching 30.97%efficiency.展开更多
基金supported by National Natural Science Foundation of China under Grant No.10562002Natural Science Foundation of Inner Mongolia under Grant Nos.200508010103 and 200711020106
文摘The results of invertibility and spectrum for some different classes of infinite-dimensional Hayniltonian operators, after a brief classification by domains. are given. By the above results, the associated infinite-dimensional Hamiltonian operator with simple supported rectangular plate is proved to be invertible. Furthermore, by a certain compactness, we find that the spectrum of this operator consists only of isolated eigenvalues with finite geometric multiplicity, which will play a significant role in finding the analytical and numerical solution based on Hamiltonian system for a class of plate bending equations.
基金funding of Natural Science Foundation of Shandong Province(ZR2013F0025),www.sdnsf.gov.cn.
文摘To implement restoration in a single motion blurred image,the PSF(Point Spread Function)is difficult to estimate and the image deconvolution is ill-posed as a result that a good recovery effect cannot be obtained.Considering that several different PSFs can get joint invertibility to make restoration wellposed,we proposed a motion-blurred image restoration method based on joint invertibility of PSFs by means of computational photography.Firstly,we designed a set of observation device which composed by multiple cameras with the same parameters to shoot the moving target in the same field of view continuously to obtain the target images with the same background.The target images have the same brightness,but different exposure time and different motion blur length.It is easy to estimate the blur PSFs of the target images make use of the sequence frames obtained by one camera.According to the motion blur superposition feature of the target and its background,the complete blurred target images can be extracted from the observed images respectively.Finally,for the same target images with different PSFs,the iterative restoration is solved by joint solution of multiple images in spatial domain.The experiments showed that the moving target observation device designed by this method had lower requirements on hardware conditions,and the observed images are more convenient to use joint-PSF solution for image restoration,and the restoration results maintained details well and had lower signal noise ratio(SNR).
文摘From the point of mathematical mapping, this paper discusses the invertibility of nonlinear systems, and presents definition, equivalence theorem, sufficient and necessary conditions of strong invertibility for single input single output systems. Then it analyzes the feasibility of inverse system control method, and yields some conclusions on feasibility.
文摘In this paper, we consider functional operators with shift in weighted H?lder spaces. We present the main idea and the scheme of proof of the conditions of invertibility for these operators. As an application, we propose to use these results for solution of equations with shift which arise in the study of cyclic models for natural systems with renewable resources.
基金supported by the National Natural Science Foundation of China.
文摘Let 3V denote the set of all possible transfer function matrices of weakly invertible linear finite automata over a given finite field F. A classification and an enumeration on the infinite set are given.
文摘We survey some recent results on linear maps on operator algebras that preserve invertibility. We also consider related problems such as the problem of the characterization of linear maps preserving spectrum, various parts of spectrum, spectral radius, quasinilpotents, etc. We present some results on elementary operators and additive operators preserving invertibility or related properties. In particular, we give a negative answer to a problem posed by Gao and Hou on characterizing spectrum-preserving elementary operators. Several open problems are also mentioned.
基金the National Natural Science Foundation of China under Grant No.12161057。
文摘In this paper,the so-called invertibility is introduced for rational univariate representations,and a characterization of the invertibility is given.It is shown that the rational univariate representations,obtained by both Rouillier’s approach and Wu’s method,are invertible.Moreover,the ideal created by a given rational univariate representation is defined.Some results on invertible rational univariate representations and created ideals are established.Based on these results,a new approach is presented for decomposing the radical of a zero-dimensional polynomial ideal into an intersection of maximal ideals.
文摘Ra, Rb transformations were successfully applied to establish invertibility theory for linear and quasi-linear finite automata over finite fields. In aprevious paper, the authors generalized R., Rb transformations to deal with nonlinear memory finite automata, and gave sufficient conditions for weak inverse andfor weakly invertible memory finite automata and inversion processes concerned;methods by transformation to generate a kind of nonlinear memory finite automatasatisfying one of these sufficient conditions were also given. This paper extends theconcepts, methods and results to general finite automata, in which states consist offinite input history, finite output history and finite 'inner state' history.
基金supported in part by a grant from the Ministry of Science of Slovenia
文摘We characterize the additive singularity preserving almost surjective maps on Mn （F）, the algebra of all n×n matrices over a field F with char F=0. We also describe additive invertibility preserving surjective maps on Mn （F） and give examples showing that all the assunlptions in these two theorems are indispensable.
文摘The weak invertibility problem of finite automata (FAs) has received continuous considerations. The weak invertibility theory has applications in cryptography, both conventional cryptosystems and public key cryptosystems. Given a finite commutative ring (?) with identity, it is known, that the weak invertibility of a linear finite automaton(LFA) over (?) depends only on its transfer function matrix. Let H be the set of all possible transfer function matrices which weakly invertible LFAs over (?) can have. Our
基金supported by the Fundamental Research Funds for the Central Universities of China(Grant No.2010121005)supported by the Scientific Research and Development Funds for Youth of Fujian University of Technology of China(Grant No.GY-Z09081)
文摘We investigate some probabilistic properties of a new class of nonlinear time series models.A sufficient condition for the existence of a unique causal,strictly and weakly stationary solution is derived.To understand the proposed models better,we further discuss the moment structure and obtain some Yule-Walker difference equations for the second and third order cumulants,which can also be used for identification purpose.A sufficient condition for invertibility is also provided.
基金the National Natural Science Foundation of China (No.10571113)
文摘In this note an alternative proof of the equivalence of Drazin invertibility of operators AB and BA is given. As an application, we will prove that σD(AB) = σD(BA) and σD(A) = σD(A), where σD(M) and ■ denote the Drazin spectrum and the Aluthge transform of an operator M ∈ B(H), respectively.
基金Supported by the Fundamental Research Funds for the Central Universities(2024ZYGXZR047)the National Natural Science Foundation of China(62373156)the Guangdong Basic and Applied Basic Research Foundation(2024A1515011736)。
文摘This article investigates the robust current tracking control problem of three-phase grid-connected inverters with LCL filter under external disturbance by a dynamic state feedback control method.First,this paper constructs an internal model to learn the information of the states and input of the grid-connected inverter under steady state.Second,by utilizing the internal model principle,the paper turns the tracking control problem into the robust stabilization control problem based on some appropriate coordinate transformations.Then,The paper designs a dynamics state feedback control law to deal with this robust stabilization problem,and thus the solution of the robust current tracking control problem of three-phase grid-connected inverters can be obtained.This control method can ensure the asymptotic stability of the closedloop system.Finally,the paper illustrates the effectiveness of the proposed control approach through several groups of simulations,and compares it with the feedforward control method to verify the robustness of the proposed control method to uncertain parameters.
基金Project supported by the National Natural Science Foundation of China.
文摘This paper gives a necessary condition for a kind of weakly invertible, invertible, weak inverse or inverse finite automata by linear RaRb transformation sequence. For such finite automata the existence of terminating RaRb transformation sequence is also established.
基金supported by the Yunnan Natural Science Foundation(Grant No.201601YA00004)supported by National Natural Science Foundation of China(Grant No.11701052)+1 种基金Chongqing Natural Science Foundation(Grant No.cstc2017jcyjAX0373)the Fundamental Research Funds for the Central Universities(Grant Nos.106112016CDJRC000080 and 106112017CDJXY100007)。
文摘Let p be an analytic polynomial on the unit disk.We obtain a necessary and sufficient condition for Toeplitz operators with the symbol z+p to be invertible on the Bergman space when all coefficients of p are real numbers.Furthermore,we establish several necessary and sufficient,easy-to-check conditions for Toeplitz operators with the symbol z+p to be invertible on the Bergman space when some coefficients of p are complex numbers.
基金financially supported by the Talent Initiation Fund of Wuxi University(550220008).
文摘With the increasing integration of renewable energy,microgrids are increasingly facing stability challenges,primarily due to the lack of inherent inertia in inverter-dominated systems,which is traditionally provided by synchronous generators.To address this critical issue,Virtual Synchronous Generator(VSG)technology has emerged as a highly promising solution by emulating the inertia and damping characteristics of conventional synchronous generators.To enhance the operational efficiency of virtual synchronous generators(VSGs),this study employs smallsignal modeling analysis,root locus methods,and synchronous generator power-angle characteristic analysis to comprehensively evaluate how virtual inertia and damping coefficients affect frequency stability and power output during transient processes.Based on these analyses,an adaptive control strategy is proposed:increasing the virtual inertia when the rotor angular velocity undergoes rapid changes,while strengthening the damping coefficient when the speed deviation exceeds a certain threshold to suppress angular velocity oscillations.To validate the effectiveness of the proposed method,a grid-connected VSG simulation platform was developed inMATLAB/Simulink.Comparative simulations demonstrate that the proposed adaptive control strategy outperforms conventional VSGmethods by significantly reducing grid frequency deviations and shortening active power response time during active power command changes and load disturbances.This approach enhances microgrid stability and dynamic performance,confirming its viability for renewable-dominant power systems.Future work should focus on experimental validation and real-world parameter optimization,while further exploring the strategy’s effectiveness in improvingVSG low-voltage ride-through(LVRT)capability and power-sharing applications in multi-parallel configurations.
基金supported by the National Natural Science Foundation of China(61904053,22279033)the National Key Research and Development Program of China(2023YFB4204502)+2 种基金the 111 Project(B16016)the Fundamental Research Funds for the Central Universities(2025MS043)the Special Foundation for Carbon Peak Carbon Neutralization Technology Innovation Program of Jiangsu Province(BE2022026).
文摘Molecular tailoring of self-assembled hole-transporting monolayers(SAMs)has been proven as an efficient approach for improving the device performance of inverted perovskite solar cells.Herein,a novel SAM with extended conjugation is designed and synthesized,named NaPh-4PACz.Compared to Ph-4PACz,NaPh-4PACz exhibits a larger adsorption energy with the ITO substrate,enabling the formation of a more uniform and dense film,thereby preventing direct contact between the perovskite and ITO.Additionally,NaPh-4PACz also has a stronger interaction with the perovskite,which can reduce buried interface defects and suppress non-radiative recombination.Consequently,NaPh-4PACz-based devices achieved a power conversion efficiency of 25.48%due to their interfacial“adhesive”ability.Importantly,the stability of the NaPh-4PACz-based devices was significantly improved.
基金supported by Natural Science Basic Research Program of Shaanxi Province of China (No. 2023-JC-YB-574)National Natural Science Foundation of China (No. 62304178)。
文摘β-Ga_(2)O_(3) MOS inverter should play a crucial role in β-Ga_(2)O_(3) electronic circuits. Enhancement-mode(E-mode) MOSFET was fabricated based on β-Ga_(2)O_(3) film grown by atomic layer deposition technology, and the β-Ga_(2)O_(3) inverter was further monolithically integrated on this basis. The β-Ga_(2)O_(3) n MOSFET exhibits excellent electrical characteristics with an on/off current ratio reaching 10^(5). The logic inverter shows outstanding voltage inversion characteristics under low-frequency from 1 to 400 Hz operation. As the frequency continues to increase to 10 K, the reverse characteristic becomes worse due to parasitic capacitance induced by processes, and the difference between the highest and lowest values of VOUT has an exponential decay relationship with the frequency. This paper provides the practice for the development of β-Ga_(2)O_(3)-based circuits.
文摘Recent progress in inverted perovskite solar cells(i PSCs)highlights the critical role of interface engineering between the charge transport layer and perovskite.Self-assembled monolayers(SAM)on transparent conductive oxide electrodes serve effectively as hole transport layers,though challenges such as energy mismatches and surface inhomogeneities remain.Here,a blended self-assembled monolayer of(2-(9H-carbazol-9-yl)ethyl)phosphonic acid(2PACz)and(4-(3,6-Dimethyl-9H-carbazol-9-yl)butyl)phosphonic acid(Me-4PACz)is developed,offering improved surface potential uniformity and interfacial energy alignment compared to individual SAMs.Interactions between the SAMs and ionic species are investigated with simulation analysis conducted,revealing the elimination of interfacial energy barriers through precise energy-level tuning.This strategy enables wide-bandgap(1.67 e V)perovskite solar cells with inverted structures with over 24%efficiency,an open-circuit voltage(V_(oc))of 1.268 V,and a certified fill factor(FF)of 86.8%,leading to a certified efficiency of 23.42%.The approach also enables high-efficiency semi-transparent devices and a mechanically stacked four-terminal perovskite/silicon tandem solar cell reaching 30.97%efficiency.
