Infinitives which consist of bare infinitive and infinitival to are imperative in linguistic studies.And both of the two kinds of infinitives do not indicate person,tense and number.This research aims to analyze the p...Infinitives which consist of bare infinitive and infinitival to are imperative in linguistic studies.And both of the two kinds of infinitives do not indicate person,tense and number.This research aims to analyze the properties,similarities and differences between bare infinitive and infinitival to from the perspective of syntax.Thus,it enables us to attain a uniform characterization of the infinitival to and bare infinitive on the syntactic level and help us to understand these two kinds of infinitives better.展开更多
The polarization properties of light are widely applied in imaging,communications,materials analy⁃sis,and life sciences.Various methods have been developed that can measure the polarization information of a target.How...The polarization properties of light are widely applied in imaging,communications,materials analy⁃sis,and life sciences.Various methods have been developed that can measure the polarization information of a target.However,conventional polarization detection systems are often bulky and complex,limiting their poten⁃tial for broader applications.To address the challenges of miniaturization,integrated polarization detectors have been extensively explored in recent years,achieving significant advancements in performance and functionality.In this review,we focus mainly on integrated polarization detectors with innovative features,including infinitely high polarization discrimination,ultrahigh sensitivity to polarization state change,full Stokes parameters measure⁃ment,and simultaneous perception of polarization and other key properties of light.Lastly,we discuss the oppor⁃tunities and challenges for the future development of integrated polarization photodetectors.展开更多
A previous paper showed that the real numbers between 0 and 1 could be represented by an infinite tree structure, called the ‘infinity tree’, which contains only a countably infinite number of nodes and arcs. This p...A previous paper showed that the real numbers between 0 and 1 could be represented by an infinite tree structure, called the ‘infinity tree’, which contains only a countably infinite number of nodes and arcs. This paper discusses how a finite-state Turing machine could, in a countably infinite number of state transitions, write all the infinite paths in the infinity tree to a countably infinite tape. Hence it is argued that the real numbers in the interval [0, 1] are countably infinite in a non-Cantorian theory of infinity based on Turing machines using countably infinite space and time. In this theory, Cantor’s Continuum Hypothesis can also be proved. And in this theory, it follows that the power set of the natural numbers P(ℕ) is countably infinite, which contradicts the claim of Cantor’s Theorem for the natural numbers. However, this paper does not claim there is an error in Cantor’s arguments that [0, 1] is uncountably infinite. Rather, this paper considers the situation as a paradox, resulting from different choices about how to represent and count the continuum of real numbers.展开更多
Let I be the set of all infinitely divisible random variables with finite second moments,I_(0)={X∈I;Var(X)>0},P_(I)=inf_(x∈I)P{|X-E[X]|≤√Var(X)}and P_(I_(0))=inf P{|X-E[X]|<√Var(X)}.Firstly,we prove that P_...Let I be the set of all infinitely divisible random variables with finite second moments,I_(0)={X∈I;Var(X)>0},P_(I)=inf_(x∈I)P{|X-E[X]|≤√Var(X)}and P_(I_(0))=inf P{|X-E[X]|<√Var(X)}.Firstly,we prove that P_(I)≥P_(I_(0))>0.Secondly,we find_(x∈I_(0))the exact values of inf P{|X-E[X]|≤√Var(X)}and inf P{|X-E[X]|<√Var(X)}for the cases that J is the set of all geometric random variables,symmetric geometric random variables,Poisson random variables and symmetric Poisson random variables,respectively.As a consequence,we obtain that P_(I)≤e^(-1)^(∞)∑_(k=0)1/2^(2k)(k!)^(2)≈0.46576 and P_(I_(0))≤e^(-1)≈0.36788.展开更多
Industrial linear accelerators often contain many bunches when their pulse widths are extended to microseconds.As they typically operate at low electron energies and high currents,the interactions among bunches cannot...Industrial linear accelerators often contain many bunches when their pulse widths are extended to microseconds.As they typically operate at low electron energies and high currents,the interactions among bunches cannot be neglected.In this study,an algorithm is introduced for calculating the space charge force of a train with infinite bunches.By utilizing the ring charge model and the particle-in-cell(PIC)method and combining analytical and numerical methods,the proposed algorithm efficiently calculates the space charge force of infinite bunches,enabling the accurate design of accelerator parameters and a comprehensive understanding of the space charge force.This is a significant improvement on existing simulation software such as ASTRA and PARMELA that can only handle a single bunch or a small number of bunches.The PIC algorithm is validated in long drift space transport by comparing it with existing models,such as the infinite-bunch,ASTRA single-bunch,and PARMELA several-bunch algorithms.The space charge force calculation results for the external acceleration field are also verified.The reliability of the proposed algorithm provides a foundation for the design and optimization of industrial accelerators.展开更多
Here,a seismic-response analysis model was proposed for evaluating the nonlinear seismic response of a pile-supported bridge pier under frozen and thawed soil conditions.The effect of a seasonally frozen soil layer on...Here,a seismic-response analysis model was proposed for evaluating the nonlinear seismic response of a pile-supported bridge pier under frozen and thawed soil conditions.The effect of a seasonally frozen soil layer on the seismic vulnerability of a pile-supported bridge pier was evaluated based on reliability theory.Although the frozen soil layer inhibited the seismic response of the ground surface to a certain extent,it exacerbated the acceleration response at the bridge pier top owing to the low radiation damping effect of the frozen soil layer.Furthermore,the frozen soil layer reduced the lateral displacement of the bridge pier top relative to the ground surface by approximately 80%,thereby preventing damage caused by earthquakes,such as falling girders.Compared to the thawed state of the ground surface,the bending moment of the bridge pier in frozen ground increases.However,the bending moment of the pile foundation in frozen ground decreases,thereby lessening the seismic vulnerability of the bridge pile foundation.The results of this can provide a reference for the seismic response analysis and seismic risk assessment of pile-supported bridges in seasonally frozen regions.展开更多
A theory based on the superposition principle is developed to uncover the basic physics of wave behavior in a finite grating of N unit cells.The theory reveals that bound states in the continuum(BICs)of infinite quali...A theory based on the superposition principle is developed to uncover the basic physics of wave behavior in a finite grating of N unit cells.The theory reveals that bound states in the continuum(BICs)of infinite quality factor(Q-factor)can be supported by such a grating when perfect reflection is introduced at its boundaries.If geometrical perturbations are introduced into the structure,the dark BICs transform into bright quasi-BICs with finite Q-factor,maintaining spectral characteristics nearly identical to those of quasi-BICs supported by infinite gratings.When the boundaries are replaced with high-reflectivity metallic mirrors,the Q-factor of the resonant mode is reduced to be finite;however,it can be much larger than that in the corresponding nanostructure with open boundaries and can be tuned over a large range by varying the number of unit cells or boundary conditions.展开更多
With the development of the Internet,image encryption technology has become critical for network security.Traditional methods often suffer from issues such as insufficient chaos,low randomness in key generation,and po...With the development of the Internet,image encryption technology has become critical for network security.Traditional methods often suffer from issues such as insufficient chaos,low randomness in key generation,and poor encryption efficiency.To enhance performance,this paper proposes a new encryption algorithm designed to optimize parallel processing and adapt to images of varying sizes and colors.The method begins by using SHA-384 to extract the hash value of the plaintext image,which is then processed to determine the chaotic system’s initial value and block size.The image is padded and divided into blocks for further processing.A novel two-dimensional infinite collapses hyperchaotic map(2DICHM)is employed to generate the intra-block scrambling sequence,while an improved variable Joseph traversal sequence is used for inter-block scrambling.After removing the padding,3D forward and backward shift diffusions,controlled by the 2D-ICHM sequences,are applied to the scrambled image,producing the ciphertext.Simulation results demonstrate that the proposed algorithm outperforms others in terms of entropy,anti-noise resilience,correlation coefficient,robustness,and encryption efficiency.展开更多
The opaque property plays an important role in the operation of a security-critical system,implying that pre-defined secret information of the system is not able to be inferred through partially observing its behavior...The opaque property plays an important role in the operation of a security-critical system,implying that pre-defined secret information of the system is not able to be inferred through partially observing its behavior.This paper addresses the verification of current-state,initial-state,infinite-step,and K-step opacity of networked discrete event systems modeled by labeled Petri nets,where communication losses and delays are considered.Based on the symbolic technique for the representation of states in Petri nets,an observer and an estimator are designed for the verification of current-state and initial-state opacity,respectively.Then,we propose a structure called an I-observer that is combined with secret states to verify whether a networked discrete event system is infinite-step opaque or K-step opaque.Due to the utilization of symbolic approaches for the state-based opacity verification,the computation of the reachability graphs of labeled Petri nets is avoided,which dramatically reduces the computational overheads stemming from networked discrete event systems.展开更多
The non-Hermitian skin effect and edge burst reflect the vital role of spatial boundaries in non-Hermitian systems from both static and dynamic perspectives.In this study,we investigate a non-Hermitian dissipative lat...The non-Hermitian skin effect and edge burst reflect the vital role of spatial boundaries in non-Hermitian systems from both static and dynamic perspectives.In this study,we investigate a non-Hermitian dissipative lattice with nonlocal coupling and demonstrate many interesting static and dynamic phenomena.In the case of global coupling with all sites coupled with each other,we observe anomalous hopping resonance,where a quantum walker initially placed at a single site almost completely escapes from the boundary of the system regardless of its initial position.In the case of non-global coupling,which is infinite-range coupling,the interplay between nonlocal hopping and the non-Hermitian skin effect results in the emergence of local bulk modes exhibiting a multipartite density distribution.The presence of local bulk modes induces the nontrivial dynamics of a quantum walker,which features multiple peaks of lost probability in spatially separated domains.Our findings demonstrate unique properties induced by nonlocal coupling in non-Hermitian systems.展开更多
This paper presents a novel model-free method to solve linear quadratic(LQ)mean-field control problems with one-dimensional state space and multiplicative noise.The focus is on the infinite horizon LQ setting,where th...This paper presents a novel model-free method to solve linear quadratic(LQ)mean-field control problems with one-dimensional state space and multiplicative noise.The focus is on the infinite horizon LQ setting,where the conditions for solution either stabilization or optimization can be formulated as two algebraic Riccati equations(AREs).The proposed approach leverages the integral reinforcement learning technique to iteratively solve the drift-coefficient-dependent stochastic ARE(SARE)and other indefinite ARE,without requiring knowledge of the system dynamics.A numerical example is given to demonstrate the effectiveness of the proposed algorithm.展开更多
Infinite matrix theory is an important branch of function analysis.Every linear operator on a complex separable infinite dimensional Hilbert space corresponds to an infinite matrix with respect a orthonormal base of t...Infinite matrix theory is an important branch of function analysis.Every linear operator on a complex separable infinite dimensional Hilbert space corresponds to an infinite matrix with respect a orthonormal base of the space,but not every infinite matrix corresponds to an operator.The classical Schur test provides an elegant and useful criterion for the boundedness of linear operators,which is considered a respectable mathematical accomplishment.In this paper,we prove the compact version of the Schur test.Moreover,we provide the Schur test for the Schatten class S_(2).It is worth noting that our main results can be applicable to the general matrix without limitation on non-negative numbers.We finally provide the Schur test for compact operators from l_(p) into l_(q).展开更多
The critical rainfall of runoff-initiated debris flows is utmost importance for local early hazard forecasting.This paper presents research on the critical rainfall of runoff-initiated debris flows through comparisons...The critical rainfall of runoff-initiated debris flows is utmost importance for local early hazard forecasting.This paper presents research on the critical rainfall of runoff-initiated debris flows through comparisons between slope gradients and three key factors,including topographic contributing area,dimensionless discharge,and Shields stress.The rainfall amount was estimated by utilizing in-situ rainfall records and a slope-dependent Shields stress model was created.The created model can predict critical Shields stress more accurately than the other two models.Furthermore,a new dimensionless discharge equation was proposed based on the corresponding discharge-gradient datasets.The new equation,along with factors such as contributing area above bed failure sites,channel width,and mean diameter of debris flow deposits,predicts a smaller rainfall amount than the in-situ measured records.Although the slope-dependent Shields stress model performs well and the estimated rainfall amount is lower than the in-situ records,the sediment initiation in the experiments falls within sheet flow regime due to a large Shields stress.Therefore,further sediment initiation experiments at a steeper slope range are expected in the future to ensure that the sediment transport belongs to mass failure regime characterized by a low level of Shields stress.Finally,a more accurate hazard forecast on the runoff-initiated debris flow holds promise when the corresponding critical slope-dependent dimensionless discharge of no motion,fluvial sediment transport,mass flow regime,and sheet flow regime are considered.展开更多
In this article,we introduce and study the class of approximately Artinian(Noetherian)C^(*)-algebras,called AR-algebras(AN-algebras),which is a simultaneous generalization of Artinian(Noetherian)C*-algebras and AF-alg...In this article,we introduce and study the class of approximately Artinian(Noetherian)C^(*)-algebras,called AR-algebras(AN-algebras),which is a simultaneous generalization of Artinian(Noetherian)C*-algebras and AF-algebras.We study properties such as the ideal property and topological dimension zero for them.In particular,we show that a faithful AR or AN algebra is strongly purely infinite iff it is purely infinite iff it is weakly purely infinite.This extends the Kirchberg's O_(∞)-absorption theorem,and implies that a weakly purely infinite C^(*)-algebra is Noetherian iff every its ideal has a full projection.展开更多
In this paper,by using the discrete Arzelá-Ascoli Lemma and the fixed-point theorem in cones,we discuss the existence of positive solutions of the following second order discrete Sturm-Liouville boundary value pr...In this paper,by using the discrete Arzelá-Ascoli Lemma and the fixed-point theorem in cones,we discuss the existence of positive solutions of the following second order discrete Sturm-Liouville boundary value problem on infinite intervals■where Δu(x)=u(x+1)-u(x)is the forward difference operator,■is continuous,a>0,B and C are nonnegative constants.展开更多
Ultrasonic transmitting, receiving and amplifying circuits are designed. Thereceived signals are sampled with the high speed ADC (analog-to-digital converter), and dealt withthe DSP (digital signal processing). A forw...Ultrasonic transmitting, receiving and amplifying circuits are designed. Thereceived signals are sampled with the high speed ADC (analog-to-digital converter), and dealt withthe DSP (digital signal processing). A forward-backward IIR (infinitive impulse response) filterwith no delay is designed to filter the sampled data, and series A and B are achieved by narrow andwide band filtering, respectively. In series A, the start point of the cycle first exceeding thethreshold is calculated accuratelyby interpolation, and the start cycle is detected by fittingcycles in series A and its inversion A' to cycles in B with variance analysis. Therefore, the startpoint of the start cycle is calculated precisely. By deriving the relationships between the traveltime in the opposite directions of three axes and the airflow velocities, the wind velocity anddirection are calculated. Experiments show that the reliability and the precision are improved, andthe circuits are simplified.展开更多
We give a proof of an explicit formula for affine coodinates of points in the Sato’s infinite Grassmannian corresponding to tau-functions for the KdV hierarchy.
文摘Infinitives which consist of bare infinitive and infinitival to are imperative in linguistic studies.And both of the two kinds of infinitives do not indicate person,tense and number.This research aims to analyze the properties,similarities and differences between bare infinitive and infinitival to from the perspective of syntax.Thus,it enables us to attain a uniform characterization of the infinitival to and bare infinitive on the syntactic level and help us to understand these two kinds of infinitives better.
基金Supported by the National Key Research and Development Program of China(2022YFA1404602)the Strategic Priority Research Program of the Chinese Academy of Sciences(XDB0580000)+3 种基金the National Natural Science Foundation of China(U23B2045,62305362)the Program of Shanghai Academic/Technology Research Leader(22XD1424400)the Fund of SITP Innovation Foundation(CX-461 and CX-522)Special Project to Seize the Commanding Heights of Science and Technology of Chinese Academy of Sciences,subtopic(GJ0090406-6).
文摘The polarization properties of light are widely applied in imaging,communications,materials analy⁃sis,and life sciences.Various methods have been developed that can measure the polarization information of a target.However,conventional polarization detection systems are often bulky and complex,limiting their poten⁃tial for broader applications.To address the challenges of miniaturization,integrated polarization detectors have been extensively explored in recent years,achieving significant advancements in performance and functionality.In this review,we focus mainly on integrated polarization detectors with innovative features,including infinitely high polarization discrimination,ultrahigh sensitivity to polarization state change,full Stokes parameters measure⁃ment,and simultaneous perception of polarization and other key properties of light.Lastly,we discuss the oppor⁃tunities and challenges for the future development of integrated polarization photodetectors.
文摘A previous paper showed that the real numbers between 0 and 1 could be represented by an infinite tree structure, called the ‘infinity tree’, which contains only a countably infinite number of nodes and arcs. This paper discusses how a finite-state Turing machine could, in a countably infinite number of state transitions, write all the infinite paths in the infinity tree to a countably infinite tape. Hence it is argued that the real numbers in the interval [0, 1] are countably infinite in a non-Cantorian theory of infinity based on Turing machines using countably infinite space and time. In this theory, Cantor’s Continuum Hypothesis can also be proved. And in this theory, it follows that the power set of the natural numbers P(ℕ) is countably infinite, which contradicts the claim of Cantor’s Theorem for the natural numbers. However, this paper does not claim there is an error in Cantor’s arguments that [0, 1] is uncountably infinite. Rather, this paper considers the situation as a paradox, resulting from different choices about how to represent and count the continuum of real numbers.
基金supported by the National Natural Science Foundation of China(12161029,12171335)the National Natural Science Foundation of Hainan Province(121RC149)+1 种基金the Science Development Project of Sichuan University(2020SCUNL201)the Natural Sciences and Engineering Research Council of Canada(4394-2018).
文摘Let I be the set of all infinitely divisible random variables with finite second moments,I_(0)={X∈I;Var(X)>0},P_(I)=inf_(x∈I)P{|X-E[X]|≤√Var(X)}and P_(I_(0))=inf P{|X-E[X]|<√Var(X)}.Firstly,we prove that P_(I)≥P_(I_(0))>0.Secondly,we find_(x∈I_(0))the exact values of inf P{|X-E[X]|≤√Var(X)}and inf P{|X-E[X]|<√Var(X)}for the cases that J is the set of all geometric random variables,symmetric geometric random variables,Poisson random variables and symmetric Poisson random variables,respectively.As a consequence,we obtain that P_(I)≤e^(-1)^(∞)∑_(k=0)1/2^(2k)(k!)^(2)≈0.46576 and P_(I_(0))≤e^(-1)≈0.36788.
基金supported by the National Key Research and Development Program(No.2022YFC2402300)。
文摘Industrial linear accelerators often contain many bunches when their pulse widths are extended to microseconds.As they typically operate at low electron energies and high currents,the interactions among bunches cannot be neglected.In this study,an algorithm is introduced for calculating the space charge force of a train with infinite bunches.By utilizing the ring charge model and the particle-in-cell(PIC)method and combining analytical and numerical methods,the proposed algorithm efficiently calculates the space charge force of infinite bunches,enabling the accurate design of accelerator parameters and a comprehensive understanding of the space charge force.This is a significant improvement on existing simulation software such as ASTRA and PARMELA that can only handle a single bunch or a small number of bunches.The PIC algorithm is validated in long drift space transport by comparing it with existing models,such as the infinite-bunch,ASTRA single-bunch,and PARMELA several-bunch algorithms.The space charge force calculation results for the external acceleration field are also verified.The reliability of the proposed algorithm provides a foundation for the design and optimization of industrial accelerators.
基金National Natural Science Foundation of China under Grant Nos.52068045,U21A2012 and 41825015。
文摘Here,a seismic-response analysis model was proposed for evaluating the nonlinear seismic response of a pile-supported bridge pier under frozen and thawed soil conditions.The effect of a seasonally frozen soil layer on the seismic vulnerability of a pile-supported bridge pier was evaluated based on reliability theory.Although the frozen soil layer inhibited the seismic response of the ground surface to a certain extent,it exacerbated the acceleration response at the bridge pier top owing to the low radiation damping effect of the frozen soil layer.Furthermore,the frozen soil layer reduced the lateral displacement of the bridge pier top relative to the ground surface by approximately 80%,thereby preventing damage caused by earthquakes,such as falling girders.Compared to the thawed state of the ground surface,the bending moment of the bridge pier in frozen ground increases.However,the bending moment of the pile foundation in frozen ground decreases,thereby lessening the seismic vulnerability of the bridge pile foundation.The results of this can provide a reference for the seismic response analysis and seismic risk assessment of pile-supported bridges in seasonally frozen regions.
基金supported by the National Natural Science Foundation of China(Grant Nos.11874270 and 12174228)the Shenzhen Basic Research Special Project(Grant No.JCYJ20240813141606009)。
文摘A theory based on the superposition principle is developed to uncover the basic physics of wave behavior in a finite grating of N unit cells.The theory reveals that bound states in the continuum(BICs)of infinite quality factor(Q-factor)can be supported by such a grating when perfect reflection is introduced at its boundaries.If geometrical perturbations are introduced into the structure,the dark BICs transform into bright quasi-BICs with finite Q-factor,maintaining spectral characteristics nearly identical to those of quasi-BICs supported by infinite gratings.When the boundaries are replaced with high-reflectivity metallic mirrors,the Q-factor of the resonant mode is reduced to be finite;however,it can be much larger than that in the corresponding nanostructure with open boundaries and can be tuned over a large range by varying the number of unit cells or boundary conditions.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.62105004 and 52174141)the College Student Innovation and Entrepreneurship Fund Project(Grant No.202210361053)+4 种基金Anhui Mining Machinery and Electrical Equipment Coordination Innovation Center,Anhui University of Science&Technology(Grant No.KSJD202304)the Anhui Province Digital Agricultural Engineering Technology Research Center Open Project(Grant No.AHSZNYGC-ZXKF021)the Talent Recruitment Special Fund of Anhui University of Science and Technology(Grant No.2024yjrc175)the Graduate Innovation Fund Project of Anhui University of Science and Technology(Grant Nos.2024cx2067,2024cx2107,and 2024cx2064)Seed Support Project for Postgraduate Innovation,Entrepreneurship and Practice at Anhui University of Science and Technology(Grant No.2024cxcysj084).
文摘With the development of the Internet,image encryption technology has become critical for network security.Traditional methods often suffer from issues such as insufficient chaos,low randomness in key generation,and poor encryption efficiency.To enhance performance,this paper proposes a new encryption algorithm designed to optimize parallel processing and adapt to images of varying sizes and colors.The method begins by using SHA-384 to extract the hash value of the plaintext image,which is then processed to determine the chaotic system’s initial value and block size.The image is padded and divided into blocks for further processing.A novel two-dimensional infinite collapses hyperchaotic map(2DICHM)is employed to generate the intra-block scrambling sequence,while an improved variable Joseph traversal sequence is used for inter-block scrambling.After removing the padding,3D forward and backward shift diffusions,controlled by the 2D-ICHM sequences,are applied to the scrambled image,producing the ciphertext.Simulation results demonstrate that the proposed algorithm outperforms others in terms of entropy,anti-noise resilience,correlation coefficient,robustness,and encryption efficiency.
基金supported by the National R&D Program of China(2018YFB 1700104)the Science and Technology Development FundMacao Special Administrative Region(MSAR)(0029/2023/RIA1)。
文摘The opaque property plays an important role in the operation of a security-critical system,implying that pre-defined secret information of the system is not able to be inferred through partially observing its behavior.This paper addresses the verification of current-state,initial-state,infinite-step,and K-step opacity of networked discrete event systems modeled by labeled Petri nets,where communication losses and delays are considered.Based on the symbolic technique for the representation of states in Petri nets,an observer and an estimator are designed for the verification of current-state and initial-state opacity,respectively.Then,we propose a structure called an I-observer that is combined with secret states to verify whether a networked discrete event system is infinite-step opaque or K-step opaque.Due to the utilization of symbolic approaches for the state-based opacity verification,the computation of the reachability graphs of labeled Petri nets is avoided,which dramatically reduces the computational overheads stemming from networked discrete event systems.
基金supported by the National Natural Science Foundation of China (Grant No.41572334)the Innovation Fund Research Project (Grant Nos.SKLGDUEK202222 and SKLGDUEK202216).
基金National Natural Science Foundation of China(Grant Nos.12074428 and 92265208)the National Key R&D Program of China(Grant No.2022YFA1405300).
文摘The non-Hermitian skin effect and edge burst reflect the vital role of spatial boundaries in non-Hermitian systems from both static and dynamic perspectives.In this study,we investigate a non-Hermitian dissipative lattice with nonlocal coupling and demonstrate many interesting static and dynamic phenomena.In the case of global coupling with all sites coupled with each other,we observe anomalous hopping resonance,where a quantum walker initially placed at a single site almost completely escapes from the boundary of the system regardless of its initial position.In the case of non-global coupling,which is infinite-range coupling,the interplay between nonlocal hopping and the non-Hermitian skin effect results in the emergence of local bulk modes exhibiting a multipartite density distribution.The presence of local bulk modes induces the nontrivial dynamics of a quantum walker,which features multiple peaks of lost probability in spatially separated domains.Our findings demonstrate unique properties induced by nonlocal coupling in non-Hermitian systems.
文摘This paper presents a novel model-free method to solve linear quadratic(LQ)mean-field control problems with one-dimensional state space and multiplicative noise.The focus is on the infinite horizon LQ setting,where the conditions for solution either stabilization or optimization can be formulated as two algebraic Riccati equations(AREs).The proposed approach leverages the integral reinforcement learning technique to iteratively solve the drift-coefficient-dependent stochastic ARE(SARE)and other indefinite ARE,without requiring knowledge of the system dynamics.A numerical example is given to demonstrate the effectiveness of the proposed algorithm.
文摘Infinite matrix theory is an important branch of function analysis.Every linear operator on a complex separable infinite dimensional Hilbert space corresponds to an infinite matrix with respect a orthonormal base of the space,but not every infinite matrix corresponds to an operator.The classical Schur test provides an elegant and useful criterion for the boundedness of linear operators,which is considered a respectable mathematical accomplishment.In this paper,we prove the compact version of the Schur test.Moreover,we provide the Schur test for the Schatten class S_(2).It is worth noting that our main results can be applicable to the general matrix without limitation on non-negative numbers.We finally provide the Schur test for compact operators from l_(p) into l_(q).
基金supported by the by the Second Tibetan Plateau Scientific Expedition and Research Program (Grant No. 2019QZKK0902)Beijing Municipal Science and Technology Project (Z191100001419015)
文摘The critical rainfall of runoff-initiated debris flows is utmost importance for local early hazard forecasting.This paper presents research on the critical rainfall of runoff-initiated debris flows through comparisons between slope gradients and three key factors,including topographic contributing area,dimensionless discharge,and Shields stress.The rainfall amount was estimated by utilizing in-situ rainfall records and a slope-dependent Shields stress model was created.The created model can predict critical Shields stress more accurately than the other two models.Furthermore,a new dimensionless discharge equation was proposed based on the corresponding discharge-gradient datasets.The new equation,along with factors such as contributing area above bed failure sites,channel width,and mean diameter of debris flow deposits,predicts a smaller rainfall amount than the in-situ measured records.Although the slope-dependent Shields stress model performs well and the estimated rainfall amount is lower than the in-situ records,the sediment initiation in the experiments falls within sheet flow regime due to a large Shields stress.Therefore,further sediment initiation experiments at a steeper slope range are expected in the future to ensure that the sediment transport belongs to mass failure regime characterized by a low level of Shields stress.Finally,a more accurate hazard forecast on the runoff-initiated debris flow holds promise when the corresponding critical slope-dependent dimensionless discharge of no motion,fluvial sediment transport,mass flow regime,and sheet flow regime are considered.
基金supported by grants from INSF(98029498,99013953)partly supported by a grant from IPM(96430215)。
文摘In this article,we introduce and study the class of approximately Artinian(Noetherian)C^(*)-algebras,called AR-algebras(AN-algebras),which is a simultaneous generalization of Artinian(Noetherian)C*-algebras and AF-algebras.We study properties such as the ideal property and topological dimension zero for them.In particular,we show that a faithful AR or AN algebra is strongly purely infinite iff it is purely infinite iff it is weakly purely infinite.This extends the Kirchberg's O_(∞)-absorption theorem,and implies that a weakly purely infinite C^(*)-algebra is Noetherian iff every its ideal has a full projection.
基金Supported by the National Natural Science Foundation of China(Grant No.12361040)the Department of Education University Innovation Fund of Gansu Province(Grant No.2021A-006)。
文摘In this paper,by using the discrete Arzelá-Ascoli Lemma and the fixed-point theorem in cones,we discuss the existence of positive solutions of the following second order discrete Sturm-Liouville boundary value problem on infinite intervals■where Δu(x)=u(x+1)-u(x)is the forward difference operator,■is continuous,a>0,B and C are nonnegative constants.
文摘Ultrasonic transmitting, receiving and amplifying circuits are designed. Thereceived signals are sampled with the high speed ADC (analog-to-digital converter), and dealt withthe DSP (digital signal processing). A forward-backward IIR (infinitive impulse response) filterwith no delay is designed to filter the sampled data, and series A and B are achieved by narrow andwide band filtering, respectively. In series A, the start point of the cycle first exceeding thethreshold is calculated accuratelyby interpolation, and the start cycle is detected by fittingcycles in series A and its inversion A' to cycles in B with variance analysis. Therefore, the startpoint of the start cycle is calculated precisely. By deriving the relationships between the traveltime in the opposite directions of three axes and the airflow velocities, the wind velocity anddirection are calculated. Experiments show that the reliability and the precision are improved, andthe circuits are simplified.
文摘We give a proof of an explicit formula for affine coodinates of points in the Sato’s infinite Grassmannian corresponding to tau-functions for the KdV hierarchy.
