It is found that when the parity–time symmetry phenomenon is introduced into the resonant optical gyro system and it works near the exceptional point,the sensitivity can in theory be significantly amplified at low an...It is found that when the parity–time symmetry phenomenon is introduced into the resonant optical gyro system and it works near the exceptional point,the sensitivity can in theory be significantly amplified at low angular rate.However,in fact,the exceptional point is easily disturbed by external environmental variables,which means that it depends on harsh experimental environment and strong control ability,so it is difficult to move towards practical application.Here,we propose a new angular rate sensor structure based on exceptional surface,which has the advantages of high sensitivity and high robustness.The system consists of two fiber-optic ring resonators and two optical loop mirrors,and one of the resonators contains a variable ratio coupler and a variable optical attenuator.We theoretically analyze the system response,and the effects of phase and coupling ratio on the system response.Finally,compared with the conventional resonant gyro,the sensitivity of this exceptional surface angular rate sensor can be improved by about 300 times at low speed.In addition,by changing the loss coefficient in the ring resonator,we can achieve a wide range of 600 rad/s.This scheme provides a new approach for the development of ultra-high sensitivity and wide range angular rate sensors in the future.展开更多
We study the exceptional-point(EP) structure and the associated quantum dynamics in a system consisting of a non-Hermitian qubit and a Hermitian qubit. We find that the system possesses two sets of EPs, which divide t...We study the exceptional-point(EP) structure and the associated quantum dynamics in a system consisting of a non-Hermitian qubit and a Hermitian qubit. We find that the system possesses two sets of EPs, which divide the systemparameter space into PT-symmetry unbroken, partially broken and fully broken regimes, each with distinct quantumdynamics characteristics. Particularly, in the partially broken regime, while the PT-symmetry is generally broken in the whole four-dimensional Hilbert space, it is preserved in a two-dimensional subspace such that the quantum dynamics in the subspace are similar to those in the PT-symmetry unbroken regime. In addition, we reveal that the competition between the inter-qubit coupling and the intra-qubit driving gives rise to a complex pattern in the EP variation with system parameters.展开更多
We propose a quasi-one-dimensional non-Hermitian Creutz ladder with an entirely flat spectrum by introducing alternating gain and loss components while maintaining inversion symmetry.Destructive interference generates...We propose a quasi-one-dimensional non-Hermitian Creutz ladder with an entirely flat spectrum by introducing alternating gain and loss components while maintaining inversion symmetry.Destructive interference generates a flat spectrum at the exceptional point,where the Creutz ladder maintains coalesced and degenerate eigenvalues with compact localized states distributed in a single plaquette.All excitations are completely confined within the localization area,unaffected by gain and loss.Single-site excitations exhibit nonunitary dynamics with intensities increasing due to level coalescence,while multiple-site excitations may display oscillating or constant intensities at the exceptional point.These results provide insights into the fascinating dynamics of non-Hermitian localization,where level coalescence and degeneracy coexist at the exceptional point.展开更多
Protection of personal information is a significant issue in the construction of legal systems in various countries in the information age.Introducing a balanced approach for protecting personal information is an impo...Protection of personal information is a significant issue in the construction of legal systems in various countries in the information age.Introducing a balanced approach for protecting personal information is an important goal of basic human rights protection and data legislation.Personal information protection involves comprehensive considerations among various values,and the balanced structure between personal information rights and other rights systems has become the key to legislation on personal information protection.The“news exception”is a prominent example representing the balanced structure of personal information protection.As a societal instrument,news not only pursues commercial value but also advocates freedom of expression and public value.There exists a natural tension between news and personal information protection.The“news exception”of the balanced structure has become a fundamental requirement and important connotation for constructing a system for protecting personal information.The balanced structure of the“news exception”requires a reasonable definition of the concept and purpose of news,and both the self-discipline within the news industry and the judicial intervention are necessary factors.China has preliminarily completed the top-level legislative design of personal information protection through laws such as the Civil Code of the People’s Republic of China(PRC)and the Personal Information Protection Law of the People’s Republic of China.However,the balanced mechanism of the“news exception”has not yet been fully established in China.A“news exception”based on the ideas of balance and the improvement of the institutional system is the fundamental principle for the development of China’s personal information protection system.展开更多
Elastic wave absorption at subwavelength scale is of significance in many engineering applications.Non-Hermitian metamaterials show the ability in high-efficiency wave absorption.However,the single functionality of me...Elastic wave absorption at subwavelength scale is of significance in many engineering applications.Non-Hermitian metamaterials show the ability in high-efficiency wave absorption.However,the single functionality of metamaterials is an important limitation on their practical applications for lack of tunability and reconfigurability.Here,we propose a tunable and reconfigurable non-Hermitian piezoelectric metamaterial bar,in which piezoelectric bars connect with resonant circuits,to achieve asymmetric unidirectional perfect absorption(UPA)and symmetric bidirectional perfect absorption(PA)at low frequencies.The two functions can be arbitrarily switched by rearranging shunted circuits.Based on the reverberation-ray matrix(RRM)method,an approach is provided to achieve UPA by setting an exceptional point(EP)in the coupled resonant bandgap.By using the transfer matrix method(TMM)and the finite element method(FEM),it is observed that a non-Hermitian pseudo-band forms between two resonant bandgaps,and the EP appears at the bottom of the pseudo-band.In addition,the genetic algorithm is used to accurately and efficiently design the shunted circuits for desired low-frequency UPA and PA.The present work may provide new strategies for vibration suppression and guided waves manipulation in wide potential applications.展开更多
We study the nonlinear perturbation of a high-order exceptional point(EP)of the order equal to the system site number L in a Hatano-Nelson model with unidirectional hopping and Kerr nonlinearity.Notably,we find a clas...We study the nonlinear perturbation of a high-order exceptional point(EP)of the order equal to the system site number L in a Hatano-Nelson model with unidirectional hopping and Kerr nonlinearity.Notably,we find a class of discrete breathers that aggregate to one boundary,here named as skin discrete breathers(SDBs).The nonlinear spectrum of these SDBs shows a hierarchical power-law scaling near the EP.Specifically,the response of nonlinear energy to the perturbation is given by E_(m)∝Γ~(α_(m)),whereα_(m)=3^(m-1)is the power with m=1,...,L labeling the nonlinear energy bands.This is in sharp contrast to the L-th root of a linear perturbation in general.These SDBs decay in a double-exponential manner,unlike the edge states or skin modes in linear systems,which decay exponentially.Furthermore,these SDBs can survive over the full range of nonlinearity strength and are continuously connected to the self-trapped states in the limit of large nonlinearity.They are also stable,as confirmed by a defined nonlinear fidelity of an adiabatic evolution from the stability analysis.As nonreciprocal nonlinear models may be experimentally realized in various platforms,such as the classical platform of optical waveguides,where Kerr nonlinearity is naturally present,and the quantum platform of optical lattices with Bose-Einstein condensates,our analytical results may inspire further exploration of the interplay between nonlinearity and non-Hermiticity,particularly on high-order EPs,and benchmark the relevant simulations.展开更多
The demand for effective interventions to improve domain-specific academic outcomes for individuals with special needs at either end of the spectrum has existed for some time.Since the earlier contributions to the lit...The demand for effective interventions to improve domain-specific academic outcomes for individuals with special needs at either end of the spectrum has existed for some time.Since the earlier contributions to the literature documenting gifted individuals who were simultaneously exhibiting disabilities,there has been some progress in our understanding.We now know that in individuals with both gifts and disabilities,potentially,either or both of the exceptionalities can obscure the effects of the other,which significantly delays the average time to receive a diagnosis.Such delays in diagnosis detrimentally impact the the form of effective interventions without a diagnosis.The purpose of this paper is t quality of life across various domains because there can be no opportunity to receive help in o determine whether effective interventions exist to improve domain-specific(i.e.,social,emotional,or academic)outcomes for people with both gifts and disabilities.A query was performed using evidence databases TRIP and PDQ for“twice-exceptional,”“Giftedness,”“Disability,”and“intervention.”The four most relevant,freely available studies in English were selected for critique.Despite identifying potential threats to validity among the studies,methodological similarities among them were strong enough to confidently conclude that not only do effective interventions exist for the population of gifted with ADHD,but the outcomes of these interventions may also carry over into other domains resulting in indirect effects.展开更多
To solve the problems that the exception handling code is hard to test and maintain and that it affects the robustness and reliability of software, a method for evaluating the exception handling of programs is present...To solve the problems that the exception handling code is hard to test and maintain and that it affects the robustness and reliability of software, a method for evaluating the exception handling of programs is presented. The exception propagation graph （EPG） that describes the large programs with exception handling constructs is proposed by simplifying the control flow graph and it is applied to a case to verify its validity. According to the EPG, the exception handling code that never executes is identified; the points that are the most critical to controlling exception propagation are found; and the irrational exception handling code is corrected. The constructing algorithm for the EPG is given; thus, this provides a basis for automatically constructing the EPG and automatically correcting the irrational exception handling code.展开更多
美国微软开发的VB.NET2005可视化程序设计语言中,有一个DivideByZeroException类,它是当程序中有整数除法运算而除数为零时发生的异常,这种异常通过"Catch e As DivideByZeroException"语句来捕捉,捕捉到后根据相应的容错处...美国微软开发的VB.NET2005可视化程序设计语言中,有一个DivideByZeroException类,它是当程序中有整数除法运算而除数为零时发生的异常,这种异常通过"Catch e As DivideByZeroException"语句来捕捉,捕捉到后根据相应的容错处理语句继续执行。但在教学实践和实际编程中发现,在整数除法运算中发生除数为零的情况时,DivideByZeroException类异常并不能发生,这反映了微软开发的VB.NET2005程序设计语言中的一个漏洞。对这个问题进行了分析,并提出了弥补该漏洞的解决方案。展开更多
In this paper, by means of the definition of Borel exceptional value method, another exceptional value of meromorphic function which is a T exceptional value is defined by linking the concept of T direction. And we co...In this paper, by means of the definition of Borel exceptional value method, another exceptional value of meromorphic function which is a T exceptional value is defined by linking the concept of T direction. And we construct a meromorphic function with zero as Borel exceptional value, but not as T exceptional value; and another meromorphic function with zero as T exceptional value, but not as Borel exceptional value.展开更多
There are rules refering to infrequent instances after the procession of attribute reductionand value reduction with traditional methods.A rough set RS based k-exception approach (RSKEA) torule reduction is presented....There are rules refering to infrequent instances after the procession of attribute reductionand value reduction with traditional methods.A rough set RS based k-exception approach (RSKEA) torule reduction is presented.Its main idea lies in a two-phase RS based rule reduction.An ordinarydecision table is attained through general method of RS knowledge reduction in the first phase.Then a k-exception candidate set is nominated according to the decision table.RS rule reduction is employed forthe reformed source data set,which remove all the instances included in the k-exception set.We apply theapproach to the automobile database.Results show that it can reduce the number and complexity of ruleswith adjustable conflict rate,which contributes to approximate rule reduction.展开更多
The notion of “exceptional family of elements (EFE)” plays a very important role in solving complementarity prob- lems. It has been applied in finite dimensional spaces and Hilbert spaces by many authors. In this pa...The notion of “exceptional family of elements (EFE)” plays a very important role in solving complementarity prob- lems. It has been applied in finite dimensional spaces and Hilbert spaces by many authors. In this paper, by using the generalized projection defined by Alber, we extend this notion from Hilbert spaces to uniformly smooth and uniformly convex Banach spaces, and apply this extension to the study of nonlinear complementarity problems in Banach spaces.展开更多
The present note is concerned with two connected and highly important fundamental questions of physics and cosmology, namely if E8E8 Lie symmetry group describes the universe and where cosmic dark energy comes from. F...The present note is concerned with two connected and highly important fundamental questions of physics and cosmology, namely if E8E8 Lie symmetry group describes the universe and where cosmic dark energy comes from. Furthermore, we reason following Wheeler, Hartle and Hawking that since the boundary of a boundary is an empty set which models the quantum wave of the cosmos, then it follows that dark energy is a fundamental physical phenomenon associated with the boundary of the holographic boundary. This leads directly to a clopen universe which is its own Penrose tiling-like multiverse with energy density in full agreement with COBE, WMAP and Type 1a supernova cosmic measurements.展开更多
Open physical systems described by the non-Hermitian Hamiltonian with parity-time-reversal(PT)symmetry show peculiar phenomena,such as the presence of an exceptional point(EP)at which the PT symmetry is broken and two...Open physical systems described by the non-Hermitian Hamiltonian with parity-time-reversal(PT)symmetry show peculiar phenomena,such as the presence of an exceptional point(EP)at which the PT symmetry is broken and two resonant modes of the Hamiltonian become degenerate.Near the EP,the system could be more sensitive to external perturbations and this may lead to enhanced sensing.In this paper,we present experimental results on the observation of PT symmetry broken transition and the EP using a tunable superconducting qubit.The quantum system of investigation is formed by the two levels of the qubit and the energy loss of the system to the environment is controlled by a method of parametric modulation of the qubit frequency.This method is simple with no requirements for additional elements or qubit device modifications.We believe it can be easily implemented on multi-qubit devices that would be suitable for further exploration of non-Hermitian physics in more complex and diverse systems.展开更多
Featured by its uniqueness and historic significance, American exceptionalism plays an indispensable role in shaping the American political,especially the foreign policies, as well as social lives. To understand the o...Featured by its uniqueness and historic significance, American exceptionalism plays an indispensable role in shaping the American political,especially the foreign policies, as well as social lives. To understand the origins of American exceptionalism, people must look into its national values-Puritanism, individualism and political system.展开更多
Objective The putative coronatean Punctatus flourished at the beginning of the Cambrian explosion, and is significant in the exploration of the origin and evolution of early life. Liu Yunhuan established a new specie...Objective The putative coronatean Punctatus flourished at the beginning of the Cambrian explosion, and is significant in the exploration of the origin and evolution of early life. Liu Yunhuan established a new species： Punctatus triangulicostalis Liu, 2006. Two questions remain： how was the special body plan of P. triangulicostalis formed？ How does P. triangulicostalis transform from embryo to the long cylindrical mature individual？ Although the study of Steiner et al. in 2004 involved the above questions, they did not explain them clearly due to the lack of fossil materials at that time. This article aims to consider the above questions based on new information from several rare specimens.展开更多
We examine the energy function with respect to the zeros of exceptional Hermite polynomials. The localization of the eigenvalues of the Hessian is given in the general case.In some special arrangements we have a more ...We examine the energy function with respect to the zeros of exceptional Hermite polynomials. The localization of the eigenvalues of the Hessian is given in the general case.In some special arrangements we have a more precise result on the behavior of the energy function. Finally we investigate the energy function with respect to the regular zeros of the exceptional Hermite polynomials.展开更多
The open quantum system can be described by either a Lindblad master equation or a non-Hermitian Hamiltonian(NHH).However,these two descriptions usually have different exceptional points(EPs),associated with the degen...The open quantum system can be described by either a Lindblad master equation or a non-Hermitian Hamiltonian(NHH).However,these two descriptions usually have different exceptional points(EPs),associated with the degeneracies in the open quantum system.Here,considering a dissipative quantum Rabi model,we study the spectral features of EPs in these two descriptions and explore their connections.We find that,although the EPs in these two descriptions are usually different,the EPs of NHH will be consistent with the EPs of master equation in the weak coupling regime.Further,we find that the quantum Fisher information(QFI),which measures the statistical distance between quantum states,can be used as a signature for the appearance of EPs.Our study may give a theoretical guidance for exploring the properties of EPs in open quantum systems.展开更多
The exceptional point（EP） is a significant and attractive phenomenon in an open quantum system. The scattering properties of light are similar to those in the open quantum system, which makes it possible to achieve ...The exceptional point（EP） is a significant and attractive phenomenon in an open quantum system. The scattering properties of light are similar to those in the open quantum system, which makes it possible to achieve EP in the optic system. Here we investigate the EP in a Fabry–P′erot（F–P） resonant coupling structure. The coupling between different types of F–P resonances leads to a near zero reflection, which results in a degeneration of eigenstates and thus the appearing of EP. Furthermore, the multi-wavelength EPs and unidirectional invisibility can be achieved which may be used in integrated photonics systems.展开更多
基金supported in part by the National Natural Science Foundation of China (Grant Nos.62273314,U21A20141,and 51821003)Fundamental Research Program of Shanxi Province (Grant No.202303021224008)Shanxi Province Key Laboratory of Quantum Sensing and Precision Measure-ment (Grant No.201905D121001).
文摘It is found that when the parity–time symmetry phenomenon is introduced into the resonant optical gyro system and it works near the exceptional point,the sensitivity can in theory be significantly amplified at low angular rate.However,in fact,the exceptional point is easily disturbed by external environmental variables,which means that it depends on harsh experimental environment and strong control ability,so it is difficult to move towards practical application.Here,we propose a new angular rate sensor structure based on exceptional surface,which has the advantages of high sensitivity and high robustness.The system consists of two fiber-optic ring resonators and two optical loop mirrors,and one of the resonators contains a variable ratio coupler and a variable optical attenuator.We theoretically analyze the system response,and the effects of phase and coupling ratio on the system response.Finally,compared with the conventional resonant gyro,the sensitivity of this exceptional surface angular rate sensor can be improved by about 300 times at low speed.In addition,by changing the loss coefficient in the ring resonator,we can achieve a wide range of 600 rad/s.This scheme provides a new approach for the development of ultra-high sensitivity and wide range angular rate sensors in the future.
基金partly funded by the Natural Science Foundation of Shandong Province of China (Grant Nos. ZR2021MA091 and ZR2018MA044)Introduction and Cultivation Plan of Youth Innovation Talents for Universities of Shandong Province (Research and Innovation Team on Materials Modification and Optoelectronic Devices at extreme conditions)。
文摘We study the exceptional-point(EP) structure and the associated quantum dynamics in a system consisting of a non-Hermitian qubit and a Hermitian qubit. We find that the system possesses two sets of EPs, which divide the systemparameter space into PT-symmetry unbroken, partially broken and fully broken regimes, each with distinct quantumdynamics characteristics. Particularly, in the partially broken regime, while the PT-symmetry is generally broken in the whole four-dimensional Hilbert space, it is preserved in a two-dimensional subspace such that the quantum dynamics in the subspace are similar to those in the PT-symmetry unbroken regime. In addition, we reveal that the competition between the inter-qubit coupling and the intra-qubit driving gives rise to a complex pattern in the EP variation with system parameters.
基金supported by the National Natural Science Foundation of China(Grant Nos.12222504 and 11975128).
文摘We propose a quasi-one-dimensional non-Hermitian Creutz ladder with an entirely flat spectrum by introducing alternating gain and loss components while maintaining inversion symmetry.Destructive interference generates a flat spectrum at the exceptional point,where the Creutz ladder maintains coalesced and degenerate eigenvalues with compact localized states distributed in a single plaquette.All excitations are completely confined within the localization area,unaffected by gain and loss.Single-site excitations exhibit nonunitary dynamics with intensities increasing due to level coalescence,while multiple-site excitations may display oscillating or constant intensities at the exceptional point.These results provide insights into the fascinating dynamics of non-Hermitian localization,where level coalescence and degeneracy coexist at the exceptional point.
文摘Protection of personal information is a significant issue in the construction of legal systems in various countries in the information age.Introducing a balanced approach for protecting personal information is an important goal of basic human rights protection and data legislation.Personal information protection involves comprehensive considerations among various values,and the balanced structure between personal information rights and other rights systems has become the key to legislation on personal information protection.The“news exception”is a prominent example representing the balanced structure of personal information protection.As a societal instrument,news not only pursues commercial value but also advocates freedom of expression and public value.There exists a natural tension between news and personal information protection.The“news exception”of the balanced structure has become a fundamental requirement and important connotation for constructing a system for protecting personal information.The balanced structure of the“news exception”requires a reasonable definition of the concept and purpose of news,and both the self-discipline within the news industry and the judicial intervention are necessary factors.China has preliminarily completed the top-level legislative design of personal information protection through laws such as the Civil Code of the People’s Republic of China(PRC)and the Personal Information Protection Law of the People’s Republic of China.However,the balanced mechanism of the“news exception”has not yet been fully established in China.A“news exception”based on the ideas of balance and the improvement of the institutional system is the fundamental principle for the development of China’s personal information protection system.
基金the National Natural Science Foundation of China(Nos.11991033 and 11890681)。
文摘Elastic wave absorption at subwavelength scale is of significance in many engineering applications.Non-Hermitian metamaterials show the ability in high-efficiency wave absorption.However,the single functionality of metamaterials is an important limitation on their practical applications for lack of tunability and reconfigurability.Here,we propose a tunable and reconfigurable non-Hermitian piezoelectric metamaterial bar,in which piezoelectric bars connect with resonant circuits,to achieve asymmetric unidirectional perfect absorption(UPA)and symmetric bidirectional perfect absorption(PA)at low frequencies.The two functions can be arbitrarily switched by rearranging shunted circuits.Based on the reverberation-ray matrix(RRM)method,an approach is provided to achieve UPA by setting an exceptional point(EP)in the coupled resonant bandgap.By using the transfer matrix method(TMM)and the finite element method(FEM),it is observed that a non-Hermitian pseudo-band forms between two resonant bandgaps,and the EP appears at the bottom of the pseudo-band.In addition,the genetic algorithm is used to accurately and efficiently design the shunted circuits for desired low-frequency UPA and PA.The present work may provide new strategies for vibration suppression and guided waves manipulation in wide potential applications.
基金Project supported by the National Key Research and Development Program of China(Grant No.2022YFA1405304)the Key-Area Research and Development Program of Guangdong Province,China(Grant No.2019B030330001)the Guangdong Provincial Key Laboratory(Grant No.2020B1212060066)。
文摘We study the nonlinear perturbation of a high-order exceptional point(EP)of the order equal to the system site number L in a Hatano-Nelson model with unidirectional hopping and Kerr nonlinearity.Notably,we find a class of discrete breathers that aggregate to one boundary,here named as skin discrete breathers(SDBs).The nonlinear spectrum of these SDBs shows a hierarchical power-law scaling near the EP.Specifically,the response of nonlinear energy to the perturbation is given by E_(m)∝Γ~(α_(m)),whereα_(m)=3^(m-1)is the power with m=1,...,L labeling the nonlinear energy bands.This is in sharp contrast to the L-th root of a linear perturbation in general.These SDBs decay in a double-exponential manner,unlike the edge states or skin modes in linear systems,which decay exponentially.Furthermore,these SDBs can survive over the full range of nonlinearity strength and are continuously connected to the self-trapped states in the limit of large nonlinearity.They are also stable,as confirmed by a defined nonlinear fidelity of an adiabatic evolution from the stability analysis.As nonreciprocal nonlinear models may be experimentally realized in various platforms,such as the classical platform of optical waveguides,where Kerr nonlinearity is naturally present,and the quantum platform of optical lattices with Bose-Einstein condensates,our analytical results may inspire further exploration of the interplay between nonlinearity and non-Hermiticity,particularly on high-order EPs,and benchmark the relevant simulations.
文摘The demand for effective interventions to improve domain-specific academic outcomes for individuals with special needs at either end of the spectrum has existed for some time.Since the earlier contributions to the literature documenting gifted individuals who were simultaneously exhibiting disabilities,there has been some progress in our understanding.We now know that in individuals with both gifts and disabilities,potentially,either or both of the exceptionalities can obscure the effects of the other,which significantly delays the average time to receive a diagnosis.Such delays in diagnosis detrimentally impact the the form of effective interventions without a diagnosis.The purpose of this paper is t quality of life across various domains because there can be no opportunity to receive help in o determine whether effective interventions exist to improve domain-specific(i.e.,social,emotional,or academic)outcomes for people with both gifts and disabilities.A query was performed using evidence databases TRIP and PDQ for“twice-exceptional,”“Giftedness,”“Disability,”and“intervention.”The four most relevant,freely available studies in English were selected for critique.Despite identifying potential threats to validity among the studies,methodological similarities among them were strong enough to confidently conclude that not only do effective interventions exist for the population of gifted with ADHD,but the outcomes of these interventions may also carry over into other domains resulting in indirect effects.
基金The National Natural Science Foundation of China(No60503020)the National Basic Research Program of China (973Program) (No2002CB312000)+1 种基金the Natural Science Foundation of Jiangsu Province (NoBK2006094)the Science Research Foundation of China University of Mining and Technology
文摘To solve the problems that the exception handling code is hard to test and maintain and that it affects the robustness and reliability of software, a method for evaluating the exception handling of programs is presented. The exception propagation graph （EPG） that describes the large programs with exception handling constructs is proposed by simplifying the control flow graph and it is applied to a case to verify its validity. According to the EPG, the exception handling code that never executes is identified; the points that are the most critical to controlling exception propagation are found; and the irrational exception handling code is corrected. The constructing algorithm for the EPG is given; thus, this provides a basis for automatically constructing the EPG and automatically correcting the irrational exception handling code.
文摘美国微软开发的VB.NET2005可视化程序设计语言中,有一个DivideByZeroException类,它是当程序中有整数除法运算而除数为零时发生的异常,这种异常通过"Catch e As DivideByZeroException"语句来捕捉,捕捉到后根据相应的容错处理语句继续执行。但在教学实践和实际编程中发现,在整数除法运算中发生除数为零的情况时,DivideByZeroException类异常并不能发生,这反映了微软开发的VB.NET2005程序设计语言中的一个漏洞。对这个问题进行了分析,并提出了弥补该漏洞的解决方案。
基金supported by the Natural Science Foundation of China(10161006)
文摘In this paper, by means of the definition of Borel exceptional value method, another exceptional value of meromorphic function which is a T exceptional value is defined by linking the concept of T direction. And we construct a meromorphic function with zero as Borel exceptional value, but not as T exceptional value; and another meromorphic function with zero as T exceptional value, but not as Borel exceptional value.
文摘There are rules refering to infrequent instances after the procession of attribute reductionand value reduction with traditional methods.A rough set RS based k-exception approach (RSKEA) torule reduction is presented.Its main idea lies in a two-phase RS based rule reduction.An ordinarydecision table is attained through general method of RS knowledge reduction in the first phase.Then a k-exception candidate set is nominated according to the decision table.RS rule reduction is employed forthe reformed source data set,which remove all the instances included in the k-exception set.We apply theapproach to the automobile database.Results show that it can reduce the number and complexity of ruleswith adjustable conflict rate,which contributes to approximate rule reduction.
文摘The notion of “exceptional family of elements (EFE)” plays a very important role in solving complementarity prob- lems. It has been applied in finite dimensional spaces and Hilbert spaces by many authors. In this paper, by using the generalized projection defined by Alber, we extend this notion from Hilbert spaces to uniformly smooth and uniformly convex Banach spaces, and apply this extension to the study of nonlinear complementarity problems in Banach spaces.
文摘The present note is concerned with two connected and highly important fundamental questions of physics and cosmology, namely if E8E8 Lie symmetry group describes the universe and where cosmic dark energy comes from. Furthermore, we reason following Wheeler, Hartle and Hawking that since the boundary of a boundary is an empty set which models the quantum wave of the cosmos, then it follows that dark energy is a fundamental physical phenomenon associated with the boundary of the holographic boundary. This leads directly to a clopen universe which is its own Penrose tiling-like multiverse with energy density in full agreement with COBE, WMAP and Type 1a supernova cosmic measurements.
基金supported by the State Key Development Program for Basic Research of China(Grant Nos.2017YFA0304300 and 2016YFA0300600)the Key-Area Research and Development Program of Guangdong Province,China(Grant No.2020B0303030001)the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDB28000000).
文摘Open physical systems described by the non-Hermitian Hamiltonian with parity-time-reversal(PT)symmetry show peculiar phenomena,such as the presence of an exceptional point(EP)at which the PT symmetry is broken and two resonant modes of the Hamiltonian become degenerate.Near the EP,the system could be more sensitive to external perturbations and this may lead to enhanced sensing.In this paper,we present experimental results on the observation of PT symmetry broken transition and the EP using a tunable superconducting qubit.The quantum system of investigation is formed by the two levels of the qubit and the energy loss of the system to the environment is controlled by a method of parametric modulation of the qubit frequency.This method is simple with no requirements for additional elements or qubit device modifications.We believe it can be easily implemented on multi-qubit devices that would be suitable for further exploration of non-Hermitian physics in more complex and diverse systems.
文摘Featured by its uniqueness and historic significance, American exceptionalism plays an indispensable role in shaping the American political,especially the foreign policies, as well as social lives. To understand the origins of American exceptionalism, people must look into its national values-Puritanism, individualism and political system.
基金supported by the National Natural Science Foundation of China (grant No.41572009)the State Key Laboratory of Palaeobiology and Stratigraphy (grant No.173121)the College Students’ Training Program of Chang’an University (201610710047, 201710710062, 201710710063, 201710710240)
文摘Objective The putative coronatean Punctatus flourished at the beginning of the Cambrian explosion, and is significant in the exploration of the origin and evolution of early life. Liu Yunhuan established a new species： Punctatus triangulicostalis Liu, 2006. Two questions remain： how was the special body plan of P. triangulicostalis formed？ How does P. triangulicostalis transform from embryo to the long cylindrical mature individual？ Although the study of Steiner et al. in 2004 involved the above questions, they did not explain them clearly due to the lack of fossil materials at that time. This article aims to consider the above questions based on new information from several rare specimens.
基金Supported by Hungarian National Foundation for Scientific Research,Grant No.K-100461
文摘We examine the energy function with respect to the zeros of exceptional Hermite polynomials. The localization of the eigenvalues of the Hessian is given in the general case.In some special arrangements we have a more precise result on the behavior of the energy function. Finally we investigate the energy function with respect to the regular zeros of the exceptional Hermite polynomials.
基金Project supported by the Key-Area Research and Development Program of GuangDong Province,China (Grant No. 2019B030330001)the National Natural Science Foundation of China (Grant Nos. 12025509, 11874434, and 11704420)+1 种基金the Science and Technology Program of Guangzhou (China)(Grant No. 201904020024)partially supported by the Guangzhou Science and Technology Projects (Grant No. 202002030459)
文摘The open quantum system can be described by either a Lindblad master equation or a non-Hermitian Hamiltonian(NHH).However,these two descriptions usually have different exceptional points(EPs),associated with the degeneracies in the open quantum system.Here,considering a dissipative quantum Rabi model,we study the spectral features of EPs in these two descriptions and explore their connections.We find that,although the EPs in these two descriptions are usually different,the EPs of NHH will be consistent with the EPs of master equation in the weak coupling regime.Further,we find that the quantum Fisher information(QFI),which measures the statistical distance between quantum states,can be used as a signature for the appearance of EPs.Our study may give a theoretical guidance for exploring the properties of EPs in open quantum systems.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.61377054 and 61675140)
文摘The exceptional point（EP） is a significant and attractive phenomenon in an open quantum system. The scattering properties of light are similar to those in the open quantum system, which makes it possible to achieve EP in the optic system. Here we investigate the EP in a Fabry–P′erot（F–P） resonant coupling structure. The coupling between different types of F–P resonances leads to a near zero reflection, which results in a degeneration of eigenstates and thus the appearing of EP. Furthermore, the multi-wavelength EPs and unidirectional invisibility can be achieved which may be used in integrated photonics systems.
