The π-tangle is used to study the behavior of entanglement of a nonmaximal tripartite state of both Dirac and scMar fields in accelerated frame. For Dirac fields, the degree of degradation with acceleration of both o...The π-tangle is used to study the behavior of entanglement of a nonmaximal tripartite state of both Dirac and scMar fields in accelerated frame. For Dirac fields, the degree of degradation with acceleration of both one-tangle of accelerated observer and π-tangle, for the same initial entanglement, is different by just interchanging the values of probability amplitudes. A fraction of both one-tangles and the π-tangle always survives for any choice of acceleration and the degree of initial entanglement. For scalar field, the one-tangle of accelerated observer depends on the choice of values of probability amplitudes and it vanishes in the range of infinite acceleration, whereas for 1r-tangle this is not always true. The dependence of π-tangle on probability amplitudes varies with acceleration. In the lower range of acceleration, its behavior changes by switching between the values of probability amplitudes and for larger values of acceleration this dependence on probability amplitudes vanishes. Interestingly, unlike bipartite entanglement, the degradation of π-tangle against acceleration in the case of sca/ar fields is slower than for Dirac fields.展开更多
In educational settings,instructors often lead students through hands-on software projects,sometimes engaging two different schools or departments.How can such collaborations be made more efficient,and how can student...In educational settings,instructors often lead students through hands-on software projects,sometimes engaging two different schools or departments.How can such collaborations be made more efficient,and how can students truly experience the importance of teamwork and the impact of organizational structure on project complexity?To answer these questions,we introduce the requirement-driven organization structure(R-DOS)approach,which tightly couples software requirements with the actual development process.By extending problem-frames modeling and focusing on requirements,R-DOS allows educators and students to(1)diagnose structural flaws early,(2)prescribe role-level and communication fixes,and(3)observe-in real time-how poor structure can derail a project while good structure accelerates learning and delivery.展开更多
Methods of quantum information processing often appear in terms of specially selected states.For example,mutually unbiased bases(MUBs)and symmetric informationally complete measurements are widely applied.Finite frame...Methods of quantum information processing often appear in terms of specially selected states.For example,mutually unbiased bases(MUBs)and symmetric informationally complete measurements are widely applied.Finite frames have found use in many areas including quantum information.Due to its specific inner structure,a single equiangular tight frame(ETF)allows one to formulate criteria to detect non-classical correlations.This study aims to approach entanglement detection with the use of mutually unbiased ETFs.Such frames are an interesting generalization of widely recognized MUBs.It still uses rank-one operators,but the number of outcomes can exceed the dimensionality.Several approaches are considered including separability criteria and entanglement witnesses.Separability criteria for multipartite systems are finally obtained.展开更多
Rapid quantification of seismic-induced damage immediately following an earthquake is critical for determining whether a structure is safe for continued occupation or requires evacuation.This study proposes a novel da...Rapid quantification of seismic-induced damage immediately following an earthquake is critical for determining whether a structure is safe for continued occupation or requires evacuation.This study proposes a novel damage identification method that utilizes limited strain data points,significantly reducing installation,maintenance,and data analysis costs compared to traditional distributed sensor networks.The approach integrates finite element(FE)modeling to generate capacity curves through pushover analysis,incorporates noise-augmented datasets for Artificial Neural Network(ANN)training,and classifies structural conditions into four damage levels:Operational(OP),Immediate Occupancy(IO),Life Safety(LS),and Collapse Prevention(CP).To evaluate the method’s accuracy and efficiency,it was applied to two reinforced concrete(RC)frames;a single-story frame tested experimentally under cyclic loading and a three-story frame analyzed under various lateral load patterns.Strain data from selected beam and column ends were used as ANN inputs,while the corresponding damage classes served as outputs.Confusion matrix results demonstrated high true positive rates(>85%for the single-story and>90%for the three-story frame),even with a reduced number of sensors.The model also exhibited strong robustness to White Gaussian Noise(SNR=2.5-5 dB)and generalized effectively to nonlinear time-history analyses under scaled ground motions(PGA=0.1-1.0 g).Feature selection using the MRMR and ANOVA algorithms further enhanced computational efficiency.Overall,the proposed ANN-based framework has strong potential for real-time structural health monitoring applications.展开更多
Modelling the turbulent flows in non-inertial frames of reference has long been a challenging task. Recently we introduced the notion of the "extended intrinsic mean spin tensor" for turbulence modelling and...Modelling the turbulent flows in non-inertial frames of reference has long been a challenging task. Recently we introduced the notion of the "extended intrinsic mean spin tensor" for turbulence modelling and pointed out that, when applying the Reynolds stress models developed in the inertial frame of reference to model-ling the turbulence in a non-inertial frame of reference, the mean spin tensor should be replaced by the extended intrinsic mean spin tensor to correctly account for the rotation effects induced by the non-inertial frame of reference, to conform in phys-ics with the Reynolds stress transport equation. To exemplify the approach, we conducted numerical simulations of the fully developed turbulent channel flow in a rotating frame of reference by employing four non-linear K-ε models. Our numerical results based on this approach at a wide range of Reynolds and Rossby numbers evince that, among the models tested, the non-linear K-ε model of Huang and Ma and the non-linear K-ε model of Craft, Launder and Suga can better capture the rotation effects and the resulting influence on the structures of turbulence, and therefore are satisfactorily applied to dealing with the turbulent flows of practical interest in engineering. The general approach worked out in this paper is also ap-plied to the second-moment closure and the large-eddy simulation of turbulence.展开更多
We investigate the role of extended intrinsic mean spin tensor introduced in this work for turbulence modelling in a non-inertial frame of reference. It is described by the Euclidean group of transformations and, in p...We investigate the role of extended intrinsic mean spin tensor introduced in this work for turbulence modelling in a non-inertial frame of reference. It is described by the Euclidean group of transformations and, in particular, its significance and importance in the approach of the algebraic Reynolds stress modelling, such as in a nonlinear K-ε model. To this end and for illustration of the effect of extended intrinsic spin tensor on turbulence modelling, we examine several recently developed nonlinear K-ε models and compare their performance in predicting the homogeneous turbulent shear flow in a rotating frame of reference with LES data. Our results and analysis indicate that, only if the deficiencies of these models and the like be well understood and properly corrected, may in the near future, more sophisticated nonlinear K-ε models be developed to better predict complex turbulent flows in a non-inertial frame of reference.展开更多
The new variational principle of Gauss's form of nonlinear nonholonomic nonpotential system relative to non-inertial reference frame is established by constructing generalized inertial potentials. Naether's th...The new variational principle of Gauss's form of nonlinear nonholonomic nonpotential system relative to non-inertial reference frame is established by constructing generalized inertial potentials. Naether's theorem and Naether's inverse theorem of the system above is presented and proved. Finally, one example is given to illustrate the application.展开更多
Stepping out of Danyang Railway Station,the large sign reading“China Danyang Optical City”immediately comes into view across the road.Inside the bustling marketplace,a dazzling array of eyeglass frames and lenses is...Stepping out of Danyang Railway Station,the large sign reading“China Danyang Optical City”immediately comes into view across the road.Inside the bustling marketplace,a dazzling array of eyeglass frames and lenses is neatly displayed in rows of shops,attracting consumers from across the country.展开更多
We connect magic(non-stabilizer)states,symmetric informationally complete positive operator valued measures(SIC-POVMs),and mutually unbiased bases(MUBs)in the context of group frames,and study their interplay.Magic st...We connect magic(non-stabilizer)states,symmetric informationally complete positive operator valued measures(SIC-POVMs),and mutually unbiased bases(MUBs)in the context of group frames,and study their interplay.Magic states are quantum resources in the stabilizer formalism of quantum computation.SIC-POVMs and MUBs are fundamental structures in quantum information theory with many applications in quantum foundations,quantum state tomography,and quantum cryptography,etc.In this work,we study group frames constructed from some prominent magic states,and further investigate their applications.Our method exploits the orbit of discrete Heisenberg-Weyl group acting on an initial fiducial state.We quantify the distance of the group frames from SIC-POVMs and MUBs,respectively.As a simple corollary,we reproduce a complete family of MUBs of any prime dimensional system by introducing the concept of MUB fiducial states,analogous to the well-known SIC-POVM fiducial states.We present an intuitive and direct construction of MUB fiducial states via quantum T-gates,and demonstrate that for the qubit system,there are twelve MUB fiducial states,which coincide with the H-type magic states.We compare MUB fiducial states and SIC-POVM fiducial states from the perspective of magic resource for stabilizer quantum computation.We further pose the challenging issue of identifying all MUB fiducial states in general dimensions.展开更多
Ensuring the secure transmission of secret messages,particularly through video—one of the most widely used media formats—is a critical challenge in the field of information security.Relying on a single-layered secur...Ensuring the secure transmission of secret messages,particularly through video—one of the most widely used media formats—is a critical challenge in the field of information security.Relying on a single-layered security approach is often insufficient for safeguarding sensitive data.This study proposes a triple-lightweight cryptographic and steganographic model that integrates the Hill Cipher Technique(HCT),Rotation Left Digits(RLD),and Discrete Wavelet Transform(DWT)to embed secret messages within video frames securely.The approach begins with encrypting the secret text using a private key matrix(PK^(1))of size 2×2 up to 6×6 via HCT.A second encryption layer is applied using a dynamic private key(PK2)derived from the RGB pixel values of the video frame,resulting in a rotated cipher.The doubly encrypted message is then embedded into the video frames using the DWT method.Upon transmission,the concealed message is extracted using inverse DWT and decrypted in two steps—first with PK2 and then with the inverse of PK^(1).Experiments conducted using MPEG video sequences and message lengths ranging from 10 to 300 bytes demonstrate strong performance in terms of Mean Square Error(MSE),Peak Signal-to-Noise Ratio(PSNR),and Correlation Coefficient(CC)between original and encrypted messages.The similarity between original and stego frames is further validated using Structural Similarity Index(SSIM),Mean Absolute Error(MAE),Number of Pixel Change Rate(NPCR),and Unified Average Changing Intensity(UACI).Results confirm that utilizing video frames to generate PK2 offers superior security compared to static key images.Moreover,the indistinguishability between original and stego frames highlights the method’s robustness against visual and statistical attacks.展开更多
Improvement of the detection ability of quantum entanglement is one of the essential tasks in quantum computing and quantum information.Finite tight frames play a fundamental role in a wide variety of areas and,genera...Improvement of the detection ability of quantum entanglement is one of the essential tasks in quantum computing and quantum information.Finite tight frames play a fundamental role in a wide variety of areas and,generally,each application requires a specific class of frames and is closely related to quantum measurement.It is worth noting that a maximal set of complex equiangular vectors is closely related to a symmetric informationally complete measurement.Hence,our goal in this work is to propose a series of separability criteria assigned to a finite tight frame and some well-known inequalities in different quantum systems,respectively.In addition,some tighter criteria to detect entanglement for many-body quantum states are presented in arbitrary dimensions.Finally,the effectiveness of the proposed entanglement detection criteria is illustrated through some detailed examples.展开更多
A relationship was discovered between the amplification factor and the number of load increments that are needed to limit the relative error to one percent in second-order elastic analyses with a predictor-corrector s...A relationship was discovered between the amplification factor and the number of load increments that are needed to limit the relative error to one percent in second-order elastic analyses with a predictor-corrector solution scheme.Previous research by the authors proposed a design equation to determine the required minimum number of load increments based on an evaluation of the elastic critical buckling load ratio.Further research has shown that an approximate amplification factor equation that is based on the B2 multiplier equation produces similar results when the amplification factor is less than approximately four.Eleven moment frames are used to verify the use of the new approximate amplification factor in the proposed design equation.展开更多
A three-dimensional beam element is derived based on the principle of stationary total potential energy for geometrically nonlinear analysis of space frames. A new tangent stiffness matrix, which allows for high order...A three-dimensional beam element is derived based on the principle of stationary total potential energy for geometrically nonlinear analysis of space frames. A new tangent stiffness matrix, which allows for high order effects of element deformations, replaces the conventional incremental secant stiffness matrix. Two deformation stiffness matrices due to the variation of axial force and bending moments are included in the tangent stiffness. They are functions of element deformations and incorporate the coupling among axial, lateral and torsional deformations. A correction matrix is added to the tangent stiffness matrix to make displacement derivatives equivalent to the commutative rotational degrees of freedom. Numerical examples show that the proposed dement is accurate and efficient in predicting the nonlinear behavior, such as axial-torsional and flexural-torsional buckling, of space frames even when fewer elements are used to model a member.展开更多
Suppose that Φ(x)∈L 2(R) with compact support and V= span{Φ(x-k)|k∈Z}. In this note, we prove that if {Φ(x-k)k|k∈Z} is tight frame with bound 1 in V, then {Φ(x-k)|k∈Z} must be an orthonormal basis of V.
In the paper, we study the stability of Hilbert space generalized frames under perturbations. We get some results that are in spirit close to classical results for discrete frames, due to OLE Christensen.
In this paper we shall offer a separation axiom for frames inspired by the Hausdorff separation axiom for topological spaces. We call it separated condition. This is a condition on topology OX equivalent to the ...In this paper we shall offer a separation axiom for frames inspired by the Hausdorff separation axiom for topological spaces. We call it separated condition. This is a condition on topology OX equivalent to the T O space X being Hausdorff. The class of separated frames includes that of strong Hausdorff frames and that of S frames. We shall show that the class of separated frames is a class closed under the formation of coproducts and subspaces, and the space Fil( L ) is Hausdorff for any separated frame L . Therefore there is a contravariant adjunction between the category TOP 2 of Hausdorff topological spaces and the category FRAM 2 of separated frames.展开更多
In this article, we introduce and characterize approximate duality for g-frames. We get some important properties and applications of approximate duals. We also obtain some new results in approximate duality of frames...In this article, we introduce and characterize approximate duality for g-frames. We get some important properties and applications of approximate duals. We also obtain some new results in approximate duality of frames, and generalize some of the known results in approximate duality of frames to g-frames. We also get some results for fusion frames, and perturbation of approximately dual g-frames. We show that approximate duals are stable under small perturbations and they are useful for erasures and reconstruction.展开更多
We use two appropriate bounded invertible operators to define a controlled frame with optimal frame bounds. We characterize those operators that produces Parseval controlled frames also we state a way to construct nea...We use two appropriate bounded invertible operators to define a controlled frame with optimal frame bounds. We characterize those operators that produces Parseval controlled frames also we state a way to construct nearly Parseval controlled frames. We intro- duce a new perturbation of controlled frames to obtain new frames from a given one. Also we reduce the distance of frames by appropriate operators and produce nearly dual frames from two given frames which are not dual frames for each other.展开更多
The workpiece frames relative to each robot base frame should be known in advance for the proper operation of twin-robot nondestructive testing system. However, when two robots are separated from the workpieces, the t...The workpiece frames relative to each robot base frame should be known in advance for the proper operation of twin-robot nondestructive testing system. However, when two robots are separated from the workpieces, the twin robots cannot reach the same point to complete the process of workpiece frame positioning. Thus, a new method is proposed to solve the problem of coincidence between workpiece frames. Transformation between two robot base frames is initiated by measuring the coordinate values of three non-collinear calibration points. The relationship between the workpiece frame and that of the slave robot base frame is then determined according to the known transformation of two robot base frames, as well as the relationship between the workpiece frame and that of the master robot base frame. Only one robot is required to actually measure the coordinate values of the calibration points on the workpiece. This requirement is beneficial when one of the robots cannot reach and measure the calibration points. The coordinate values of the calibration points are derived by driving the robot hand to the points and recording the values of top center point（TCP） coordinates. The translation and rotation matrices relate either the two robot base frames or the workpiece and master robot. The coordinated are solved using the measured values of the calibration points according to the Cartesian transformation principle. An optimal method is developed based on exponential mapping of Lie algebra to ensure that the rotation matrix is orthogonal. Experimental results show that this method involves fewer steps, offers significant advantages in terms of operation and time-saving. A method used to synchronize workpiece frames in twin-robot system automatically is presented.展开更多
In this paper,a Littlewood-Paley function characterization of the spaces L p（R）,1〈p〈∞,is first established by means of the equivalent conditions of tight wavelet frames,wherein the Littlewood-Paley function is as...In this paper,a Littlewood-Paley function characterization of the spaces L p（R）,1〈p〈∞,is first established by means of the equivalent conditions of tight wavelet frames,wherein the Littlewood-Paley function is associated with a tight wavelet frame generated by the so-called extension principles.With the above characterization,another characterization of L p（R）,1〈p〈∞,is also established in terms of the weighted l 2-norm of the wavelet frame coefficients,which can be a useful tool in harmonic analysis,approximation theory,and image processing.展开更多
文摘The π-tangle is used to study the behavior of entanglement of a nonmaximal tripartite state of both Dirac and scMar fields in accelerated frame. For Dirac fields, the degree of degradation with acceleration of both one-tangle of accelerated observer and π-tangle, for the same initial entanglement, is different by just interchanging the values of probability amplitudes. A fraction of both one-tangles and the π-tangle always survives for any choice of acceleration and the degree of initial entanglement. For scalar field, the one-tangle of accelerated observer depends on the choice of values of probability amplitudes and it vanishes in the range of infinite acceleration, whereas for 1r-tangle this is not always true. The dependence of π-tangle on probability amplitudes varies with acceleration. In the lower range of acceleration, its behavior changes by switching between the values of probability amplitudes and for larger values of acceleration this dependence on probability amplitudes vanishes. Interestingly, unlike bipartite entanglement, the degradation of π-tangle against acceleration in the case of sca/ar fields is slower than for Dirac fields.
基金supported by the National Natural Science Foundation of China(No.62362006)Guangxi Science and Technology Project(Key Research&Development)(No.GuiKeAB24010343)+1 种基金Guangxi“Bagui Scholar”Teams for Innovation and Research,Innovation Project of Guangxi Graduate Education(No.YCSW2025193)Guangxi Collaborative Innovation Center of Multi-source Information Integration and Intelligent Processing.
文摘In educational settings,instructors often lead students through hands-on software projects,sometimes engaging two different schools or departments.How can such collaborations be made more efficient,and how can students truly experience the importance of teamwork and the impact of organizational structure on project complexity?To answer these questions,we introduce the requirement-driven organization structure(R-DOS)approach,which tightly couples software requirements with the actual development process.By extending problem-frames modeling and focusing on requirements,R-DOS allows educators and students to(1)diagnose structural flaws early,(2)prescribe role-level and communication fixes,and(3)observe-in real time-how poor structure can derail a project while good structure accelerates learning and delivery.
文摘Methods of quantum information processing often appear in terms of specially selected states.For example,mutually unbiased bases(MUBs)and symmetric informationally complete measurements are widely applied.Finite frames have found use in many areas including quantum information.Due to its specific inner structure,a single equiangular tight frame(ETF)allows one to formulate criteria to detect non-classical correlations.This study aims to approach entanglement detection with the use of mutually unbiased ETFs.Such frames are an interesting generalization of widely recognized MUBs.It still uses rank-one operators,but the number of outcomes can exceed the dimensionality.Several approaches are considered including separability criteria and entanglement witnesses.Separability criteria for multipartite systems are finally obtained.
基金funded by UTM Fundamental Research Grant(PY/2024/01221,Cost centre no.:Q.J130000.3822.23H73)HiCoE Grant Scheme(Cost centre no.:R.J130000.7822.4J738)。
文摘Rapid quantification of seismic-induced damage immediately following an earthquake is critical for determining whether a structure is safe for continued occupation or requires evacuation.This study proposes a novel damage identification method that utilizes limited strain data points,significantly reducing installation,maintenance,and data analysis costs compared to traditional distributed sensor networks.The approach integrates finite element(FE)modeling to generate capacity curves through pushover analysis,incorporates noise-augmented datasets for Artificial Neural Network(ANN)training,and classifies structural conditions into four damage levels:Operational(OP),Immediate Occupancy(IO),Life Safety(LS),and Collapse Prevention(CP).To evaluate the method’s accuracy and efficiency,it was applied to two reinforced concrete(RC)frames;a single-story frame tested experimentally under cyclic loading and a three-story frame analyzed under various lateral load patterns.Strain data from selected beam and column ends were used as ANN inputs,while the corresponding damage classes served as outputs.Confusion matrix results demonstrated high true positive rates(>85%for the single-story and>90%for the three-story frame),even with a reduced number of sensors.The model also exhibited strong robustness to White Gaussian Noise(SNR=2.5-5 dB)and generalized effectively to nonlinear time-history analyses under scaled ground motions(PGA=0.1-1.0 g).Feature selection using the MRMR and ANOVA algorithms further enhanced computational efficiency.Overall,the proposed ANN-based framework has strong potential for real-time structural health monitoring applications.
文摘Modelling the turbulent flows in non-inertial frames of reference has long been a challenging task. Recently we introduced the notion of the "extended intrinsic mean spin tensor" for turbulence modelling and pointed out that, when applying the Reynolds stress models developed in the inertial frame of reference to model-ling the turbulence in a non-inertial frame of reference, the mean spin tensor should be replaced by the extended intrinsic mean spin tensor to correctly account for the rotation effects induced by the non-inertial frame of reference, to conform in phys-ics with the Reynolds stress transport equation. To exemplify the approach, we conducted numerical simulations of the fully developed turbulent channel flow in a rotating frame of reference by employing four non-linear K-ε models. Our numerical results based on this approach at a wide range of Reynolds and Rossby numbers evince that, among the models tested, the non-linear K-ε model of Huang and Ma and the non-linear K-ε model of Craft, Launder and Suga can better capture the rotation effects and the resulting influence on the structures of turbulence, and therefore are satisfactorily applied to dealing with the turbulent flows of practical interest in engineering. The general approach worked out in this paper is also ap-plied to the second-moment closure and the large-eddy simulation of turbulence.
文摘We investigate the role of extended intrinsic mean spin tensor introduced in this work for turbulence modelling in a non-inertial frame of reference. It is described by the Euclidean group of transformations and, in particular, its significance and importance in the approach of the algebraic Reynolds stress modelling, such as in a nonlinear K-ε model. To this end and for illustration of the effect of extended intrinsic spin tensor on turbulence modelling, we examine several recently developed nonlinear K-ε models and compare their performance in predicting the homogeneous turbulent shear flow in a rotating frame of reference with LES data. Our results and analysis indicate that, only if the deficiencies of these models and the like be well understood and properly corrected, may in the near future, more sophisticated nonlinear K-ε models be developed to better predict complex turbulent flows in a non-inertial frame of reference.
文摘The new variational principle of Gauss's form of nonlinear nonholonomic nonpotential system relative to non-inertial reference frame is established by constructing generalized inertial potentials. Naether's theorem and Naether's inverse theorem of the system above is presented and proved. Finally, one example is given to illustrate the application.
文摘Stepping out of Danyang Railway Station,the large sign reading“China Danyang Optical City”immediately comes into view across the road.Inside the bustling marketplace,a dazzling array of eyeglass frames and lenses is neatly displayed in rows of shops,attracting consumers from across the country.
基金supported by the National Key R&D Program of China,Grant No.2020YFA0712700the National Natural Science Foundation of China‘Mathematical Basic Theory of Quantum Computing’special project,Grant No.12341103。
文摘We connect magic(non-stabilizer)states,symmetric informationally complete positive operator valued measures(SIC-POVMs),and mutually unbiased bases(MUBs)in the context of group frames,and study their interplay.Magic states are quantum resources in the stabilizer formalism of quantum computation.SIC-POVMs and MUBs are fundamental structures in quantum information theory with many applications in quantum foundations,quantum state tomography,and quantum cryptography,etc.In this work,we study group frames constructed from some prominent magic states,and further investigate their applications.Our method exploits the orbit of discrete Heisenberg-Weyl group acting on an initial fiducial state.We quantify the distance of the group frames from SIC-POVMs and MUBs,respectively.As a simple corollary,we reproduce a complete family of MUBs of any prime dimensional system by introducing the concept of MUB fiducial states,analogous to the well-known SIC-POVM fiducial states.We present an intuitive and direct construction of MUB fiducial states via quantum T-gates,and demonstrate that for the qubit system,there are twelve MUB fiducial states,which coincide with the H-type magic states.We compare MUB fiducial states and SIC-POVM fiducial states from the perspective of magic resource for stabilizer quantum computation.We further pose the challenging issue of identifying all MUB fiducial states in general dimensions.
文摘Ensuring the secure transmission of secret messages,particularly through video—one of the most widely used media formats—is a critical challenge in the field of information security.Relying on a single-layered security approach is often insufficient for safeguarding sensitive data.This study proposes a triple-lightweight cryptographic and steganographic model that integrates the Hill Cipher Technique(HCT),Rotation Left Digits(RLD),and Discrete Wavelet Transform(DWT)to embed secret messages within video frames securely.The approach begins with encrypting the secret text using a private key matrix(PK^(1))of size 2×2 up to 6×6 via HCT.A second encryption layer is applied using a dynamic private key(PK2)derived from the RGB pixel values of the video frame,resulting in a rotated cipher.The doubly encrypted message is then embedded into the video frames using the DWT method.Upon transmission,the concealed message is extracted using inverse DWT and decrypted in two steps—first with PK2 and then with the inverse of PK^(1).Experiments conducted using MPEG video sequences and message lengths ranging from 10 to 300 bytes demonstrate strong performance in terms of Mean Square Error(MSE),Peak Signal-to-Noise Ratio(PSNR),and Correlation Coefficient(CC)between original and encrypted messages.The similarity between original and stego frames is further validated using Structural Similarity Index(SSIM),Mean Absolute Error(MAE),Number of Pixel Change Rate(NPCR),and Unified Average Changing Intensity(UACI).Results confirm that utilizing video frames to generate PK2 offers superior security compared to static key images.Moreover,the indistinguishability between original and stego frames highlights the method’s robustness against visual and statistical attacks.
基金supported by the Natural Science Foundation of Sichuan Province(Grant No.25QNJJ4066)。
文摘Improvement of the detection ability of quantum entanglement is one of the essential tasks in quantum computing and quantum information.Finite tight frames play a fundamental role in a wide variety of areas and,generally,each application requires a specific class of frames and is closely related to quantum measurement.It is worth noting that a maximal set of complex equiangular vectors is closely related to a symmetric informationally complete measurement.Hence,our goal in this work is to propose a series of separability criteria assigned to a finite tight frame and some well-known inequalities in different quantum systems,respectively.In addition,some tighter criteria to detect entanglement for many-body quantum states are presented in arbitrary dimensions.Finally,the effectiveness of the proposed entanglement detection criteria is illustrated through some detailed examples.
文摘A relationship was discovered between the amplification factor and the number of load increments that are needed to limit the relative error to one percent in second-order elastic analyses with a predictor-corrector solution scheme.Previous research by the authors proposed a design equation to determine the required minimum number of load increments based on an evaluation of the elastic critical buckling load ratio.Further research has shown that an approximate amplification factor equation that is based on the B2 multiplier equation produces similar results when the amplification factor is less than approximately four.Eleven moment frames are used to verify the use of the new approximate amplification factor in the proposed design equation.
文摘A three-dimensional beam element is derived based on the principle of stationary total potential energy for geometrically nonlinear analysis of space frames. A new tangent stiffness matrix, which allows for high order effects of element deformations, replaces the conventional incremental secant stiffness matrix. Two deformation stiffness matrices due to the variation of axial force and bending moments are included in the tangent stiffness. They are functions of element deformations and incorporate the coupling among axial, lateral and torsional deformations. A correction matrix is added to the tangent stiffness matrix to make displacement derivatives equivalent to the commutative rotational degrees of freedom. Numerical examples show that the proposed dement is accurate and efficient in predicting the nonlinear behavior, such as axial-torsional and flexural-torsional buckling, of space frames even when fewer elements are used to model a member.
文摘Suppose that Φ(x)∈L 2(R) with compact support and V= span{Φ(x-k)|k∈Z}. In this note, we prove that if {Φ(x-k)k|k∈Z} is tight frame with bound 1 in V, then {Φ(x-k)|k∈Z} must be an orthonormal basis of V.
文摘In the paper, we study the stability of Hilbert space generalized frames under perturbations. We get some results that are in spirit close to classical results for discrete frames, due to OLE Christensen.
文摘In this paper we shall offer a separation axiom for frames inspired by the Hausdorff separation axiom for topological spaces. We call it separated condition. This is a condition on topology OX equivalent to the T O space X being Hausdorff. The class of separated frames includes that of strong Hausdorff frames and that of S frames. We shall show that the class of separated frames is a class closed under the formation of coproducts and subspaces, and the space Fil( L ) is Hausdorff for any separated frame L . Therefore there is a contravariant adjunction between the category TOP 2 of Hausdorff topological spaces and the category FRAM 2 of separated frames.
文摘In this article, we introduce and characterize approximate duality for g-frames. We get some important properties and applications of approximate duals. We also obtain some new results in approximate duality of frames, and generalize some of the known results in approximate duality of frames to g-frames. We also get some results for fusion frames, and perturbation of approximately dual g-frames. We show that approximate duals are stable under small perturbations and they are useful for erasures and reconstruction.
文摘We use two appropriate bounded invertible operators to define a controlled frame with optimal frame bounds. We characterize those operators that produces Parseval controlled frames also we state a way to construct nearly Parseval controlled frames. We intro- duce a new perturbation of controlled frames to obtain new frames from a given one. Also we reduce the distance of frames by appropriate operators and produce nearly dual frames from two given frames which are not dual frames for each other.
基金Supported by International S&T Cooperation Program of China(Grant No.2012DFA70260)High-end CNC Machine and Basic Manufacturing Equipment of Chinese Key National Science and Technology(Grant No.2011ZX04014-081)
文摘The workpiece frames relative to each robot base frame should be known in advance for the proper operation of twin-robot nondestructive testing system. However, when two robots are separated from the workpieces, the twin robots cannot reach the same point to complete the process of workpiece frame positioning. Thus, a new method is proposed to solve the problem of coincidence between workpiece frames. Transformation between two robot base frames is initiated by measuring the coordinate values of three non-collinear calibration points. The relationship between the workpiece frame and that of the slave robot base frame is then determined according to the known transformation of two robot base frames, as well as the relationship between the workpiece frame and that of the master robot base frame. Only one robot is required to actually measure the coordinate values of the calibration points on the workpiece. This requirement is beneficial when one of the robots cannot reach and measure the calibration points. The coordinate values of the calibration points are derived by driving the robot hand to the points and recording the values of top center point（TCP） coordinates. The translation and rotation matrices relate either the two robot base frames or the workpiece and master robot. The coordinated are solved using the measured values of the calibration points according to the Cartesian transformation principle. An optimal method is developed based on exponential mapping of Lie algebra to ensure that the rotation matrix is orthogonal. Experimental results show that this method involves fewer steps, offers significant advantages in terms of operation and time-saving. A method used to synchronize workpiece frames in twin-robot system automatically is presented.
基金Supported by the National High Technology Research and Development Program of China (863 Program) (2009AA12Z203,2008AA 12Z201)
文摘In this paper,a Littlewood-Paley function characterization of the spaces L p（R）,1〈p〈∞,is first established by means of the equivalent conditions of tight wavelet frames,wherein the Littlewood-Paley function is associated with a tight wavelet frame generated by the so-called extension principles.With the above characterization,another characterization of L p（R）,1〈p〈∞,is also established in terms of the weighted l 2-norm of the wavelet frame coefficients,which can be a useful tool in harmonic analysis,approximation theory,and image processing.
