We-map is an interactive mobile map that can be easily communicated and applied on personal electronic devices,such as personal computers and mobile phones.Therefore,the study of direction systems and coordinate syste...We-map is an interactive mobile map that can be easily communicated and applied on personal electronic devices,such as personal computers and mobile phones.Therefore,the study of direction systems and coordinate systems is critical,and exploring reference frames is essential in direction and coordinate systems.Despite its significance,existing research on We-map lacks specific solutions for the exploration of reference frames is indispensable for the establishment of accurate direction and coordinate systems.In this paper,we endeavor to address this gap by elucidating the significance of We-map reference frames,defining them with mathematical constraints,summarizing their nature and characteristics,deriving their transformation relationships and representing them through mathematical formulars and equations.Our work contributes to the fundamental theory of We-map and provides valuable systems and support for the mathematical foundation of We-map,map production,and platform development.Ultimately,this research serves to advance the development of We-map.展开更多
A resilience-incorporated risk assessment framework is proposed and demonstrated in this study to manifest the advantageous seismic resilience of precast concrete frame(PCF)structures with“dry”connections in terms o...A resilience-incorporated risk assessment framework is proposed and demonstrated in this study to manifest the advantageous seismic resilience of precast concrete frame(PCF)structures with“dry”connections in terms of their low damage and rapid recovery.The framework integrates various uncertainties in the seismic hazard,fragility,capacity,demand,loss functions,and post-earthquake recovery.In this study,the PCF structures are distinguished from ordinary reinforced concrete frame(RCF)structures by characterizing multiple limit states for the PCF based on its unique damage mechanisms.Accordingly,probabilistic story-wise pushover analyses are performed to yield story-wise capacities for the predefined limit states.In the seismic resilience analysis,a step-wise recovery model is proposed to idealize the functionality recovery process,with separate considerations of the repair and non-repair events.The recovery model leverages the economic loss and downtime to delineate the stochastic post-earthquake recovery curves for the resilience loss estimation.As such,contingencies in the probabilistic post-earthquake repairs are incorporated and the empirical judgments on the recovery parameters are largely circumvented.The proposed framework is demonstrated through a comparative study between two“dry”connected PCFs and one RCF designed as alternative structural systems for a prototype building.The results from the risk quantification indicate that the PCFs show reduced loss hazards and lower expected losses relative to the RCF.Particularly,the PCF equipped with energy dissipation devices at the“dry”connections largely reduces the expected economic loss,downtime,and resilience loss by 29%,56%,and 60%,respectively,compared to the RCF.展开更多
Plug-and-play priors are popular for solving illposed imaging inverse problems. Recent efforts indicate that the convergence guarantee of the imaging algorithms using plug-andplay priors relies on the assumption of bo...Plug-and-play priors are popular for solving illposed imaging inverse problems. Recent efforts indicate that the convergence guarantee of the imaging algorithms using plug-andplay priors relies on the assumption of bounded denoisers. However, the bounded properties of existing plugged Gaussian denoisers have not been proven explicitly. To bridge this gap, we detail a novel provable bounded denoiser termed as BMDual,which combines a trainable denoiser using dual tight frames and the well-known block-matching and 3D filtering(BM3D)denoiser. We incorporate multiple dual frames utilized by BMDual into a novel regularization model induced by a solver. The proposed regularization model is utilized for compressed sensing magnetic resonance imaging(CSMRI). We theoretically show the bound of the BMDual denoiser, the bounded gradient of the CSMRI data-fidelity function, and further demonstrate that the proposed CSMRI algorithm converges. Experimental results also demonstrate that the proposed algorithm has a good convergence behavior, and show the effectiveness of the proposed algorithm.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 covariant derivative is a generalization of differentiating vectors.The Euclidean derivative is a special case of the covariant derivative in Euclidean space.The covariant derivative gathers broad attention,partic...The covariant derivative is a generalization of differentiating vectors.The Euclidean derivative is a special case of the covariant derivative in Euclidean space.The covariant derivative gathers broad attention,particularly when computing vector derivatives on curved surfaces and volumes in various applications.Covariant derivatives have been computed using the metric tensor from the analytically known curved axes.However,deriving the global axis for the domain has been mathematically and computationally challenging for an arbitrary two-dimensional(2D)surface.Consequently,computing the covariant derivative has been difficult or even impossible.A novel high-order numerical scheme is proposed for computing the covariant derivative on any 2D curved surface.A set of orthonormal vectors,known as moving frames,expand vectors to compute accurately covariant derivatives on 2D curved surfaces.The proposed scheme does not require the construction of curved axes for the metric tensor or the Christoffel symbols.The connectivity given by the Christoffel symbols is equivalently provided by the attitude matrix of orthonormal moving frames.Consequently,the proposed scheme can be extended to the general 2D curved surface.As an application,the Helmholtz‐Hodge decomposition is considered for a realistic atrium and a bunny.展开更多
The rotation-minimizing frame is the main research object for a spatial curve. Although the mathematical description is not complicated, it is not easy to directly make an exact minimizing-rotation frame for the Euler...The rotation-minimizing frame is the main research object for a spatial curve. Although the mathematical description is not complicated, it is not easy to directly make an exact minimizing-rotation frame for the Euler-Rodrigues frame. The condition for the non-normalized Euler-Rodrigues frame of the Pythagorean-Hodograph curve to become the rotation-minimizing frame is given in this article, which is an ordinary differential equation with rational form, the analytical solution that does not always exist. To avoid calculating the solution of ordinary differential equations, a global optimization algorithm for the conditions is proposed, that has a weight function in the objective function. The quintic Pythagorean-Hodograph curve is analyzed concretely with the method, and its objective function and constraint conditions of optimization are clarified. The example is analyzed by using this method with different weight functions and contrasting that approach with its exact value.展开更多
This paper is concerned with the characterization of the duals of wavelet frames of L(2)(R). The sufficient and necessary conditions for them are obtained.
The most valuable resource on the planet is no longer oil,but data.The transmission of this data securely over the internet is another challenge that comes with its ever-increasing value.In order to transmit sensitive...The most valuable resource on the planet is no longer oil,but data.The transmission of this data securely over the internet is another challenge that comes with its ever-increasing value.In order to transmit sensitive information securely,researchers are combining robust cryptography and steganographic approaches.The objective of this research is to introduce a more secure method of video steganography by using Deoxyribonucleic acid(DNA)for embedding encrypted data and an intelligent frame selection algorithm to improve video imperceptibility.In the previous approach,DNA was used only for frame selection.If this DNA is compromised,then our frames with the hidden and unencrypted data will be exposed.Moreover the frame selected in this way were random frames,and no consideration was made to the contents of frames.Hiding data in this way introduces visible artifacts in video.In the proposed approach rather than using DNA for frame selection we have created a fakeDNA out of our data and then embedded it in a video file on intelligently selected frames called the complex frames.Using chaotic maps and linear congruential generators,a unique pixel set is selected each time only from the identified complex frames,and encrypted data is embedded in these random locations.Experimental results demonstrate that the proposed technique shows minimum degradation of the stenographic video hence reducing the very first chances of visual surveillance.Further,the selection of complex frames for embedding and creation of a fake DNA as proposed in this research have higher peak signal-to-noise ratio(PSNR)and reduced mean squared error(MSE)values that indicate improved results.The proposed methodology has been implemented in Matlab.展开更多
In this paper,using Parseval frames we generalize Sun’s results to g-frames in Hilbert C^(*)-modules.Moreover,for g-frames in Hilbert spaces,we present some characterizations in terms of a family of frames,not only f...In this paper,using Parseval frames we generalize Sun’s results to g-frames in Hilbert C^(*)-modules.Moreover,for g-frames in Hilbert spaces,we present some characterizations in terms of a family of frames,not only for orthonormal bases.Also,we have a note about a comment and a relation in the proof of Proposition 5.3 in[D.Li et al.,On weaving g-frames for Hilbert spaces,Complex Analysis and Operator Theory,2020].Finally,we have some results for g-Riesz bases,woven and P-woven g-frames.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
Operator-valued frames （or g-frames） are generalizations of frames and fusion frames and have been used in packets encoding, quantum computing, theory of coherent states and more. In this article, we give a new form...Operator-valued frames （or g-frames） are generalizations of frames and fusion frames and have been used in packets encoding, quantum computing, theory of coherent states and more. In this article, we give a new formula for operator-valued frames for finite dimensional Hilbert spaces. As an application, we derive in a simple manner a recent result of A. Najati concerning the approximation of g-frames by Parseval ones. We obtain also some results concerning the best approximation of operator-valued frames by its alternate duals, with optimal estimates.展开更多
A frame is an orthonormal basis-like collection of vectors in a Hilbert space, but need not be a basis or orthonormal. A fusion frame （frame of subspaces） is a frame-like collection of subspaces in a Hilbert space, ...A frame is an orthonormal basis-like collection of vectors in a Hilbert space, but need not be a basis or orthonormal. A fusion frame （frame of subspaces） is a frame-like collection of subspaces in a Hilbert space, thereby constructing a frame for the whole space by joining sequences of frames for subspaces. Moreover the notion of fusion frames provide a framework for applications and providing efficient and robust information processing algorithms.In this paper we study the conditions under which removing an element from a fusion frame, again we obtain another fusion frame. We give another proof of [5, Corollary 3.3（iii）] with extra information about the bounds.展开更多
2-frames in 2-Hilbert spaces are studied and some results on it are presented. The tensor product of 2-frames in 2-Hilbert spaces is introduced. It is shown that the tensor product of two 2-frames is a 2-frame for the...2-frames in 2-Hilbert spaces are studied and some results on it are presented. The tensor product of 2-frames in 2-Hilbert spaces is introduced. It is shown that the tensor product of two 2-frames is a 2-frame for the tensor product of Hilbert spaces. Some results on tensor product of 2-frames are established.展开更多
Accurate estimates of ductility demands on buckling-restrained braced frames(BRBFs)are crucial to performance-based design of BRBFs.An analytical study on the seismic behavior of BRBFs has been conducted at the ATLSS ...Accurate estimates of ductility demands on buckling-restrained braced frames(BRBFs)are crucial to performance-based design of BRBFs.An analytical study on the seismic behavior of BRBFs has been conducted at the ATLSS Center,Lehigh University to prepare for an upcoming experimental program.The analysis program DRAIN-2DX was used to model a one-bay,four-story prototype BRBF including material and geometric nonlinearities.The buckling- restrained brace(BRB)model incorporates both isotropic and kinematic hardening.Nonlinear static pushover and time- history analyses were performed on the prototype BRBF.Performance objectives for the BRBs were defined and used to evaluate the time-history analysis results.Particular emphasis was placed on global ductility demands and ductility demands on the BRBs.These demands were compared with anticipated ductility capacities.The analysis results,along with results from similar previous studies,are used to evaluate the BRBF design provisions that have been recommended for codification in the United States.The results show that BRB maximum ductility demands can be as high as 20 to 25.These demands significantly exceed those anticipated by the BRBF recommended provisions.Results from the static pushover and time- history analyses are used to demonstrate why the ductility demands exceed those anticipated by the recommended provisions. The BRB qualification testing protocol contained in the BRBF recommended provisions is shown to be inadequate because it requires only a maximum ductility demand of at most 7.5.Modifications to the testing protocol are recommended.展开更多
To consider the bending collapse of the pipes in the latticed frames, based on the multi-scale simulation, the collapsed parts of the pipe are meshed by the shell elements as micro-scaled models, and the other parts a...To consider the bending collapse of the pipes in the latticed frames, based on the multi-scale simulation, the collapsed parts of the pipe are meshed by the shell elements as micro-scaled models, and the other parts are meshed by beam elements macro-models. The incremental displacement constraint equations for the nodes on the section between the two models are established based on the plane section premise of classical beam theory. The method to introduce the constraint equations is derived based on the Updated Largrangian method. The location of the micro-model is predicted by the stress field of the beam element, and the length of the collapsed part is adjusted by the plastic energy in the micro model. Several examples are included to illustrate the efficiency and accuracy of this method.展开更多
The seismic behavior of planar frames with concrete-filled T-section columns to steel beam was experimentally and numerically studied. A finite element analysis （FEA） model was developed to investigate the engineeri...The seismic behavior of planar frames with concrete-filled T-section columns to steel beam was experimentally and numerically studied. A finite element analysis （FEA） model was developed to investigate the engineering properties of the planar frames. Two 1：2.5 reduced-scale specimens of T-section concrete-filled steel tubular column and steel beam of single-story and single-bay plane frames were designed and fabricated based on the design principles of strong-column, weak-beam and stronger-joint. One three-dimensional entity model of the investigated frame structure was built using a large-scale nonlinear finite-element analysis software ABAQUS. Experimental results show that the axial compression ratio has no effect on the failure mode of the structure, while with the increase of axial compression ratio and the dissipated energy ability increasing, the structural ductility decreased. The results from both experiments and simulations agree with each other, which verifies the validity and accuracy of the developed finite element model. Furthermore, the developed finite element model helps to reflect the detailed stress status of the investigated frame at different time and different positions.展开更多
This study investigates the efficiency of two types of rehabilitation methods based on economic justification that can lead to logical decision making between the retrofitting schemes. Among various rehabilitation met...This study investigates the efficiency of two types of rehabilitation methods based on economic justification that can lead to logical decision making between the retrofitting schemes. Among various rehabilitation methods, concentric chevron bracing（CCB） and cylindrical friction damper（CFD） were selected. The performance assessment procedure of the frames is divided into two distinct phases. First, the limit state probabilities of the structures before and after rehabilitation are investigated. In the second phase, the seismic risk of structures in terms of life safety and financial losses（decision variables） using the recently published FEMA P58 methodology is evaluated. The results show that the proposed retrofitting methods improve the serviceability and life safety performance levels of steel and RC structures at different rates when subjected to earthquake loads. Moreover, these procedures reveal that financial losses are greatly decreased, and were more tangible by the application of CFD rather than using CCB. Although using both retrofitting methods reduced damage state probabilities, incorporation of a site-specific seismic hazard curve to evaluate mean annual occurrence frequency at the collapse prevention limit state caused unexpected results to be obtained. Contrary to CFD, the collapse probability of the structures retrofitted with CCB increased when compared with the primary structures.展开更多
A procedure is proposed whereby input and hysteretic energy spectra developed for single-degree-of-freedom （SDOF） systems are applied to multi-degree-of-freedom （MDOF） steel moment resisting frames. The proposed p...A procedure is proposed whereby input and hysteretic energy spectra developed for single-degree-of-freedom （SDOF） systems are applied to multi-degree-of-freedom （MDOF） steel moment resisting frames. The proposed procedure is verified using four frames, viz., frame with three-, five-, seven- and nine-stories, each of which is subjected to the fault- normal and fault-parallel components of three actual earthquakes. A very good estimate for the three- and five-story frames, and a reasonably acceptable estimate for the seven-, and nine-story frames, have been obtained. A method for distributing the hysteretic energy over the frame height is also proposed. This distribution scheme allows for the determination of the energy demand component of a proposed energy-based seismic design （EBSD） procedure for each story. To address the capacity component of EBSD, a story-wise optimization design procedure is developed by utilizing the energy dissipating capacity from plastic hinge formation/rotation for these moment frames. The proposed EBSD procedure is demonstrated in the design of a three-story one-bay steel moment frame.展开更多
In this paper, we consider data separation problem, where the original signal is composed of two distinct subcomponents, via dual frames based Split-analysis approach. We show that the two distinct subcomponents, whic...In this paper, we consider data separation problem, where the original signal is composed of two distinct subcomponents, via dual frames based Split-analysis approach. We show that the two distinct subcomponents, which are sparse in two diff erent general frames respectively, can be exactly recovered with high probability, when the measurement matrix is a Weibull random matrix （not Gaussian） and the two frames satisfy a mutual coherence property. Our result may be significant for analysing Split-analysis model for data separation.展开更多
基金Industrial Support and Program Project of Universities in Gansu Province(No.2022CYZC-30)National Natural Science Foundation of China(Nos.42430108,41930101)China Scholarship Council(No.202306180085).
文摘We-map is an interactive mobile map that can be easily communicated and applied on personal electronic devices,such as personal computers and mobile phones.Therefore,the study of direction systems and coordinate systems is critical,and exploring reference frames is essential in direction and coordinate systems.Despite its significance,existing research on We-map lacks specific solutions for the exploration of reference frames is indispensable for the establishment of accurate direction and coordinate systems.In this paper,we endeavor to address this gap by elucidating the significance of We-map reference frames,defining them with mathematical constraints,summarizing their nature and characteristics,deriving their transformation relationships and representing them through mathematical formulars and equations.Our work contributes to the fundamental theory of We-map and provides valuable systems and support for the mathematical foundation of We-map,map production,and platform development.Ultimately,this research serves to advance the development of We-map.
基金National Key Research and Development Program of China under Grant No.2022YFC3803004Postgraduate Research&Practice Innovation Program of Jiangsu Province under Grant No.SJCX20_0031Fundamental Research Funds for the Central Universities under Grant No.3205002108D。
文摘A resilience-incorporated risk assessment framework is proposed and demonstrated in this study to manifest the advantageous seismic resilience of precast concrete frame(PCF)structures with“dry”connections in terms of their low damage and rapid recovery.The framework integrates various uncertainties in the seismic hazard,fragility,capacity,demand,loss functions,and post-earthquake recovery.In this study,the PCF structures are distinguished from ordinary reinforced concrete frame(RCF)structures by characterizing multiple limit states for the PCF based on its unique damage mechanisms.Accordingly,probabilistic story-wise pushover analyses are performed to yield story-wise capacities for the predefined limit states.In the seismic resilience analysis,a step-wise recovery model is proposed to idealize the functionality recovery process,with separate considerations of the repair and non-repair events.The recovery model leverages the economic loss and downtime to delineate the stochastic post-earthquake recovery curves for the resilience loss estimation.As such,contingencies in the probabilistic post-earthquake repairs are incorporated and the empirical judgments on the recovery parameters are largely circumvented.The proposed framework is demonstrated through a comparative study between two“dry”connected PCFs and one RCF designed as alternative structural systems for a prototype building.The results from the risk quantification indicate that the PCFs show reduced loss hazards and lower expected losses relative to the RCF.Particularly,the PCF equipped with energy dissipation devices at the“dry”connections largely reduces the expected economic loss,downtime,and resilience loss by 29%,56%,and 60%,respectively,compared to the RCF.
基金supported in part by the National Natural Science Foundation of China (62371414,61901406)the Hebei Natural Science Foundation (F2020203025)+2 种基金the Young Talent Program of Universities and Colleges in Hebei Province (BJ2021044)the Hebei Key Laboratory Project (202250701010046)the Central Government Guides Local Science and Technology Development Fund Projects(216Z1602G)。
文摘Plug-and-play priors are popular for solving illposed imaging inverse problems. Recent efforts indicate that the convergence guarantee of the imaging algorithms using plug-andplay priors relies on the assumption of bounded denoisers. However, the bounded properties of existing plugged Gaussian denoisers have not been proven explicitly. To bridge this gap, we detail a novel provable bounded denoiser termed as BMDual,which combines a trainable denoiser using dual tight frames and the well-known block-matching and 3D filtering(BM3D)denoiser. We incorporate multiple dual frames utilized by BMDual into a novel regularization model induced by a solver. The proposed regularization model is utilized for compressed sensing magnetic resonance imaging(CSMRI). We theoretically show the bound of the BMDual denoiser, the bounded gradient of the CSMRI data-fidelity function, and further demonstrate that the proposed CSMRI algorithm converges. Experimental results also demonstrate that the proposed algorithm has a good convergence behavior, and show the effectiveness of the proposed algorithm.
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the National Research Foundation of Korea(NRF-2021R1A2C109297811).
文摘The covariant derivative is a generalization of differentiating vectors.The Euclidean derivative is a special case of the covariant derivative in Euclidean space.The covariant derivative gathers broad attention,particularly when computing vector derivatives on curved surfaces and volumes in various applications.Covariant derivatives have been computed using the metric tensor from the analytically known curved axes.However,deriving the global axis for the domain has been mathematically and computationally challenging for an arbitrary two-dimensional(2D)surface.Consequently,computing the covariant derivative has been difficult or even impossible.A novel high-order numerical scheme is proposed for computing the covariant derivative on any 2D curved surface.A set of orthonormal vectors,known as moving frames,expand vectors to compute accurately covariant derivatives on 2D curved surfaces.The proposed scheme does not require the construction of curved axes for the metric tensor or the Christoffel symbols.The connectivity given by the Christoffel symbols is equivalently provided by the attitude matrix of orthonormal moving frames.Consequently,the proposed scheme can be extended to the general 2D curved surface.As an application,the Helmholtz‐Hodge decomposition is considered for a realistic atrium and a bunny.
文摘The rotation-minimizing frame is the main research object for a spatial curve. Although the mathematical description is not complicated, it is not easy to directly make an exact minimizing-rotation frame for the Euler-Rodrigues frame. The condition for the non-normalized Euler-Rodrigues frame of the Pythagorean-Hodograph curve to become the rotation-minimizing frame is given in this article, which is an ordinary differential equation with rational form, the analytical solution that does not always exist. To avoid calculating the solution of ordinary differential equations, a global optimization algorithm for the conditions is proposed, that has a weight function in the objective function. The quintic Pythagorean-Hodograph curve is analyzed concretely with the method, and its objective function and constraint conditions of optimization are clarified. The example is analyzed by using this method with different weight functions and contrasting that approach with its exact value.
文摘This paper is concerned with the characterization of the duals of wavelet frames of L(2)(R). The sufficient and necessary conditions for them are obtained.
基金Taif University Researchers Supporting Project number(TURSP-2020/98),Taif University,Taif,Saudi Arabia.
文摘The most valuable resource on the planet is no longer oil,but data.The transmission of this data securely over the internet is another challenge that comes with its ever-increasing value.In order to transmit sensitive information securely,researchers are combining robust cryptography and steganographic approaches.The objective of this research is to introduce a more secure method of video steganography by using Deoxyribonucleic acid(DNA)for embedding encrypted data and an intelligent frame selection algorithm to improve video imperceptibility.In the previous approach,DNA was used only for frame selection.If this DNA is compromised,then our frames with the hidden and unencrypted data will be exposed.Moreover the frame selected in this way were random frames,and no consideration was made to the contents of frames.Hiding data in this way introduces visible artifacts in video.In the proposed approach rather than using DNA for frame selection we have created a fakeDNA out of our data and then embedded it in a video file on intelligently selected frames called the complex frames.Using chaotic maps and linear congruential generators,a unique pixel set is selected each time only from the identified complex frames,and encrypted data is embedded in these random locations.Experimental results demonstrate that the proposed technique shows minimum degradation of the stenographic video hence reducing the very first chances of visual surveillance.Further,the selection of complex frames for embedding and creation of a fake DNA as proposed in this research have higher peak signal-to-noise ratio(PSNR)and reduced mean squared error(MSE)values that indicate improved results.The proposed methodology has been implemented in Matlab.
文摘In this paper,using Parseval frames we generalize Sun’s results to g-frames in Hilbert C^(*)-modules.Moreover,for g-frames in Hilbert spaces,we present some characterizations in terms of a family of frames,not only for orthonormal bases.Also,we have a note about a comment and a relation in the proof of Proposition 5.3 in[D.Li et al.,On weaving g-frames for Hilbert spaces,Complex Analysis and Operator Theory,2020].Finally,we have some results for g-Riesz bases,woven and P-woven g-frames.
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.
基金The final work of P.Gǎvruta on this article was supported by a grant of Romanian National Authority for Scientific Research,CNCS-UEFISCDI,project number PN-II-ID-JRP-2011-2/11-RO-FR/01.03.2013
文摘Operator-valued frames （or g-frames） are generalizations of frames and fusion frames and have been used in packets encoding, quantum computing, theory of coherent states and more. In this article, we give a new formula for operator-valued frames for finite dimensional Hilbert spaces. As an application, we derive in a simple manner a recent result of A. Najati concerning the approximation of g-frames by Parseval ones. We obtain also some results concerning the best approximation of operator-valued frames by its alternate duals, with optimal estimates.
文摘A frame is an orthonormal basis-like collection of vectors in a Hilbert space, but need not be a basis or orthonormal. A fusion frame （frame of subspaces） is a frame-like collection of subspaces in a Hilbert space, thereby constructing a frame for the whole space by joining sequences of frames for subspaces. Moreover the notion of fusion frames provide a framework for applications and providing efficient and robust information processing algorithms.In this paper we study the conditions under which removing an element from a fusion frame, again we obtain another fusion frame. We give another proof of [5, Corollary 3.3（iii）] with extra information about the bounds.
文摘2-frames in 2-Hilbert spaces are studied and some results on it are presented. The tensor product of 2-frames in 2-Hilbert spaces is introduced. It is shown that the tensor product of two 2-frames is a 2-frame for the tensor product of Hilbert spaces. Some results on tensor product of 2-frames are established.
文摘Accurate estimates of ductility demands on buckling-restrained braced frames(BRBFs)are crucial to performance-based design of BRBFs.An analytical study on the seismic behavior of BRBFs has been conducted at the ATLSS Center,Lehigh University to prepare for an upcoming experimental program.The analysis program DRAIN-2DX was used to model a one-bay,four-story prototype BRBF including material and geometric nonlinearities.The buckling- restrained brace(BRB)model incorporates both isotropic and kinematic hardening.Nonlinear static pushover and time- history analyses were performed on the prototype BRBF.Performance objectives for the BRBs were defined and used to evaluate the time-history analysis results.Particular emphasis was placed on global ductility demands and ductility demands on the BRBs.These demands were compared with anticipated ductility capacities.The analysis results,along with results from similar previous studies,are used to evaluate the BRBF design provisions that have been recommended for codification in the United States.The results show that BRB maximum ductility demands can be as high as 20 to 25.These demands significantly exceed those anticipated by the BRBF recommended provisions.Results from the static pushover and time- history analyses are used to demonstrate why the ductility demands exceed those anticipated by the recommended provisions. The BRB qualification testing protocol contained in the BRBF recommended provisions is shown to be inadequate because it requires only a maximum ductility demand of at most 7.5.Modifications to the testing protocol are recommended.
基金Funded by the Key Science and Technology Project of State Grid Corporation of China under Grant No.GC-10-1006
文摘To consider the bending collapse of the pipes in the latticed frames, based on the multi-scale simulation, the collapsed parts of the pipe are meshed by the shell elements as micro-scaled models, and the other parts are meshed by beam elements macro-models. The incremental displacement constraint equations for the nodes on the section between the two models are established based on the plane section premise of classical beam theory. The method to introduce the constraint equations is derived based on the Updated Largrangian method. The location of the micro-model is predicted by the stress field of the beam element, and the length of the collapsed part is adjusted by the plastic energy in the micro model. Several examples are included to illustrate the efficiency and accuracy of this method.
基金Projects(51378077,51478047,51778066)supported by the National Natural Science Foundation of ChinaProject(D20151304)supported by Science and Technology Research Project of Education Department of Hubei Province,ChinaProject(2017CFA070)supported by Hubei Provincial Natural Science Foundation,China
文摘The seismic behavior of planar frames with concrete-filled T-section columns to steel beam was experimentally and numerically studied. A finite element analysis （FEA） model was developed to investigate the engineering properties of the planar frames. Two 1：2.5 reduced-scale specimens of T-section concrete-filled steel tubular column and steel beam of single-story and single-bay plane frames were designed and fabricated based on the design principles of strong-column, weak-beam and stronger-joint. One three-dimensional entity model of the investigated frame structure was built using a large-scale nonlinear finite-element analysis software ABAQUS. Experimental results show that the axial compression ratio has no effect on the failure mode of the structure, while with the increase of axial compression ratio and the dissipated energy ability increasing, the structural ductility decreased. The results from both experiments and simulations agree with each other, which verifies the validity and accuracy of the developed finite element model. Furthermore, the developed finite element model helps to reflect the detailed stress status of the investigated frame at different time and different positions.
文摘This study investigates the efficiency of two types of rehabilitation methods based on economic justification that can lead to logical decision making between the retrofitting schemes. Among various rehabilitation methods, concentric chevron bracing（CCB） and cylindrical friction damper（CFD） were selected. The performance assessment procedure of the frames is divided into two distinct phases. First, the limit state probabilities of the structures before and after rehabilitation are investigated. In the second phase, the seismic risk of structures in terms of life safety and financial losses（decision variables） using the recently published FEMA P58 methodology is evaluated. The results show that the proposed retrofitting methods improve the serviceability and life safety performance levels of steel and RC structures at different rates when subjected to earthquake loads. Moreover, these procedures reveal that financial losses are greatly decreased, and were more tangible by the application of CFD rather than using CCB. Although using both retrofitting methods reduced damage state probabilities, incorporation of a site-specific seismic hazard curve to evaluate mean annual occurrence frequency at the collapse prevention limit state caused unexpected results to be obtained. Contrary to CFD, the collapse probability of the structures retrofitted with CCB increased when compared with the primary structures.
文摘A procedure is proposed whereby input and hysteretic energy spectra developed for single-degree-of-freedom （SDOF） systems are applied to multi-degree-of-freedom （MDOF） steel moment resisting frames. The proposed procedure is verified using four frames, viz., frame with three-, five-, seven- and nine-stories, each of which is subjected to the fault- normal and fault-parallel components of three actual earthquakes. A very good estimate for the three- and five-story frames, and a reasonably acceptable estimate for the seven-, and nine-story frames, have been obtained. A method for distributing the hysteretic energy over the frame height is also proposed. This distribution scheme allows for the determination of the energy demand component of a proposed energy-based seismic design （EBSD） procedure for each story. To address the capacity component of EBSD, a story-wise optimization design procedure is developed by utilizing the energy dissipating capacity from plastic hinge formation/rotation for these moment frames. The proposed EBSD procedure is demonstrated in the design of a three-story one-bay steel moment frame.
基金Supported by the National Natural Science Foundation of China(11171299 and 91130009)
文摘In this paper, we consider data separation problem, where the original signal is composed of two distinct subcomponents, via dual frames based Split-analysis approach. We show that the two distinct subcomponents, which are sparse in two diff erent general frames respectively, can be exactly recovered with high probability, when the measurement matrix is a Weibull random matrix （not Gaussian） and the two frames satisfy a mutual coherence property. Our result may be significant for analysing Split-analysis model for data separation.
