Some equalities and inequalities of g-continuous frames

In this paper,we derive some equalities and inequalities about g-continuous frames,which are an extension to g-frames and continuous frames.We also discuss the stability of the perturbation of a g-continuous frame.

Cascaded ELM-Based Joint Frame Synchronization and Channel Estimation over Rician Fading Channel with Hardware Imperfections

Due to the interdependency of frame synchronization(FS)and channel estimation(CE),joint FS and CE(JFSCE)schemes are proposed to enhance their functionalities and therefore boost the overall performance of wireless communication systems.Although traditional JFSCE schemes alleviate the influence between FS and CE,they show deficiencies in dealing with hardware imperfection(HI)and deterministic line-of-sight(LOS)path.To tackle this challenge,we proposed a cascaded ELM-based JFSCE to alleviate the influence of HI in the scenario of the Rician fading channel.Specifically,the conventional JFSCE method is first employed to extract the initial features,and thus forms the non-Neural Network(NN)solutions for FS and CE,respectively.Then,the ELMbased networks,named FS-NET and CE-NET,are cascaded to capture the NN solutions of FS and CE.Simulation and analysis results show that,compared with the conventional JFSCE methods,the proposed cascaded ELM-based JFSCE significantly reduces the error probability of FS and the normalized mean square error(NMSE)of CE,even against the impacts of parameter variations.

Dynamic interactive bitwise meta-holography with ultra-high computational and display frame rates

Interactive holography offers unmatched levels of immersion and user engagement in the field of future display.Despite of the substantial progress has been made in dynamic meta-holography,the realization of real-time,highly smooth interactive holography remains a significant challenge due to the computational and display frame rate limitations.In this study,we introduced a dynamic interactive bitwise meta-holography with ultra-high computational and display frame rates.To our knowledge,this is the first reported practical dynamic interactive metasurface holographic system.We spa-tially divided the metasurface device into multiple distinct channels,each projecting a reconstructed sub-pattern.The switching states of these channels were mapped to bitwise operations on a set of bit values,which avoids complex holo-gram computations,enabling an ultra-high computational frame rate.Our approach achieves a computational frame rate of 800 kHz and a display frame rate of 23 kHz on a low-power Raspberry Pi computational platform.According to this methodology,we demonstrated an interactive dynamic holographic Tetris game system that allows interactive gameplay,color display,and on-the-fly hologram creation.Our technology presents an inspiration for advanced dynamic meta-holography,which is promising for a broad range of applications including advanced human-computer interaction,real-time 3D visualization,and next-generation virtual and augmented reality systems.

Resilience-incorporated seismic risk assessment of precast concrete frames with“dry”connections

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.

Defining the We-map Reference Frames and Providing Mathematical Expressions for Transformation Relations

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.

Experimental and numerical study regarding H-steel all-bolted connection steel frame with composite wall boards

H-steel all-bolted connection steel frame structures with heat preservation and decoration composite wall boards were investigated and the seismic performances of three scaled specimens were studied.The failure modes,hysteresis curves,bearing capacity,ductility,energy dissipation capacity,stiffness degradation and strain distribution were discussed.The calculation method of structural theoretical internal force was presented.The results showed that the overall structural seismic performance was better,and the structural ductility met the demands of elastic-plastic inter-story drift angle for seismic design.The H-steel weak-axis connection structure obtained better energy dissipation capacity,and its bearing capacity and stiffness were slightly different from the strong-axis connection.The heat preservation and decoration performance of composite wallboard and the all-bolted connection of the steel frame realized prefabrication during the whole construction period.The plastic hinge of the steel beam can be moved outwards because of the L-angles,which effectively avoids stress concentration in joint areas and expands the plastic hinge range.The errors between the theoretical structural capacity calculated by the plastic analysis method and the test results were within 2.44%.In addition,structural failure mechanisms and bearing capacities were verified by the finite element(FE)analysis,and the effects of the main parameters on the structures were investigated.The FE verification results were the same as in the test.The research results provide theoretical support and technical guidance for the application of thermal insulation and decorative composite wall panels in H-shaped steel all-bolted steel frames.

Evaluation of the seismic behavior of reinforced concrete structures with flat slab-column gravity frame and shear walls through nonlinear analysis methods

This paper presents an investigation of the seismic behavior of reinforced concrete(RC)structures in which shear walls are the main lateral load-resisting elements and the participation of flat slab floor systems is not considered in the seismic design procedure.In this regard,the behavior of six prototype structures(with different heights and plan layouts)is investigated through nonlinear static and time history analyses,implemented in the OpenSees platform.The results of the analyses are presented in terms of the behavior of the slab-column connections and their mode of failure at different loading stages.Moreover,the global response of the buildings is discussed in terms of some parameters,such as lateral overstrength due to the gravity flat slab-column frames.According to the nonlinear static analyses,in structures in which the slab-column connections were designed only for gravity loads,the slab-column connections exhibited a punching mode of failure even in the early stages of loading.However,the punching failure was eliminated in structures in which a minimum transverse reinforcement recommended in ACI 318(2019)was provided in the slabs at joint regions.Furthermore,despite neglecting the contribution of gravity flat slab-column frames in the lateral load resistance of the structures,a relatively significant overstrength was imposed on the structures by the gravity frames.

Field Load Test Based SHM System Safety Standard Determination for Rigid Frame Bridge

The deteriorated continuous rigid frame bridge is strengthened by external prestressing. Static loading tests wereconducted before and after the bridge rehabilitation to verify the effectiveness of the rehabilitation process. Thestiffness of the repaired bridge is improved, and the maximum deflection of the load test is reduced from 37.9 to27.6 mm. A bridge health monitoring system is installed after the bridge is reinforced. To achieve an easy assessmentof the bridge’s safety status by directly using transferred data, a real-time safety warning system is createdbased on a five-level safety standard. The threshold for each safety level will be determined by theoretical calculationsand the outcomes of static loading tests. The highest risk threshold will be set at the ultimate limit statevalue. The remaining levels, namely middle risk, low risk, and very low risk, will be determined usingreduction coefficients of 0.95, 0.9, and 0.8, respectively.

Frame Length Dependency for Fundamental Frequency Extraction in Noisy Speech

The fundamental frequency plays a significant part in understanding and perceiving the pitch of a sound. The pitch is a fundamental attribute employed in numerous speech-related works. For fundamental frequency extraction, several algorithms have been developed which one to use relies on the signal’s characteristics and the surrounding noise. Thus, the algorithm’s noise resistance becomes more critical than ever for precise fundamental frequency estimation. Nonetheless, numerous state-of-the-art algorithms face struggles in achieving satisfying outcomes when confronted with speech recordings that are noisy with low signal-to-noise ratio (SNR) values. Also, most of the recent techniques utilize different frame lengths for pitch extraction. From this point of view, This research considers different frame lengths on male and female speech signals for fundamental frequency extraction. Also, analyze the frame length dependency on the speech signal analytically to understand which frame length is more suitable and effective for male and female speech signals specifically. For the validation of our idea, we have utilized the conventional autocorrelation function (ACF), and state-of-the-art method BaNa. This study puts out a potent idea that will work better for speech processing applications in noisy speech. From experimental results, the proposed idea represents which frame length is more appropriate for male and female speech signals in noisy environments.

Real-Time Mosaic Method of Aerial Video Based on Two-Stage Key Frame Selection Method

A two-stage automatic key frame selection method is proposed to enhance stitching speed and quality for UAV aerial videos. In the first stage, to reduce redundancy, the overlapping rate of the UAV aerial video sequence within the sampling period is calculated. Lagrange interpolation is used to fit the overlapping rate curve of the sequence. An empirical threshold for the overlapping rate is then applied to filter candidate key frames from the sequence. In the second stage, the principle of minimizing remapping spots is used to dynamically adjust and determine the final key frame close to the candidate key frames. Comparative experiments show that the proposed method significantly improves stitching speed and accuracy by more than 40%.

远程开放教育中移动学习的接受与学习体验探究——基于COI和FRAME综合模式的考察

随着智能手机的普及、移动互联网的发展和云平台的应用,移动学习已成为我国远程开放教育普遍采用的学习形式,移动学习的接受和学习体验成为亟待研究的课题。本研究借鉴西方移动学习理论,通过批判性综合探究社区理论(COI)和移动学习理性分析框架(FRAME),进行问卷调查。结果表明,远程开放教育移动学习的教学设计需要充分考虑设备维度的限制,加强内容碎片化和输入方式多元化设计,增强移动学习交流与互信,提升合作学习探究效果,加强导学课或线上学习素养课的实施。远程开放教育需要面对新的移动社会的变化,持续思考,更新、优化、整合教育系统,以进一步激发学习者在移动学习中发挥、利用、实现自己的潜能。

Improved Video Steganography with Dual Cover Medium,DNA and Complex Frames

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.

一种基于模板匹配的芯片Frame图像分割算法

针对背景复杂、边界模糊以及芯片相连等特征的芯片Frame图像,提出了一种基于模板匹配的芯片Frame图像分割算法。首先,对整幅芯片Frame图像预分割出多个区域模块;然后,基于区域模块图像采取模板匹配算法匹配单芯片图像;最后,通过合并单芯片的重叠匹配框并记录合并框的坐标信息的方式分割出单芯片图像。实验结果表明:选取合适的模板和阈值,能使该算法的分割准确率达到100%,并且比不基于区域模块匹配的分割算法节省了至少45.76%的分割时间,满足芯片Frame高精度和高速度的分割需求,为芯片图像分割算法的研究提供了一种新思路。

Regularization by Multiple Dual Frames for Compressed Sensing Magnetic Resonance Imaging With Convergence Analysis

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.

CHARACTEIZATIONS OF WOVENT g-FRAMES AND WEAVING g-FRAMES IN HILBERT SPACESS AND C^(*)-MODULES

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.

Experimental and Numerical Study on Progressive Collapse Analysis of a Glulam Frame Structure:I.Side Column Exposed to Fire

This paper presents experimental and numerical investigations on progressive collapse behavior of a two-story glulam frame when the side column is exposed to ISO834 standard fire.The collapse mechanism initiated by fire is identified.The experimental results show that the progressive collapse of a glulam frame could be described for three stages,namely bending effect stage,catenary effect stage and failure stage,respectively.These stages are discussed in detail to understand the structural behavior before and during collapse.It is demonstrated that the entire frame slopes towards the side of the heated column,and the“overturning”collapse occurs eventually.The catenary effect of beams is the main reason for the progressive collapse of the frame.In addition,a finite element model of a glulam frame is established to simulate the progressive collapse behavior.The effects of axial loads on the columns are summarized.The numerical simulation results agree well with the experimental results,which could verify the effectiveness and practicability of finite element simulation.Furthermore,the progressive collapse resistance of the frame in practical design were proposed.

Video Frame Prediction by Joint Optimization of Direct Frame Synthesis and Optical-Flow Estimation

Video prediction is the problem of generating future frames by exploiting the spatiotemporal correlation from the past frame sequence.It is one of the crucial issues in computer vision and has many real-world applications,mainly focused on predicting future scenarios to avoid undesirable outcomes.However,modeling future image content and object is challenging due to the dynamic evolution and complexity of the scene,such as occlusions,camera movements,delay and illumination.Direct frame synthesis or optical-flow estimation are common approaches used by researchers.However,researchers mainly focused on video prediction using one of the approaches.Both methods have limitations,such as direct frame synthesis,usually face blurry prediction due to complex pixel distributions in the scene,and optical-flow estimation,usually produce artifacts due to large object displacements or obstructions in the clip.In this paper,we constructed a deep neural network Frame Prediction Network(FPNet-OF)with multiplebranch inputs(optical flow and original frame)to predict the future video frame by adaptively fusing the future object-motion with the future frame generator.The key idea is to jointly optimize direct RGB frame synthesis and dense optical flow estimation to generate a superior video prediction network.Using various real-world datasets,we experimentally verify that our proposed framework can produce high-level video frame compared to other state-ofthe-art framework.

Global Optimization Method to Comprise Rotation-Minimizing Euler-Rodrigues Frames of Pythagorean-Hodograph Curve

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.

Characteristics and C-E Translation Methods of the Four-Character Frame in the Subtitles of the Documentary Daming Palace

This paper studies the four-character frame in the subtitle of the documentary Daming Palace, aiming to provide a reference for the translation of the documentary four-character case as well as better spread Chinese culture. By analyzing, researching and summarizing the subtitle of Daming Palace and reading a lot of literature, the author has found that in Daming Palace the four-character frame is characterized by the use of the absolute four-character frames and the recurrence of some four-character frames, and that C-E translation methods of the four-character frame are mainly literal translation, free translation, provincial translation and concise translation.

High-Order Method with Moving Frames to Compute the Covariant Derivatives of Vectors on General 2D Curved Surfaces

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.