Convex Reconstruction of Structured Matrix Signals from Linear Measurements:Theoretical Results

The problem of reconstructing n-by-n structured matrix signal X=(x1,...,xn)via convex optimization is investigated,where each column xj is a vector of s-sparsity and all columns have the same l1-norm value.In this paper,the convex programming problem was solved with noise-free or noisy measurements.The uniform sufficient conditions were established which are very close to necessary conditions and non-uniform conditions were also discussed.In addition,stronger conditions were investigated to guarantee the reconstructed signal’s support stability,sign stability and approximation-error robustness.Moreover,with the convex geometric approach in random measurement setting,one of the critical ingredients in this contribution is to estimate the related widths’bounds in case of Gaussian and non-Gaussian distributions.These bounds were explicitly controlled by signal’s structural parameters r and s which determined matrix signal’s column-wise sparsity and l1-column-flatness respectively.This paper provides a relatively complete theory on column-wise sparse and l1-column-flat matrix signal reconstruction,as well as a heuristic foundation for dealing with more complicated high-order tensor signals in,e.g.,statistical big data analysis and related data-intensive applications.

Robust signal recovery algorithm for structured perturbation compressive sensing

It is understood that the sparse signal recovery with a standard compressive sensing（CS） strategy requires the measurement matrix known as a priori. The measurement matrix is, however, often perturbed in a practical application.In order to handle such a case, an optimization problem by exploiting the sparsity characteristics of both the perturbations and signals is formulated. An algorithm named as the sparse perturbation signal recovery algorithm（SPSRA） is then proposed to solve the formulated optimization problem. The analytical results show that our SPSRA can simultaneously recover the signal and perturbation vectors by an alternative iteration way, while the convergence of the SPSRA is also analytically given and guaranteed. Moreover, the support patterns of the sparse signal and structured perturbation shown are the same and can be exploited to improve the estimation accuracy and reduce the computation complexity of the algorithm. The numerical simulation results verify the effectiveness of analytical ones.

Systematic Elastostatic Stiffness Model of Over-Constrained Parallel Manipulators Without Additional Constraint Equations

The establishment of an elastostatic stiffness model for over constrained parallel manipulators(PMs),particularly those with over constrained subclosed loops,poses a challenge while ensuring numerical stability.This study addresses this issue by proposing a systematic elastostatic stiffness model based on matrix structural analysis(MSA)and independent displacement coordinates(IDCs)extraction techniques.To begin,the closed-loop PM is transformed into an open-loop PM by eliminating constraints.A subassembly element is then introduced,which considers the flexibility of both rods and joints.This approach helps circumvent the numerical instability typically encountered with traditional constraint equations.The IDCs and analytical constraint equations of nodes constrained by various joints are summarized in the appendix,utilizing multipoint constraint theory and singularity analysis,all unified within a single coordinate frame.Subsequently,the open-loop mechanism is efficiently closed by referencing the constraint equations presented in the appendix,alongside its elastostatic model.The proposed method proves to be both modeling and computationally efficient due to the comprehensive summary of the constraint equations in the Appendix,eliminating the need for additional equations.An example utilizing an over constrained subclosed loops demonstrate the application of the proposed method.In conclusion,the model proposed in this study enriches the theory of elastostatic stiffness modeling of PMs and provides an effective solution for stiffness modeling challenges they present.

Quantum and classical correlations for a two-qubit X structure density matrix

We derive explicit expressions for quantum discord and classical correlation for an X structure density matrix. Based on the characteristics of the expressions, the quantum discord and the classical correlation are easily obtained and compared under different initial conditions using a novel analytical method. We explain the relationships among quantum discord, classical correlation, and entanglement, and further find that the quantum discord is not always larger than the entanglement measured by concurrence in a general two-qubit X state. The new method, which is different from previous approaches, has certain guiding significance for analysing quantum discord and classical correlation of a two-qubit X state, such as a mixed state.

EFFECT OF NITROGEN ON MATRIX STRUCTURE OF GRAY CAST IRON

Effect of nitrogen on matrix structure of 3 different varieties of gray cast iron,i.e., sub-eutectic Fe-C-Si,near-eutectic Fe-C-Si and Fe-C-Si-Mn,has been investigated. The eutectie colony structure of gray cast iron may be refined,the pearlite content increased and the micro-hardness of pearlite and ferrite raised with an addition of nitrogen.The influ- ence of nitrogen on the transformation temperature of the equilibrium and non-equilibrium phases,as well as,the solution of nitrogen in ferrite and cementite seem to be the major rea- sons to strengthening the matrix structure of gray cast iron.

Structure of Hamiltonian Matrix and the Shape of Eigenfunctions：Nuclear Octupole Deformation Model

The structure of a Hamiltonian matrix for a quantum chaotic system, the nuclear octupole deformation model, has been discussed in detail. The distribution of the eigenfunctions of this system expanded by the eigenstates of a quantum integrable system is studied with the help of generalized Brillouin?Wigner perturbation theory. The results show that a significant randomness in this distribution can be observed when its classical counterpart is under the strong chaotic condition. The averaged shape of the eigenfunctions fits with the Gaussian distribution only when the effects of the symmetry have been removed.

A Matrix-Based Approach for Sustainability in Product Design

The paper proposes a matrix-based approach that a designer can use to evaluate the sustainability of one or more design solutions in the conceptual phase of a product development process. The methodology is structured in two main phases. In the first one, a data structure, called Augmented-DSM （Design Structure Matrix）, has to be drawn in order to collect design information such as functional links among product components, indicators that provide information about the life cycle of each element, connections with the environment and toward other systems. The matrix is based on a DSM format, where new records were introduced to store and organize different types of data and an editing protocol was formalized. In the second stage, a set of procedures have to be applied in order to evaluate sustainability of a design solution and compare it with the others. The presented procedures, in fact, allow designers to assess a product in its proper characteristics, evaluate a device during its use stage and verify the coherence of links present in the functional model. This new approach is conceived to manage different performance indicators and, as a support tool, it is an attempt to aid designers in a quantitative evaluation.

Schedule Model for Project Portfolio Based on Design Structure Matrix

To improve the enterprise resource utilization and shorten the cycle of the whole project portfolio, a scheduling model based on Design Structure Matrix （DSM） is built. By setting the project activity weight index system and calculating the activity weight for the project portfolio, the constraint relationship between project portfolio information and resource utilization, as the two dimensions of the DSM, are fully reflected in the sched- ule model to determine the order of these activities of project portfolio. A project portfolio example is given to il- lustrate the applicability and effectiveness of the schedule model.

An Efficient CPE Preconditioner for Cyclic Structured Matrices

A new cyclic pseudo-elimination(CPE,in brief)preconditioner,which combines the pseudoelimination(PE)technique and LU factorization together,is proposed for a kind of cyclic structured matrices.For the case of M-matrices,some theoretical results of convergence and estimation of the condition number are presented.Numerical experiments show that the CPE preconditioner performs the best with respect to the reduction of number of iterations.Moreover,it costs much less time than the ILUT and block Jacobi(BJ)preconditioners in a whole in all tested cases.

Microstructure and Mechanical Performance of Cu-SnO_2-rGO based Composites Prepared by Plasma Activated Sintering

A novel chemical technique combined with unique plasma activated sintering（PAS） was utilized to prepare consolidated copper matrix composites（CMCs） by adding Cu-SnO2-rGO layered micro powders as reinforced fillers into Cu matrix. The repeating Cu-SnO2-rGO structure was composed of inner dispersed reduced graphene oxide（r GO）, SnO2 as intermedia and outer Cu coating. SnO2 was introduced to the surface of rGO sheets in order to prevent the graphene aggregation with SnO2 serving as spacer and to provide enough active sites for subsequent Cu deposition. This process can guarantee rGO sheets to suffi ciently disperse and Cu nanoparticles to tightly and uniformly anchor on each layer of rGO by means of the SnO2 active sites as well as strictly control the reduction speed of Cu^2＋. The complete cover of Cu nanoparticles on rGO sheets thoroughly avoids direct contact among rGO layers. Hence, the repeating structure can simultaneously solve the wettability problem between rGO and Cu matrix as well as improve the bonding strength between rGO and Cu matrix at the well-bonded Cu-SnO2-rGO interface. The isolated rGO can effectively hinder the glide of dislocation at Cu-rGO interface and support the applied loads. Finally, the compressive strength of CMCs was enhanced when the strengthening effi ciency reached up to 41.

Effect of Different Conditions on the Structural Color of Konjac Glucomannan Particles

In this paper,molecular dynamics simulation was applied to synthesize a layered structural color from Konjac glucomannan（KGM） and the effect of particle diameter and temperature were investigated. A series of methods such as high voltage electric field treatment,the transfer matrix method and the CIE standard colorimetric system were simulated to obtain the chromaticity coordinates and to analyze the color changes of KGM particles. The results revealed that as the particle diameter increases,the structural color of KGM particles deflects towards the yellow wavelength within the visible spectrum; and as the reaction temperature rises,the structural color deflects towards the blue and violet wavelengths within the visible spectrum.

Study on DSM-based task planning of product cooperative development

The results of analyzing the managerial characteristics and complexity of product cooperative development suggest that task planning is an important aspect for process management of product cooperative development and the method for planning tasks should be able to model the dependency between tasks and iterations during the development process. In this paper, a DSM-based method and its corresponding optimization algorithms are developed. At first the coupled task sets and uncoupled task sets are identified, and the tasks are then optimized by the corresponding algorithms. The optimal tasks plan will reduce the development time and cost. Considering the practical requirements in real world, a Multilayer DSM is proposed, and its information communication techniques between DSM and traversing principle are described in details.

Conceptual Design Process for LEO Satellite Constellations Based on System Engineering Disciplines

Satellite design process is an interdisciplinary subject in which the need for collaboration among various science and engineering disciplines is evident.Meanwhile,finding an optimal process for conceptual design of a satellite,which can optimize time and cost,is still an important issue.In this paper,based on system engineering approach,an optimal design process is proposed for LEO satellite constellations.In the proposed method,design process,design sequences,and data flow are established.In this regard,the conceptual design process is divided into two levels of mission(or constellation)and system(or satellite)as well as 15 main activities based on the mission profile,previous experiences of the authors,and existing literature.Then,the relationships between these activities have been determined by considering the importance of relationships according to their priority.Finally,these relations are optimized based on design structure matrix(DSM).By utilizing this approach,system design process of a telecommunication satellite constellation in LEO is formulated in conceptual design phase.Performance and capability of the proposed approach in optimal design process of the satellite constellation are investigated by comparing the outcome with existing results in the literature.

THE THEORY OF STATIC DECAY IN COMPUTATIONAL MECHANICS

In this paper, a new mathematical form, matrix, continued fraction (MCF) is introduced to describe the decay of effects of an equilibrant system of forces acting on a sphere of an elastic body. By this way, the famous Saint-Venant's principle is proved often but not always valid in computational mechanics.

Mill scale structure and damp heat corrosion performance of four 510L hot-rolled strips

In this study, the matrix structure, state and composition of the mill scales of four typical domestically made 510L hot-rolled strips were observed and analyzed by means of optical microscopy （OM） ,scanning electron microscopy （SEM） and X-ray diffraction （XRD）. The corrosion behavior of the steels with and without mill scales were investigated by means of hot-humid corrosion tests under the condition of relative humidity （ RH ） of 95% at 50℃ and 70℃, respectively. The results show that the matrix structures, state, composition and thickness of mill scales vary in the strips. The rusting starting time of the specimens with scales is generally a bit longer than that of the specimens without scales, but their corrosion mass-gain is higher. For these two kinds of specimens ,their corrosion rate increases significantly with the increase of temperature. The rusting behavior of the 510L strips produced by various plants is different due to the variations of hot-rolling processes and designed chemical compositions. Various relevant aspects should be taken into account in the evaluation of the corrosion behavior of hot-rolled strips.

A New Approach to Analyzing Behavioral Change Propagation in Redesigning of Drone Camera Stabilizer

Redesigning of complex products is not an easy task. Engineering change requirements can be extracted at any stage of the product redesign process, and it makes the management of engineering change become a challenging mission. The motivation for this study is to find the shortest path of behavioral change propagation (BCP), minimize the BCP, access to the special behavioral elements in order to better managing the BCP and classifying the behavioral attribute of the elements in terms of their relationship to change by betweenness centrality coefficient (BNCC), clustering coefficient (CLC), reachability coefficient (RC) and change propagation index (CPI). In this article, the procedure of managerial decision-making is proposed by combining system restrictions in behavioral clustering design structure matrix (BCDSM) with optimization algorithms. The practicality of suggested method is verified in redesign procedure of a phantom drone camera stabilizer as a case study. The results, indicate that the absorption of change by behavioral elements is dominant in the mechanical (63.9%), electrical (61.1%) and thermal (38.9%) behaviors of the drone camera stabilizer system in redesign process. These elements are best candidates for reducing the cost and time of behavioral changes in the system redesign and are desirable for the designer.

Structure Evolution of China Aviation Network Based on Hierarchical Model

The annual passenger volume of airport reflected its passenger transport scale and the role in aviation network.The airports in whole country were divided into three layers:first layer airports,second layer airports and third layer airports.The airlines from the first layer airports consisted the first layer aviation network.The airlines from the second layer airports consisted the second layer aviation network.The airlines from the third layer airports consisted the third layer aviation network.The structure and function of different layer aviation network had significant differences.These differences were shown in the number of airlines,average number of airlines of each airport,annual passenger volume of airport and average passenger volume of each airline.National aviation network hierarchical model was constructed to describe the whole country aviation network.The matrix was built to describe the airline number,annual passenger volume,average number of airlines,average passenger volume of each airport and airline rate of aviation network.The index of national aviation network structure was constructed to show the ratio of index between different aviation network layer to describe the aviation network structure.The structure index was built to illustrate the macrostructural features of national aviation network.The statistics data in year 1988,1994,2001,2008 and 2015 of China aviation network were analyzed and basic data matrixes,basic index matrixes and structure index matrixes were calculated.The trend of ratio of corresponding index between the first layer and the second layer showed the change of basic structure of China aviation network.At meantime,the tendency of ratio of corresponding index between the third layer and the second layer also showed the change of basic structure.The trend of network general structure index illustrated that the large scaled new airports and airlines construction had significant influence on the national aviation network structure.

LIE ALGEBRAIC STRUCTURE OF AKNS MATRIX SYSTEM

For an AKNS matrix system,Lie algebraic structure and its mastersymmetry are obtained by a purely algebraic approach;and by using the reduced technique,two similar algebraic structures for MKdV and KdV matrix systems are given.

Analytical Derivations of Single-Particle Matrix Elements in Nuclear Shell Model

We present analytical method to calculate single particle matrix elements used in atomic and nuclear physics. We show seven different formulas of matrix elements of the operator f(r)d_r^m where f(r) = r~μ, r~μjJ(qr), V(r)corresponding to the Gaussian and the Yukawa potentials used in nuclear shell models and nuclear structure. In addition,we take into account a general integral formula of the matrix element 〈 n′ l′|f(r) d_r^(m) |n l〉 that covers all seven matrix elements obtained analytically.

An architecture decomposition method of pneumatic catapult system based on OPM and DSM

The architecture strategy of the Unmanned Aerial Vehicle(UAV)pneumatic launch system should continue to evolve to adapt to complex and variable operating environments.Architecture representation,decomposition perspective,and cluster analysis play a vital role in the early phase of system architecture development.In order for the system to emerge anticipated and desirable intrinsic functional properties,an architecture decomposition method based on the ObjectProcess Methodology(OPM)and Design Structure Matrix(DSM)is put forward in this paper.The OPM is proposed to model the UAV launch process formally,and the matrix representation of the architecture of the pneumatic launch system is established.After the extension of the definition and operations of DSM,with the Idicula-Gutierrez-Thebeau Algorithm plus(IGTA+)clustering algorithm,the transformation of the pneumatic launch system architecture from process decomposition to function decomposition is demonstrated in this paper.The analysis shows that the architecture decomposition of the pneumatic launch system meets the functional requirements of stakeholders.