Matrix Form Research Articles

Energy decomposition analysis method using density matrix formulation.

In this work, an energy decomposition analysis (EDA) method with the strategy of density matrix, called DM-EDA, is proposed on the basis of single reference electronic structure calculations. Different from traditional EDA methods, instead of an intermediate state wave function, the EDA terms in DM-EDA are expressed in the forms of the density matrix. This method can be carried out with various kinds of density matrices. With the efficient implementation, DM-EDA not only greatly improves the computational efficiency but also provides quantitative knowledge of intermolecular interactions with a large number of monomers.

Synchronization of delayed stochastic reaction–diffusion Hopfield neural networks via sliding mode control

Synchronization of stochastic reaction–diffusion Hopfield neural networks with s-delays via sliding mode control is investigated in this article. To begin with, we choose suitable functional space for state variables, then the system is transformed into a functional differential equation in an infinite-dimensional Hilbert space by using appropriate functional analysis technique. Based on above preliminary preparation, sliding mode control (SMC) is constructed to drive the error trajectory into the designed switching surface. Specifically, the switching surface is constructed as linear combination of state variables, which is related to control gains. Then novel SMC law is designed which involving delay, reaction diffusion term, and reaching law. Furthermore, the criterion of mean-square exponential synchronization for stochastic delayed reaction–diffusion Hopfield neural networks with s-delays is given in the form of matrix form. This criterion is less restrictive and easy to check in computer. Meanwhile, a different novel Lyapunov–Krasovskii functional (LKF) mixed with Itô’s formula, Young inequality, Hanalay inequality is employed in this proof procedure. At last, a numerical example is presented to validate the availability of theoretical result. The simulation is based on the finite difference method, and numerical result coincides with the theoretical result proposed.

The Numerical Solutions of weakly singular Fredholm integral equations of the Second kind Using Chebyshev Polynomials of the Second Kind

In this study, the second kind Chebyshev Polynomials were utilized to acquire interpolated solutions for the second kind Fredholm integral equations with weakly singular kernel. To accomplish this, the data, unknown, and kernel functions were converted into matrix form, and consequently we completely isolated the singularity of the kernel. The primary benefit of this method is the ability to change the form of integral equation to an equivalent algebraic system, which is easier to solve. The effectiveness of our technique was evaluated by applying it to three illustrated examples, and it was observed that the solutions obtained exhibit strong convergence towards the exact solutions.

The Role of Tenascin-C on the Structural Plasticity of Perineuronal Nets and Synaptic Expression in the Hippocampus of Male Mice.

Neuronal plasticity is a crucial mechanism for an adapting nervous system to change. It is shown to be regulated by perineuronal nets (PNNs), the condensed forms of the extracellular matrix (ECM) around neuronal bodies. By assessing the changes in the number, intensity, and structure of PNNs, the ultrastructure of the PNN mesh, and the expression of inhibitory and excitatory synaptic inputs on these neurons, we aimed to clarify the role of an ECM glycoprotein, tenascin-C (TnC), in the dorsal hippocampus. To enhance neuronal plasticity, TnC-deficient (TnC-/-) and wild-type (TnC+/+) young adult male mice were reared in an enriched environment (EE) for 8 weeks. Deletion of TnC in TnC-/- mice showed an ultrastructural reduction of the PNN mesh and an increased inhibitory input in the dentate gyrus (DG), and an increase in the number of PNNs with a rise in the inhibitory input in the CA2 region. EE induced an increased inhibitory input in the CA2, CA3, and DG regions; in DG, the change was also followed by an increased intensity of PNNs. No changes in PNNs or synaptic expression were found in the CA1 region. We conclude that the DG and CA2 regions emerged as focal points of alterations in PNNs and synaptogenesis with EE as mediated by TnC.

A general method for twin element analysis and its application in Cu–Zn–Al shape memory alloys with M18R martensite

Twins play a crucial role in elucidating the structure and deformation characteristics of materials. However, in materials with low-symmetry crystal structures, solving the twin relationships remains a challenging task. In this study, we propose a general method for determining twin elements K1, η1, K2, and η2, which are essential for twin analysis. The proposed method involves three main steps: (1) representing misorientation data measured by electron back-scattered diffraction (EBSD) and transmission electron microscopy (TEM) in matrix form, (2) identifying additional 180° rotation elements related to twin elements K1 or η1 by traversing all symmetrically equivalent misorientations, and (3) using a minimum and crystal structure-dependent uniform shear as the constraint to determine the other twin elements (K2andη2). By combining the experimental data and the proposed method, we systematically analyze the complex twin relationships of Cu–Zn–Al shape memory alloys (SMAs) with monoclinic martensite (M18R). This methodology has been demonstrated to be effective and possesses broad applicability.

Computing a compact local Smith–McMillan form

We define a compact local Smith–McMillan form of a rational matrix R ( λ ) as the diagonal matrix whose diagonal elements are the nonzero entries of a local Smith-McMillan form of R ( λ ) . We show that a recursive rank search procedure, applied to a block-Toeplitz matrix built on the Laurent expansion of R ( λ ) around an arbitrary complex point λ 0 , allows us to compute a compact local Smith-McMillan form of that rational matrix R ( λ ) at the point λ 0 , provided we keep track of the transformation matrices used in the rank search. It also allows us to recover the root polynomials of a polynomial matrix and root vectors of a rational matrix, at an expansion point λ 0 . Numerical tests illustrate the promising performance of the resulting algorithm.

Direction-of-Arrival Estimation via Sparse Bayesian Learning Exploiting Hierarchical Priors with Low Complexity.

For direction-of-arrival (DOA) estimation problems in a sparse domain, sparse Bayesian learning (SBL) is highly favored by researchers owing to its excellent estimation performance. However, traditional SBL-based methods always assign Gaussian priors to parameters to be solved, leading to moderate sparse signal recovery (SSR) effects. The reason is Gaussian priors play a similar role to l2 regularization in sparsity constraint. Therefore, numerous methods are developed by adopting hierarchical priors that are used to perform better than Gaussian priors. However, these methods are in straitened circumstances when multiple measurement vector (MMV) data are adopted. On this basis, a block-sparse SBL method (named BSBL) is developed to handle DOA estimation problems in MMV models. The novelty of BSBL is the combination of hierarchical priors and block-sparse model originating from MMV data. Therefore, on the one hand, BSBL transfers the MMV model to a block-sparse model by vectorization so that Bayesian learning is directly performed, regardless of the prior independent assumption of different measurement vectors and the inconvenience caused by the solution of matrix form. On the other hand, BSBL inherited the advantage of hierarchical priors for better SSR ability. Despite the benefit, BSBL still has the disadvantage of relatively large computation complexity caused by high dimensional matrix operations. In view of this, two operations are implemented for low complexity. One is reducing the matrix dimension of BSBL by approximation, generating a method named BSBL-APPR, and the other is embedding the generalized approximate message passing (GAMB) technique into BSBL so as to decompose matrix operations into vector or scale operations, named BSBL-GAMP. Moreover, BSBL is able to suppress temporal correlation and handle wideband sources easily. Extensive simulation results are presented to prove the superiority of BSBL over other state-of-the-art algorithms.

Thermoelastic wave scattering by a multi-layered object

In this work the scattering of time-harmonic thermoelastic waves by a multi-layered thermoelastic body is considered. The mathematical formulation of the scattering problem is presented in a unified four-dimensional form. Using the thermoelastic analogue of Betti's identity, the transmission conditions and asymptotic analysis in the dyadic fundamental solution of thermoelasticity, an integral representation of the scattered field as well as formulas of the thermoelastic far-field patterns containing the physical parameters of the scatterer's layers are constructed. Via the Rellich's Lemma for vector fields, the Helmholtz decomposition of thermoelastic waves and the Kupradze's radiation conditions, uniqueness of solution is proved. Setting the solution to be a linear combination of single- and double- layer thermoelastic potentials and using their jump relations, the scattering problem is transformed into a system of integral equations written in a matrix form. Using the regularity properties of the potentials and the Riesz-Fredholm's theory existence of solution is obtained.

Inverse Estimation of Thermal Contact Resistance Between Two Layers of Cylindrical Wall

This study presents a method for estimating the space-dependent thermal contact resistance between the two-layer walls of a furnace using the boundary element method (BEM) and conjugate gradient method (CGM) for the heat conduction problem. The global solution equation in matrix form is derived using the interface conditions, and the BEM is used to solve the direct problem. The CGM minimizes the objective function and calculates the sensitivity coefficients with the complex variable derivation method (CVDM). Comparative results show that the present approach is more accurate, stable, and efficient than the conventional CGM, which is attributed to the calculation of the sensitivity coefficients by CVDM. The effects of the value of thermal contact resistance, thermal conductivity ratio, Biot number, initial guess, measurement error, and the number and position of measurement points on the inversion results are also analyzed. Finally, the effectiveness of this approach is demonstrated through numerical examples, and the inversion results show its stability, efficiency, and accuracy in identifying different and complex distributions of thermal contact resistance. Furthermore, this approach is feasible for nonintrusive measurement, which is very meaningful in practical applications.

Low-complexity GFDM transmission scheme for low earth orbit satellite communications

As a promising multi-carrier modulation scheme, Generalized Frequency Division Multiplexing (GFDM) has certain advantages in low earth orbit satellite communications. However, the cost of GFDM to obtain these advantages is the self-interference caused by non-orthogonality and the increase of computational complexity. This paper proposes two low-complexity transceiver schemes for GFDM based on matrix sparsity. Firstly, the paper summarizes two GFDM modulation structures, referred to as structure types I and II, based on modulation data. Next, the modulation matrix in both structures is divided into sub-matrices, and the modulation sub-matrix is made sparse by leveraging the properties of the Fourier transform, so as to reduce the complexity of the transmitter. Similarly, by performing sparse processing on the received matrix and converting it into a block diagonal matrix form, the complexity of the receiver can be effectively reduced. The computational costs of our proposed schemes are analyzed in detail and compared with the existing solutions that are known to have the lowest complexity. The simulation results demonstrate that the two proposed schemes can provide satisfactory low-complexity performance depending on the time–frequency structure.

Extraction of Emergency Elements and Business Process Model of Urban Rail Transit Plans

The emergency plan of the urban rail transit (URT) system is a guiding document for dealing with emergencies and formulating emergency plans. However, the emergency plan text described in natural language has some problems, such as poor visibility and enforceability. Effective help is difficult to provide for the rapid implementation of emergency response. Therefore, obtaining key emergency task information from the emergency response plan and visualizing the emergency disposal workflow are the main challenges. In this article, we propose a method of extracting emergency elements (EELs) from emergency plans and constructing a business process model. First, a nested entity extraction model incorporating adversarial training is proposed to extract EELs from the complex sentences in the emergency plan text. Second, the EELs are combined into emergency task units, and then the relations between emergency task units are identified to form the emergency task sequence flow, which is stored in matrix form. Finally, the emergency disposal workflow model is generated based on the emergency task sequence flow and the BPMN modeling method. Taking the actual emergency plan text as an example, the process from the extraction of EELs to the construction of the disposal workflow model is demonstrated. Experimental results prove that this method has advantages in comprehensively extracting EELs, visualizing the emergency disposal workflow, and improving the enforceability of emergency plans.

Online Magneto-Thermal Coupled Model of PMECCs Using Measured Boundaries

Online modeling of the magneto-thermal coupled field (MCF) in permanent magnet eddy current couplings (PMECCs) has long been challenging since it exists in the copper layer and cannot be directly measured. This article proposes an online magneto-thermal coupled model (OMCM) to reconstruct the MCF using measured boundaries. The magnetic field (MF), eddy current field (ECF), and temperature field (TF) in the MCF are coupled in an identical space-time united discretization system. Virtual boundary nodes are added to the system, which can adapt to different boundary conditions in electromagnetic and thermal analysis. The measured data of single-point sensors are spanned to continuous boundary conditions. An approximate solution of the MCF is derived based on the measured boundaries and the general solutions of Laplace's equation and Poisson's equation in magneto-thermal analysis. The three-dimensional distribution of the MF, ECF, and TF at each spatial node and time segment can be simultaneously calculated in matrix form by the OMCM. Furthermore, the output torque is estimated and compared with the conventional methods. A verification process is carried out to assess the reconstructed results, showing that the OMCM can yield results close to the verification sensors for various slips and air gaps.

Dynamic Event-Triggered Synchronization of Markov Jump Neural Networks via Sliding Mode Control.

This article proposes an asynchronous and dynamic event-based sliding mode control strategy to efficiently address the synchronization problem of Markov jump neural networks. By designing an adaptive law, and a triggered threshold in the form of a diagonal matrix, a special dynamic event-triggered scheme is applied to send the control signals only at triggered moments. An asynchronous sliding mode controller with gain uncertainty is designed by constructing a specified sliding manifold. Then, linear matrix inequalities are used to represent sufficient conditions for guaranteeing system synchronization. The error system trajectories are pushed onto the sliding surface by the controller. Eventually, the availability of the presented control strategy is demonstrated by an illustrative example.

Using the State Space Method for Calculating Electromechanical Transients

The state space method is widely used for the analysis and synthesis of automatic control systems in a wide variety of industries. It was revealed that the analysis of electromechanical processes in electrical systems is associated with the solution of a system of nonlinear differential equations by very laborious mathematical methods. It is shown how to represent a system of differential equations describing electromechanical transients in synchronous machines in d, q, 0 – coordinates, in matrix form. An algorithm for calculating electromechanical transients by the state space method is considered. The transit matrix of states is represented by a decomposition formula, the terms of which are determined by matrices with constant elements. Comparison with known numerical calculation methods allows us to conclude that the state space method is a fairly effective way to analyze electromechanical transients in synchronous machines.

RANKING METHOD OF A TEAM OF SCIENTISTS BY THEIR PUBLICATION ACTIVITY IN SCIENTIFIC JOURNALS OF QUARTILE SYSTEMATICS AND INDEXED IN RSCI DATABASE

The article offers a more complex and effective method of assessing the publication activity of scientists in comparison with existing algorithms for the formation of the Hirsch index and its modifications. The method involves structuring all published works of the scientist and their citations, as well as a mathematical description of the algorithm of index construction. The results of the scientist’s publication activities are structured using the matrix form of recording statistical raw data from the RSCI (Russian Science Citation Index). The index algorithm is based on summing all publications and citations, taking into account the weight of journals and the number of authors. The weight of the journals in which the articles are published and links to them are set depending on their quartiles. The method allows, with the help of the proposed complex index, to establish the ratings of scientists in their teams.

Technology independent optimization when implementing sparse systems of disjunctive normal forms of Boolean functions in ASIC

Objectives. The problem of choosing the best methods and programs for circuit implementation as part of digital ASIC (Application-Specific Integrated Circuit) sparse systems of disjunctive normal forms (DNF) of completely defined Boolean functions is considered. For matrix forms of sparse DNF systems, the ternary matrix specifying elementary conjunctions contains a large proportion of undefined values corresponding to missing literals of Boolean input variables, and the Boolean matrix specifying the occurrences of conjunctions in DNF functions contains a large proportion of zero values.Methods. It is proposed to investigate various methods of technologically independent logical optimization performed at the first stage of logical synthesis: joint minimization of systems of functions in the DNF class, separate and joint minimization in classes of multilevel representations in the form of Boolean networks and BDD representations using mutually inverse cofactors, as well as the division of a system of functions into subsystems with a limited number of input variables and the method of block cover of DNF systems, focused on minimizing the total area of the blocks forming the cover.Results. When implementing sparse DNF systems of Boolean functions in ASIC, along with traditional methods of joint minimization of systems of functions in the DNF class, methods for optimizing multilevel representations of Boolean function systems based on Shannon expansions can be used for technologically independent optimization, while separate minimization and joint minimization of the entire system as a whole turn out to be less effective compared with block partitions and coatings of the DNF system and subsequent minimization of multilevel representations. Schemes obtained as a result of synthesis using minimized representations of Boolean networks often have a smaller area than schemes obtained using minimized BDD representations.Conclusion. For the design of digital ASIC, the effectiveness of combined approach is shown, when initially the block coverage programs of the DNF system is used, followed by the use of programs to minimize multilevel block representations in the form of Boolean networks minimized based on Shannon expansion.

ЭНЕРГЕТИЧЕСКИЕ СВОЙСТВА СИММЕТРИЧНЫХ ДЕФОРМИРУЕМЫХ СИСТЕМ

Energy methods for calculating structures, which have become popular for a century, are based on the Lagrange principle and have the meaning of equality of work of external forces and internal forces. Having proved their effectiveness in the overwhelming majority of problems of structural mechanics, they became the dominant approach in formulating the problems of studying solid deformable systems and gave rise to the main methodology for solving problems. As a result, a situation has arisen that the internal potential energy of a deformed body remains insufficiently studied.
 The paper develops an approach to the study of the symmetric structure at critical levels of strain energy. The criterion of critical levels of strain energy, based on the concepts of "self-stress" ("self-balance") of a deformable body. Limiting values of the structure strain energy may get by varying the reactions and deflections in the nodal points. The extreme values of forces and displacements of the rods are calculated in matrix form from the values of nodal reactions (displacements).
 Methodology for studying the energy properties of a system is shown on the examples of the study of symmetric rod systems without involving the concept of external forces. The technique is based on matrix methods of structural mechanics and the mathematical apparatus of eigenvalue problems. The comparison of structural design and structural analysis solution of structural mechanics tasks by traditional methods and with the proposed methodology is carried out.

The Role of Network Topology on Electro‐Thermal and Optical Characteristics of Transparent Thermal Heaters Based on Embedded Random Metallic Mesh

AbstractTransparent thermal heaters based on metallic networks have gained considerable attention in the last few years as a result of their superior response time, low sheet resistance, and low cost of manufacturing. To increase the mechanical stability and reliability of the thermal heater, it is desirable to embed the metallic network in some form of matrix. Embedding the network, however, changes the nature of thermal conduction making both in‐plane and out‐of‐plane thermal conduction important for ensuring reliability and uniform thermal distribution. The performance of embedded thermal heaters is also significantly influenced by the geometry of the metallic network, both in terms of optical transparency and thermal performance. In this paper, a coupled electro‐thermal model and an electromagnetic model are developed to investigate the properties of an embedded metallic mesh in a polymer matrix. Infrared thermal imaging and ultraviolet‐visible spectrophotometry are used to quantify thermal transport and transparency in the system and to verify the performance of finite element models. A systematic study is then performed to assess the role of network topology both on in‐plane and out‐of‐plane thermal distribution and optical performance. According to numerical analysis, a structure‐property relationship is established which can provide desirable network configurations to optimize performance.

Inverse dynamics analysis of a 6-RR-RP-RR parallel manipulator with offset universal joints

AbstractThis paper presents an algorithm for solving the inverse dynamics of a parallel manipulator (PM) with offset universal joints (RR–joints) via the Newton–Euler method. The PM with RR–joints increase the joint stiffness and enlarge the workspace but introduces additional joint parameters and constraint torques, rendering the dynamics more complex. Unlike existing studies on PMs with RR–joints, which emphasize the kinematics and joint performance, this paper studies the dynamical model. First, an iterative algorithm is established through a rigid body velocity transformation, which calculates the input parameters of the link velocity and acceleration. A linear system of equations in matrix form is then established for the entire PM through the Newton–Euler method. By using the generalized minimal residual method (GMRES) to solve the equation system, all the forces and torques on the joints can be obtained, from which the required actuation force can be derived. This method is validated through numerical simulations using the automatic dynamic analysis of multibody systems software. The proposed method is suitable for establishing the dynamic model of complex PMs with redundant or hybrid structures.

A unified impact response analysis for FG-CNTRC and 3D-GrF sandwich composite sector- rectangular coupled plates

This paper proposes a general method for analyzing the dynamic response characteristics of sector- rectangular coupled plates subjected to external impacts. This method combines the method of reverberation-ray matrix (MRRM) with the strip transfer function method, referred to as the strip method of reverberation-ray matrix (S-MRRM). The traditional MRRM has some limitations for the dynamic modeling of the sector structure and also requires the Lévy-type exact solution, leading to simply supported boundary conditions in certain direction of the structure. The present method can not only address the aforementioned limitations but also maintain the efficiency advantage of the wave method for solution. The investigated structure consists of sandwich panels composed of functionally graded carbon nanotube reinforced (FG-CNTRC) panels and the three-dimensional graphene foam (3D-GrF) core. The structure is discretized into several strip elements by the strip transfer function method, and the whole dynamic model of the structure is obtained through matrix assembly. The motion differential equation in matrix form is derived by using Hamilton principle, followed by obtaining the matrix-form wave number equation. Upon deriving the wave solution of the structure based on this equation, the transient and steady-state responses of the structure are obtained by employing MRRM. Convergence analysis is conducted on these calculation results, followed by comparison with FEM results to validate its prediction accuracy. Finally, through a comprehensive parametric study, the impacts of various factors such as CNTs distribution form, CNTs volume fraction, 3D-GrF pore distribution form, 3D-GrF porosity, and sandwich panel thickness ratio on both transient and steady-state responses of these structures were investigated, thereby providing guidance for engineering applications.