Elements Of Matrices Research Articles

Data Security System of Text Messaging Based on Android Mobile Devices Using Advanced Encrytion Standard Dynamic S-BOX

Most of the recent technologies are turning to mobile platforms, Android becames one of the most widely used OS. Eventhough it has complete features, even it's not safe enough such like Chat Messenger. The security of messages distribution is a challenge to increase of vulnerable distribution of information through the network today. Therefore, a data security or cryptographic algorithm is needed to secure the messages so that it cannot be read by irresponsible people. National Institute of Standard and Technology (NIST) established the Advanced Encrytion Standard (AES) cryptographic algorithm as a standard encryption algorithm that is safe and can be used globally. AES algorithm is included in block cipher cryptography that uses substitution boxes (S-BOX) in its operations, so that algorithmically can make input and output unrelated. So, it can provide more varied output in the process, we need a dynamic S-BOX. In this research, dynamic S-BOX generalized using XOR operations from affine transformations with 8-bit binary element matrices arranged and randomly to produce as many as 256 S-Boxes. The application of dynamic AES with S-BOX algorithm on Android-based messenger chat application is built using the Java programming language and database hierarchy for data storage. The implementation results showed that the algorithm was running well and could encrypt the text of the message to ciphertext and decrypt the ciphertext to the original message. This research can be used as a reference so that further researchers can merge the AES algorithm with other algorithms to improve the security of encryption in text files, documents, images, videos or other types of files.

FAMILY OF SHAPE PRESERVING FRACTAL-LIKE BÉZIER CURVES

Subdivision schemes generate self-similar curves and surfaces for which it has a familiar connection between fractal curves and surfaces generated by iterated function systems (IFS). Overveld [Comput.-Aided Des. 22(9) (1990) 591–597] proved that the subdivision matrices can be perturbated in such a way that it is possible to get fractal-like curves that are perturbated Bézier cubic curves. In this work, we extend the Overveld scheme to [Formula: see text]th degree curves, and deduce the condition for curvature continuity and convex hull property. We find the conditions for positive preserving fractal-like Bézier curves in the proposed subdivision matrices. The resulting 2D/3D curves from these binary subdivision matrices resemble with fractal images. Finally, the dependence of the shape of these fractal-like curves on the elements of subdivision matrices is demonstrated with suitably chosen examples.

Nonlocal biased random walks and fractional transport on directed networks.

In this paper, we study nonlocal random walk strategies generated with the fractional Laplacian matrix of directed networks. We present a general approach to analyzing these strategies by defining the dynamics as a discrete-time Markovian process with transition probabilities between nodes expressed in terms of powers of the Laplacian matrix. We analyze the elements of the transition matrices and their respective eigenvalues and eigenvectors, the mean first passage times and global times to characterize the random walk strategies. We apply this approach to the study of particular local and nonlocal ergodic random walks on different directed networks; we explore circulant networks, the biased transport on rings and the dynamics on random networks. We study the efficiency of a fractional random walker with bias on these structures. Effects of ergodicity loss which occur when a directed network is not any more strongly connected are also discussed.

Estimating a Change Point in a Sequence of Very High-Dimensional Covariance Matrices

This article considers the problem of estimating a change point in the covariance matrix in a sequence of high-dimensional vectors, where the dimension is substantially larger than the sample size. A two-stage approach is proposed to efficiently estimate the location of the change point. The first step consists of a reduction of the dimension to identify elements of the covariance matrices corresponding to significant changes. In a second step, we use the components after dimension reduction to determine the position of the change point. Theoretical properties are developed for both steps, and numerical studies are conducted to support the new methodology. Supplementary materials for this article are available online.

Development of an equivalent shell finite element for modelling damped multi-layered composite structures

A new equivalent shell finite element (FE) for modelling damped multi-layered structures is presented in this study. The method used for developing the new FE for such structures is based on the idea that the strain energy of the equivalent single-layer FE must be equal to the sum of the strain energies of individual layers. The so-called energy coefficients are defined for this purpose for the extensional, bending and shear deformations of the composite structure. These coefficients are then determined and used as correction multipliers during stacking the elemental matrices of individual layers. Two approaches, based on second-order strain or stress distribution assumption through the composite thickness, are investigated for deriving the shear energy coefficients. The damping capability of the FE developed here originates from using complex Young’s modulus to define the material properties of individual layers. The resulting equivalent single-layer shell element with four nodes has six degrees-of-freedom per node. The accuracy, advantages and limitations of the composite FE developed in this work are investigated using experimental as well as theoretical results. In the light of the finding of these investigations, further enhancement in the formulation is made by also utilising a new shear correction factor for the individual layers in the equivalent shell element. Final results for free- and constrained-layered structures confirm that the equivalent shell FE developed here can be used effectively for the prediction of the modal properties of damped multi-layered structures.

Uncertainty quantification of bladed disc systems using data driven stochastic reduced order models

This study focusses on the development of stochastic reduced order model for probabilistic characterisation of bladed disc systems with random spatial inhomogeneities. High fidelity finite element modelling is used to mathematically model the system. A two step reduction strategy is applied involving reduction in the state space dimension and reduction in the stochastic dimensions. Information of the spatial inhomogeneities are assumed to be available from limited in situ measurements across the spatial extent and are modelled as non-Gaussian random fields. The stochastic version of the finite element matrices are developed using a polynomial chaos based framework, which optimizes the stochastic dimensionality of the problem. The uncertainties in the input propagates through the system into the response, which are also random. Surrogate models for these response quantities are obtained as PCE and are constructed using the method of stochastic collocations. Challenges involved in application of PCE on complex geometrically irregular spatial domains are addressed. The efficacy of the proposed framework is demonstrated through two numerical examples -an academic bladed disc system and an industrial turbine rotor blade.

Nonlinear forced vibration analysis of composite beam combined with DQFEM and IHB

In this paper, a forced vibration model of composite beams under the action of periodic excitation force considering geometric nonlinearity is proposed. For the strain–displacement relationship, Timoshenko beam theory is used, and the element and system matrices are developed using the differential quadrature finite element method. Each node has 3 degrees of freedom. The incremental harmonic balance method is used to solve the nonlinear forced vibration equation. In order to prove the validity of the proposed model, the solution of the Duffing equation is calculated using the analytical method and the proposed method. Next, linear forced vibration analysis of the beam made of isotropic material is performed and compared with the result of ABAQUS. The results are very close. Based on these comparisons, nonlinear vibration phenomena of composite beams are studied under the action of periodic forces.

Exact free vibration analysis for membrane assemblies with general classical boundary conditions

This paper proposes exact dynamic stiffness formulations for membranes and their assemblies under any arbitrary classical boundary conditions. First, by taking exact solutions in one direction satisfying all possible opposite edge supports, we can derive exact general solutions of the Helmholtz equation for membrane vibration. Then, generic force and displacement boundary conditions in the other direction are expressed in terms of the general solutions. Finally, the dynamic stiffness matrices of rectangular membrane elements are formulated, which can be assembled directly and allows applications of arbitrary boundary conditions. As an accurate and efficient modal solution technique, the Wittrick-Williams (WW) algorithm is applied onto the global dynamic stiffness matrix of the final structure. The most important issue of the WW algorithm, J0 count, has been resolved with the analytical expressions derived for all possible cases. The proposed dynamic stiffness method (DSM) is then applied to several examples including individual membranes and their assemblies. High accuracy and exactness of the proposed method within the whole frequency range is demonstrated by comparison with the finite element method. Besides, interesting findings have been observed on repeated eigenvalues with distinct mode shapes corresponding to certain aspect ratio and tension ratio, where physical and mathematical understanding has been provided.

A segregated spectral element method for the 2D transient incompressible Navier-Stokes equations

In this paper, a spectral element method for the solution of the two-dimensional transient incompressible Navier-Stokes equations is introduced, which combines the segregated velocity-pressure equal-order formulation originated from the SIMPLE (semi-implicit method for pressure linked equations) algorithm. In contrast to previous segregated finite element method based on the SIMPLE algorithm, the pressure equation is derived from the momentum and continuity equations using the element matrices to ensure the convergence of the pressure. High-order element basis functions are adopted to construct the discrete form that presents arbitrary order or accuracy. The validation test with analytical solution verifies the high accuracy of the method. The flow in a lid-driven cavity with different inclination angles and the flow over a backward-facing step are investigated to further illustrate the property of the scheme. The computed results are in excellent agreement with the benchmark solutions, even if fewer grid points are used. The almost periodic solution for the flow of Re=10000 in a lid-driven square cavity is also captured by the present scheme. The numerical results indicate that the proposed high-order method can significantly reduce the number of grid points used in the calculation.

GPU-based matrix-free finite element solver exploiting symmetry of elemental matrices

Matrix-free solvers for finite element method (FEM) avoid assembly of elemental matrices and replace sparse matrix-vector multiplication required in iterative solution method by an element level dense matrix-vector product. In this paper, a novel matrix-free strategy for FEM is proposed which computes element level matrix-vector product by using only the symmetric part of the elemental matrices. The proposed strategy is developed to take advantage of the massive parallelism of Graphics Processing Unit (GPU). A unique data structure is also introduced which ensures localized and coalesced memory access suitable for a GPU while storing only the symmetric part of the elemental matrices. In addition, the proposed strategy emphasizes the efficient use of register cache, uniform workload distribution, reducing thread synchronization, and maintaining sufficient granularity to make the best use of GPU resources. The performance of the proposed strategy is evaluated by solving elasticity and heat conduction problems using 4-noded quadrilateral element with two degrees of freedom (DOFs) and one DOF per node, respectively. The performance is compared with the matrix-free solver strategies on GPU from the literature. It is found that a maximum speedup of 4.9 $$\times $$ is obtained for the elasticity problem and a maximum of 3.2 $$\times $$ speedup for the heat conduction problem. Further, the proposed strategy takes the least amount of GPU memory as compared to the existing strategies.

Ternary tree-based structural twin support tensor machine for clustering

Most of the real-life applications usually involve complex data, e.g., grayscale images, where information is distributed spatially in the form of two-dimensional matrices (elements of second-order tensor space). Traditional vector-based clustering models such as k-means and support vector clustering rely on low-dimensional features representations for identifying patterns and are prone to loss of useful information which is present in spatial structure of the data. To overcome this limitation, tensor-based clustering models can be utilized for identifying relevant patterns in matrix data as they take advantage of structural information present in multi-dimensional framework and reduce computational overheads as well. However, despite these numerous advantages, tensor clustering has still remained relatively unexplored research area. In this paper, we propose a novel clustering framework, termed as Ternary Tree-based Structural Least Squares Support Tensor Clustering (TT-SLSTWSTC), that builds a cluster model as a hierarchical ternary tree, where at each node non-ambiguous data are dealt separately from ambiguous data points using the proposed Ternary Structural Least Squares Support Tensor Machine (TS-LSTWSTM). The TS-LSTWSTM classifier considers the structural risk minimization of data alongside a symmetrical L2-norm loss function. Also, initialization framework based on tensor k-means has been used in order to overcome the instability disseminated by random initialization. To validate the efficacy of the proposed framework, computational experiments have been performed on human activity recognition and image recognition problems. Experimental results show that our method is not only fast but yields significantly better generalization performance and is comparatively more robust in order to handle heteroscedastic noise and outliers when compared to related methods.

Extended continuum model for dynamic analysis of beam-like truss structures with geometrical nonlinearity

An approach to extend the application of the continuum model to beam-like lattice truss structures with geometrical nonlinearity is presented in this paper. The geometrical nonlinearity within the truss structures is accounted for by dividing it into substructures and introducing a co-rotational coordinate system to decompose the substructure motion into rigid body motion and pure deformations. The linear continuum model of each substructure is derived using the continuum model based on the small deformation hypothesis in the local coordinate system, in which the deformation of the truss structure is still small. Then, the linear mass and stiffness matrices of the continuum elements are converted into the nonlinear equivalent mass and stiffness matrices for the global coordinate system. The equations of motion for the truss structure are established using Lagrange's equations. Three numerical simulation examples are considered and the results show that the proposed model requires fewer degrees of freedom and has better efficiency than the finite element model based on the truss elements while also obtaining the desired accuracy.

Extending epipolar geometry for real-time structured light illumination

Structured light illumination, scanning along both horizontal and vertical directions, achieves more robust accuracy. By introducing the constraint of epipolar geometry, we previously proposed real-time 3D reconstruction using lookup tables; however, we only knew these offline derived tables were the combinations of the elements in calibration matrices of a camera and a projector, and suffered from long-time computation. In this Letter, by parameterizing the line perspectively mapping a 3D world coordinate into the camera and projector spaces, we propose to extend the epipolar analysis by defining phase and optical poles. Thus, we can geometrically address these parameters via analytic closed-form equations, with which we can (1) directly derive lookup tables in real time from the calibration matrices and (2) optimally reduce the number of tables from 11 to 5 to save much more memory space while further accelerating the processing rate. Experiments show that with the same level of accuracy, we significantly reduce the time to compute the lookup tables from more than 20 min to 20 ms, and increase the speed of computing point clouds from approximately 320 to 492 fps.

Color image compression and encryption scheme based on compressive sensing and double random encryption strategy

Based on compressive sensing and double random encryption strategy, a novel color image compression and encryption scheme is proposed in this paper. The architecture of compression, confusion and diffusion is adopted. Firstly, the red, green and blue components of color plain image are converted to three sparse coefficient matrices by discrete wavelet transform (DWT), and then a double random position permutation (DRPP) is introduced to confuse the coefficient matrices. Subsequently, Logistic-Tent system is utilized to generate the asymptotic deterministic random measurement matrix based on chaotic system and plain image (ADMMCP), which is used to measure the coefficient matrices to obtain measurement value matrices. Moreover, simultaneous double random pixel diffusion between inter-intra components (SDRDIC) is presented to modify the elements of measurement value matrices to obtain the final cipher image. A 4-D hyperchaotic system is applied to produce chaotic sequences for confusion and diffusion, the initial conditions of the used chaotic systems are controlled by the SHA 512 hash value of plain image and external keys, such that the proposed image cryptosystem may withstand known-plaintext and chosen-plaintext attacks. Experimental results and security analyses verify the effectiveness of the proposed cipher.

KHARKIV TEST PLATFORM FOR RESEARCH AND DEVELOPMENT OF Si SPECTROMETRIC PLANAR DETECTORS AND DETECTORS ARRAYS FOR MEDICAL APPLICATION

A universal test platform for research and development of planar radiation detectors for use in medicine has been created having the possibility of obtaining complete information about the characteristics of the detector before creating a detecting module with specialized electronics. 5 jobs were created with the ability to perform the following work: measurement of the electrophysical characteristics of individual detectors and selected detection elements of the matrices based on the station with manual movement of microprobes; determination of the yield of suitable detector elements of matrices using a test station with automated microprobe movement and automated collection and processing of electrophysical measurement data; measurement of the energy resolution (ER) of individual silicon detectors, “scintillator-silicon photosensor” type detectors and measurement of the ER of selected matrix elements before creating a detection module with specialized electronics.

Dynamic analysis of viscoelastic functionally graded porous thick beams under pulse load

Due to the significant effect of porosity on the mechanical response of functionally graded (FG) structures, this paper presents a comprehensive model to investigate the vibration response of FG porous thick beam under the dynamic sine pulse load including the damping effect by using adopted finite element model, for the first time. The multilayer thick beam is modeled as two-dimensional plane stress problem. The distribution of material gradation through the graded layer is described by the power law function, and the porosity is depicted by three different distributions (i.e., symmetric-distribution, X-distribution and O-distribution). The damping effect is included in the model by using the Kelvin–Voigt viscoelastic constitutive model. Constitutive equations, gradation and porosity functions are described in detail. Forced motion equations are derived by using Lagrange energy principles. Twelve-node 2D plane element with 3 × 3 integration points is proposed to discretize the beam and get the element matrices and force vectors. The numerical time integration method of Newmark is proposed to solve the system numerical and get the displacement response of the structure. Effects of layer stacking sequence, material gradation index and porosity parameter on the dynamic’s response of thick FG porous damped beam are presented. The presented mathematical model is useful in analysis and design of nuclear, marine, vehicle and aerospace structures those manufactured from functionally graded materials.

Model-based clustering with determinant-and-shape constraint

Model-based approaches to cluster analysis and mixture modeling often involve maximizing classification and mixture likelihoods. Without appropriate constrains on the scatter matrices of the components, these maximizations result in ill-posed problems. Moreover, without constrains, non-interesting or “spurious” clusters are often detected by the EM and CEM algorithms traditionally used for the maximization of the likelihood criteria. Considering an upper bound on the maximal ratio between the determinants of the scatter matrices seems to be a sensible way to overcome these problems by affine equivariant constraints. Unfortunately, problems still arise without also controlling the elements of the “shape” matrices. A new methodology is proposed that allows both control of the scatter matrices determinants and also the shape matrices elements. Some theoretical justification is given. A fast algorithm is proposed for this doubly constrained maximization. The methodology is also extended to robust model-based clustering problems.

Hydroelastic responses of floating composite plates under moving loads using a hybrid moving element-boundary element method

Responses of floating plates with the impact of moving excitations have been previously studied by several scholars. Generally, such structures were often assumed to be isotropic. Nonetheless, the directional-dependent bending stiffness should be considered for designing practical floating structures, especially for very large floating structures. Accordingly, this article aims to analyze hydroelastic responses of floating composite plates subjected to moving loads for the first time. For this, a novel numerical approach as a combination of boundary element method and moving element method which is named the BEM–MEM is proposed. In the this approach, governing equations of motion, moving element, and fluid matrices are formulated in a relative coordinate system traveling with moving loads. Consequently, the suggested paradigm can effectively eliminate difficulties in addressing the bound of computational domain and tracking the location of contact points which often encounter in the traditional finite element method owing to utilizing a fixed coordinate system. Several numerical examples are exhibited to demonstrate the performance and ability of the boundary element method-moving element method . Gained results are compared with those by the Fourier transform method and the asymptotic expression to verify the accuracy of the proposed methodology. The outcomes indicate that the speed of moving loads considerably affects the plate deflection. In addition, as the speed is larger than the minimum celerity of the free surface of hydroelastic system ( Cmin), the influence of anisotropy on the deflection becomes significant.

An Efficient and Rapid Numerical Quadrature to generate element matrices for quadrilateral and hexahedral elements in Functionally Graded Materials (FGMs)

This research paper introduces a robust, efficient and stabilized midpoint quadrature to generate element stiffness matrices for quadrilateral and hexahedral elements in finite element method (FEM). This new quadrature is established based on Passive Richardson extrapolation which has the inherent ability to stabilize and improve the accuracy of the extrapolated results. The new quadrature includes a simple artificial stabilizing function with Gauss one-point quadrature (1GP) as an anti-hourglass effect. For the first approximation, the 1GP (sampling point to be considered at origin (0,0)) is done to evaluate element matrices (thermal conductivity matrices, capacitance matrices etc.,) in the 4-square element ( [-2, 2] x [-2, 2] ) in the (ξ, η) plane. As a stabilizing function, sampling points are considered to be either at the center of the four element edges or center of the four quadrants in the reference square element with appropriate constant weighting functions. For hexahedral elements also, the element stiffness coefficients are calculated only in the center of the element and center of all the octants of the reference cubic element ([-2, 2] x [-2, 2] x [-2, 2]), the proposed method deals mostly with integer variables and sampling at (0,0,0), whereas Gauss quadrature uses lengthy float variables corresponding to irrational numbers in terms of decimals in the stiffness matrix calculations, thus consuming time. A number of standard example problems are demonstrated to assess the efficiency of the proposed method. The results of all the numerical examples are found to be in good agreement with the exact results and conventional Gauss quadrature results.

A Novel Lyapunov functional with application to stability analysis of neutral systems with nonlinear disturbances

It is well-known that the global asymptotic stability analysis of neutral systems is an important concept in designing the appropriate controllers or filters for this class of systems. This paper carries out a delay-independent stability analysis of neutral systems possessing discrete time delays in the states and discrete neutral delays in the time derivative of the states in the presence of nonlinear disturbances. Some new global asymptotic stability criteria are proposed by introducing a novel Lyapunov functional. The obtained delay-independent stability criteria establish some simple and easily verifiable mathematical expressions involving the elements of the system matrices and the disturbance parameters of the neutral system. Different from the most of the previously reported stability results for neutral systems, the conditions obtained in this paper are not expressed in terms the Linear Matrix Inequalities (LMIs). Therefore, the criteria presented in this paper can be considered as the alternative results to previously published stability results stated in the LMI forms. A comparison between the results of this paper and some of previously published corresponding stability results is made to substantiate the significant improvement of the proposed results. A constructive numerical example is also presented to show applicability and the effectiveness of the proposed stability condition.