Search results for: Hankel matrices

Authors: Ivan Baravy

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Interpolation problem, as it was initially posed in terms of polynomials, is well researched. However, further mathematical developments extended it significantly. Trigonometric interpolation is widely used in Fourier analysis, while its generalized representation as exponential interpolation is applicable to such problem of mathematical physics as modelling of Ziegler-Biersack-Littmark repulsive interatomic potentials. Formulated for finite fields, this problem arises in decoding Reed--Solomon codes. This paper shows the relation between different interpretations of the problem through the class of matrices of special structure - Hankel matrices.

Keywords: Berlekamp-Massey algorithm, exponential interpolation, finite fields, Hankel matrices, Hankel polynomials

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Authors: Celina Pestano-Gabino, Concepcion Gonzalez-Concepcion, M. Candelaria Gil-Fariña

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Some estimation methods for VARMA models, and Multivariate Time Series Models in general, rely on the use of a Hankel matrix. It is known that if the data sample is populous enough and the dimension of the Hankel matrix is unnecessarily large, this may result in an unnecessary number of computations as well as in numerical problems. In this sense, the aim of this paper is two-fold. First, we provide some theoretical results for these matrices which translate into a lower dimension for the matrices normally used in the algorithms. This contribution thus serves to improve those methods from a numerical and, presumably, statistical point of view. Second, we have chosen an estimation algorithm to illustrate in practice our improvements. The results we obtained in a simulation of VARMA models show that an increase in the size of the Hankel matrix beyond the theoretical bound proposed as valid does not necessarily lead to improved practical results. Therefore, for future research, we propose conducting similar studies using any of the linear system estimation methods that depend on Hankel matrices.

Keywords: covariances Hankel matrices, Kronecker indices, system identification, VARMA models

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Authors: Brando Vagenende, Marie-Anne Guerry

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For stochastic matrices of any order, the geometric description of the convex set of eigenvalues is completely known. The purpose of this study is to investigate the subset of the monotone matrices. This type of matrix appears in contexts such as intergenerational occupational mobility, equal-input modeling, and credit ratings-based systems. Monotone matrices are stochastic matrices in which each row stochastically dominates the previous row. The monotonicity property of a stochastic matrix can be expressed by a nonnegative lower-order matrix with the same eigenvalues as the original monotone matrix (except for the eigenvalue 1). Specifically, the aim of this research is to focus on the properties of eigenvalues of monotone matrices. For those matrices up to order 3, there already exists a complete description of the convex set of eigenvalues. For monotone matrices of order at least 4, this study gives, through simulations, more insight into the geometric description of their eigenvalues. Furthermore, this research treats in a geometric and algebraic way the properties of eigenvalues of monotone matrices of order at least 4.

Keywords: eigenvalues of matrices, finite Markov chains, monotone matrices, nonnegative matrices, stochastic matrices

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Authors: Manideepa Saha, Jahnavi Chakrabarty

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Generalized Jacobi (GJ) and Generalized Gauss-Seidel (GGS) methods are most effective than conventional Jacobi and Gauss-Seidel methods for solving linear system of equations. It is known that GJ and GGS methods converge for strictly diagonally dominant (SDD) and for M-matrices. In this paper, we study the convergence of GJ and GGS converge for symmetric positive definite (SPD) matrices, L-matrices and H-matrices. We introduce a generalization of successive overrelaxation (SOR) method for solving linear systems and discuss its convergence for the classes of SDD matrices, SPD matrices, M-matrices, L-matrices and for H-matrices. Advantages of generalized SOR method are established through numerical experiments over GJ, GGS, and SOR methods.

Keywords: convergence, Gauss-Seidel, iterative method, Jacobi, SOR

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Authors: Qinyi Mei, Li-Ping Wang

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MDS matrices are of great significance in the design of block ciphers and hash functions. In the present paper, we investigate the problem of constructing MDS matrices which are both lightweight and low-latency. We propose a new method of constructing lightweight MDS matrices using circulant matrices which can be implemented efficiently in hardware. Furthermore, we provide circulant MDS matrices with as few bit XOR operations as possible for the classical dimensions 4 × 4, 8 × 8 over the space of linear transformations over finite field F42 . In contrast to previous constructions of MDS matrices, our constructions have achieved fewer XORs.

Keywords: linear diffusion layer, circulant matrix, lightweight, maximum distance separable (MDS) matrix

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Authors: Ric Joseph R. Murillo, Edna N. Gueco, Dennis I. Merino

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Let F be C or R, where C and R are the set of complex numbers and real numbers, respectively, and n be a natural number. An n-by-n matrix A over the field F is called an α-involutory matrix or an α-involution if there exists an α in the field such that the square of the matrix is equal to αI, where I is the n-by-n identity matrix. If α is a complex number or a nonnegative real number, then an n-by-n matrix A over the field F can be written as a sum of n-by-n α-involutory matrices over the field F if and only if the trace of that matrix is an integral multiple of the square root of α. Meanwhile, if α is a negative real number, then a 2n-by-2n matrix A over R can be written as a sum of 2n-by-2n α-involutory matrices over R if and only the trace of the matrix is zero. Some other properties of α-involutory matrices are also determined

Keywords: α-involutory Matrices, sum of α-involutory Matrices, Trace, Matrix Theory

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Authors: Divyesh Patel, Tanuja Srivastava

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This paper considers the NP-hard problem of reconstructing binary matrices satisfying exactly-1-4-adjacency constraint from its row and column projections. This problem is formulated into a maximization problem. The objective function gives a measure of adjacency constraint for the binary matrices. The maximization problem is solved by the simulated annealing algorithm and experimental results are presented.

Keywords: discrete tomography, exactly-1-4-adjacency, simulated annealing, binary matrices

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Authors: Jose D. Herrera, Mario A. Rios

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This paper deals with the coordinated tuning of the Power System Stabilizer (PSS) controller and Power Oscillation Damping (POD) Controller of Flexible AC Transmission System (FACTS) in a multi-machine power systems. The coordinated tuning is based on the critical eigenvalues of the power system and a model reduction technique where the Hankel Singular Value method is applied. Through the linearized system model and the parameter-constrained nonlinear optimization algorithm, it can compute the parameters of both controllers. Moreover, the parameters are optimized simultaneously obtaining the gains of both controllers. Then, the nonlinear simulation to observe the time response of the controller is performed.

Keywords: electromechanical oscillations, power system stabilizers, power oscillation damping, hankel singular values

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Authors: Anuj Abraham, N. Pappa, Daniel Honc, Rahul Sharma

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In this paper, an analysis of some model order reduction techniques is presented. A new hybrid algorithm for model order reduction of linear time invariant systems is compared with the conventional techniques namely Balanced Truncation, Hankel Norm reduction and Dominant Pole Algorithm (DPA). The proposed hybrid algorithm is known as Clustering Dominant Pole Algorithm (CDPA) is able to compute the full set of dominant poles and its cluster center efficiently. The dominant poles of a transfer function are specific eigenvalues of the state space matrix of the corresponding dynamical system. The effectiveness of this novel technique is shown through the simulation results.

Keywords: balanced truncation, clustering, dominant pole, Hankel norm, model reduction

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Authors: Dariusz Jacek Jakóbczak

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Mathematics and computer science are interested in methods of 2D curve interpolation and extrapolation using the set of key points (knots). A proposed method of Hurwitz- Radon Matrices (MHR) is such a method. This novel method is based on the family of Hurwitz-Radon (HR) matrices which possess columns composed of orthogonal vectors. Two-dimensional curve is interpolated via different functions as probability distribution functions: polynomial, sinus, cosine, tangent, cotangent, logarithm, exponent, arcsin, arccos, arctan, arcctg or power function, also inverse functions. It is shown how to build the orthogonal matrix operator and how to use it in a process of curve reconstruction.

Keywords: 2D data interpolation, hurwitz-radon matrices, MHR method, probabilistic modeling, curve extrapolation

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Authors: K. M. Aldossari, W. A. Elsaigh, M. J. Shannag

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An experimental study was conducted to investigate the effect of hooked-end steel fibers on the flexural behavior of normal and high strength concrete matrices. The fiber content appropriate for the concrete matrices investigated was also determined based on flexural tests on standard prisms. Parameters investigated include: Matrix compressive strength ranging from 45 MPa to 70 MPa, corresponding to normal and high strength concrete matrices respectively; Fiber volume fraction including 0, 0.5%, 0.76%, and 1%, equivalent to 0, 40, 60, and 80 kg/m3 of hooked-end steel fibers respectively. Test results indicated that flexural strength and toughness of normal and high strength concrete matrices were significantly improved with the increase in the fiber content added; Whereas a slight improvement in compressive strength was observed for the same matrices. Furthermore, the test results indicated that the effect of increasing the fiber content was more pronounced on increasing the flexural strength of high strength concrete than that of normal concrete.

Keywords: concrete, flexural strength, toughness, steel fibers

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Authors: Yang Zhong, Meijie Xue

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The purpose of this paper is to investigate the stresses and excess pore fluid pressure induced by the moving wheel pressure on saturated asphalt pavements, which is one of the reasons for a damage phenomenon in flexible pavement denoted stripping. The saturated asphalt pavement is modeled as multilayered poroelastic half space exerted by a wheel pressure, which is moving at a constant velocity along the surface of the pavement. The governing equations for the proposed analysis are based on the Biot’s theory of dynamics in saturated poroelastic medium. The governing partial differential equations are solved by using Laplace and Hankel integral transforms. The solutions for the stresses and excess pore pressure are expressed in the forms of numerical inversion Laplace and Hankel integral transforms. The numerical simulation results clearly demonstrate the induced deformation and water flow in the asphalt pavement.

Keywords: saturated asphalt pavements, moving loads, excess pore fluid pressure, stress of pavement, biot theory, stress and strain of pavement

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Authors: Emine Tuğba Akyüz

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In this study, the analysis of Hadamard matrices, which is a special type of matrix, was made under three headings: norms, singular values, condition number. Six norm types was applied to Hadamard matrices and the relationship between the results and the size of the matrix has been studied. As a result of the investigation when 2-norm was used on the problem Hx =f, the equation ‖x‖_2= ‖f‖_2/√n was shown (H is n-dimensional Hadamard matrix). Related with this, the relationship between the the singular value of H and 2-norm and eigenvalues was shown. Then, the evaluation of condition number for Hx =f was made.

Keywords: condition number, Hadamard matrix, norm, singular value

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Authors: Malika Yaici, Kamel Hariche

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In control engineering, systems described by matrix fractions are studied through properties of block roots, also called solvents. These solvents are usually dealt with in a block Vandermonde matrix form. Inverses and determinants of Vandermonde matrices and block Vandermonde matrices are used in solving problems of numerical analysis in many domains but require costly computations. Even though Vandermonde matrices are well known and method to compute inverse and determinants are many and, generally, based on interpolation techniques, methods to compute the inverse and determinant of a block Vandermonde matrix have not been well studied. In this paper, some properties of these matrices and iterative algorithms to compute the determinant and the inverse of a block Vandermonde matrix are given. These methods are deducted from the partitioned matrix inversion and determinant computing methods. Due to their great size, parallelization may be a solution to reduce the computations cost, so a parallelization of these algorithms is proposed and validated by a comparison using algorithmic complexity.

Keywords: block vandermonde matrix, solvents, matrix polynomial, matrix inverse, matrix determinant, parallelization

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Authors: Mostafa Shahriari, Sergio Rojas, David Pardo, Angel Rodriguez- Rozas, Shaaban A. Bakr, Victor M. Calo, Ignacio Muga

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Logging-While Drilling (LWD) is a technique to record down-hole logging measurements while drilling the well. Nowadays, LWD devices (e.g., nuclear, sonic, resistivity) are mostly used commercially for geo-steering applications. Modern borehole resistivity tools are able to measure all components of the magnetic field by incorporating tilted coils. The depth of investigation of LWD tools is limited compared to the thickness of the geological layers. Thus, it is a common practice to approximate the Earth’s subsurface with a sequence of 1D models. For a 1D model, we can reduce the dimensionality of the problem using a Hankel transform. We can solve the resulting system of ordinary differential equations (ODEs) either (a) analytically, which results in a so-called semi-analytic method after performing a numerical inverse Hankel transform, or (b) numerically. Semi-analytic methods are used by the industry due to their high performance. However, they have major limitations, namely: -The analytical solution of the aforementioned system of ODEs exists only for piecewise constant resistivity distributions. For arbitrary resistivity distributions, the solution of the system of ODEs is unknown by today’s knowledge. -In geo-steering, we need to solve inverse problems with respect to the inversion variables (e.g., the constant resistivity value of each layer and bed boundary positions) using a gradient-based inversion method. Thus, we need to compute the corresponding derivatives. However, the analytical derivatives of cross-bedded formation and the analytical derivatives with respect to the bed boundary positions have not been published to the best of our knowledge. The main contribution of this work is to overcome the aforementioned limitations of semi-analytic methods by solving each 1D model (associated with each Hankel mode) using an efficient multi-scale finite element method. The main idea is to divide our computations into two parts: (a) offline computations, which are independent of the tool positions and we precompute only once and use them for all logging positions, and (b) online computations, which depend upon the logging position. With the above method, (a) we can consider arbitrary resistivity distributions along the 1D model, and (b) we can easily and rapidly compute the derivatives with respect to any inversion variable at a negligible additional cost by using an adjoint state formulation. Although the proposed method is slower than semi-analytic methods, its computational efficiency is still high. In the presentation, we shall derive the mathematical variational formulation, describe the proposed multi-scale finite element method, and verify the accuracy and efficiency of our method by performing a wide range of numerical experiments and comparing the numerical solutions to semi-analytic ones when the latest are available.

Keywords: logging-While-Drilling, resistivity measurements, multi-scale finite elements, Hankel transform

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Authors: Ali N. Suri, Ahmad A. Al-Makhlufi

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In this paper the problem of buckling of plates on foundation of finite length and with different side support is studied. The Finite Strip Method is used as tool for the analysis. This method uses finite strip elastic, foundation, and geometric matrices to build the assembly matrices for the whole structure, then after introducing boundary conditions at supports, the resulting reduced matrices is transformed into a standard Eigenvalue-Eigenvector problem. The solution of this problem will enable the determination of the buckling load, the associated buckling modes and the buckling wave length. To carry out the buckling analysis starting from the elastic, foundation, and geometric stiffness matrices for each strip a computer program FORTRAN list is developed. Since stiffness matrices are function of wave length of buckling, the computer program used an iteration procedure to find the critical buckling stress for each value of foundation modulus and for each boundary condition. The results showed the use of elastic medium to support plates subject to axial load increase a great deal the buckling load, the results found are very close with those obtained by other analytical methods and experimental work. The results also showed that foundation compensates the effect of the weakness of some types of constraint of side support and maximum benefit found for plate with one side simply supported the other free.

Keywords: buckling, finite strip, different sides support, plates on foundation

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Authors: Khosrow Maleknejad, Yaser Rostami

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In this paper, semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions.

Keywords: ıntegro-differential equations, quartic B-spline wavelet, operational matrices, dual functions

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Authors: Damir Latypov

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A hybrid classical-quantum algorithm to solve boundary integral equations (BIE) arising in problems of electromagnetic and acoustic scattering is proposed. The quantum speed-up is due to a Quantum Linear System Algorithm (QLSA). The original QLSA of Harrow et al. provides an exponential speed-up over the best-known classical algorithms but only in the case of sparse systems. Due to the non-local nature of integral operators, matrices arising from discretization of BIEs, are, however, dense. A QLSA for dense matrices was introduced in 2017. Its runtime as function of the system's size N is bounded by O(√Npolylog(N)). The run time of the best-known classical algorithm for an arbitrary dense matrix scales as O(N².³⁷³). Instead of exponential as in case of sparse matrices, here we have only a polynomial speed-up. Nevertheless, sufficiently high power of this polynomial, ~4.7, should make QLSA an appealing alternative. Unfortunately for the QLSA, the asymptotic separability of the Green's function leads to high compressibility of the BIEs matrices. Classical fast algorithms such as Multilevel Fast Multipole Method (MLFMM) take advantage of this fact and reduce the runtime to O(Nlog(N)), i.e., the QLSA is only quadratically faster than the MLFMM. To be truly impactful for computational electromagnetics and acoustics engineers, QLSA must provide more substantial advantage than that. We propose a computational scheme which combines elements of the classical fast algorithms with the QLSA to achieve the required performance.

Keywords: quantum linear system algorithm, boundary integral equations, dense matrices, electromagnetic scattering theory

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Authors: D. Mehdizadeh, M. Rahimian, M. Eskandari-Ghadi

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This article is concerned with the determination of the static interaction of a vertically loaded rigid circular disc embedded at the interface of a horizontal layer sandwiched in between two different transversely isotropic half-spaces called as tri-material full-space. The axes of symmetry of different regions are assumed to be normal to the horizontal interfaces and parallel to the movement direction. With the use of a potential function method, and by implementing Hankel integral transforms in the radial direction, the government partial differential equation for the solely scalar potential function is transformed to an ordinary 4th order differential equation, and the mixed boundary conditions are transformed into a pair of integral equations called dual integral equations, which can be reduced to a Fredholm integral equation of the second kind, which is solved analytically. Then, the displacements and stresses are given in the form of improper line integrals, which is due to inverse Hankel integral transforms. It is shown that the present solutions are in exact agreement with the existing solutions for a homogeneous full-space with transversely isotropic material. To confirm the accuracy of the numerical evaluation of the integrals involved, the numerical results are compared with the solutions exists for the homogeneous full-space. Then, some different cases with different degrees of material anisotropy are compared to portray the effect of degree of anisotropy.

Keywords: transversely isotropic, rigid disc, elasticity, dual integral equations, tri-material full-space

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Authors: Ahmed Noor Al-qayyim, Barlas Özden Çağlayan

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Structural failure is caused mainly by damage that often occurs on structures. Many researchers focus on obtaining very efficient tools to detect the damage in structures in the early state. In the past decades, a subject that has received considerable attention in literature is the damage detection as determined by variations in the dynamic characteristics or response of structures. This study presents a new damage identification technique. The technique detects the damage location for the incomplete structure system using output data only. The method indicates the damage based on the free vibration test data by using “Two Points - Condensation (TPC) technique”. This method creates a set of matrices by reducing the structural system to two degrees of freedom systems. The current stiffness matrices are obtained from optimization of the equation of motion using the measured test data. The current stiffness matrices are compared with original (undamaged) stiffness matrices. High percentage changes in matrices’ coefficients lead to the location of the damage. TPC technique is applied to the experimental data of a simply supported steel beam model structure after inducing thickness change in one element. Where two cases are considered, the method detects the damage and determines its location accurately in both cases. In addition, the results illustrate that these changes in stiffness matrix can be a useful tool for continuous monitoring of structural safety using ambient vibration data. Furthermore, its efficiency proves that this technique can also be used for big structures.

Keywords: damage detection, optimization, signals processing, structural health monitoring, two points–condensation

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Authors: Jaroslav Krutil, František Pochylý, Simona Fialová, Vladimír Habán

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A mathematical model of the additional effects of the liquid in the hydrodynamic gap is presented in the paper. An in-compressible viscous fluid is considered. Based on computational modeling are determined the matrices of mass, stiffness and damping. The mathematical model is experimentally verified.

Keywords: computational modeling, mathematical model, hydrodynamic gap, matrices of mass, stiffness and damping

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Authors: Daniela Rivera-Tobar Mario Perez-Won, Roberto Lemus-Mondaca, Gipsy Tabilo-Munizaga

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Different dietary trends worldwide seek to consume foods with anti-inflammatory properties, rich in antioxidants, proteins, and unsaturated fatty acids that lead to better metabolic, intestinal, mental, and cardiac health. In this sense, food matrices with high protein content based on macro and microalgae are an excellent alternative to meet the new needs of consumers. An emerging and environmentally friendly technology for producing protein matrices is ultrasonic agglomeration. It consists of the formation of permanent bonds between particles, improving the agglomeration of the matrix compared to conventionally agglomerated products (compression). Among the advantages of this process are the reduction of nutrient loss and the avoidance of binding agents. The objective of this research was to optimize the ultrasonic agglomeration process in matrices composed of Spirulina (Arthrospira platensis) powder and Cochayuyo (Durvillae Antartica) flour, by means of the response variable (Young's modulus) and the independent variables were the process conditions (percentage of ultrasonic amplitude: 70, 80 and 90; ultrasonic agglomeration times and cycles: 20, 25 and 30 seconds, and 3, 4 and 5). It was evaluated using a central composite design and analyzed using response surface methodology. In addition, the effects of agglomeration on thermophysical and microstructural properties were evaluated. It was determined that ultrasonic compression with 80 and 90% amplitude caused conformational changes according to Fourier infrared spectroscopy (FTIR) analysis, the best condition with respect to observed microstructure images (SEM) and differential scanning calorimetry (DSC) analysis, was the condition of 90% amplitude 25 and 30 seconds with 3 and 4 cycles of ultrasound. In conclusion, the agglomerated matrices present good macro and microstructural properties which would allow the design of food systems with better nutritional and functional properties.

Keywords: ultrasonic agglomeration, physical properties of food, protein matrices, macro and microalgae

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Authors: Obaid Algahtani

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An interval may be defined as a convex combination as follows: I=[a,b]={x_α=(1-α)a+αb: α∈[0,1]}. Consequently, we may adopt interval operations by applying the scalar operation point-wise to the corresponding interval points: I ∙J={x_α∙y_α ∶ αϵ[0,1],x_α ϵI ,y_α ϵJ}, With the usual restriction 0∉J if ∙ = ÷. These operations are associative: I+( J+K)=(I+J)+ K, I*( J*K)=( I*J )* K. These two properties, which are missing in the usual interval operations, will enable the extension of the usual linear system concepts to the interval setting in a seamless manner. The arithmetic introduced here avoids such vague terms as ”interval extension”, ”inclusion function”, determinants which we encounter in the engineering literature that deal with interval linear systems. On the other hand, these definitions were motivated by our attempt to arrive at a definition of interval random variables and investigate the corresponding statistical properties. We feel that they are the natural ones to handle interval systems. We will enable the extension of many results from usual state space models to interval state space models. The interval state space model we will consider here is one of the form X_((t+1) )=AX_t+ W_t, Y_t=HX_t+ V_t, t≥0, where A∈ 〖IR〗^(k×k), H ∈ 〖IR〗^(p×k) are interval matrices and 〖W 〗_t ∈ 〖IR〗^k,V_t ∈〖IR〗^p are zero – mean Gaussian white-noise interval processes. This feeling is reassured by the numerical results we obtained in a simulation examples.

Keywords: interval analysis, interval matrices, state space model, Kalman Filter

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Authors: Mustafa Abu Ghalia, Yaser Dahman

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A new class of polyurethane (PU) reinforced with green bacterial cellulose nanofibers (BC) were prepared using a solvent casting method, with the goal of fabricating green nanocomposites. Four series classes of BC (1, 2.5, 5, and 10 wt%) were reinforced into PU matrices via BC surface modification and subsequently BC-grafted into PU throughout silane coupling agent to improve BC dispersion and its interfacial interaction. The experiment results from the tensile tester were evaluated according to the response surface method (RSM) for optimizing the impacts of variable parameters, pore size, porosity, and BC contents on the mechanical properties. The compressive strength for PU-5 BC wt% was about 9.8 MPa, and decrease when being generated prosperity to recorded at 4.9 MPa. Nielson model was applied to investigate the BC stress concentration on the PU matrices. Likewise, krenche and Hapli-Tasi model were employed to evaluate the BC nanofiber reinforcement potential and BC orientation into PU matrices. The analysis of variance (ANOVA) demonstrated that only BC loading has a significant effect in increases tensile strength, young’s modulus, and a flexural modulus of the PU-BC nanocomposites. The optimal factors of the variables experiment confirmed to be 5 wt% for BC, 230 for pore size, and 80 % for porosity. Scanning electron microscopy (SEM) micrographs showed that the uniform distribution of nanofibers in the PU matrices with the addition of BC 5 wt %. Hydrolytic degradation revealed that the weight loss in PU-BC scaffold is higher than PU-BC wt %.

Keywords: polyurethane scaffold, mechanical properties, tissue engineering, polyurethane

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Authors: Hebert Montegranario, Mauricio Londoño

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Solutions of Helmholtz equation are essential in seismic imaging methods like full wave inversion, which needs to solve many times the wave equation. Traditional methods like Finite Element Method (FEM) or Finite Differences (FD) have sparse matrices but may suffer the so called pollution effect in the numerical solutions of Helmholtz equation for large values of the wave number. On the other side, global radial basis functions have a better accuracy but produce full matrices that become unstable. In this research we combine the virtues of both approaches to find numerical solutions of Helmholtz equation, by applying a meshless method that produce sparse matrices by local radial basis functions. We solve the equation with absorbing boundary conditions of the kind Clayton-Enquist and PML (Perfect Matched Layers) and compared with results in standard literature, showing a promising performance by tackling both the pollution effect and matrix instability.

Keywords: Helmholtz equation, meshless methods, seismic imaging, wavefield inversion

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Authors: Silvia Gastaldello, Maria Grillo, Luca Tassoni, Claudio Maran, Stefano Balbo

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Antioxidants are nowadays attractive not only for the countless benefits to the human and animal health, but also for the perspective of use as food preservative instead of synthetic chemical molecules. In this study, the radical scavenging activity of six protein extracts from pulse and oleaginous seeds was evaluated. The selected matrices are Pisum sativum (yellow pea from two different origins), Carthamus tinctorius (safflower), Helianthus annuus (sunflower), Lupinus luteus cv Mister (lupin) and Glycine max (soybean), since they are economically interesting for both human and animal nutrition. The seeds were grinded and proteins extracted from 20mg powder with a specific vegetal-extraction kit. Proteins have been quantified through Bradford protocol and scavenging activity was revealed using DPPH assay, based on radical DPPH (2,2-diphenyl-1-picrylhydrazyl) absorbance decrease in the presence of antioxidants molecules. Different concentrations of the protein extract (1, 5, 10, 50, 100, 500 µg/ml) were mixed with DPPH solution (DPPH 0,004% in ethanol 70% v/v). Ascorbic acid was used as a scavenging activity standard reference, at the same six concentrations of protein extracts, while DPPH solution was used as control. Samples and standard were prepared in triplicate and incubated for 30 minutes in dark at room temperature, the absorbance was read at 517nm (ABS30). Average and standard deviation of absorbance values were calculated for each concentration of samples and standard. Statistical analysis using t-students and p-value were performed to assess the statistical significance of the scavenging activity difference between the samples (or standard) and control (ABSctrl). The percentage of antioxidant activity has been calculated using the formula [(ABSctrl-ABS30)/ABSctrl]*100. The obtained results demonstrate that all matrices showed antioxidant activity. Ascorbic acid, used as standard, exhibits a 96% scavenging activity at the concentration of 500 µg/ml. At the same conditions, sunflower, safflower and yellow peas revealed the highest antioxidant performance among the matrices analyzed, with an activity of 74%, 68% and 70% respectively (p < 0.005). Although lupin and soybean exhibit a lower antioxidant activity compared to the other matrices, they showed a percentage of 46 and 36 respectively. All these data suggest the possibility to use undervalued edible matrices as antioxidants source. However, further studies are necessary to investigate a possible synergic effect of several matrices as well as the impact of industrial processes for a large-scale approach.

Keywords: antioxidants, DPPH assay, natural matrices, vegetal proteins

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Authors: Sonia Kudlacik-Kramarczyk, Anna Drabczyk, Dagmara Malina, Bozena Tyliszczak, Agnieszka Sobczak-Kupiec

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Introduction: In the preparation of polymer materials, compounds of natural origin are currently gaining more and more interest. This is particularly noticeable in the case of synthesis of materials considered for biomedical use. Then, selected material has to meet many requirements. It should be characterized by non-toxicity, biodegradability and biocompatibility. Therefore special attention is directed to substances such as polysaccharides, proteins or substances that are the basic building components of proteins, i.e. amino acids. These compounds may be crosslinked with other reagents that leads to the preparation of polymer matrices. Such amino acids as e.g. cysteine or histidine. On the other hand, previously mentioned requirements may be met by polymers obtained as a result of biosynthesis, e.g. polyhydroxybutyrate. This polymer belongs to the group of aliphatic polyesters that is synthesized by microorganisms (selected strain of bacteria) under specific conditions. It is possible to modify matrices based on given polymer with substances of various origin. Such a modification may result in the change of their properties or/and in providing the material with new features desirable in viewpoint of specific application. Described materials are synthesized using UV radiation. Process of photopolymerization is fast, waste-free and enables to obtain final products with favorable properties. Methodology: Polymer matrices have been prepared by means of photopolymerization. First step involved the preparation of solutions of particular reagents and mixing them in the appropriate ratio. Next, crosslinking agent and photoinitiator have been added to the reaction mixture and the whole was poured into the Petri dish and treated with UV radiation. After the synthesis, polymer samples were dried at room temperature and subjected to the numerous analyses aimed at the determining their physicochemical properties. Firstly, sorption properties of obtained polymer matrices have been determined. Next, mechanical properties have been characterized, i.e. tensile strength. The ability to deformation under applied stress of all prepared polymer matrices has been checked. Such a property is important in viewpoint of the application of analyzed materials e.g. as wound dressings. Wound dressings have to be elastic because depending on the location of the wound and its mobility, such a dressing has to adhere properly to the wound. Furthermore, considering the use of the materials for biomedical purposes it is essential to determine its behavior in environments simulating these ones occurring in human body. Therefore incubation studies using selected liquids have also been conducted. Conclusions: As a result of photopolymerization process, polymer matrices based on natural compounds have been prepared. These exhibited favorable mechanical properties and swelling ability. Moreover, biocompatibility in relation to simulated body fluids has been stated. Therefore it can be concluded that analyzed polymer matrices constitute an interesting materials that may be considered for biomedical use and may be subjected to the further more advanced analyses using specific cell lines.

Keywords: photopolymerization, polymer matrices, simulated body fluids, swelling properties

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Authors: Somveer Singh, Vineet Kumar Singh

Abstract:

We present a new model based on viscoelasticity for the Non-Newtonian fluids.We use a matrix formulated algorithm to approximate solutions of a class of partial integro-differential equations with the given initial and boundary conditions. Some numerical results are presented to simplify application of operational matrix formulation and reduce the computational cost. Convergence analysis, error estimation and numerical stability of the method are also investigated. Finally, some test examples are given to demonstrate accuracy and efficiency of the proposed method.

Keywords: Legendre Wavelets, operational matrices, partial integro-differential equation, viscoelasticity

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Authors: Archana Sharma, Vijayashree Nayak, Ashok Kumar

Abstract:

Three-dimensional matrices were fabricated from blend of natural-natural polymers like carrageenan-gelatin and synthetic -natural polymers such as PEG- gelatin (PEG of different molecular weights (2,000 and 6,000) using two different crosslinkers; glutaraldehyde and EDC-NHS by cryogelation technique. Blends represented a feasible approach to design 3-D scaffolds with controllable mechanical, physical and biochemical properties without compromising biocompatibility and biodegradability. These matrices possessed interconnected porous structure, good mechanical strength, biodegradable nature, constant swelling kinetics, ability to withstand high temperature and visco-elastic behavior. Hemocompatibility of cryogel matrices was determined by coagulation assays and hemolytic activity assay which demonstrated that these cryogels have negligible effects on coagulation time and have excellent blood compatibility. In vitro biocompatibility (cell-matrix interaction) inferred good cell adhesion, proliferation, and secretion of ECM on matrices. These matrices provide a microenvironment for the growth, proliferation, differentiation and secretion of ECM of different cell types such as IMR-32, C2C12, Cos-7, rat bone marrow derived MSCs and human bone marrow MSCs. Hoechst 33342 and PI staining also confirmed that the cells were uniformly distributed, adhered and proliferated properly on the cryogel matrix. An ideal scaffold used for tissue engineering application should allow the cells to adhere, proliferate and maintain their functionality. Neurotransmitter analysis has been done which indicated that IMR-32 cells adhered, proliferated and secreted neurotransmitters when they interacted with these matrices which showed restoration of their functionality. The cell-matrix interaction up to molecular level was also evaluated so to check genotoxicity and protein expression profile which indicated that these cryogel matrices are non-genotoxic and maintained biofunctionality of cells growing on these matrices. All these cryogels, when implanted subcutaneously in balb/c mice, showed no adverse systemic or local toxicity effects at implantation site. There was no significant increase in inflammatory cell count has otherwise been observed after scaffold implantation. These cryogels are supermacroporous and this porous structure allows cell infiltration and proliferation of host cells. This showed the integration and presence of infiltrated cells into the cryogel implants. Histological analysis confirmed that the implanted cryogels do not have any adverse effect in spite of host immune system recognition at the site of implantation, on its surrounding tissues and other vital host organs. In vivo biocompatibility study after in vitro biocompatibility analysis has also concluded that these synthesized cryogels act as important biological substitutes, more adaptable and appropriate for transplantation. Thus, these cryogels showed their potential for soft tissue engineering applications.

Keywords: cryogelation, hemocompatibility, in vitro biocompatibility, in vivo biocompatibility, soft tissue engineering applications

Procedia PDF Downloads 189

Authors: Somveer Singh, Vineet Kumar Singh

Abstract:

This work contributes a numerical method based on Legendre wavelet approximation for the treatment of partial integro-differential equation (PIDE). Operational matrices of Legendre wavelets reduce the solution of PIDE into the system of algebraic equations. Some useful results concerning the computational order of convergence and error estimates associated to the suggested scheme are presented. Illustrative examples are provided to show the effectiveness and accuracy of proposed numerical method.

Keywords: legendre wavelets, operational matrices, partial integro-differential equation, viscoelasticity

Procedia PDF Downloads 401