Search results for: block linear multistep methods

Authors: J. P. Chollom, G. M. Kumleng, S. Longwap

Abstract:

The search for higher order A-stable linear multi-step methods has been the interest of many numerical analysts and has been realized through either higher derivatives of the solution or by inserting additional off step points, supper future points and the likes. These methods are suitable for the solution of stiff differential equations which exhibit characteristics that place a severe restriction on the choice of step size. It becomes necessary that only methods with large regions of absolute stability remain suitable for such equations. In this paper, high order block implicit multi-step methods of the hybrid form up to order twelve have been constructed using the multi-step collocation approach by inserting one or more off step points in the multi-step method. The accuracy and stability properties of the new methods are investigated and are shown to yield A-stable methods, a property desirable of methods suitable for the solution of stiff ODE’s. The new High Order Block Implicit Multistep methods used as block integrators are tested on stiff differential systems and the results reveal that the new methods are efficient and compete favourably with the state of the art Matlab ode23 code.

Keywords: block linear multistep methods, high order, implicit, stiff differential equations

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Authors: James Adewale, Joshua Sunday

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In this paper, we developed a linear multistep method, which is implemented in predictor corrector-method. The corrector is developed by method of collocation and interpretation of power series approximate solutions at some selected grid points, to give a continuous linear multistep method, which is evaluated at some selected grid points to give a discrete linear multistep method. The predictors were also developed by method of collocation and interpolation of power series approximate solution, to give a continuous linear multistep method. The continuous linear multistep method is then solved for the independent solution to give a continuous block formula, which is evaluated at some selected grid point to give discrete block method. Basic properties of the corrector were investigated and found to be zero stable, consistent and convergent. The efficiency of the method was tested on some linear, non-learn, oscillatory and stiff problems of first order, initial value problems of ordinary differential equations. The results were found to be better in terms of computer time and error bound when compared with the existing methods.

Keywords: predictor, corrector, collocation, interpolation, approximate solution, independent solution, zero stable, consistent, convergent

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Authors: A. M. Sagir

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The aim of this paper is to investigate the performance of the developed linear multistep block method for solving first order initial value problem of Ordinary Differential Equations (ODEs). The method calculates the numerical solution at three points simultaneously and produces three new equally spaced solution values within a block. The continuous formulations enable us to differentiate and evaluate at some selected points to obtain three discrete schemes, which were used in block form for parallel or sequential solutions of the problems. A stability analysis and efficiency of the block method are tested on ordinary differential equations involving practical applications, and the results obtained compared favorably with the exact solution. Furthermore, comparison of error analysis has been developed with the help of computer software.

Keywords: block method, first order ordinary differential equations, linear multistep, self-starting

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Authors: A. A. James, A. O. Adesanya, M. R. Odekunle, D. G. Yakubu

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This paper examines the development of one step, five hybrid point method for the solution of first order initial value problems. We adopted the method of collocation and interpolation of power series approximate solution to generate a continuous linear multistep method. The continuous linear multistep method was evaluated at selected grid points to give the discrete linear multistep method. The method was implemented using a constant order predictor of order seven over an overlapping interval. The basic properties of the derived corrector was investigated and found to be zero stable, consistent and convergent. The region of absolute stability was also investigated. The method was tested on some numerical experiments and found to compete favorably with the existing methods.

Keywords: interpolation, approximate solution, collocation, differential system, half step, converges, block method, efficiency

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Authors: Mohamed Suleiman, Zarina Bibi Ibrahim, Nor Ain Azeany, Khairil Iskandar Othman

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In this paper, a class of variable order fully implicit multistep Block Backward Differentiation Formulas (VOBBDF) using uniform step size for the numerical solution of stiff ordinary differential equations (ODEs) is developed. The code will combine three multistep block methods of order four, five and six. The order selection is based on approximation of the local errors with specific tolerance. These methods are constructed to produce two approximate solutions simultaneously at each iteration in order to further increase the efficiency. The proposed VOBBDF is validated through numerical results on some standard problems found in the literature and comparisons are made with single order Block Backward Differentiation Formula (BBDF). Numerical results shows the advantage of using VOBBDF for solving ODEs.

Keywords: block backward differentiation formulas, uniform step size, ordinary differential equations

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Authors: Adamu S. Salawu, Ibrahim O. Isah

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Direct solution to several forms of fourth-order ordinary differential equations is not easily obtained without first reducing them to a system of first-order equations. Thus, numerical methods are being developed with the underlying techniques in the literature, which seeks to approximate some classes of fourth-order initial value problems with admissible error bounds. Multistep methods present a great advantage of the ease of implementation but with a setback of several functions evaluation for every stage of implementation. However, hybrid methods conventionally show a slightly higher order of truncation for any k-step linear multistep method, with the possibility of obtaining solutions at off mesh points within the interval of solution. In the light of the foregoing, we propose the continuous form of a hybrid multistep method with Chebyshev polynomial as a basis function for the numerical integration of fourth-order initial value problems of ordinary differential equations. The basis function is interpolated and collocated at some points on the interval [0, 2] to yield a system of equations, which is solved to obtain the unknowns of the approximating polynomial. The continuous form obtained, its first and second derivatives are evaluated at carefully chosen points to obtain the proposed block method needed to directly approximate fourth-order initial value problems. The method is analyzed for convergence. Implementation of the method is done by conducting numerical experiments on some test problems. The outcome of the implementation of the method suggests that the method performs well on problems with oscillatory or trigonometric terms since the approximations at several points on the solution domain did not deviate too far from the theoretical solutions. The method also shows better performance compared with an existing hybrid method when implemented on a larger interval of solution.

Keywords: Chebyshev polynomial, collocation, hybrid multistep method, initial value problems, interpolation

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Authors: T. A. Biala

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This paper deals with the numerical integration of the general second order multipoint boundary value problems. This has been achieved by the development of a continuous linear multistep method (LMM). The continuous LMM is used to construct a main discrete method to be used with some initial and final methods (also obtained from the continuous LMM) so that they form a discrete analogue of the continuous second order boundary value problems. These methods are used as boundary value methods and adapted to cope with the integration of the general second order multipoint boundary value problems. The convergence, the use and the region of absolute stability of the methods are discussed. Several numerical examples are implemented to elucidate our solution process.

Keywords: linear multistep methods, boundary value methods, second order multipoint boundary value problems, convergence

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Authors: A. M. Sagir

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Discrete linear multistep block method of uniform order for the solution of first order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: block method, first order ordinary differential equations, hybrid, self-starting

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Authors: A. M. Sagir

Abstract:

This paper derived four newly schemes which are combined in order to form an accurate and efficient block method for parallel or sequential solution of third order ordinary differential equations of the form y^'''= f(x,y,y^',y^'' ), y(α)=y_0,〖y〗^' (α)=β,y^('' ) (α)=μ with associated initial or boundary conditions. The implementation strategies of the derived method have shown that the block method is found to be consistent, zero stable and hence convergent. The derived schemes were tested on stiff and non-stiff ordinary differential equations, and the numerical results obtained compared favorably with the exact solution.

Keywords: block method, hybrid, linear multistep, self-starting, third order ordinary differential equations

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Authors: Y. A. Yahaya, Ahmad Tijjani Asabe

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This paper focuses on the formulation of 3-step hybrid Adams type method for the solution of first order differential equation (ODE). The methods which was derived on both grid and off grid points using multistep collocation schemes and also evaluated at some points to produced Block Adams type method and Adams moulton method respectively. The method with the highest order was selected to serve as the corrector. The convergence was valid and efficient. The numerical experiments were carried out and reveal that hybrid Adams type methods performed better than the conventional Adams moulton method.

Keywords: adam-moulton type (amt), corrector method, off-grid, block method, convergence analysis

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Authors: Hudson Akewe

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We prove that the convergence of explicit Mann, explicit Ishikawa, explicit Noor, explicit SP, explicit multistep and explicit multistep-SP fixed point iterative procedures are equivalent for the classes of multi-valued phi-contraction, phi-Zamfirescu and phi-quasi-contractive mappings in the framework of modular function spaces. Our results complement equivalence results on normed and metric spaces in the literature as they elegantly cut out the triangle inequality.

Keywords: multistep iterative procedures, multivalued mappings, equivalence results, fixed point

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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: Abubakar Danbaba

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Sudoku squares have been widely used to design an experiment where each treatment occurs exactly once in each row, column or sub-block. For some experiments, the size of row (or column or sub-block) may be larger than the number of treatments. Since each treatment appears only once in each row (column or sub-block) with an additional empty cell such designs are partially balanced Sudoku designs (PBSD) with NP-complete structures. This paper proposed methods for constructing PBSD of prime order of treatments by a modified Kronecker product and swap of matrix row (or column) in cyclic order. In addition, linear model and procedure for the analysis of data for PBSD are proposed.

Keywords: sudoku design, partial sudoku, NP-complete, Kronecker product, row and column swap

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Authors: Khairil I. Othman, Mahfuzah Mahayaddin, Zarina Bibi Ibrahim

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We develop and demonstrate a computationally efficient numerical technique to solve first order stiff differential equations. This technique is based on block method whereby three approximate points are calculated. The Cholistani of varied step sizes are presented in divided difference form. Stability regions of the formulae are briefly discussed in this paper. Numerical results show that this block method perform very well compared to existing methods.

Keywords: block method, divided difference, stiff, computational

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Authors: Khairil Iskandar Othman, Nadhirah Kamal, Zarina Bibi Ibrahim

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Block methods for solving stiff systems of ordinary differential equations (ODEs) are based on backward differential formulas (BDF) with PE(CE)2 and Newton method. In this paper, we introduce Modified Newton as a new strategy to get more efficient result. The derivation of BBDF using modified block Newton method is presented. This new block method with predictor-corrector gives more accurate result when compared to the existing BBDF.

Keywords: modified Newton, stiff, BBDF, Jacobian matrix

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Authors: Amin Saeidi

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Using a representation-theoretic approach and considering G to be a finite primitive permutation group of degree n, our aim is to determine linear codes of length n that admit G as a permutation automorphism group. We can show that in some cases, every binary linear code admitting G as a permutation automorphism group is a submodule of a permutation module defined by a primitive action of G. As an illustration of the method, we consider the sporadic simple group M₁₁ and the unitary group U(3,3). We also construct some point- and block-primitive 1-designs from the supports of some codewords of the codes in the discussion.

Keywords: linear code, permutation representation, support design, simple group

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Authors: A. Danbaba

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Samurai Sudoku consists of five Sudoku square designs each having nine treatments in each row (column or sub-block) only once such the five Sudoku designs overlaps. Two or more Samurai designs can be joint together to give an extended Samurai design. In addition, two Samurai designs, each containing five Sudoku square designs, are mutually orthogonal (Graeco). If we superimpose two Samurai designs and obtained a pair of Latin and Greek letters in each row (column or sub-block) of the five Sudoku designs only once, then we have Graeco Samurai design. In this paper, simple method of constructing Samurai designs and mutually orthogonal Samurai design are proposed. In addition, linear models and methods of data analysis for the designs are proposed.

Keywords: samurai design, graeco samurai design, sudoku design, row or column swap

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Authors: Jan-Tore H. Horn, Jørgen Juncher Jensen

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Uncertainties related to fatigue damage estimation of non-linear systems are highly dependent on the tail behaviour and extreme values of the stress range distribution. By using a combination of the First Order Reliability Method (FORM) and Monte Carlo simulations (MCS), the accuracy of the fatigue estimations may be improved for the same computational efforts. The method is applied to a bottom-fixed, monopile-supported large offshore wind turbine, which is a non-linear and dynamically sensitive system. Different curve fitting techniques to the fatigue damage distribution have been used depending on the sea-state dependent response characteristics, and the effect of a bi-linear S-N curve is discussed. Finally, analyses are performed on several environmental conditions to investigate the long-term applicability of this multistep method. Wave loads are calculated using state-of-the-art theory, while wind loads are applied with a simplified model based on rotor thrust coefficients.

Keywords: fatigue damage, FORM, monopile, Monte Carlo, simulation, wind turbine

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Authors: E. Tchandao Mangamana, V. Cariou, E. Vigneau, R. Glele Kakai, E. M. Qannari

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A new definition of a latent variable associated with a dataset makes it possible to propose variants of the PLS2 regression and the multi-block PLS (MB-PLS). We shall refer to these variants as Rd-PLS regression and Rd-MB-PLS respectively because they are inspired by both Redundancy analysis and PLS regression. Usually, a latent variable t associated with a dataset Z is defined as a linear combination of the variables of Z with the constraint that the length of the loading weights vector equals 1. Formally, t=Zw with ‖w‖=1. Denoting by Z' the transpose of Z, we define herein, a latent variable by t=ZZ’q with the constraint that the auxiliary variable q has a norm equal to 1. This new definition of a latent variable entails that, as previously, t is a linear combination of the variables in Z and, in addition, the loading vector w=Z’q is constrained to be a linear combination of the rows of Z. More importantly, t could be interpreted as a kind of projection of the auxiliary variable q onto the space generated by the variables in Z, since it is collinear to the first PLS1 component of q onto Z. Consider the situation in which we aim to predict a dataset Y from another dataset X. These two datasets relate to the same individuals and are assumed to be centered. Let us consider a latent variable u=YY’q to which we associate the variable t= XX’YY’q. Rd-PLS consists in seeking q (and therefore u and t) so that the covariance between t and u is maximum. The solution to this problem is straightforward and consists in setting q to the eigenvector of YY’XX’YY’ associated with the largest eigenvalue. For the determination of higher order components, we deflate X and Y with respect to the latent variable t. Extending Rd-PLS to the context of multi-block data is relatively easy. Starting from a latent variable u=YY’q, we consider its ‘projection’ on the space generated by the variables of each block Xk (k=1, ..., K) namely, tk= XkXk'YY’q. Thereafter, Rd-MB-PLS seeks q in order to maximize the average of the covariances of u with tk (k=1, ..., K). The solution to this problem is given by q, eigenvector of YY’XX’YY’, where X is the dataset obtained by horizontally merging datasets Xk (k=1, ..., K). For the determination of latent variables of order higher than 1, we use a deflation of Y and Xk with respect to the variable t= XX’YY’q. In the same vein, extending Rd-MB-PLS to the path modeling setting is straightforward. Methods are illustrated on the basis of case studies and performance of Rd-PLS and Rd-MB-PLS in terms of prediction is compared to that of PLS2 and MB-PLS.

Keywords: multiblock data analysis, partial least squares regression, path modeling, redundancy analysis

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Authors: Nazia Nazir

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Background: The benefits of regional anesthetic techniques are well established. Use of additives to local anesthetics can prolong these benefits. The aim of this study was to observe the effect of adding dexmedetomidine to bupivacaine for the supraclavicular block. Methods (Design): In this randomized, double-blind study, seventy ASA I & II patients of either sex undergoing elective surgeries on the upper limb were given supraclavicular block under ultrasound guidance. Group C (n=35), received 38 mL 0.25% bupivacaine + 2mL normal saline and group D received 38 mL 0.25% bupivacaine + 1 µg/kg dexmedetomidine (2mL). Patients were observed for onset, duration of motor and sensory block, duration of analgesia, sedation score, hemodynamic changes and any adverse events. Results: In group D the onset was faster (P < 0.001), duration of sensory and motor block, as well as duration of analgesia, was prolonged as compared to group C (P < 0.0001). There was significant drop in heart rate (HR) from the baseline in group D (P < 0.05) at 30, 60, 90 and 120 min, however, none of the patients dropped HR below 50/min. Mean arterial Pressure (MAP) remained unaffected. The patients in group D were effectively sedated than those in group C (P < 0.05). No adverse event was reported in either group. Conclusion: Dexmedetomidine as adjuvant to bupivacaine in supraclavicular block resulted in faster action, prolonged motor and sensory block, prolonged analgesia with hemodynamic stability and adequate sedation.

Keywords: Analgesia, bupivacaine, dexmedetomidine, supraclavicular block

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Authors: Gram Y. Rivas Sanchez

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The seismic design codes in the world allow the analysis of structures considering an elastic-linear behavior; however, against earthquakes, the structures exhibit non-linear behaviors that induce damage to their elements. For this reason, it is necessary to use non-linear methods to analyze these structures, being the dynamic methods that provide more reliable results but require a lot of computational costs; on the other hand, non-linear static methods do not have this disadvantage and are being used more and more. In the present work, the nonlinear static analysis (pushover) of RC frame buildings of three, five, and seven stories is carried out considering models of concentrated plasticity using plastic hinges; and the seismic performance points are determined using ATC-40, FEMA 356, and FEMA 440 guidelines. Using this last standard, the highest inelastic displacements and basal shears are obtained, providing designs that are more conservative.

Keywords: pushover, nonlinear, RC building, FEMA 440, ATC 40

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Authors: Asabe Ahmad Tijani, Y. A. Yahaya

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The paper considers the derivation of implicit Adams-Moulton type method, with k=4 and 5. We adopted the method of interpolation and collocation of power series approximation to generate the continuous formula which was evaluated at off-grid and some grid points within the step length to generate the proposed block schemes, the schemes were investigated and found to be consistent and zero stable. Finally, the methods were tested with numerical experiments to ascertain their level of accuracy.

Keywords: Adam-Moulton Type (AMT), off-grid, block method, consistent and zero stable

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Authors: Fedili Benamar, Beloulou Mohamed Lamine, Ouahes Hassane, Ghattas Samir

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 Background and aims: Peripheral regional anesthesia has been integrated into most analgesia protocols for total knee arthroplasty which considered among the most painful surgeries with a huge potential for chronicization. The adductor canal block (ACB) has gained popularity. Similarly, the IPACK block has been described to provide analgesia of the posterior knee capsule. This study aimed to evaluate the analgesic efficacy of this block in patients undergoing primary PTG. Methods: 90 patients were randomized to receive either an IPACK, an anterior sciatic block, or a sham block (30 patients in each group + multimodal analgesia and a catheter in the KCA adductor canal). GROUP 1 KCA GROUP 2 KCA+BSA GROUP 3 KCA+IPACK The analgesic blocks were done under echo-guidance preoperatively respecting the safety rules, the dose administered was 20 cc of ropivacaine 0.25% was used. We were to assess posterior knee pain 6 hours after surgery. Other endpoints included quality of recovery after surgery, pain scores, opioid requirements (PCA morphine)(EPI info 7.2 analysis). Results: -groups were matched -A predominance of women (4F/1H). -average age: 68 +/-7 years -the average BMI =31.75 kg/m2 +/- 4. -70% of patients ASA2 ,20% ASA3. -The average duration of the intervention: 89 +/- 19 minutes. -Morphine consumption (PCA) significantly higher in group 1 (16mg) & group 2 (8mg) group 3 (4mg) - The groups were matched . -There was a correlation between the use of the ipack block and postoperative pain Conclusions :In a multimodal analgesic protocol, the addition of IPACK block decreased pain scores and morphine consumption ,

Keywords: regional anesthesia, analgesia, total knee arthroplasty, the adductor canal block (acb), the ipack block, pain

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Authors: C. V. Pietreanu, S. E. Zaharia, C. Dinu

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The present research is built on three major pillars, commencing by making some considerations on accident investigation methods and pointing out both defining aspects and differences between linear and non-linear analysis. The traditional linear focus on accident analysis describes accidents as a sequence of events, while the latest systemic models outline interdependencies between different factors and define the processes evolution related to a specific (normal) situation. Linear and non-linear accident analysis methods have specific limitations, so the second point of interest is mirrored by the aim to discover the drawbacks of systemic models which becomes a starting point for developing new directions to identify risks or data closer to the cause of incidents/accidents. Since communication represents a critical issue in the interaction of human factor and has been proved to be the answer of the problems made by possible breakdowns in different communication procedures, from this focus point, on the third pylon a new error-modeling instrument suitable for risk assessment/accident analysis will be elaborated.

Keywords: accident analysis, multi-factorial error modeling, risk, systemic methods

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Authors: Maciej Major, Izabela Major

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The aim of this paper is a numerical analysis of three-layered block design to walls construction subjected to the dynamic load. The block consists of the layers: concrete with rubber pads in shape of crosses, space filled with air and concrete with I-shape rubber pads. The main purpose of rubber inserts embedded during the production process is additional protection against the transversal dynamic load. For the analysis, as rubber, the Zahorski hyperelastic incompressible material model was assumed. A concentrated force as dynamic load applied to the external block surface was investigated. The results for the considered block observed as the stress distribution plot were compared to the results obtained for the solid concrete block. In order to estimate the percentage damping of proposed composite, rubber-concrete block in relation to the solid block the numerical analysis with the use of finite element method based on ADINA software was performed.

Keywords: dynamics, composite, rubber, Zahorski

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Authors: Hae-Yeoun Lee

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Mosaic refers to a technique that makes image by gathering lots of small materials in various colours. This paper presents an automatic algorithm that makes the photomosaic image using photos. The algorithm is composed of four steps: Partition and feature extraction, block matching, redundancy removal and colour adjustment. The input image is partitioned in the small block to extract feature. Each block is matched to find similar photo in database by comparing similarity with Euclidean difference between blocks. The intensity of the block is adjusted to enhance the similarity of image by replacing the value of light and darkness with that of relevant block. Further, the quality of image is improved by minimizing the redundancy of tiles in the adjacent blocks. Experimental results support that the proposed algorithm is excellent in quantitative analysis and qualitative analysis.

Keywords: photomosaic, Euclidean distance, block matching, intensity adjustment

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Authors: Khairil I. Othman, Nur N. Kamal, Zarina B. Ibrahim

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In this paper, we present modified Newton method as a new strategy for improving the efficiency of Two Point Block Backward Differentiation Formulas (BBDF) when solving stiff systems of ordinary differential equations (ODEs). These methods are constructed to produce two approximate solutions simultaneously at each iteration The detailed implementation of the predictor corrector BBDF with PE(CE)2 with modified Newton are discussed. The proposed modification of BBDF is validated through numerical results on some standard problems found in the literature and comparisons are made with the existing Block Backward Differentiation Formula. Numerical results show the advantage of using the new strategy for solving stiff ODEs in improving the accuracy of the solution.

Keywords: newton method, two point, block, accuracy

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Authors: Mukesh K., Siddiqui A. K., Abbas H., Gupta R.

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Background: General Anesthesia is a standard for breast onco-surgery. The issue of postoperative pain and the occurrence of nausea and vomiting has prompted the quest for a superior methodology with fewer complications. Over the recent couple of years, paravertebral block (PVB) has acquired huge fame either in combination with GA or alone for anesthetic management. In this study, we aim to evaluate the efficacy of morphine and clonidine as an adjunct to ropivacaine in a paravertebral block in breast cancer patients undergoing modified radical mastectomy. Methods: In this study, total 90 patients were divided into three groups (30 each) on the basis of computer-generated randomization. Group C (Control): Paravertebral block with 0.25% ropivacaine (19ml) and 1 ml saline; Group M- Paravertebral block with 0.25% ropivacaine(19ml) + 20 microgram/kg body weight morphine; Group N: Paravertebral block with 0.25% ropivacaine(19ml) +1.0 microgram/kg body weight clonidine. The postoperative pain intensity was recorded using the visual analog scale (VAS) and Sedation was observed by the Ramsay Sedation score (RSS). Results: The VAS was similar at 0hr, 2hr and 4 hr in the postoperative period among all the groups. There was a significant (p=0.003) difference in VAS from 6 hr to 20 hr in the postoperative period among the groups. A significant (p<0.05) difference was observed among the groups at 8 hr to 20 hr). The first requirement of analgesia was significantly (p=0.001) higher in Group N (7.70±1.74) than in Group C (4.43±1.43) and Group M (7.33±2.21). Conclusion: The morphine in the paravertebral block provides better postoperative analgesia. The consumption of rescue analgesia was significantly reduced in the morphine group as compared to the clonidine group. The procedure also proved to be safe as no complication was encountered in the paravertebral block in our study.

Keywords: ropivacaine, morphine, clonidine, paravertebral block

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Authors: Young-Hun Ko, Seung-Jun Kim, Khaqan Baluch, Hyung- Sik Yang

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In this study, the polymer gel was used as coupling material in a blasting hole and its comparison was made with other coupling materials like sand, water, and air. Trazul lead block test and AUTODYN numerical analysis were conducted to analyze the effects of the coupling materials on the intensity of the explosion, as well as the verification tests were conducted by using concrete block test. The emulsion explosives were used in decoupling conditions, sand, water, and polymer gel were used as the coupling materials. The lead block test and the numerical analysis showed that the expansion of the blast hole in the lead block was similar to that of the water and gelatin and followed by sand and air conditions. The validation of concrete block test result showed the similar result as Trazul lead block test and the explosion strength was measured at 0.8 for polymer gel, 0.7 for sand, and 0.6 for no coupling material, in comparison to the full charge (1.0) case.

Keywords: Trazul lead block test, AUTODYN numerical analysis, coupling material, polymer gel, soil covering concrete block explosion test

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Authors: Mohamed Korany, Azza Gazy, Essam Khamis, Marwa Adel, Miranda Fawzy

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Background: Two new, simple and specific methods; First, a Zero-crossing first-derivative technique and second, a chemometric-assisted spectrophotometric artificial neural network (ANN) were developed and validated in accordance with ICH guidelines. Both methods were used for the simultaneous estimation of the two closely related antioxidant nutraceuticals ; Coenzyme Q10 (Q) ; also known as Ubidecarenone or Ubiquinone-10, and Vitamin E (E); alpha-tocopherol acetate, in their pharmaceutical binary mixture. Results: For first method: By applying the first derivative, both Q and E were alternatively determined; each at the zero-crossing of the other. The D1 amplitudes of Q and E, at 285 nm and 235 nm respectively, were recorded and correlated to their concentrations. The calibration curve is linear over the concentration range of 10-60 and 5.6-70 μg mL-1 for Q and E, respectively. For second method: ANN (as a multivariate calibration method) was developed and applied for the simultaneous determination of both analytes. A training set (or a concentration set) of 90 different synthetic mixtures containing Q and E, in wide concentration ranges between 0-100 µg/mL and 0-556 µg/mL respectively, were prepared in ethanol. The absorption spectra of the training sets were recorded in the spectral region of 230–300 nm. A Gradient Descend Back Propagation ANN chemometric calibration was computed by relating the concentration sets (x-block) to their corresponding absorption data (y-block). Another set of 45 synthetic mixtures of the two drugs, in defined range, was used to validate the proposed network. Neither chemical separation, preparation stage nor mathematical graphical treatment were required. Conclusions: The proposed methods were successfully applied for the assay of Q and E in laboratory prepared mixtures and combined pharmaceutical tablet with excellent recoveries. The ANN method was superior over the derivative technique as the former determined both drugs in the non-linear experimental conditions. It also offers rapidity, high accuracy, effort and money saving. Moreover, no need for an analyst for its application. Although the ANN technique needed a large training set, it is the method of choice in the routine analysis of Q and E tablet. No interference was observed from common pharmaceutical additives. The results of the two methods were compared together

Keywords: coenzyme Q10, vitamin E, chemometry, quantitative analysis, first derivative spectrophotometry, artificial neural network

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