Search results for: Gauss-Seidel iteration

Authors: Kholod Mohammad Abualnaja

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A new algorithm is presented to find some new iterative methods for solving nonlinear equations F(x)=0 by using the variational iteration method. The efficiency of the considered method is illustrated by example. The results show that the proposed iteration technique, without linearization or small perturbation, is very effective and convenient.

Keywords: variational iteration method, nonlinear equations, Lagrange multiplier, algorithms

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Authors: O. M. Bamigbola, A. A. Ibrahim

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Analysis of real life problems often results in linear systems of equations for which solutions are sought. The method to employ depends, to some extent, on the properties of the coefficient matrix. It is not always feasible to solve linear systems of equations by direct methods, as such the need to use an iterative method becomes imperative. Before an iterative method can be employed to solve a linear system of equations there must be a guaranty that the process of solution will converge. This guaranty, which must be determined a priori, involve the use of some criterion expressible in terms of the entries of the coefficient matrix. It is, therefore, logical that the convergence criterion should depend implicitly on the algebraic structure of such a method. However, in deference to this view is the practice of conducting convergence analysis for Gauss-Seidel iteration on a criterion formulated based on the algebraic structure of Jacobi iteration. To remedy this anomaly, the Gauss-Seidel iteration was studied for its algebraic structure and contrary to the usual assumption, it was discovered that some property of the iteration matrix of Gauss-Seidel method is only diagonally dominant in its first row while the other rows do not satisfy diagonal dominance. With the aid of this structure we herein fashion out an improved version of Gauss-Seidel iteration with the prospect of enhancing convergence and robustness of the method. A numerical section is included to demonstrate the validity of the theoretical results obtained for the improved Gauss-Seidel method.

Keywords: linear algebraic system, Gauss-Seidel iteration, algebraic structure, convergence

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Authors: M. O. Olayiwola

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Numerical solutions of the generalized Burger-Fisher are obtained using a Modified Variational Iteration Method (MVIM) with minimal computational efforts. The computed results with this technique have been compared with other results. The present method is seen to be a very reliable alternative method to some existing techniques for such nonlinear problems.

Keywords: burger-fisher, modified variational iteration method, lagrange multiplier, Taylor’s series, partial differential equation

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Authors: Alemayehu Geremew Geremew

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We prove the weak convergence of Mann iteration for a hybrid pair of maps to a common fixed point of a selfmap f and a multivalued f nonexpansive mapping T in Banach space E.

Keywords: common fixed point, Mann iteration, multivalued mapping, weak convergence

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Authors: Yixun Shi

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Many interior point methods for convex programming solve an (n+m)x(n+m)linear system in each iteration. Many implementations solve this system in each iteration by considering an equivalent mXm system (4) as listed in the paper, and thus the job is reduced into solving the system (4). However, the system(4) has to be solved exactly since otherwise the error would be entirely passed onto the last m equations of the original system. Often the Cholesky factorization is computed to obtain the exact solution of (4). One Cholesky factorization is to be done in every iteration, resulting in higher computational costs. In this paper, two iterative methods for solving linear systems using vector division are combined together and embedded into interior point methods. Instead of computing one Cholesky factorization in each iteration, it requires only one Cholesky factorization in the entire procedure, thus significantly reduces the amount of computation needed for solving the problem. Based on that, a hybrid algorithm for solving convex programming problems is proposed.

Keywords: convex programming, interior point method, linear systems, vector division

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Authors: Olayiwola Moruf Oyedunsi

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This paper discusses the Modified Variational Iteration Method (MVIM) for the solution of nonlinear Burgers’ equation arising in longitudinal dispersion phenomena in fluid flow through porous media. The method is an elegant combination of Taylor’s series and the variational iteration method (VIM). Using Maple 18 for implementation, it is observed that the procedure provides rapidly convergent approximation with less computational efforts. The result shows that the concentration C(x,t) of the contaminated water decreases as distance x increases for the given time t.

Keywords: modified variational iteration method, Burger’s equation, porous media, partial differential equation

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Authors: Taysir Soliman

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One of the current popular clustering techniques is Spectral Clustering (SC) because of its advantages over conventional approaches such as hierarchical clustering, k-means, etc. and other techniques as well. However, one of the disadvantages of SC is the time consuming process because it requires computing the eigenvectors. In the past to overcome this disadvantage, a number of attempts have been proposed such as the Power Iteration Clustering (PIC) technique, which is one of versions from SC; some of PIC advantages are: 1) its scalability and efficiency, 2) finding one pseudo-eigenvectors instead of computing eigenvectors, and 3) linear combination of the eigenvectors in linear time. However, its worst disadvantage is an inter-class collision problem because it used only one pseudo-eigenvectors which is not enough. Previous researchers developed Deflation-based Power Iteration Clustering (DPIC) to overcome problems of PIC technique on inter-class collision with the same efficiency of PIC. In this paper, we developed Parallel DPIC (PDPIC) to improve the time and memory complexity which is run on apache spark framework using sparse matrix. To test the performance of PDPIC, we compared it to SC, ESCG, ESCALG algorithms on four small graph benchmark datasets and nine large graph benchmark datasets, where PDPIC proved higher accuracy and better time consuming than other compared algorithms.

Keywords: spectral clustering, power iteration clustering, deflation-based power iteration clustering, Apache spark, large graph

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Authors: Nicholas D. Assimakis

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In linear estimation, the traditional Kalman filter uses the Kalman filter gain in order to produce estimation and prediction of the n-dimensional state vector using the m-dimensional measurement vector. The computation of the Kalman filter gain requires the inversion of an m x m matrix in every iteration. In this paper, a variation of the Kalman filter eliminating the Kalman filter gain is proposed. In the time varying case, the elimination of the Kalman filter gain requires the inversion of an n x n matrix and the inversion of an m x m matrix in every iteration. In the time invariant case, the elimination of the Kalman filter gain requires the inversion of an n x n matrix in every iteration. The proposed Kalman filter gain elimination algorithm may be faster than the conventional Kalman filter, depending on the model dimensions.

Keywords: discrete time, estimation, Kalman filter, Kalman filter gain

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Authors: A. W. Gbolagade, M. O. Olayiwola, K. O. Kareem

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In this paper, further to our result on recent paper on the solution of nonlinear advection equations, we present further results on the nonlinear nonhomogeneous advection equations using a modified variational iteration method.

Keywords: lagrange multiplier, non-homogeneous equations, advection equations, mathematics

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Authors: Desmond Adair, Kairat Ismailov, Martin Jaeger

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Modelling of Timoshenko beams on elastic foundations has been widely used in the analysis of buildings, geotechnical problems, and, railway and aerospace structures. For the elastic foundation, the most widely used models are one-parameter mechanical models or two-parameter models to include continuity and cohesion of typical foundations, with the two-parameter usually considered the better of the two. Knowledge of free vibration characteristics of beams on an elastic foundation is considered necessary for optimal design solutions in many engineering applications, and in this work, the efficient and accurate variational iteration method is developed and used to calculate natural frequencies of a Timoshenko beam on a two-parameter foundation. The variational iteration method is a technique capable of dealing with some linear and non-linear problems in an easy and efficient way. The calculations are compared with those using a finite-element method and other analytical solutions, and it is shown that the results are accurate and are obtained efficiently. It is found that the effect of the presence of the two-parameter foundation is to increase the beam’s natural frequencies and this is thought to be because of the shear-layer stiffness, which has an effect on the elastic stiffness. By setting the two-parameter model’s stiffness parameter to zero, it is possible to obtain a one-parameter foundation model, and so, comparison between the two foundation models is also made.

Keywords: Timoshenko beam, variational iteration method, two-parameter elastic foundation model

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Authors: Soyoon Bak, Sunyoung Bu, Philsu Kim

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In this paper, a backward semi-Lagrangian scheme combined with the second-order backward difference formula is designed to calculate the numerical solutions of nonlinear advection-diffusion equations. The primary aims of this paper are to remove any iteration process and to get an efficient algorithm with the convergence order of accuracy 2 in time. In order to achieve these objects, we use the second-order central finite difference and the B-spline approximations of degree 2 and 3 in order to approximate the diffusion term and the spatial discretization, respectively. For the temporal discretization, the second order backward difference formula is applied. To calculate the numerical solution of the starting point of the characteristic curves, we use the error correction methodology developed by the authors recently. The proposed algorithm turns out to be completely iteration-free, which resolves the main weakness of the conventional backward semi-Lagrangian method. Also, the adaptability of the proposed method is indicated by numerical simulations for Burgers’ equations. Throughout these numerical simulations, it is shown that the numerical results are in good agreement with the analytic solution and the present scheme offer better accuracy in comparison with other existing numerical schemes. Semi-Lagrangian method, iteration-free method, nonlinear advection-diffusion equation, second-order backward difference formula

Keywords: Semi-Lagrangian method, iteration free method, nonlinear advection-diffusion equation, second-order backward difference formula

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Authors: O. Acan, Y. Keskin

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In this study, we will carry out a comparative study between the reduced differential transform method, the adomian decomposition method, the variational iteration method and the homotopy analysis method. These methods are used in many fields of engineering. This is been achieved by handling a kind of 2-Dimensional and forth-order partial differential equations called the Kuramoto–Sivashinsky equations. Three numerical examples have also been carried out to validate and demonstrate efficiency of the four methods. Furthermost, it is shown that the reduced differential transform method has advantage over other methods. This method is very effective and simple and could be applied for nonlinear problems which used in engineering.

Keywords: reduced differential transform method, adomian decomposition method, variational iteration method, homotopy analysis method

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Authors: Wided Batita, Stéphane Roche, Claude Caron

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Geodesign is an emergent term related to a new and complex process. Hence, it needs to rethink tools, technologies and platforms in order to efficiently achieve its goals. A few tools have emerged since 2010 such as CommunityViz, GeoPlanner, etc. In the era of Web 2.0 and collaboration, WikiGIS has been proposed as a new category of tools. In this paper, we present WikiGIS functionalities dealing mainly with the iteration and traceability management to support the collaboration of the Geodesign process. Actually, WikiGIS is built on GeoWeb 2.0 technologies —and primarily on wiki— and aims at managing the tracking of participants’ editing. This paper focuses on a simplified simulation to illustrate the strength of WikiGIS in the management of traceability and in the access to history in a Geodesign process. Indeed, a cartographic user interface has been implemented, and then a hypothetical use case has been imagined as proof of concept.

Keywords: geodesign, history, traceability, tracking of participants’ editing, WikiGIS

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Authors: Liang Liu, Xiaopeng Luo

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In this paper, we propose an accelerated stochastic gradient method with momentum. The momentum term is the weighted average of generated gradients, and the weights decay inverse proportionally with the iteration times. Stochastic gradient descent with momentum (SGDM) uses weights that decay exponentially with the iteration times to generate the momentum term. Using exponential decay weights, variants of SGDM with inexplicable and complicated formats have been proposed to achieve better performance. However, the momentum update rules of our method are as simple as that of SGDM. We provide theoretical convergence analyses, which show both the exponential decay weights and our inverse proportional decay weights can limit the variance of the parameter moving directly to a region. Experimental results show that our method works well with many practical problems and outperforms SGDM.

Keywords: exponential decay rate weight, gradient descent, inverse proportional decay rate weight, momentum

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Authors: David C. Ni

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In the previous efforts, we constructed N-Body Systems by an extended Blaschke product (EBP), which represents a non-temporal and nonlinear extension of Lorentz transformation. In this construction, we rely only on two parameters, nonlinear degree, and relative momentum to characterize the systems. We further explored root computation via iteration with an algorithm extended from Jenkins-Traub method. The solution sets demonstrate a form of σ+ i [-t, t], where σ and t are the real numbers, and the [-t, t] shows various canonical distributions. In this paper, we correlate the convergent sets in the original domain with solution sets, which demonstrating large-deviation distributions in the codomain. We proceed to compare our approach with the formula or principles, such as Donsker-Varadhan and Wentzell-Freidlin theories. The deterministic model based on this construction allows us to explore applications in the areas of finance and statistical mechanics.

Keywords: nonlinear Lorentz transformation, Blaschke equation, iteration solutions, root computation, large deviation distribution, deterministic model

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Authors: Sanjay Rathee, Arti Kashyap

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Extraction of useful information from large datasets is one of the most important research problems. Association rule mining is one of the best methods for this purpose. Finding possible associations between items in large transaction based datasets (finding frequent patterns) is most important part of the association rule mining. There exist many algorithms to find frequent patterns but Apriori algorithm always remains a preferred choice due to its ease of implementation and natural tendency to be parallelized. Many single-machine based Apriori variants exist but massive amount of data available these days is above capacity of a single machine. Therefore, to meet the demands of this ever-growing huge data, there is a need of multiple machines based Apriori algorithm. For these types of distributed applications, MapReduce is a popular fault-tolerant framework. Hadoop is one of the best open-source software frameworks with MapReduce approach for distributed storage and distributed processing of huge datasets using clusters built from commodity hardware. However, heavy disk I/O operation at each iteration of a highly iterative algorithm like Apriori makes Hadoop inefficient. A number of MapReduce-based platforms are being developed for parallel computing in recent years. Among them, two platforms, namely, Spark and Flink have attracted a lot of attention because of their inbuilt support to distributed computations. Earlier we proposed a reduced- Apriori algorithm on Spark platform which outperforms parallel Apriori, one because of use of Spark and secondly because of the improvement we proposed in standard Apriori. Therefore, this work is a natural sequel of our work and targets on implementing, testing and benchmarking Apriori and Reduced-Apriori and our new algorithm ReducedAll-Apriori on Apache Flink and compares it with Spark implementation. Flink, a streaming dataflow engine, overcomes disk I/O bottlenecks in MapReduce, providing an ideal platform for distributed Apriori. Flink's pipelining based structure allows starting a next iteration as soon as partial results of earlier iteration are available. Therefore, there is no need to wait for all reducers result to start a next iteration. We conduct in-depth experiments to gain insight into the effectiveness, efficiency and scalability of the Apriori and RA-Apriori algorithm on Flink.

Keywords: apriori, apache flink, Mapreduce, spark, Hadoop, R-Apriori, frequent itemset mining

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Authors: Mohammad Sahadet Hossain, Shamsil Arifeen, Mehrab Hossian Likhon

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In this paper, we analyze a linear time invariant (LTI) descriptor system of large dimension. Since these systems are difficult to simulate, compute and store, we attempt to reduce this large system using Low Rank Cholesky Factorized Alternating Directions Implicit (LRCF-ADI) iteration followed by Square Root Balanced Truncation. LRCF-ADI solves the dual Lyapunov equations of the large system and gives low-rank Cholesky factors of the gramians as the solution. Using these cholesky factors, we compute the Hankel singular values via singular value decomposition. Later, implementing square root balanced truncation, the reduced system is obtained. The bode plots of original and lower order systems are used to show that the magnitude and phase responses are same for both the systems.

Keywords: low-rank cholesky factor alternating directions implicit iteration, LTI Descriptor system, Lyapunov equations, Square-root balanced truncation

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Authors: Hong Lu, Xiong Xiao

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Shaft parts are widely used in machinery industry, however, bending deformation often occurred when this kind of parts is being heat treated. This parts needs to be straightened to meet the requirement of straightness. As for the pressure straightening process, a good straightening stroke algorithm is related to the precision and efficiency of straightening process. In this paper, the relationship between straightening load and deflection during the straightening process is analyzed, and the mathematical model of the straightening process has been established. By the mathematical model, the iterative method is used to solve the straightening stroke. Compared to the traditional straightening stroke algorithm, straightening stroke calculated by this method is much more precise; because it can adapt to the change of material performance parameters. Considering that the straightening method is widely used in the mass production of the shaft parts, knowledge base is used to store the data of the straightening process, and a straightening stroke algorithm based on empirical data is set up. In this paper, the straightening process control model which combine the straightening stroke method based on iteration and straightening stroke algorithm based on empirical data has been set up. Finally, an experiment has been designed to verify the straightening process control model.

Keywords: straightness, straightening stroke, deflection, shaft parts

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Authors: E. Behmanesh, J. Pannek

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Logistics network design is known as one of the strategic decision problems. As these kinds of problems belong to the category of NP-hard problems, traditional ways are failed to find an optimal solution in short time. In this study, we attempt to involve reverse flow through an integrated design of forward/reverse supply chain network that formulated into a mixed integer linear programming. This Integrated, multi-stages model is enriched by three different delivery path which makes the problem more complex. To tackle with such an NP-hard problem a revised random path direct encoding method based memetic algorithm is considered as the solution methodology. Each algorithm has some parameters that need to be investigate to reveal the best performance. In this regard, Taguchi method is adapted to identify the optimum operating condition of the proposed memetic algorithm to improve the results. In this study, four factors namely, population size, crossover rate, local search iteration and a number of iteration are considered. Analyzing the parameters and improvement in results are the outlook of this research.

Keywords: integrated logistics network, flexible path, memetic algorithm, Taguchi method

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Authors: Sie Long Kek, Wah June Leong, Kok Lay Teo

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Linear quadratic Gaussian model is a standard mathematical model for the stochastic optimal control problem. The combination of the linear quadratic estimation and the linear quadratic regulator allows the state estimation and the optimal control policy to be designed separately. This is known as the separation principle. In this paper, an efficient computational method is proposed to solve the linear quadratic Gaussian problem. In our approach, the Hamiltonian function is defined, and the necessary conditions are derived. In addition to this, the output error is defined and the least-square optimization problem is introduced. By determining the first-order necessary condition, the gradient of the sum squares of output error is established. On this point of view, the stochastic approximation approach is employed such that the optimal control policy is updated. Within a given tolerance, the iteration procedure would be stopped and the optimal solution of the linear-quadratic Gaussian problem is obtained. For illustration, an example of the linear-quadratic Gaussian problem is studied. The result shows the efficiency of the approach proposed. In conclusion, the applicability of the approach proposed for solving the linear quadratic Gaussian problem is highly demonstrated.

Keywords: iteration procedure, least squares solution, linear quadratic Gaussian, output error, stochastic approximation

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Authors: Abdulrahman Abdulrahman

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Critical depth meters, such as abroad crested weir, Venture Flume and combined control flume are standard devices for measuring flow in open channels. The discharge relation for these devices cannot be solved directly, but it needs iteration process to account for the approach velocity head. In this paper, analytical solution was developed to calculate the discharge in a combined critical depth-meter namely, a hump combined with lateral contraction in rectangular channel with subcritical approach flow including energy losses. Also analytical formulae were derived for approach velocity head coefficient for different types of critical depth meters. The solution was derived by solving a standard cubic equation considering energy loss on the base of trigonometric identity. The advantage of this technique is to avoid iteration process adopted in measuring flow by these devices. Numerical examples are chosen for demonstration of the proposed solution.

Keywords: broad crested weir, combined control meter, control structures, critical flow, discharge measurement, flow control, hydraulic engineering, hydraulic structures, open channel flow

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Authors: Hancy Issac, Gerben Keijzers, Ian Yang, Clint Moloney, Jackie Lea, Melissa Taylor

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Introduction: Chronic obstructive pulmonary disease guideline non-adherence is associated with a reduction in health-related quality of life in patients (HRQoL). Improving guideline adherence has the potential to mitigate fragmented care thereby sustaining pulmonary function, preventing acute exacerbations, reducing economic health burdens, and enhancing HRQoL. The development of an electronic proforma stemming from expert consensus, including digital guideline resources and direct interdisciplinary referrals is hypothesised to improve guideline adherence and patient outcomes for emergency department (ED) patients with COPD. Aim: The aim of this study was to develop consensus among ED and respiratory staff for the correct composition of a COPD electronic proforma that aids in guideline adherence and management in the ED. Methods: This study adopted a mixed-method design to develop the most important indicators of care in the ED. The study involved three phases: (1) a systematic literature review and qualitative interdisciplinary staff interviews to assess barriers and solutions for guideline adherence and qualitative interdisciplinary staff interviews, (2) a modified Delphi panel to select interventions for the proforma, and (3) a consensus process through three rounds of scoring through a quantitative survey (ED and Respiratory consensus) and qualitative thematic analysis on each indicator. Results: The electronic proforma achieved acceptable and good internal consistency through all iterations from national emergency department and respiratory department interdisciplinary experts. Cronbach’s alpha score for internal consistency (α) in iteration 1 emergency department cohort (EDC) (α = 0.80 [CI = 0.89%]), respiratory department cohort (RDC) (α = 0.95 [CI = 0.98%]). Iteration 2 reported EDC (α = 0.85 [CI = 0.97%]) and RDC (α = 0.86 [CI = 0.97%]). Iteration 3 revealed EDC (α = 0.73 [CI = 0.91%]) and RDC (α = 0.86 [CI = 0.95%]), respectively. Conclusion: Electronic proformas have the potential to facilitate direct referrals from the ED leading to reduced hospital admissions, reduced length of hospital stays, holistic care, improved health care and quality of life and improved interdisciplinary guideline adherence.

Keywords: COPD, electronic proforma, modified delphi study, interdisciplinary, guideline adherence, COPD-X plan

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Authors: Tsui-Tsai Lin

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Cooperative orthogonal frequency division multiplexing (OFDM) transmission, which possesses the advantages of better connectivity, expanded coverage, and resistance to frequency selective fading, has been a more powerful solution for the physical layer in wireless communications. However, such a hybrid scheme suffers from the carrier frequency offset (CFO) effects inherited from the OFDM-based systems, which lead to a significant degradation in performance. In addition, insertion of a cyclic prefix (CP) at each symbol block head for combating inter-symbol interference will lead to a reduction in spectral efficiency. The design on the CFO estimation for the cooperative OFDM system without CP is a suspended problem. This motivates us to develop a low complexity CFO estimator for the cooperative OFDM decode-and-forward (DF) communication system without CP over the multipath fading channel. Especially, using a block-type pilot, the CFO estimation is first derived in accordance with the least square criterion. A reliable performance can be obtained through an exhaustive two-dimensional (2D) search with a penalty of heavy computational complexity. As a remedy, an alternative solution realized with an iteration approach is proposed for the CFO estimation. In contrast to the 2D-search estimator, the iterative method enjoys the advantage of the substantially reduced implementation complexity without sacrificing the estimate performance. Computer simulations have been presented to demonstrate the efficacy of the proposed CFO estimation.

Keywords: cooperative transmission, orthogonal frequency division multiplexing (OFDM), carrier frequency offset, iteration

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Authors: Guenther Schuh, Michael Riesener, Jan Kantelberg

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Due to the fugacity of markets and the reduction of product lifecycles, manufacturing companies from high-wage countries are nowadays faced with the challenge to place more innovative products within even shorter development time on the market. At the same time, volatile customer requirements have to be satisfied in order to successfully differentiate from market competitors. One potential approach to address the explained challenges is provided by agile values and principles. These agile values and principles already proofed their success within software development projects in the form of management frameworks like Scrum or concrete procedure models such as Extreme Programming or Crystal Clear. Those models lead to significant improvements regarding quality, costs and development time and are therefore used within most software development projects. Motivated by the success within the software industry, manufacturing companies have tried to transfer agile mechanisms of action to the development of hardware products ever since. Though first empirical studies show similar effects in the agile development of hardware products, no comprehensive procedure model for the design of development iterations has been developed for hardware development yet due to different constraints of the domains. For this reason, this paper focusses on the design of agile product development processes by transferring mechanisms of action used in agile software development towards product development. This is conducted by decomposing the individual systems 'product development' and 'agile software development' into relevant elements and symbiotically composing the elements of both systems in respect of the design of agile product development processes afterwards. In a first step, existing product development processes are described following existing approaches of the system theory. By analyzing existing case studies from industrial companies as well as academic approaches, characteristic objectives, activities and artefacts are identified within a target-, action- and object-system. In partial model two, mechanisms of action are derived from existing procedure models of agile software development. These mechanisms of action are classified in a superior strategy level, in a system level comprising characteristic, domain-independent activities and their cause-effect relationships as well as in an activity-based element level. Within partial model three, the influence of the identified agile mechanism of action towards the characteristic system elements of product development processes is analyzed. For this reason, target-, action- and object-system of the product development are compared with the strategy-, system- and element-level of agile mechanism of action by using the graph theory. Furthermore, the necessity of existence of activities within iteration can be determined by defining activity-specific degrees of freedom. Based on this analysis, agile product development processes are designed in form of different types of iterations within a last step. By defining iteration-differentiating characteristics and their interdependencies, a logic for the configuration of activities, their form of execution as well as relevant artefacts for the specific iteration is developed. Furthermore, characteristic types of iteration for the agile product development are identified.

Keywords: activity-based process model, agile mechanisms of action, agile product development, degrees of freedom

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Authors: Nidal Ali

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Consider an algebraic number field K of degree n, A0 K is its ring of integers and a prime number p inert in K. Let F(u1, . . . , un, x) be the generic polynomial of integers of K. We will study in advance the stability of this polynomial and then, we will apply it in order to obtain all the monic irreducible polynomials in Fp[x] of degree d dividing n.

Keywords: generic polynomial, irreducibility, iteration, stability, inert prime, totally ramified

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Authors: Young Hee Geum

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We compare optimal quartic order method for the multiple zeros of nonlinear equations illustrating the basins of attraction. To construct basins of attraction effectively, we take a 600×600 uniform grid points at the origin of the complex plane and paint the initial values on the basins of attraction with different colors according to the iteration number required for convergence.

Keywords: basins of attraction, convergence, multiple-root, nonlinear equation

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Authors: Anne M. Denton, Rahul Gomes, David W. Franzen

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High-resolution elevation data are becoming increasingly available, but typical approaches for computing topographic features, like slope and curvature, still assume small sliding windows, for example, of size 3x3. That means that the digital elevation model (DEM) has to be resampled to the scale of the landform features that are of interest. Any higher resolution is lost in this resampling. When the topographic features are computed through regression that is performed at the resolution of the original data, the accuracy can be much higher, and the reported result can be adjusted to the length scale that is relevant locally. Slope and variance are calculated for overlapping windows, meaning that one regression result is computed per raster point. The number of window centers per area is the same for the output as for the original DEM. Slope and variance are computed by performing regression on the points in the surrounding window. Such an approach is computationally feasible because of the additive nature of regression parameters and variance. Any doubling of window size in each direction only takes a single pass over the data, corresponding to a logarithmic scaling of the resulting algorithm as a function of the window size. Slope and variance are stored for each aggregation step, allowing the reported slope to be selected to minimize variance. The approach thereby adjusts the effective window size to the landform features that are characteristic to the area within the DEM. Starting with a window size of 2x2, each iteration aggregates 2x2 non-overlapping windows from the previous iteration. Regression results are stored for each iteration, and the slope at minimal variance is reported in the final result. As such, the reported slope is adjusted to the length scale that is characteristic of the landform locally. The length scale itself and the variance at that length scale are also visualized to aid in interpreting the results for slope. The relevant length scale is taken to be half of the window size of the window over which the minimum variance was achieved. The resulting process was evaluated for 1-meter DEM data and for artificial data that was constructed to have defined length scales and added noise. A comparison with ESRI ArcMap was performed and showed the potential of the proposed algorithm. The resolution of the resulting output is much higher and the slope and aspect much less affected by noise. Additionally, the algorithm adjusts to the scale of interest within the region of the image. These benefits are gained without additional computational cost in comparison with resampling the DEM and computing the slope over 3x3 images in ESRI ArcMap for each resolution. In summary, the proposed approach extracts slope and aspect of DEMs at the lengths scales that are characteristic locally. The result is of higher resolution and less affected by noise than existing techniques.

Keywords: high resolution digital elevation models, multi-scale analysis, slope calculation, window-based regression

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Authors: T. Frawley, G. O'Kelly

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The UCD School of Nursing, Midwifery and Health Systems Higher Diploma in Mental Health (HDMH) nursing programme commenced in January 2017. Forty students successfully completed the programme. Programme evaluation was conducted from the outset. Research ethics approval was granted by the UCD Human Research Ethics Committee – Sciences in November 2016 (LS-E-16-163). Plan for Sustainability: Each iteration of the programme continues to be evaluated and adjusted accordingly. Aims: The ultimate purpose of the HDMH programme is to prepare registered nurses (registered children’s nurse (RCN), registered nurse in intellectual disability (RNID) and registered general nurse (RGN)) to function as effective registered psychiatric nurses in all settings which provide care and treatment for people experiencing mental health difficulties. Curriculum evaluation is essential to ensure that the programme achieves its purpose, that aims and expected outcomes are met and that required changes are highlighted for the programme’s continuing positive development. Methods: Both quantitative and qualitative methods were used in the evaluation. A series of questionnaires were used (the majority pre and post programme) to determine student perceptions of the programme, behaviour and attitudinal change from commencement to completion. These included the student assessment of learning gains (SALG); mental health knowledge schedule (MAKS); mental health clinician attitudes scale (MICA); reported and intended behaviour scale (RIBS); and community attitudes towards the mentally ill (CAMI). In addition, student and staff focus groups were conducted. Evaluation methods also incorporated module feedback. Outcome/Results: The evaluation highlighted a very positive response in relation to the achievement of programme outcomes and preparation for future work as registered psychiatric nursing. Some areas were highlighted for further development, which have been taken cognisance of in the 2019 iteration of the programme.

Keywords: learning gains, mental health, nursing, stigma

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Authors: Dewi Retno Sari Saputro, Purnami Widyaningsih, Hendrika Handayani

Abstract:

Extreme data on an observation can occur due to unusual circumstances in the observation. The data can provide important information that can’t be provided by other data so that its existence needs to be further investigated. The method for obtaining extreme data is one of them using maxima block method. The distribution of extreme data sets taken with the maxima block method is called the distribution of extreme values. Distribution of extreme values is Gumbel distribution with two parameters. The parameter estimation of Gumbel distribution with maximum likelihood method (ML) is difficult to determine its exact value so that it is necessary to solve the approach. The purpose of this study was to determine the parameter estimation of Gumbel distribution with quasi-Newton BFGS method. The quasi-Newton BFGS method is a numerical method used for nonlinear function optimization without constraint so that the method can be used for parameter estimation from Gumbel distribution whose distribution function is in the form of exponential doubel function. The quasi-New BFGS method is a development of the Newton method. The Newton method uses the second derivative to calculate the parameter value changes on each iteration. Newton's method is then modified with the addition of a step length to provide a guarantee of convergence when the second derivative requires complex calculations. In the quasi-Newton BFGS method, Newton's method is modified by updating both derivatives on each iteration. The parameter estimation of the Gumbel distribution by a numerical approach using the quasi-Newton BFGS method is done by calculating the parameter values that make the distribution function maximum. In this method, we need gradient vector and hessian matrix. This research is a theory research and application by studying several journals and textbooks. The results of this study obtained the quasi-Newton BFGS algorithm and estimation of Gumbel distribution parameters. The estimation method is then applied to daily rainfall data in Purworejo District to estimate the distribution parameters. This indicates that the high rainfall that occurred in Purworejo District decreased its intensity and the range of rainfall that occurred decreased.

Keywords: parameter estimation, Gumbel distribution, maximum likelihood, broyden fletcher goldfarb shanno (BFGS)quasi newton

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Authors: Ahmad Alhawarat, Mustafa Mamat, Mohd Rivaie, Ismail Mohd

Abstract:

Conjugate gradient method has been enormously used to solve large scale unconstrained optimization problems due to the number of iteration, memory, CPU time, and convergence property, in this paper we find a new class of nonlinear conjugate gradient coefficient with global convergence properties proved by exact line search. The numerical results for our new βK give a good result when it compared with well-known formulas.

Keywords: conjugate gradient method, conjugate gradient coefficient, global convergence

Procedia PDF Downloads 407