Search results for: initial value problems

Authors: Ogunrinde Roseline Bosede

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This paper presents the development, analysis and implementation of an inverse polynomial numerical method which is well suitable for solving initial value problems in first order ordinary differential equations with applications to sample problems. We also present some basic concepts and fundamental theories which are vital to the analysis of the scheme. We analyzed the consistency, convergence, and stability properties of the scheme. Numerical experiments were carried out and the results compared with the theoretical or exact solution and the algorithm was later coded using MATLAB programming language.

Keywords: differential equations, numerical, polynomial, initial value problem, differential equation

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Authors: Luke Ukpebor, C. E. Abhulimen

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Stiff initial value problems in ordinary differential equations are problems for which a typical solution is rapidly decaying exponentially, and their numerical investigations are very tedious. Conventional numerical integration solvers cannot cope effectively with stiff problems as they lack adequate stability characteristics. In this article, we developed a new family of four-step second derivative exponentially fitted method of order six for the numerical integration of stiff initial value problem of general first order differential equations. In deriving our method, we employed the idea of breaking down the general multi-derivative multistep method into predator and corrector schemes which possess free parameters that allow for automatic fitting into exponential functions. The stability analysis of the method was discussed and the method was implemented with numerical examples. The result shows that the method is A-stable and competes favorably with existing methods in terms of efficiency and accuracy.

Keywords: A-stable, exponentially fitted, four step, predator-corrector, second derivative, stiff initial value problems

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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: Eugene Stepanov, Arcady Ponosov

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To model gene regulatory networks one uses ordinary differential equations with switching nonlinearities, where the initial value problem is known to be well-posed if the trajectories cross the discontinuities transversally. Otherwise, the initial value problem is usually ill-posed, which lead to theoretical and numerical complications. In the presentation, it is proposed to apply the theory of hybrid dynamical systems, rather than switched ones, to regularize the problem. 'Hybridization' of the switched system means that one attaches a dynamic discrete component ('automaton'), which follows the trajectories of the original system and governs its dynamics at the points of ill-posedness of the initial value problem making it well-posed. The construction of the automaton is based on the classification of the attractors of the specially designed adjoint dynamical system. Several examples are provided in the presentation, which support the suggested analysis. The method can also be of interest in other applied fields, where differential equations contain switchings, e.g. in neural field models.

Keywords: hybrid dynamical systems, ill-posed problems, singular perturbation analysis, switching nonlinearities

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Authors: Alexander P. Vazhenin, Mikhail M. Lavrentiev, Alexey A. Romanenko, Pavel V. Tatarintsev

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One of the problems obstructing effective tsunami modelling is the lack of information about initial wave shape at source. The existing methods; geological, sea radars, satellite images, contain an important part of uncertainty. Therefore, direct measurement of tsunami waves obtained at the deep water bottom peruse recorders is also used. In this paper we propose a new method to reconstruct the initial sea surface displacement at tsunami source by the measured signal (marigram) approximation with the help of linear combination of synthetic marigrams from the selected set of unit sources, calculated in advance. This method has demonstrated good precision and very high performance. The mathematical model and results of numerical tests are here described.

Keywords: numerical tests, orthogonal decomposition, Tsunami Initial Sea Surface Displacement

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Authors: Lina E. Homman, Alexis C. Edwards, Seung Bin Cho, Danielle M. Dick, Kenneth S. Kendler

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Research supports an association between alcohol problems and internalising symptoms, but the understanding of how the two phenotypes relate to each other is poor. It has been hypothesized that the relationship between the phenotypes is causal; however investigations in regards to direction are inconsistent. Clarity of the relationship between the two phenotypes may be provided by investigating the phenotypes developmental inter-relationships longitudinally. The objective of the study was to investigate a) changes in alcohol problems and internalising symptoms in college students across time and b) the direction of effect of growth between alcohol problems and internalising symptoms from late adolescent to emerging adulthood c) possible gender differences. The present study adds to the knowledge of comorbidity of alcohol problems and internalising symptoms by examining a longitudinal sample of college students and by examining the simultaneous development of the symptoms. A sample of college students is of particular interest as symptoms of both phenotypes often have their onset around this age. A longitudinal sample of college students from a large, urban, public university in the United States was used. Data was collected over a time period of 2 years at 3 time points. Latent growth models were applied to examine growth trajectories. Parallel process growth models were used to assess whether initial level and rate of change of one symptom affected the initial level and rate of change of the second symptom. Possible effects of gender and ethnicity were investigated. Alcohol problems significantly increased over time, whereas internalizing symptoms remained relatively stable. The two phenotypes were significantly correlated in each wave, correlations were stronger among males. Initial level of alcohol problems was significantly positively correlated with initial level of internalising symptoms. Rate of change of alcohol problems positively predicted rate of change of internalising symptoms for females but not for males. Rate of change of internalising symptoms did not predict rate of change of alcohol problems for either gender. Participants of Black and Asian ethnicities indicated significantly lower levels of alcohol problems and a lower increase of internalising symptoms across time, compared to White participants. Participants of Black ethnicity also reported significantly lower levels of internalising symptoms compared to White participants. The present findings provide additional support for a positive relationship between alcohol problems and internalising symptoms in youth. Our findings indicated that both internalising symptoms and alcohol problems increased throughout the sample and that the phenotypes were correlated. The findings mainly implied a bi-directional relationship between the phenotypes in terms of significant associations between initial levels as well as rate of change. No direction of causality was indicated in males but significant results were found in females where alcohol problems acted as the main driver for the comorbidity of alcohol problems and internalising symptoms; alcohol may have more detrimental effects in females than in males. Importantly, our study examined a population-based longitudinal sample of college students, revealing that the observed relationships are not limited to individuals with clinically diagnosed mental health or substance use problems.

Keywords: alcohol, comorbidity, internalising symptoms, longitudinal modelling

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Authors: Li Ni, Pen ManMan, Li KenLi

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Clustering is an intensive research for some years because of its multifaceted applications, such as biology, information retrieval, medicine, business and so on. The expectation maximization (EM) is a kind of algorithm framework in clustering methods, one of the ten algorithms of machine learning. Traditionally, optimization of objective function has been the standard approach in EM. Hence, research has investigated the utility of evolutionary computing and related techniques in the regard. Chemical Reaction Optimization (CRO) is a recently established method. So the property embedded in CRO is used to solve optimization problems. This paper presents an algorithm framework (EM-CRO) with modified CRO operators based on EM cluster problems. The hybrid algorithm is mainly to solve the problem of initial value sensitivity of the objective function optimization clustering algorithm. Our experiments mainly take the EM classic algorithm:k-means and fuzzy k-means as an example, through the CRO algorithm to optimize its initial value, get K-means-CRO and FKM-CRO algorithm. The experimental results of them show that there is improved efficiency for solving objective function optimization clustering problems.

Keywords: chemical reaction optimization, expection maimization, initia, objective function clustering

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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: 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: Olusola Ezekiel Abolarin, Gift E. Noah

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This research work considered an innovative procedure to numerically approximate higher-order Initial value problems (IVP) of ordinary differential equations (ODE) using the Legendre polynomial as the basis function. The proposed method is a half-step, self-starting Block integrator employed to approximate fourth and fifth order IVPs without reduction to lower order. The method was developed through a collocation and interpolation approach. The basic properties of the method, such as convergence, consistency and stability, were well investigated. Several test problems were considered, and the results compared favorably with both exact solutions and other existing methods.

Keywords: initial value problem, ordinary differential equation, implicit off-grid block method, collocation, interpolation

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Authors: Noufe H. Aljahdaly

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The Laplace homotopy perturbation method (LHPM) is an approximate method that help to compute the approximate solution for partial differential equations. The method has been used for solving several problems in science. It requires the initial condition, so it solves the initial value problem. In physics, when some important terms are taken in account, we may obtain non-integrable partial differential equations that do not have analytical integrals. This type of PDEs do not have exact solution, therefore, we need to compute the solution without initial condition. In this work, we improved the LHPM to be able to solve non-integrable problem, especially the damped PDEs, which are the PDEs that include a damping term which makes the PDEs non-integrable. We improved the LHPM by setting a perturbation parameter and an embedding parameter as the damping parameter and using the initial condition for damped PDE as the initial condition for non-damped PDE.

Keywords: non-integrable PDEs, modified Kawahara equation;, laplace homotopy perturbation method, damping term

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Authors: Flavia Smarrazzo

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Initial-boundary value problems for nonlinear parabolic equations having a Radon measure as initial data have been widely investigated, looking for solutions which for positive times take values in some function space. On the other hand, if the diffusivity degenerates too fast at infinity, it is well known that function-valued solutions may not exist, singularities may persist, and it looks very natural to consider solutions which, roughly speaking, for positive times describe an orbit in the space of the finite Radon measures. In this general framework, our purpose is to introduce a concept of measure-valued solution which is consistent with respect to regularizing and smoothing approximations, in order to develop an existence theory which does not depend neither on the level of degeneracy of diffusivity at infinity nor on the choice of the initial measures. In more detail, we prove existence of suitably defined measure-valued solutions to the homogeneous Dirichlet initial-boundary value problem for a class of nonlinear parabolic equations without strong coerciveness. Moreover, we also discuss some qualitative properties of the constructed solutions concerning the evolution of their singular part, including conditions (depending both on the initial data and on the strength of degeneracy) under which the constructed solutions are in fact unction-valued or not.

Keywords: degenerate parabolic equations, measure-valued solutions, Radon measures, young measures

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Authors: Mohammad H. Almomani

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In this paper, we argue the effect of the initial sample size, and the increment in simulation samples on the performance of a sequential approach that used in selecting the top m designs when the number of alternative designs is very large. The sequential approach consists of two stages. In the first stage the ordinal optimization is used to select a subset that overlaps with the set of actual best k% designs with high probability. Then in the second stage the optimal computing budget is used to select the top m designs from the selected subset. We apply the selection approach on a generic example under some parameter settings, with a different choice of initial sample size and the increment in simulation samples, to explore the impacts on the performance of this approach. The results show that the choice of initial sample size and the increment in simulation samples does affect the performance of a selection approach.

Keywords: Large Scale Problems, Optimal Computing Budget Allocation, ordinal optimization, simulation optimization

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Authors: Yu Menshikov

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In this paper the influence of errors of function derivatives in initial time which have been obtained by experiment (uncontrollable inaccuracy) to the results of inverse problem solution was investigated. It was shown that these errors distort the inverse problem solution as a rule near the beginning of interval where the solution are analyzed. Several methods for remove the influence of uncontrollable inaccuracy have been suggested.

Keywords: inverse problems, filtration, uncontrollable inaccuracy

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Authors: Youngji Lee, Yonghyeon Jeon, Sunyoung Bu, Philsu Kim

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The aim of this paper is to construct an algorithm of time step control for the error correction method most recently developed by one of the authors for solving stiff initial value problems. It is achieved with the generalized Chebyshev polynomial and the corresponding error correction method. The main idea of the proposed scheme is in the usage of the duplicated node points in the generalized Chebyshev polynomials of two different degrees by adding necessary sample points instead of re-sampling all points. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. The constructed algorithm controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method. Two stiff problems are numerically solved to assess the effectiveness of the proposed scheme.

Keywords: stiff initial value problem, error correction method, generalized Chebyshev polynomial, node points

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Authors: Dmitri Terzi

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The article presents the results of an algorithmic study of a special optimization problem of the transport type (traveling salesman problem): 1) To solve the problem, a new natural algorithm has been developed based on the decomposition of the initial data into convex hulls, which has a number of advantages; it is applicable for a fairly large dimension, does not require a large amount of memory, and has fairly good performance. The relevance of the algorithm lies in the fact that, in practice, programs for problems with the number of traversal points of no more than twenty are widely used. For large-scale problems, the availability of algorithms and programs of this kind is difficult. The proposed algorithm is natural because the optimal solution found by the exact algorithm is not always feasible due to the presence of many other factors that may require some additional restrictions. 2) Another inverse problem solved here is to describe a class of traveling salesman problems that have a predetermined optimal solution. The constructed algorithm 2 allows us to characterize the structure of traveling salesman problems, as well as construct test problems to evaluate the effectiveness of algorithms and other purposes. 3) The appendix presents a software implementation of Algorithm 1 (in MATLAB), which can be used to solve practical problems, as well as in the educational process on operations research and optimization methods.

Keywords: traveling salesman problem, solution construction algorithm, convex hulls, optimality verification

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Authors: Nai-Jiin Yang, Tyler Renshaw

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Prior research has suggested that youth internalizing and externalizing problems significantly correlate with student subjective wellbeing (SSW) and achievement problems (SAP). Yet, only a few studies have used data from mental health screener based on the dual-factor model to explore the empirical relationships among internalizing problems, externalizing problems, academic problems, and student wellbeing. This study was conducted through a secondary analysis of previously collected data in school-wide mental health screening activities across secondary schools within a suburban school district in the western United States. The data set included 1880 student responses from a total of two schools. Findings suggest that both internalizing and externalizing problems are substantial predictors of both student wellbeing and academic problems. However, compared to internalizing problems, externalizing problems were a much stronger predictor of academic problems. Moreover, this study did not support academic problems that moderate the relationship between SSW and youth internalizing problems (YIP) and between youth externalizing problems (YEP) and SSW. Lastly, SAP is the strongest predictor of SSW than YIP and YEP.

Keywords: academic problems, externalizing problems, internalizing problems, school mental health, student wellbeing, universal mental health screening

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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: Ranadhir Roy

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Inverse problems arise in medical (molecular) imaging. These problems are characterized by large in three dimensions, and by the diffusion equation which models the physical phenomena within the media. The inverse problems are posed as a nonlinear optimization where the unknown parameters are found by minimizing the difference between the predicted data and the measured data. To obtain a unique and stable solution to an ill-posed inverse problem, a priori information must be used. Mathematical conditions to obtain stable solutions are established in Tikhonov’s regularization method, where the a priori information is introduced via a stabilizing functional, which may be designed to incorporate some relevant information of an inverse problem. Effective determination of the Tikhonov regularization parameter requires knowledge of the true solution, or in the case of optical imaging, the true image. Yet, in, clinically-based imaging, true image is not known. To alleviate these difficulties we have applied the penalty/modified barrier function (PMBF) method instead of Tikhonov regularization technique to make the inverse problems well-posed. Unlike the Tikhonov regularization method, the constrained optimization technique, which is based on simple bounds of the optical parameter properties of the tissue, can easily be implemented in the PMBF method. Imposing the constraints on the optical properties of the tissue explicitly restricts solution sets and can restore uniqueness. Like the Tikhonov regularization method, the PMBF method limits the size of the condition number of the Hessian matrix of the given objective function. The accuracy and the rapid convergence of the PMBF method require a good initial guess of the Lagrange multipliers. To obtain the initial guess of the multipliers, we use a least square unconstrained minimization problem. Three-dimensional images of fluorescence absorption coefficients and lifetimes were reconstructed from contact and noncontact experimentally measured data.

Keywords: constrained minimization, ill-conditioned inverse problems, Tikhonov regularization method, penalty modified barrier function method

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Authors: César Huiliñir, Danilo Villanueva, Pedro Iván Alvarez, Francisco Cubillos

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Biodrying aims at removing water from biowastes and has been mostly studied for municipal solid wastes (MSW), while few studies have dealt with secondary sludge from the paper and pulp industry. The goal of this study was to investigate the effect of initial moisture content (MC) on the batch biodrying of pulp and paper secondary sludge, using rice husks as bulking agents. Three initial MCs were studied (54, 65, and 74% w.b.) in closed batch laboratory-scale reactors under adiabatic conditions and with a constant air-flow rate (0.65 l min-1 kg-1 wet solid). The initial MC of the mixture of secondary sludge and rice husks showed a significant effect on the biodrying process. Using initial moisture content between 54-65% w.b., the solid moisture content was reduce up to 37 % w.b. in ten days, getting calorific values between 8000-9000 kJ kg-1. It was concluded that a decreasing of initial MC improves the drying rate and decreases the solid volatile consumption, therefore, the optimization of biodrying should consider this parameter.

Keywords: biodrying, secondary sludge, initial moisture content, pulp and paper industry, rice husk

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Authors: Lawrence A. Farinola

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Four point implicit schemes for the approximation of the first and pure second order derivatives for the solution of the Dirichlet problem for one dimensional Schrodinger equation with respect to the time variable t were constructed. Also, special four-point implicit difference boundary value problems are proposed for the first and pure second derivatives of the solution with respect to the spatial variable x. The Grid method is also applied to the mixed second derivative of the solution of the Linear Schrodinger time-dependent equation. It is assumed that the initial function belongs to the Holder space C⁸⁺ᵃ, 0 < α < 1, the Schrodinger wave function given in the Schrodinger equation is from the Holder space Cₓ,ₜ⁶⁺ᵃ, ³⁺ᵃ/², the boundary functions are from C⁴⁺ᵃ, and between the initial and the boundary functions the conjugation conditions of orders q = 0,1,2,3,4 are satisfied. It is proven that the solution of the proposed difference schemes converges uniformly on the grids of the order O(h²+ k) where h is the step size in x and k is the step size in time. Numerical experiments are illustrated to support the analysis made.

Keywords: approximation of derivatives, finite difference method, Schrödinger equation, uniform error

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Authors: Chih-Hsiang Chang, I-Fan Ho

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This study examines the credibility of the signaling as explanation for IPO initial underpricing. Findings reveal the initial underpricing and the long-term underperformance of IPOs in Taiwan. However, we only find weak support for signaling as explanation of IPO underpricing.

Keywords: signaling, IPO initial underpricing, IPO long-term underperformance, Taiwan’s stock market

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Authors: Bolatbek Rysbaiuly, Aliya S. Azhibekova

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Problems concerning the interpretation of the well testing results belong to the class of inverse problems of subsurface hydromechanics. The distinctive feature of such problems is that additional information is depending on the capabilities of oilfield experiments. Another factor that should not be overlooked is the existence of errors in the test data. To determine reservoir properties, some inverse problems for parabolic equations were investigated. An approach to solving the inverse problems based on the method of regularization is proposed.

Keywords: iterative approach, inverse problem, parabolic equation, reservoir properties

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Authors: Ayşe Yurdakul, Eckehard Schnieder

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Because of the growing multidisciplinarity and multilinguality, communication problems in different technical fields grows more and more. Therefore, each technical field has its own specific language, terminology which is characterised by the different definition of terms. In addition to definition problems, there are also relation problems between terms. Among these problems of relation, there are the synonymy, antonymy, hypernymy/hyponymy, ambiguity, risk of confusion, and translation problems etc. Thus, the terminology management system iglos of the Institute for Traffic Safety and Automation Engineering of the Technische Universität Braunschweig has the target to solve these problems by a methodological standardisation of term definitions with the aid of the iglos sign model and iglos relation types. The focus of this paper should be on solving definition and relation problems between terms in English navigation terminology.

Keywords: iglos, iglos sign model, methodological resolutions, navigation terminology, common language, technical language, positioning, definition problems, relation problems

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Authors: Claudia Ehrentraut, Osama Ibrahim, Hercules Dalianis

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Policy making situations are real-world problems that exhibit complexity in that they are composed of many interrelated problems and issues. To be effective, policies must holistically address the complexity of the situation rather than propose solutions to single problems. Formulating and understanding the situation and its complex dynamics, therefore, is a key to finding holistic solutions. Analysis of text based information on the policy problem, using Natural Language Processing (NLP) and Text analysis techniques, can support modelling of public policy problem situations in a more objective way based on domain experts knowledge and scientific evidence. The objective behind this study is to support modelling of public policy problem situations, using text analysis of verbal descriptions of the problem. We propose a formal methodology for analysis of qualitative data from multiple information sources on a policy problem to construct a causal diagram of the problem. The analysis process aims at identifying key variables, linking them by cause-effect relationships and mapping that structure into a graphical representation that is adequate for designing action alternatives, i.e., policy options. This study describes the outline of an algorithm used to automate the initial step of a larger methodological approach, which is so far done manually. In this initial step, inferences about key variables and their interrelationships are extracted from textual data to support a better problem structuring. A small prototype for this step is also presented.

Keywords: public policy, problem structuring, qualitative analysis, natural language processing, algorithm, inference extraction

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Authors: Jui-Ting Hsu, Heng-Li Huang, Ming-Tzu Tsai, Kuo-Chih Su, Lih-Jyh Fuh

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The objectives of this study were to measure the initial stability of the dental implant (ISQ and PTV) in the artificial foam bone block with three different quality levels. In addition, the 3D bone to implant contact percentage (BIC%) was measured based on the micro-computed tomography images. Furthermore, the relation between the initial stability of dental implant (ISQ and PTV) and BIC% were calculated. The experimental results indicated that enhanced the material property of the artificial foam bone increased the initial stability of the dental implant. The Pearson’s correlation coefficient between the BIC% and the two approaches (ISQ and PTV) were 0.652 and 0.745.

Keywords: dental implant, implant stability quotient, peak insertion torque, bone-implant contact, micro-computed tomography

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Authors: N. Guruprasad

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This paper presents a modification of approximation method for transportation problems. The initial basic feasible solution can be computed using either Russel's or Vogel's approximation methods. Russell’s approximation method provides another excellent criterion that is still quick to implement on a computer (not manually) In most cases Russel's method yields a better initial solution, though it takes longer than Vogel's method (finding the next entering variable in Russel's method is in O(n1*n2), and in O(n1+n2) for Vogel's method). However, Russel's method normally has a lesser total running time because less pivots are required to reach the optimum for all but small problem sizes (n1+n2=~20). With this motivation behind we have incorporated a variation of the same – what we have proposed it has TMC (Total Modified Cost) to obtain fast and efficient solutions.

Keywords: computation, efficiency, modified cost, Russell’s approximation method, transportation, Vogel’s approximation method

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Authors: Hichem Kmimech, Achref Jabeur Telmoudi, Lotfi Nabli

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The estimation of the initial marking minimum (MIM) is a crucial problem in labeled Petri nets. In the case of multiple choices, the search for the initial marking leads to a problem of optimization of the minimum allocation of resources with two constraints. The first concerns the firing sequence that could be legal on the initial marking with respect to the firing vector. The second deals with the total number of tokens that can be minimal. In this article, the MIM problem is solved by the meta-heuristic particle swarm optimization (PSO). The proposed approach presents the advantages of PSO to satisfy the two previous constraints and find all possible combinations of minimum initial marking with the best computing time. This method, more efficient than conventional ones, has an excellent impact on the resolution of the MIM problem. We prove through a set of definitions, lemmas, and examples, the effectiveness of our approach.

Keywords: marking, production system, labeled Petri nets, particle swarm optimization

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Authors: Raif Parlakkaya, Huseyin Cetin, Halil Akmese, Mesut Murat Adabali

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As the economies of other countries in the Mediterranean Basin, the tourism sector in our country has a high denominator in economics. Tourism businesses, which are building blocks of tourism, sector faces with a variety of problems during their activities. These problems faced make business efficiency and competition conditions of the businesses difficult. Most of the problems faced by the tourism businesses and the information of consumers about consumers’ rights were used in this study, which is conducted to determine the problems of tourism businesses in the Central Anatolia Region. It is aimed to contribute the awareness of staff and executives working at tourism sector and to attract attention of businesses active concurrently with tourism sector and legislators.

Keywords: financial problems, the problems of tourism businesses, tourism businesses, tourism sector in Turkey

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Authors: Sunila John, B. Rajashekhar

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Initial letter fluency tasks are one of the simple behavioral measures to evaluate the complex nature of word retrieval ability. This task requires the participant to retrieve as many words as possible beginning with a particular letter in a fixed time frame. Though the task of verbal fluency is popular among adult clinical conditions, its role in children has been less emphasized. There exists a lack of in-depth understanding of processes underlying verbal fluency performance in typically developing children. The present study, therefore, aims to delineate the developmental trend on initial letter fluency task observed in typically developing Malayalam speaking children. The participants were aged between 5 to 10 years and categorized into three groups: Group I (class I and II, mean (SD) age years: 6.44(.78)), Group II (class III and IV, mean (SD) age years: 8.59 (.83)) and group III (class V and VI, mean (SD) age years: 10.28 (.80). On two tasks of initial letter fluency, the verbal fluency outcome measures were analyzed. The study findings revealed a distinct pattern of initial letter fluency development which may enhance its usefulness in clinical and research settings.

Keywords: children, development, initial letter fluency, word retrieval

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