Search results for: hyperbolic problem

Authors: A. H. Choudhury

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In this paper, a highly accurate numerical method for the solution of one-dimensional fourth-order wave equation is derived. This hyperbolic problem is solved by using semidiscrete approximations. The space direction is discretized by wavelet-Galerkin method, and the time variable is discretized by using Newmark schemes.

Keywords: hyperbolic problem, semidiscrete approximations, stability, Wavelet-Galerkin Method

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Authors: Xuezhang Hou

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In the present paper, a hybrid hyperbolic dynamic system formulated by partial differential equations with initial and boundary conditions is considered. First, the system is transformed to an abstract evolution system in an appropriate Hilbert space, and spectral analysis and semigroup generation of the system operator is discussed. Subsequently, a sliding model control problem is proposed and investigated, and an equivalent control method is introduced and applied to the system. Finally, a significant result that the state of the system can be approximated by an ideal sliding mode under control in any accuracy is derived and examined.

Keywords: hyperbolic dynamic system, sliding model control, semigroup of linear operators, partial differential equations

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Authors: Adilson Elias Xavier, Otto Corrêa Rotunno Filho, Paulo Canedo De Magalhães

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This paper addresses the issue of automatic parameter estimation in conceptual rainfall-runoff (CRR) models. Due to threshold structures commonly occurring in CRR models, the associated mathematical optimization problems have the significant characteristic of being strongly non-differentiable. In order to face this enormous task, the resolution method proposed adopts a smoothing strategy using a special C∞ differentiable class function. The final estimation solution is obtained by solving a sequence of differentiable subproblems which gradually approach the original conceptual problem. The use of this technique, called Hyperbolic Smoothing Method (HSM), makes possible the application of the most powerful minimization algorithms, and also allows for the main difficulties presented by the original CRR problem to be overcome. A set of computational experiments is presented for the purpose of illustrating both the reliability and the efficiency of the proposed approach.

Keywords: rainfall-runoff models, automatic calibration, hyperbolic smoothing method

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Authors: Jose Juan Peña, J. Morales, J. García-Ravelo

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In the search of potential models applied in the theoretical treatment of diatomic molecules, some of them have been constructed by using standard hyperbolic functions as well as from the so-called q-deformed hyperbolic functions (sc q-dhf) for displacing and modifying the shape of the potential under study. In order to transcend the scope of hyperbolic functions, in this work, a kind of generalized q-deformed hyperbolic functions (g q-dhf) is presented. By a suitable transformation, through the q deformation parameter, it is shown that these g q-dhf can be expressed in terms of their corresponding standard ones besides they can be reduced to the sc q-dhf. As a useful application of the proposed approach, and considering a class of exactly solvable multi-parameter exponential-type potentials, some new q-deformed quantum interactions models that can be used as interesting alternative in quantum physics and quantum states are presented. Furthermore, due that quantum potential models are conditioned on the q-dependence of the parameters that characterize to the exponential-type potentials, it is shown that many specific cases of q-deformed potentials are obtained as particular cases from the proposal.

Keywords: diatomic molecules, exponential-type potentials, hyperbolic functions, q-deformed potentials

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Authors: S. O. Oyamakin, A. U. Chukwu,

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We proposed a Hyperbolic Gompertz Growth Model (HGGM), which was developed by introducing a stabilizing parameter called θ using hyperbolic sine function into the classical gompertz growth equation. The resulting integral solution obtained deterministically was reprogrammed into a statistical model and used in modeling the height and diameter of Pines (Pinus caribaea). Its ability in model prediction was compared with the classical gompertz growth model, an approach which mimicked the natural variability of height/diameter increment with respect to age and therefore provides a more realistic height/diameter predictions using goodness of fit tests and model selection criteria. The Kolmogorov-Smirnov test and Shapiro-Wilk test was also used to test the compliance of the error term to normality assumptions while using testing the independence of the error term using the runs test. The mean function of top height/Dbh over age using the two models under study predicted closely the observed values of top height/Dbh in the hyperbolic gompertz growth models better than the source model (classical gompertz growth model) while the results of R2, Adj. R2, MSE, and AIC confirmed the predictive power of the Hyperbolic Monomolecular growth models over its source model.

Keywords: height, Dbh, forest, Pinus caribaea, hyperbolic, gompertz

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Authors: S. O. Oyamakin, A. U. Chukwu

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Richard's growth equation being a generalized logistic growth equation was improved upon by introducing an allometric parameter using the hyperbolic sine function. The integral solution to this was called hyperbolic Richard's growth model having transformed the solution from deterministic to a stochastic growth model. Its ability in model prediction was compared with the classical Richard's growth model an approach which mimicked the natural variability of heights/diameter increment with respect to age and therefore provides a more realistic height/diameter predictions using the coefficient of determination (R2), Mean Absolute Error (MAE) and Mean Square Error (MSE) results. The Kolmogorov-Smirnov test and Shapiro-Wilk test was also used to test the behavior of the error term for possible violations. The mean function of top height/Dbh over age using the two models under study predicted closely the observed values of top height/Dbh in the hyperbolic Richard's nonlinear growth models better than the classical Richard's growth model.

Keywords: height, Dbh, forest, Pinus caribaea, hyperbolic, Richard's, stochastic

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Authors: Samuel Oluwafemi Oyamakin, Angela Unna Chukwu

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Richrads growth equation being a generalized logistic growth equation was improved upon by introducing an allometric parameter using the hyperbolic sine function. The integral solution to this was called hyperbolic Richards growth model having transformed the solution from deterministic to a stochastic growth model. Its ability in model prediction was compared with the classical Richards growth model an approach which mimicked the natural variability of heights/diameter increment with respect to age and therefore provides a more realistic height/diameter predictions using the coefficient of determination (R2), Mean Absolute Error (MAE) and Mean Square Error (MSE) results. The Kolmogorov-Smirnov test and Shapiro-Wilk test was also used to test the behavior of the error term for possible violations. The mean function of top height/Dbh over age using the two models under study predicted closely the observed values of top height/Dbh in the hyperbolic Richards nonlinear growth models better than the classical Richards growth model.

Keywords: height, diameter at breast height, DBH, hyperbolic sine function, Pinus caribaea, Richards' growth model

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Authors: M. O. Durojaye, J. T. Agee

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This paper is on the one-dimensional, positive temperature coefficient (PTC) thermistor model with a hyperbolic tangent function approximation for the electrical conductivity. The method of asymptotic expansion was adopted to obtain the steady state solution and the unsteady-state response was obtained using the method of lines (MOL) which is a well-established numerical technique. The approach is to reduce the partial differential equation to a vector system of ordinary differential equations and solve numerically. Our analysis shows that the hyperbolic tangent approximation introduced is well suitable for the electrical conductivity. Numerical solutions obtained also exhibit correct physical characteristics of the thermistor and are in good agreement with the exact steady state solutions.

Keywords: electrical conductivity, hyperbolic tangent function, PTC thermistor, method of lines

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Authors: Lana Horvat Dmitrović

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The main purpose of this paper is to study the box dimension as fractal property of bifurcations of discrete dynamical systems in higher dimensions. The paper contains the fractal analysis of the orbits near the hyperbolic and non-hyperbolic fixed points in discrete dynamical systems. It is already known that in one-dimensional case the orbit near the hyperbolic fixed point has the box dimension equal to zero. On the other hand, the orbit near the non-hyperbolic fixed point has strictly positive box dimension which is connected to the non-degeneracy condition of certain bifurcation. One of the main results in this paper is the generalisation of results about box dimension near the hyperbolic and non-hyperbolic fixed points to higher dimensions. In the process of determining box dimension, the restriction of systems to stable, unstable and center manifolds, Lipschitz property of box dimension and the notion of projective box dimension are used. The analysis of the bifurcations in higher dimensions with one multiplier on the unit circle is done by using the normal forms on one-dimensional center manifolds. This specific change in box dimension of an orbit at the moment of bifurcation has already been explored for some bifurcations in one and two dimensions. It was shown that specific values of box dimension are connected to appropriate bifurcations such as fold, flip, cusp or Neimark-Sacker bifurcation. This paper further explores this connection of box dimension as fractal property to some specific bifurcations in higher dimensions, such as fold-flip and flip-Neimark-Sacker. Furthermore, the application of the results to the unit time map of continuous dynamical system near hyperbolic and non-hyperbolic singularities is presented. In that way, box dimensions which are specific for certain bifurcations of continuous systems can be obtained. The approach to bifurcation analysis by using the box dimension as specific fractal property of orbits can lead to better understanding of bifurcation phenomenon. It could also be useful in detecting the existence or nonexistence of bifurcations of discrete and continuous dynamical systems.

Keywords: bifurcation, box dimension, invariant manifold, orbit near fixed point

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Authors: Mamyrbek A. Beisenbi, Nurgul M. Kissikova, Saltanat E. Beisembina, Salamat T. Suleimenova, Samal A. Kaliyeva

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The paper proposes a method for constructing a self-organizing control system for unstable and deterministic chaotic processes in the class of catastrophe “hyperbolic umbilic” for objects with m-inputs and n-outputs. The self-organizing control system is investigated by the universal gradient-velocity method of Lyapunov vector functions. The conditions for self-organization of the control system in the class of catastrophes “hyperbolic umbilic” are shown in the form of a system of algebraic inequalities that characterize the aperiodic robust stability in the stationary states of the system.

Keywords: gradient-velocity method of Lyapunov vector-functions, hyperbolic umbilic, self-organizing control system, stability

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Authors: Ashis Mallick, Rajeev Ranjan

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The closed form solution for thermal stresses in an annular fin with hyperbolic profile is derived using Adomian decomposition method (ADM). The conductive-convective fin with variable thermal conductivity is considered in the analysis. The nonlinear heat transfer equation is efficiently solved by ADM considering insulated convective boundary conditions at the tip of fin. The constant of integration in the solution is to be estimated using minimum decomposition error method. The solution of temperature field is represented in a polynomial form for convenience to use in thermo-elasticity equation. The non-dimensional thermal stress fields are obtained using the ADM solution of temperature field coupled with the thermo-elasticity solution. The influence of the various thermal parameters in temperature field and stress fields are presented. In order to show the accuracy of the ADM solution, the present results are compared with the results available in literature. The stress fields in fin with hyperbolic profile are compared with those of uniform thickness profile. Result shows that hyperbolic fin profile is better choice for enhancing heat transfer. Moreover, less thermal stresses are developed in hyperbolic profile as compared to rectangular profile. Next, Nelder-Mead based simplex search method is employed for the inverse estimation of unknown non-dimensional thermal parameters in a given stress fields. Owing to the correlated nature of the unknowns, the best combinations of the model parameters which are satisfying the predefined stress field are to be estimated. The stress fields calculated using the inverse parameters give a very good agreement with the stress fields obtained from the forward solution. The estimated parameters are suitable to use for efficient and cost effective fin designing.

Keywords: Adomian decomposition, inverse analysis, hyperbolic fin, variable thermal conductivity

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Authors: Telesphore Tiendrebeogo, Oumarou Sié

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Cloud computing technologies have attracted considerable interest in recent years. Thus, these latters have become more important for many existing database applications. It provides a new mode of use and of offer of IT resources in general. Such resources can be used “on demand” by anybody who has access to the internet. Particularly, the Cloud platform provides an ease to use interface between providers and users, allow providers to develop and provide software and databases for users over locations. Currently, there are many Cloud platform providers support large scale database services. However, most of these only support simple keyword-based queries and can’t response complex query efficiently due to lack of efficient in multi-attribute index techniques. Existing Cloud platform providers seek to improve performance of indexing techniques for complex queries. In this paper, we define a new cloud computing architecture based on a Distributed Hash Table (DHT) and design a prototype system. Next, we perform and evaluate our cloud computing indexing structure based on a hyperbolic tree using virtual coordinates taken in the hyperbolic plane. We show through our experimental results that we compare with others clouds systems to show our solution ensures consistence and scalability for Cloud platform.

Keywords: virtual coordinates, cloud, hyperbolic plane, storage, scalability, consistency

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Authors: Hazem M. Al-Mofleh

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In this paper, a new four-parameter univariate continuous distribution called the Normal-Generalized Hyperbolic Secant Distribution (NGHS) is defined and studied. Some general and structural distributional properties are investigated and discussed, including: central and non-central n-th moments and incomplete moments, quantile and generating functions, hazard function, Rényi and Shannon entropies, shapes: skewed right, skewed left, and symmetric, modality regions: unimodal and bimodal, maximum likelihood (MLE) estimators for the parameters. Finally, two real data sets are used to demonstrate empirically its flexibility and prove the strength of the new distribution.

Keywords: bimodality, estimation, hazard function, moments, Shannon’s entropy

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Authors: Gozel Judakova, Markus Bause

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We present and analyze reliable numerical techniques for simulating complex flow and transport phenomena related to natural gas transportation in pipelines. Such kind of problems are of high interest in the field of petroleum and environmental engineering. Modeling and understanding natural gas flow and transformation processes during transportation is important for the sake of physical realism and the design and operation of pipeline systems. In our approach a two fluid flow model based on a system of coupled hyperbolic conservation laws is considered for describing natural gas flow undergoing hydratization. The accurate numerical approximation of two-phase gas flow remains subject of strong interest in the scientific community. Such hyperbolic problems are characterized by solutions with steep gradients or discontinuities, and their approximation by standard finite element techniques typically gives rise to spurious oscillations and numerical artefacts. Recently, stabilized and discontinuous Galerkin finite element techniques have attracted researchers’ interest. They are highly adapted to the hyperbolic nature of our two-phase flow model. In the presentation a streamline upwind Petrov-Galerkin approach and a discontinuous Galerkin finite element method for the numerical approximation of our flow model of two coupled systems of Euler equations are presented. Then the efficiency and reliability of stabilized continuous and discontinous finite element methods for the approximation is carefully analyzed and the potential of the either classes of numerical schemes is investigated. In particular, standard benchmark problems of two-phase flow like the shock tube problem are used for the comparative numerical study.

Keywords: discontinuous Galerkin method, Euler system, inviscid two-fluid model, streamline upwind Petrov-Galerkin method, twophase flow

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Authors: Clarinda V. Nhangumbe, Ercília Sousa

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Weather Derivatives are financial instruments used to cover non-catastrophic weather events and can be expressed in the form of standard or plain vanilla products, structured or exotics products. The underlying asset, in this case, is the weather index, such as temperature, rainfall, humidity, wind, and snowfall. The complexity of the Weather Derivatives structure shows the weakness of the Black Scholes framework. Therefore, under the risk-neutral probability measure, the option price of a weather contract can be given as a unique solution of a two-dimensional partial differential equation (parabolic in one direction and hyperbolic in other directions), with an initial condition and subjected to adequate boundary conditions. To calculate the price of the option, one can use numerical methods such as the Monte Carlo simulations and implicit finite difference schemes conjugated with Semi-Lagrangian methods. This paper is proposed two explicit methods, namely, first-order upwind in the hyperbolic direction combined with Lax-Wendroff in the parabolic direction and first-order upwind in the hyperbolic direction combined with second-order upwind in the parabolic direction. One of the advantages of these methods is the fact that they take into consideration the boundary conditions obtained from the financial interpretation and deal efficiently with the different choices of the convection coefficients.

Keywords: incomplete markets, numerical methods, partial differential equations, stochastic process, weather derivatives

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Authors: Yinwei Lin, Cha'o-Kuang Chen

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In this article, the Laplace Adomian transform method (LADM) and double decomposition method (DDM) are used to solve the annular hyperbolic profile fins with variable thermal conductivity. As the thermal conductivity parameter ε is relatively large, the numerical solution using DDM become incorrect. Moreover, when the terms of DDM are more than seven, the numerical solution using DDM is very complicated. However, the present method can be easily calculated as terms are over seven and has more precisely numerical solutions. As the thermal conductivity parameter ε is relatively large, LADM also has better accuracy than DDM.

Keywords: fins, thermal conductivity, Laplace transform, Adomian, nonlinear

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Authors: Roberta Martino, Viviana Ventre

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Every day we face choices whose consequences are deferred in time. These types of choices are the intertemporal choices and play an important role in the social, economic, and financial world. The Discounted Utility Model is the mathematical model of reference to calculate the utility of intertemporal prospects. The discount rate is the main element of the model as it describes how the individual perceives the indeterminacy of subsequent periods. Empirical evidence has shown a discrepancy between the behavior expected from the predictions of the model and the effective choices made from the decision makers. In particular, the term temporal inconsistency indicates those choices that do not remain optimal with the passage of time. This phenomenon has been described with hyperbolic models of the discount rate which, unlike the linear or exponential nature assumed by the discounted utility model, is not constant over time. This paper explores the problem of inconsistency by tracing the decision-making process through the concept of impatience. The degree of impatience and the degree of decrease of impatience are two parameters that allow to quantify the weight of emotional factors and cognitive limitations during the evaluation and selection of alternatives. In fact, although the theory assumes perfectly rational decision makers, behavioral finance and cognitive psychology have made it possible to understand that distortions in the decision-making process and emotional influence have an inevitable impact on the decision-making process. The degree to which impatience is diminished is the focus of the first part of the study. By comparing consistent and inconsistent preferences over time, it was possible to verify that some anomalies in the discounted utility model are a result of the combination of cognitive bias and emotional factors. In particular: the delay effect and the interval effect are compared through the concept of misperception of time; starting from psychological considerations, a criterion is proposed to identify the causes of the magnitude effect that considers the differences in outcomes rather than their ratio; the sign effect is analyzed by integrating in the evaluation of prospects with negative outcomes the psychological aspects of loss aversion provided by Prospect Theory. An experiment implemented confirms three findings: the greatest variation in the degree of decrease in impatience corresponds to shorter intervals close to the present; the greatest variation in the degree of impatience occurs for outcomes of lower magnitude; the variation in the degree of impatience is greatest for negative outcomes. The experimental phase was implemented with the construction of the hyperbolic factor through the administration of questionnaires constructed for each anomaly. This work formalizes the underlying causes of the discrepancy between the discounted utility model and the empirical evidence of preference reversal.

Keywords: decreasing impatience, discount utility model, hyperbolic discount, hyperbolic factor, impatience

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Authors: Jana Abu Ahmada, Zaineb Mohamed, Ilyasse Aksikas

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The linear quadratic control system of hyperbolic first order partial differential equations (PDEs) are presented. The aim of this research is to control chemical reactions. This is achieved by converting the PDEs system to ordinary differential equations (ODEs) using the method of characteristics to reduce the system to control it by using the integral reinforcement learning. The designed controller is applied to a catalytic cracking reactor. Background—Transport-Reaction systems cover a large chemical and bio-chemical processes. They are best described by nonlinear PDEs derived from mass and energy balances. As a main application to be considered in this work is the catalytic cracking reactor. Indeed, the cracking reactor is widely used to convert high-boiling, high-molecular weight hydrocarbon fractions of petroleum crude oils into more valuable gasoline, olefinic gases, and others. On the other hand, control of PDEs systems is an important and rich area of research. One of the main control techniques is feedback control. This type of control utilizes information coming from the system to correct its trajectories and drive it to a desired state. Moreover, feedback control rejects disturbances and reduces the variation effects on the plant parameters. Linear-quadratic control is a feedback control since the developed optimal input is expressed as feedback on the system state to exponentially stabilize and drive a linear plant to the steady-state while minimizing a cost criterion. The integral reinforcement learning policy iteration technique is a strong method that solves the linear quadratic regulator problem for continuous-time systems online in real time, using only partial information about the system dynamics (i.e. the drift dynamics A of the system need not be known), and without requiring measurements of the state derivative. This is, in effect, a direct (i.e. no system identification procedure is employed) adaptive control scheme for partially unknown linear systems that converges to the optimal control solution. Contribution—The goal of this research is to Develop a characteristics-based optimal controller for a class of hyperbolic PDEs and apply the developed controller to a catalytic cracking reactor model. In the first part, developing an algorithm to control a class of hyperbolic PDEs system will be investigated. The method of characteristics will be employed to convert the PDEs system into a system of ODEs. Then, the control problem will be solved along the characteristic curves. The reinforcement technique is implemented to find the state-feedback matrix. In the other half, applying the developed algorithm to the important application of a catalytic cracking reactor. The main objective is to use the inlet fraction of gas oil as a manipulated variable to drive the process state towards desired trajectories. The outcome of this challenging research would yield the potential to provide a significant technological innovation for the gas industries since the catalytic cracking reactor is one of the most important conversion processes in petroleum refineries.

Keywords: PDEs, reinforcement iteration, method of characteristics, riccati equation, cracking reactor

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Authors: Tayo P. Ogundunmade, Adedayo A. Adepoju

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Terrorist attacks in liberal democracies bring about a few pessimistic results, for example, sabotaged public support in the governments they target, disturbing the peace of a protected environment underwritten by the state, and a limitation of individuals from adding to the advancement of the country, among others. Hence, seeking for techniques to understand the different factors involved in terrorism and how to deal with those factors in order to completely stop or reduce terrorist activities is the topmost priority of the government in every country. This research aim is to develop an efficient deep learning-based predictive model for the prediction of future terrorist activities in Nigeria, addressing low-quality prediction accuracy problems associated with the existing solution methods. The proposed predictive AI-based model as a counterterrorism tool will be useful by governments and law enforcement agencies to protect the lives of individuals in society and to improve the quality of life in general. A Heterogeneous Bayesian Neural Network (HETBNN) model was derived with Gaussian error normal distribution. Three primary transfer functions (HOTTFs), as well as two derived transfer functions (HETTFs) arising from the convolution of the HOTTFs, are namely; Symmetric Saturated Linear transfer function (SATLINS ), Hyperbolic Tangent transfer function (TANH), Hyperbolic Tangent sigmoid transfer function (TANSIG), Symmetric Saturated Linear and Hyperbolic Tangent transfer function (SATLINS-TANH) and Symmetric Saturated Linear and Hyperbolic Tangent Sigmoid transfer function (SATLINS-TANSIG). Data on the Terrorist activities in Nigeria gathered through questionnaires for the purpose of this study were used. Mean Square Error (MSE), Mean Absolute Error (MAE) and Test Error are the forecast prediction criteria. The results showed that the HETFs performed better in terms of prediction and factors associated with terrorist activities in Nigeria were determined. The proposed predictive deep learning-based model will be useful to governments and law enforcement agencies as an effective counterterrorism mechanism to understand the parameters of terrorism and to design strategies to deal with terrorism before an incident actually happens and potentially causes the loss of precious lives. The proposed predictive AI-based model will reduce the chances of terrorist activities and is particularly helpful for security agencies to predict future terrorist activities.

Keywords: activation functions, Bayesian neural network, mean square error, test error, terrorism

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Authors: Po-Jen Su, Huann-Ming Chou

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In this article we uses the residual correction method to deal with transient thermoelastic problems with a hollow spherical region when the continuum medium possesses spherically isotropic thermoelastic properties. Based on linear thermoelastic theory, the equations of hyperbolic heat conduction and thermoelastic motion were combined to establish the thermoelastic dynamic model with consideration of the deformation acceleration effect and non-Fourier effect under the condition of transient thermal shock. The approximate solutions of temperature and displacement distributions are obtained using the residual correction method based on the maximum principle in combination with the finite difference method, making it easier and faster to obtain upper and lower approximations of exact solutions. The proposed method is found to be an effective numerical method with satisfactory accuracy. Moreover, the result shows that the effect of transient thermal shock induced by deformation acceleration is enhanced by non-Fourier heat conduction with increased peak stress. The influence on the stress increases with the thermal relaxation time.

Keywords: maximum principle, non-Fourier heat conduction, residual correction method, thermo-elastic response

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Authors: S. Aditya, K. T. Nideesh, N. Guruprasad

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Being a subclass of linear programing problem, the Transportation Problem is a classic Operations Research problem where the objective is to determine the schedule for transporting goods from source to destination in a way that minimizes the shipping cost while satisfying supply and demand constraints. In this paper, we are representing the transportation problem for various warehouses along with various dealers situated in Bangalore city to reduce the transportation cost incurred by them as of now. The problem is solved by obtaining the Initial Basic feasible Solution through various methods and further proceeding to obtain optimal cost.

Keywords: NW method, optimum utilization, transportation problem, Vogel’s approximation method

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Authors: Jai Heui Kim, Sotheara Veng

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This paper studies the portfolio optimization problem for a pension fund under a hybrid model of stochastic volatility and constant elasticity of variance (CEV) using asymptotic analysis method. When the volatility component is fast mean-reverting, it is able to derive asymptotic approximations for the value function and the optimal strategy for general utility functions. Explicit solutions are given for the exponential and hyperbolic absolute risk aversion (HARA) utility functions. The study also shows that using the leading order optimal strategy results in the value function, not only up to the leading order, but also up to first order correction term. A practical strategy that does not depend on the unobservable volatility level is suggested. The result is an extension of the Merton's solution when stochastic volatility and elasticity of variance are considered simultaneously.

Keywords: asymptotic analysis, constant elasticity of variance, portfolio optimization, stochastic optimal control, stochastic volatility

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Authors: Jianhong Xiang, Hao Xiang, Linyu Wang

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Compressed sensing (CS) has a wide range of applications in sparse signal reconstruction. Aiming at the problems of low recovery accuracy and long reconstruction time of existing reconstruction algorithms in medical imaging, this paper proposes a corrected smoothing L0 algorithm based on compressed sensing (CSL0). First, an approximate hyperbolic tangent function (AHTF) that is more similar to the L0 norm is proposed to approximate the L0 norm. Secondly, in view of the "sawtooth phenomenon" in the steepest descent method and the problem of sensitivity to the initial value selection in the modified Newton method, the use of the steepest descent method and the modified Newton method are jointly optimized to improve the reconstruction accuracy. Finally, the CSL0 algorithm is simulated on various images. The results show that the algorithm proposed in this paper improves the reconstruction accuracy of the test image by 0-0. 98dB.

Keywords: smoothed L0, compressed sensing, image processing, sparse reconstruction

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Authors: Keng Keh Lim, Zaleha Ismail, Yudariah Mohammad Yusof

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This paper aims to find out how students using convergent and divergent thinking in creative problem solving to solve mathematical problems creatively. Eight engineering undergraduates in a local university took part in this study. They were divided into two groups. They solved the mathematical problems with the use of creative problem solving skills. Their solutions were collected and analyzed to reveal all the processes of problem solving, namely: problem definition, ideas generation, ideas evaluation, ideas judgment, and solution implementation. The result showed that the students were able to solve the mathematical problem with the use of creative problem solving skills.

Keywords: convergent thinking, divergent thinking, creative problem solving, creativity

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Authors: G. Sirbiladze, B. Ghvaberidze, B. Matsaberidze

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A fuzzy vehicle routing problem is considered in the possibilistic environment. A new criterion, maximization of expectation of reliability for movement on closed routes is constructed. The objective of the research is to implement a two-stage scheme for solution of this problem. Based on the algorithm of preferences on the first stage, the sample of so-called “promising” routes will be selected. On the second stage, for the selected promising routes new bi-criteria problem will be solved - minimization of total traveled distance and maximization of reliability of routes. The problem will be stated as a fuzzy-partitioning problem. Two possible solutions of this scheme are considered.

Keywords: vehicle routing problem, fuzzy partitioning problem, multiple-criteria optimization, possibility theory

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Authors: Alireza Akbari, Gelareh Babaee Khou

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Ground Penetrating Radar (GPR) is an important nondestructive remote sensing tool that has been used in both military and civilian fields. Recently, GPR imaging has attracted lots of attention in detection of subsurface shallow small targets such as landmines and unexploded ordnance and also imaging behind the wall for security applications. For the monostatic arrangement in the space-time GPR image, a single point target appears as a hyperbolic curve because of the different trip times of the EM wave when the radar moves along a synthetic aperture and collects reflectivity of the subsurface targets. With this hyperbolic curve, the resolution along the synthetic aperture direction shows undesired low resolution features owing to the tails of hyperbola. However, highly accurate information about the size, electromagnetic (EM) reflectivity, and depth of the buried objects is essential in most GPR applications. Therefore hyperbolic curve behavior in the space-time GPR image is often willing to be transformed to a focused pattern showing the object's true location and size together with its EM scattering. The common goal in a typical GPR image is to display the information of the spatial location and the reflectivity of an underground object. Therefore, the main challenge of GPR imaging technique is to devise an image reconstruction algorithm that provides high resolution and good suppression of strong artifacts and noise. In this paper, at first, the standard back-projection (BP) algorithm that was adapted to GPR imaging applications used for the image reconstruction. The standard BP algorithm was limited with against strong noise and a lot of artifacts, which have adverse effects on the following work like detection targets. Thus, an improved BP is based on cross-correlation between the receiving signals proposed for decreasing noises and suppression artifacts. To improve the quality of the results of proposed BP imaging algorithm, a weight factor was designed for each point in region imaging. Compared to a standard BP algorithm scheme, the improved algorithm produces images of higher quality and resolution. This proposed improved BP algorithm was applied on the simulation and the real GPR data and the results showed that the proposed improved BP imaging algorithm has a superior suppression artifacts and produces images with high quality and resolution. In order to quantitatively describe the imaging results on the effect of artifact suppression, focusing parameter was evaluated.

Keywords: algorithm, back-projection, GPR, remote sensing

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Authors: Terence Soule, Tami Al Ghamdi

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To study how the partial knowledge transfer may affect the Genetic Algorithm (GA) performance, we model the Transfer Learning (TL) process using GA as the model solver. The objective of the TL is to transfer the knowledge from one problem to another related problem. This process imitates how humans think in their daily life. In this paper, we proposed to study a case where the knowledge transferred from the S problem has less information than what the T problem needs. We sampled the transferred population using different strategies of TL. The results showed transfer part of the knowledge is helpful and speeds the GA process of finding a solution to the problem.

Keywords: transfer learning, partial transfer, evolutionary computation, genetic algorithm

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Authors: Kenza Aida Amara, Bachir Djebbar

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We treat the two-dimensional bin packing problem which involves packing a given set of rectangles into a minimum number of larger identical rectangles called bins. This combinatorial problem is NP-hard. We propose a pretreatment for the oriented version of the problem that allows the valorization of the lost areas in the bins and the reduction of the size problem. A heuristic method based on the strategy first-fit adapted to this problem is presented. We present an approach of resolution by bee colony optimization. Computational results express a comparison of the number of bins used with and without pretreatment.

Keywords: bee colony optimization, bin packing, heuristic algorithm, pretreatment

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Authors: Sukhveer Singh, Sandeep Singh

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A bi-objective fuzzy transportation problem with the objectives to minimize the total fuzzy cost and fuzzy time of transportation without according priorities to them is considered. To the best of our knowledge, there is no method in the literature to find efficient solutions of the bi-objective transportation problem under uncertainty. In this paper, a bi-objective transportation problem in an uncertain environment has been formulated. An algorithm has been proposed to find efficient solutions of the bi-objective transportation problem under uncertainty. The proposed algorithm avoids the degeneracy and gives the optimal solution faster than other existing algorithms for the given uncertain transportation problem.

Keywords: uncertain transportation problem, efficient solution, ranking function, fuzzy transportation problem

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Authors: Ravneil Nand

Abstract:

Cooperative coevolution uses problem decomposition methods to solve a larger problem. The problem decomposition deals with breaking down the larger problem into a number of smaller sub-problems depending on their method. Different problem decomposition methods have their own strengths and limitations depending on the neural network used and application problem. In this paper we are introducing a new problem decomposition method known as Hidden-Neuron Level Decomposition (HNL). The HNL method is competing with established problem decomposition method in time series prediction. The results show that the proposed approach has improved the results in some benchmark data sets when compared to the standalone method and has competitive results when compared to methods from literature.

Keywords: cooperative coevaluation, feed forward network, problem decomposition, neuron, synapse

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