Search results for: exponential smoothing methods

Authors: Benalia Nadia, Bensiali Nadia, Zerzouri Noura

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This paper presents an analysis of the effects of parameters np and nq for exponential load on the transmission line voltage profile, transferred power and transmission losses for different shunt compensation size. For different values for np and nq in which active and reactive power vary with it is terminal voltages as in exponential form, variations of the load voltage for different sizes of shunt capacitors are simulated with a simple two-bus power system using Matlab SimPowerSystems Toolbox. It is observed that the compensation level is significantly affected by the voltage sensitivities of loads.

Keywords: static load model, shunt compensation, transmission system, exponentiel load model

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

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It is known that by introducing alternative forms of exponential and logarithmic functions, the Tsallis entropy Sq is itself a generalization of Shannon entropy S. In this work, from a deformation through a scaling function applied to the differential operator, it is possible to generate a q-deformed calculus as well as a q-deformed arithmetic, which not only allows generalizing the exponential and logarithmic functions but also any other standard function. The updated q-deformed differential operator leads to an updated integral operator under which the functions are integrated together with a weight function. For each differentiable function, it is possible to identify its q-deformed partner, which is useful to generalize other algebraic relations proper of the original functions. As an application of this proposal, in this work, a generalization of exponential and logarithmic functions is studied in such a way that their relationship with the thermodynamic functions, particularly the entropy, allows us to have a q-deformed expression of these. As a result, from a particular scaling function applied to the differential operator, a q-deformed arithmetic is obtained, leading to the generalization of the Tsallis entropy.

Keywords: q-calculus, q-deformed arithmetic, entropy, exponential functions, thermodynamic functions

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Authors: Cletus Abhulimen, L. A. Ukpebor

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In this paper, we construct a class of four-step third derivative exponential fitting integrator of order six for the numerical integration of stiff initial-value problems of the type: y’= f(x,y); y(x₀) =y₀. The implicit method has free parameters which allow it to be fitted automatically to exponential functions. For the purpose of effective implementation of the proposed method, we adopted the techniques of splitting the method into predictor and corrector schemes. The numerical analysis of the stability of the new method was discussed; the results show that the method is A-stable. Finally, numerical examples are presented, to show the efficiency and accuracy of the new method.

Keywords: third derivative four-step, exponentially fitted, a-stable, stiff differential equations

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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: W. K. Zahra, M. A. El-Beltagy, R. R. Elkhadrawy

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So many practical problems in science and technology developed over the past decays. For instance, the mathematical boundary layer theory or the approximation of solution for different problems described by differential equations. When such problems consider large or small parameters, they become increasingly complex and therefore require the use of asymptotic methods. In this work, we consider the singularly perturbed boundary value problems which contain very small parameters. Moreover, we will consider these perturbation parameters as random variables. We propose a numerical method to solve this kind of problems. The proposed method is based on an exponential spline, Shishkin mesh discretization, and polynomial chaos expansion. The polynomial chaos expansion is used to handle the randomness exist in the perturbation parameter. Furthermore, the Monte Carlo Simulations (MCS) are used to validate the solution and the accuracy of the proposed method. Numerical results are provided to show the applicability and efficiency of the proposed method, which maintains a very remarkable high accuracy and it is ε-uniform convergence of almost second order.

Keywords: singular perturbation problem, polynomial chaos expansion, Shishkin mesh, two small parameters, exponential spline

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Authors: Sheena K. J., Jyoti Badge, Sayed Mohammed Zeeshan

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A Comparative Study of Exponential and Logistic Population Growth Models in India India is the second most populous city in the world, just behind China, and is going to be in the first place by next year. The Indian population has remarkably at higher rate than the other countries from the past 20 years. There were many scientists and demographers who has formulated various models of population growth in order to study and predict the future population. Some of the models are Fibonacci population growth model, Exponential growth model, Logistic growth model, Lotka-Volterra model, etc. These models have been effective in the past to an extent in predicting the population. However, it is essential to have a detailed comparative study between the population models to come out with a more accurate one. Having said that, this research study helps to analyze and compare the two population models under consideration - exponential and logistic growth models, thereby identifying the most effective one. Using the census data of 2011, the approximate population for 2016 to 2031 are calculated for 20 Indian states using both the models, compared and recorded the data with the actual population. On comparing the results of both models, it is found that logistic population model is more accurate than the exponential model, and using this model, we can predict the future population in a more effective way. This will give an insight to the researchers about the effective models of population and how effective these population models are in predicting the future population.

Keywords: population growth, population models, exponential model, logistic model, fibonacci model, lotka-volterra model, future population prediction, demographers

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Authors: Abdulrahman Abdulrahman

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The specific energy equation has many applications in practical channels, such as exponential channels. In this paper, the governing equation of alternate depth ratio for exponential channels, in general, was investigated towards obtaining analytical solution for the alternate depth ratio in three exponential channel shapes, viz., rectangular, triangular, and parabolic channels. The alternate depth ratio for rectangular channels is quadratic; hence it is very simple to solve. While for parabolic and triangular channels, the alternate depth ratio is cubic and quartic equations, respectively, analytical solution for these equations may be achieved easily for a given Froud number. Different examples are solved to prove the efficiency of the proposed solution. Such analytical solution can be easily used in natural rivers and most of practical channels.

Keywords: alternate depth, analytical solution, specific energy, parabolic channel, rectangular channel, triangular channel, open channel flow

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Authors: M. Mueller, M. Kuehn, M. Voelker

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In small and medium-sized enterprises (SMEs), the challenge is to create a well-grounded and reliable basis for process analysis, optimization and planning due to a lack of data. SMEs have limited access to methods with which they can effectively and efficiently analyse processes and identify cause-and-effect relationships in order to generate the necessary database and derive optimization potential from it. The implementation of digitalization within the framework of Industry 4.0 thus becomes a particular necessity for SMEs. For these reasons, the abstract presents an analysis methodology that is subject to the objective of developing an SME-appropriate methodology for efficient, temporarily feasible data collection and evaluation in flexible production and logistics systems as a basis for process analysis and optimization. The overall methodology focuses on retrospective, event-based tracing and analysis of material flow objects. The technological basis consists of Bluetooth low energy (BLE)-based transmitters, so-called beacons, and smart mobile devices (SMD), e.g. smartphones as receivers, between which distance data can be measured and derived motion profiles. The distance is determined using the Received Signal Strength Indicator (RSSI), which is a measure of signal field strength between transmitter and receiver. The focus is the development of a software-based methodology for interpretation of relative movements of transmitters and receivers based on distance data. The main research is on selection and implementation of pattern recognition methods for automatic process recognition as well as methods for the visualization of relative distance data. Due to an existing categorization of the database regarding process types, classification methods (e.g. Support Vector Machine) from the field of supervised learning are used. The necessary data quality requires selection of suitable methods as well as filters for smoothing occurring signal variations of the RSSI, the integration of methods for determination of correction factors depending on possible signal interference sources (columns, pallets) as well as the configuration of the used technology. The parameter settings on which respective algorithms are based have a further significant influence on result quality of the classification methods, correction models and methods for visualizing the position profiles used. The accuracy of classification algorithms can be improved up to 30% by selected parameter variation; this has already been proven in studies. Similar potentials can be observed with parameter variation of methods and filters for signal smoothing. Thus, there is increased interest in obtaining detailed results on the influence of parameter and factor combinations on data quality in this area. The overall methodology is realized with a modular software architecture consisting of independently modules for data acquisition, data preparation and data storage. The demonstrator for initialization and data acquisition is available as mobile Java-based application. The data preparation, including methods for signal smoothing, are Python-based with the possibility to vary parameter settings and to store them in the database (SQLite). The evaluation is divided into two separate software modules with database connection: the achievement of an automated assignment of defined process classes to distance data using selected classification algorithms and the visualization as well as reporting in terms of a graphical user interface (GUI).

Keywords: event-based tracing, machine learning, process classification, parameter settings, RSSI, signal smoothing

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Authors: Diqin Qi, Jiaming Li, Siman Li

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Based on the use of the three-point smoothing method for selectively processing original data columns, this paper establishes a group of grey GM(1,1) models to predict the concentration ranges of four major air pollutants in Shanghai from 2023 to 2024. The results indicate that PM₁₀, SO₂, and NO₂ maintain the national Grade I standards, while the concentration of PM₂.₅ has decreased but still remains within the national Grade II standards. Combining the forecast results, recommendations are provided for the Shanghai municipal government's efforts in air pollution prevention and control.

Keywords: atmospheric pollutant prediction, Grey GM(1, 1), model group, three-point smoothing method

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Authors: Korpapa Srisamai, Pawee Siriruk

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The purpose of this study is to forecast product demands and develop appropriate and adequate procurement plans to meet customer needs and reduce costs. When the product exceeds customer demands or does not move, it requires the company to support insufficient storage spaces. Moreover, some items, when stored for a long period of time, cause deterioration to dead stock. A case study of the wholesale company of electronic equipment and components, which has uncertain customer demands, is considered. The actual purchasing orders of customers are not equal to the forecast provided by the customers. In some cases, customers have higher product demands, resulting in the product being insufficient to meet the customer's needs. However, some customers have lower demands for products than estimates, causing insufficient storage spaces and dead stock. This study aims to reduce the loss of sales opportunities and the number of remaining goods in the warehouse, citing 30 product samples of the company's most popular products. The data were collected during the duration of the study from January to October 2022. The methods used to forecast are simple moving averages, weighted moving average, and exponential smoothing methods. The economic ordering quantity and reorder point are used to calculate to meet customer needs and track results. The research results are very beneficial to the company. The company can reduce the loss of sales opportunities by 20% so that the company has enough products to meet customer needs and can reduce unused products by up to 10% dead stock. This enables the company to order products more accurately, increasing profits and storage space.

Keywords: demand forecast, reorder point, lost sale, dead stock

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Authors: O. W. Lawal, L. O. Ahmed, Y. K. Ali

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The unsteady MHD Poiseuille flow of a third grade fluid between two parallel horizontal nonconducting porous plates is studied with heat transfer. The two plates are fixed but maintained at different constant temperature with the Joule and viscous dissipation taken into consideration. The fluid motion is produced by a sudden uniform exponential decaying pressure gradient and external uniform magnetic field that is perpendicular to the plates. The momentum and energy equations governing the flow are solved numerically using Maple program. The effects of magnetic field and third grade fluid parameters on velocity and temperature profile are examined through several graphs.

Keywords: exponential decaying pressure gradient, MHD flow, Poiseuille flow, third grade fluid

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Authors: Prayas Sharma

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This paper proposed a generalized class of estimators, an exponential class of estimators based on the adaption of Sharma and Singh (2015) and Solanki and Singh (2013), and a simple difference estimator for estimating unknown population mean in the case of Poisson distributed population in simple random sampling without replacement. The expressions for mean square errors of the proposed classes of estimators are derived from the first order of approximation. It is shown that the adapted version of Solanki and Singh (2013), the exponential class of estimator, is always more efficient than the usual estimator, ratio, product, exponential ratio, and exponential product type estimators and equally efficient to simple difference estimator. Moreover, the adapted version of Sharma and Singh's (2015) estimator is always more efficient than all the estimators available in the literature. In addition, theoretical findings are supported by an empirical study to show the superiority of the constructed estimators over others with an application to earthquake data of Turkey.

Keywords: auxiliary attribute, point bi-serial, mean square error, simple random sampling, Poisson distribution

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Authors: Anastasiia Yu. Timofeeva

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Two new algorithms for nonparametric estimation of errors-in-variables models are proposed. The first algorithm is based on penalized regression spline. The spline is represented as a piecewise-linear function and for each linear portion orthogonal regression is estimated. This algorithm is iterative. The second algorithm involves locally weighted regression estimation. When the independent variable is measured with error such estimation is a complex nonlinear optimization problem. The simulation results have shown the advantage of the second algorithm under the assumption that true smoothing parameters values are known. Nevertheless the use of some indexes of fit to smoothing parameters selection gives the similar results and has an oversmoothing effect.

Keywords: grade point average, orthogonal regression, penalized regression spline, locally weighted regression

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Authors: Fatemah A. Alqallaf, Debasis Kundu

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The aim of this paper is to introduce a bivariate inverse generalized exponential distribution which has a singular component. The proposed bivariate distribution can be used when the marginals have heavy-tailed distributions, and they have non-monotone hazard functions. Due to the presence of the singular component, it can be used quite effectively when there are ties in the data. Since it has four parameters, it is a very flexible bivariate distribution, and it can be used quite effectively for analyzing various bivariate data sets. Several dependency properties and dependency measures have been obtained. The maximum likelihood estimators cannot be obtained in closed form, and it involves solving a four-dimensional optimization problem. To avoid that, we have proposed to use an EM algorithm, and it involves solving only one non-linear equation at each `E'-step. Hence, the implementation of the proposed EM algorithm is very straight forward in practice. Extensive simulation experiments and the analysis of one data set have been performed. We have observed that the proposed bivariate inverse generalized exponential distribution can be used for modeling dependent competing risks data. One data set has been analyzed to show the effectiveness of the proposed model.

Keywords: Block and Basu bivariate distributions, competing risks, EM algorithm, Marshall-Olkin bivariate exponential distribution, maximum likelihood estimators

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Authors: Panudet Saengseedam, Nanthachai Kantanantha

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This paper proposes a linear mixed model (LMM) with spatial effects to forecast rice and cassava yields in Thailand at the same time. A multivariate conditional autoregressive (MCAR) model is assumed to present the spatial effects. A Bayesian method is used for parameter estimation via Gibbs sampling Markov Chain Monte Carlo (MCMC). The model is applied to the rice and cassava yields monthly data which have been extracted from the Office of Agricultural Economics, Ministry of Agriculture and Cooperatives of Thailand. The results show that the proposed model has better performance in most provinces in both fitting part and validation part compared to the simple exponential smoothing and conditional auto regressive models (CAR) from our previous study.

Keywords: Bayesian method, linear mixed model, multivariate conditional autoregressive model, spatial time series

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Authors: Yupaporn Areepong

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The main goal of this paper is to study Statistical Process Control (SPC) with Exponentially Weighted Moving Average (EWMA) control chart when observations are serially-correlated. The characteristic of control chart is Average Run Length (ARL) which is the average number of samples taken before an action signal is given. Ideally, an acceptable ARL of in-control process should be enough large, so-called (ARL0). Otherwise it should be small when the process is out-of-control, so-called Average of Delay Time (ARL1) or a mean of true alarm. We find explicit formulas of ARL for EWMA control chart for Seasonal Autoregressive and Moving Average processes (SARMA) with Exponential white noise. The results of ARL obtained from explicit formula and Integral equation are in good agreement. In particular, this formulas for evaluating (ARL0) and (ARL1) be able to get a set of optimal parameters which depend on smoothing parameter (λ) and width of control limit (H) for designing EWMA chart with minimum of (ARL1).

Keywords: average run length, optimal parameters, exponentially weighted moving average (EWMA), control chart

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Authors: Abdelhadi Elharfi

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A problem of boundary feedback (exponential) stabilization of an overhead crane model represented by a PDE is considered. For any $r>0$, the exponential stability at the desired decay rate $r$ is solved in semi group setting by a collocated-type stabiliser of a target system combined with a term involving the solution of an appropriate PDE.

Keywords: feedback stabilization, semi group and generator, overhead crane system

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Authors: Mounir Belattar

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In this paper the Analysis of voltage waves that propagate along a lossless exponential nonuniform line is presented. For this analysis the parameters of this line are assumed to be varying function of the distance x along the line from the source end. The approach is based on the tow-port networks cascading presentation to derive the ABDC parameters of transmission using Picard-Carson Method which is a powerful method in getting a power series solution for distributed network because it is easy to calculate poles and zeros and solves differential equations such as telegrapher equations by an iterative sequence. So the impedance, admittance voltage and current along the line are expanded as a Taylor series in x/l where l is the total length of the line to obtain at the end, the main transmission line parameters such as voltage response and transmission and reflexion coefficients represented by scattering parameters in frequency domain.

Keywords: ABCD parameters, characteristic impedance exponential nonuniform transmission line, Picard-Carson's method, S parameters, Taylor's series

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Authors: Dimitri Golenko-Ginzburg

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A CPM network project with deterministic activity durations, in which activities require homogenous resources with fixed capacities, is considered. The problem is to determine the optimal schedule of starting times for all network activities within their maximal allowable limits (in order not to exceed the network's critical time) to minimize the maximum required resources for the project at any point in time. In case when a non-critical activity may start only at discrete moments with the pregiven time span, the problem becomes NP-complete and an optimal solution may be obtained via a look-over algorithm. For the case when a look-over requires much computational time an approximate algorithm is suggested. The algorithm's performance ratio, i.e., the relative accuracy error, is determined. Experimentation has been undertaken to verify the suggested algorithm.

Keywords: resource smoothing problem, CPM network, lookover algorithm, lexicographical order, approximate algorithm, accuracy estimate

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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: Daoudi Abdelaziz, Mahmoudi Saïd, Chikh Mohamed Amine

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This paper presents a fully automatic segmentation method of the left ventricle at End Systolic (ES) and End Diastolic (ED) in the ultrasound images by means of an implicit deformable model (level set) based on Geodesic Active Contour model. A pre-processing Gaussian smoothing stage is applied to the image, which is essential for a good segmentation. Before the segmentation phase, we locate automatically the area of the left ventricle by using a detection approach based on the Hough Transform method. Consequently, the result obtained is used to automate the initialization of the level set model. This initial curve (zero level set) deforms to search the Endocardial border in the image. On the other hand, quantitative evaluation was performed on a data set composed of 15 subjects with a comparison to ground truth (manual segmentation).

Keywords: level set method, transform Hough, Gaussian smoothing, left ventricle, ultrasound images.

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Authors: Muhammad Gillfran Samual, Rinaldy Dalimi, Fauzan Hanif Jufri, Budi Sudiarto, Ismi Rosyiana Fitri

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Solar energy is increasingly recognized as an important future energy source due to its abundant availability and renewable nature. However, the intermittent nature of solar energy can cause fluctuations in the electricity produced, making it difficult to guarantee a stable and reliable electricity supply. One solution that can be implemented is to use batteries in a photovoltaic solar power plant system with a Moving Average control algorithm, which can help smooth and reduce fluctuations in solar power output power. The parameter that can be adjusted in the Moving Average algorithm is the window size or the arithmetic average width of the photovoltaic output power over time. This research evaluates the effect of a change of window size parameter in the Moving Average algorithm on the resulting smoothed photovoltaic output power and the technical effects on batteries, i.e., power and energy usage. Based on the evaluation, it is found that the increase of window size parameter will slow down the response of photovoltaic output power to changes in irradiation and increase the smoothing quality of the intermittent photovoltaic output power. In addition, increasing the window size will reduce the maximum power received on the load side, and the amount of energy used by the battery during the power smoothing process will increase, which, in turn, increases the required battery capacity.

Keywords: battery, intermittent, moving average, photovoltaic, power smoothing

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Authors: Kritika Bansal, Akwinder Kaur, Shruti Gujral

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In this paper, the approach of denoising is solved by using a new hybrid technique which associates the different denoising methods. Wavelet thresholding and anisotropic diffusion filter are the two different filters in our hybrid techniques. The Wavelet thresholding removes the noise by removing the high frequency components with lesser edge preservation, whereas an anisotropic diffusion filters is based on partial differential equation, (PDE) to remove the speckle noise. This PDE approach is used to preserve the edges and provides better smoothing. So our new method proposes a combination of these two filtering methods which performs better results in terms of peak signal to noise ratio (PSNR), coefficient of correlation (COC) and equivalent no of looks (ENL).

Keywords: denoising, anisotropic diffusion filter, multiplicative noise, speckle, wavelets

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Authors: Nikolaos Vassilas, Theocharis Tsenoglou, Djamchid Ghazanfarpour

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In this work we explore the capability of the mean shift algorithm as a powerful preprocessing tool for improving the quality of spatial data, acquired from airborne scanners, from densely built urban areas. On one hand, high resolution image data corrupted by noise caused by lossy compression techniques are appropriately smoothed while at the same time preserving the optical edges and, on the other, low resolution LiDAR data in the form of normalized Digital Surface Map (nDSM) is upsampled through the joint mean shift algorithm. Experiments on both the edge-preserving smoothing and upsampling capabilities using synthetic RGB-z data show that the mean shift algorithm is superior to bilateral filtering as well as to other classical smoothing and upsampling algorithms. Application of the proposed methodology for 3D reconstruction of buildings of a pilot region of Athens, Greece results in a significant visual improvement of the 3D building block model.

Keywords: 3D buildings reconstruction, data fusion, data upsampling, mean shift

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Authors: Ahmadur Rahman, Showkat Ahmad Lone, Ariful Islam

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In this article, we have estimated the parameters for the failure times of units based on the sampling technique adaptive type-I progressive hybrid censoring under the step-stress partially accelerated life tests for competing risk. The failure times of the units are assumed to follow an exponential distribution. Maximum likelihood estimation technique is used to estimate the unknown parameters of the distribution and tampered coefficient. Confidence interval also obtained for the parameters. A simulation study is performed by using Monte Carlo Simulation method to check the authenticity of the model and its assumptions.

Keywords: adaptive type-I hybrid progressive censoring, competing risks, exponential distribution, simulation, step-stress partially accelerated life tests

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Authors: Gabriel I. Loaiza Ossa, Carlos A. Cadavid Moreno, Juan C. Arango Parra

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It is known that the Riemannian manifold determined by the family of inverse Gaussian distributions endowed with the Fisher metric has negative constant curvature κ= -1/2, as does the family of usual Gaussian distributions. In the present paper, firstly, we arrive at this result by following a different path, much simpler than the previous ones. We first put the family in exponential form, thus endowing the family with a new set of parameters, or coordinates, θ₁, θ₂; then we determine the matrix of the Fisher metric in terms of these parameters; and finally we compute this matrix in the original parameters. Secondly, we define the inverse q-Gaussian distribution family (q < 3) as the family obtained by replacing the usual exponential function with the Tsallis q-exponential function in the expression for the inverse Gaussian distribution and observe that it supports two possible geometries, the Fisher and the q-Fisher geometry. And finally, we apply our strategy to obtain results about the Fisher and q-Fisher geometry of the inverse q-Gaussian distribution family, similar to the ones obtained in the case of the inverse Gaussian distribution family.

Keywords: base of changes, information geometry, inverse Gaussian distribution, inverse q-Gaussian distribution, statistical manifolds

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Authors: Kamel Al-Khaled

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A comparative study of the Sinc-Galerkin and Sinc-Collocation methods for solving the Kuramoto-Sivashinsky equation is given. Both approaches depend on using Sinc basis functions. Firstly, a numerical scheme using Sinc-Galerkin method is developed to approximate the solution of Kuramoto-Sivashinsky equation. Sinc approximations to both derivatives and indefinite integrals reduces the solution to an explicit system of algebraic equations. The error in the solution is shown to converge to the exact solution at an exponential. The convergence proof of the solution for the discrete system is given using fixed-point iteration. Secondly, a combination of a Crank-Nicolson formula in the time direction, with the Sinc-collocation in the space direction is presented, where the derivatives in the space variable are replaced by the necessary matrices to produce a system of algebraic equations. The methods are tested on two examples. The demonstrated results show that both of the presented methods more or less have the same accuracy.

Keywords: Sinc-Collocation, nonlinear PDEs, numerical methods, fixed-point

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Authors: Morteza Habibi, Reza Amrollahi

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The Aluminum made targets were placed at the central part of a Fillipov type (90KJ) plasma focus cathode. These targets were exposed to perpendicular dense plasma stream incidence. Melt layer erosion by melt motion, surface smoothing, and bubble formation were some of different effects caused by diverse working conditions. Micro hardness of surface layer tends to decrease particularly in the central region of the sample where destruction is more intense. The most pronouced melt motion is registered in the region of the maximum gradient of pressure and the etching of aluminium surface is noticeable in the central part of target. The crater with a maximum depth of 200µm, and the diameter of about 8.5mm is observed close to the mountains. Adding Krypton admixture to the Deuterium gas lead to collapsing bubbles and greater surface damage.

Keywords: fillipov type plasma focus, al target interaction, bubbling effect, melt layer motion, surface smoothing

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Authors: Suparman Suparman

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A white noise in autoregressive (AR) model is often assumed to be normally distributed. In application, the white noise usually do not follows a normal distribution. This paper aims to estimate a parameter of AR model that has a exponential white noise. A Bayesian method is adopted. A prior distribution of the parameter of AR model is selected and then this prior distribution is combined with a likelihood function of data to get a posterior distribution. Based on this posterior distribution, a Bayesian estimator for the parameter of AR model is estimated. Because the order of AR model is considered a parameter, this Bayesian estimator cannot be explicitly calculated. To resolve this problem, a method of reversible jump Markov Chain Monte Carlo (MCMC) is adopted. A result is a estimation of the parameter AR model can be simultaneously calculated.

Keywords: autoregressive (AR) model, exponential white Noise, bayesian, reversible jump Markov Chain Monte Carlo (MCMC)

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Authors: Luiz G. Véras, Felipe L. Medeiros, Lamartine F. Guimarães

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This work approaches the automatic planning of paths for Unmanned Aerial Vehicles (UAVs) through the application of the Rapidly Exploring Random Tree Star-Smart (RRT*-Smart) algorithm. RRT*-Smart is a sampling process of positions of a navigation environment through a tree-type graph. The algorithm consists of randomly expanding a tree from an initial position (root node) until one of its branches reaches the final position of the path to be planned. The algorithm ensures the planning of the shortest path, considering the number of iterations tending to infinity. When a new node is inserted into the tree, each neighbor node of the new node is connected to it, if and only if the extension of the path between the root node and that neighbor node, with this new connection, is less than the current extension of the path between those two nodes. RRT*-smart uses an intelligent sampling strategy to plan less extensive routes by spending a smaller number of iterations. This strategy is based on the creation of samples/nodes near to the convex vertices of the navigation environment obstacles. The planned paths are smoothed through the application of the method called quintic pythagorean hodograph curves. The smoothing process converts a route into a dynamically-viable one based on the kinematic constraints of the vehicle. This smoothing method models the hodograph components of a curve with polynomials that obey the Pythagorean Theorem. Its advantage is that the obtained structure allows computation of the curve length in an exact way, without the need for quadratural techniques for the resolution of integrals.

Keywords: path planning, path smoothing, Pythagorean hodograph curve, RRT*-Smart

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