Search results for: potential function

Authors: R. Noori, F. Feizi, M.R. Jafari

Abstract:

Khatunabad area is situated geologically in Urmieh- Dokhtar magmatic belt in NW of Iran. In this research, studied area has been investigated in order to recognize the potential copper and molybdenum-bearing target areas. The survey layers include the lithologic units, alteration, geochemical result, tectonics and copper and molybdenum occurrence. As an accurate decision can have a considerable effect on exploration plans, so in this efforts have been made to make use of new combination method. For this purpose, the analytical hierarchy process was used and revealed highly potential copper and molybdenum mineralization areas. Based on achieved results, geological perspective in north of studied area is appropriate for advance stage, especially for subsurface exploration in future.

Keywords: Analytical hierarchy process, Potential targets, Khatunabad, Iran

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Authors: Ashish Payal, C. S. Rai, B. V. R. Reddy

Abstract:

With the increasing use and application of Wireless Sensor Networks (WSN), need has arisen to explore them in more effective and efficient manner. An important area which can bring efficiency to WSNs is the localization process, which refers to the estimation of the position of wireless sensor nodes in an ad hoc network setting, in reference to a coordinate system that may be internal or external to the network. In this paper, we have done comparison and analysed Sigmoidal Feedforward Artificial Neural Networks (SFFANNs) and Radial Basis Function (RBF) networks for developing localization framework in WSNs. The presented work utilizes the Received Signal Strength Indicator (RSSI), measured by static node on 100 x 100 m² grid from three anchor nodes. The comprehensive evaluation of these approaches is done using MATLAB software. The simulation results effectively demonstrate that FFANNs based sensor motes will show better localization accuracy as compared to RBF.

Keywords: Localization, wireless sensor networks, artificial neural network, radial basis function, multi-layer perceptron, backpropagation, RSSI.

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Authors: Jaemyoung Lee

Abstract:

We present a method to set up system functions through a near filed communication (NFC) of a smartphone. The short communication distance of the NFC which is usually less than 4 cm could prevent any interferences from other devices and establish a secure communication channel between a system and the smartphone. The proposed set-up method for system function values is demonstrated for a blacbox system in a car. In demonstration, system functions of a blackbox which is manipulated through NFC of a smartphone are controls of image quality, sound level, shock sensing level to store images, etc. The proposed set-up method for system function values can be used for any devices with NFC.

Keywords: System set-up, near field communication, smartphone, Android.

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Authors: Yehjune Heo

Abstract:

As biometric systems become widely deployed, the security of identification systems can be easily attacked by various spoof materials. This paper contributes to finding a reliable and practical anti-spoofing method using Convolutional Neural Networks (CNNs) based on the types of loss functions and optimizers. The types of CNNs used in this paper include AlexNet, VGGNet, and ResNet. By using various loss functions including Cross-Entropy, Center Loss, Cosine Proximity, and Hinge Loss, and various loss optimizers which include Adam, SGD, RMSProp, Adadelta, Adagrad, and Nadam, we obtained significant performance changes. We realize that choosing the correct loss function for each model is crucial since different loss functions lead to different errors on the same evaluation. By using a subset of the Livdet 2017 database, we validate our approach to compare the generalization power. It is important to note that we use a subset of LiveDet and the database is the same across all training and testing for each model. This way, we can compare the performance, in terms of generalization, for the unseen data across all different models. The best CNN (AlexNet) with the appropriate loss function and optimizers result in more than 3% of performance gain over the other CNN models with the default loss function and optimizer. In addition to the highest generalization performance, this paper also contains the models with high accuracy associated with parameters and mean average error rates to find the model that consumes the least memory and computation time for training and testing. Although AlexNet has less complexity over other CNN models, it is proven to be very efficient. For practical anti-spoofing systems, the deployed version should use a small amount of memory and should run very fast with high anti-spoofing performance. For our deployed version on smartphones, additional processing steps, such as quantization and pruning algorithms, have been applied in our final model.

Keywords: Anti-spoofing, CNN, fingerprint recognition, loss function, optimizer.

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Authors: R. Kongnuy, E. Naowanich, T. Kruehong

Abstract:

An important technique in stability theory for differential equations is known as the direct method of Lyapunov. In this work we deal global stability properties of Leptospirosis transmission model by age group in Thailand. First we consider the data from Division of Epidemiology Ministry of Public Health, Thailand between 1997-2011. Then we construct the mathematical model for leptospirosis transmission by eight age groups. The Lyapunov functions are used for our model which takes the forms of an Ordinary Differential Equation system. The globally asymptotically for equilibrium states are analyzed.

Keywords: Age Group, Leptospirosis, Lyapunov Function, Ordinary Differential Equation.

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Authors: Meiyuan Zheng, Jingwu He, Yuexi Xiong

Abstract:

A universal multi-function leaf spring main landing gear was designed for light aircraft. The main landing gear combined with the leaf spring, skidding, and wheels enables it to have a good takeoff and landing performance on various grounds such as the hard, snow, grass and sand grounds. Firstly, the characteristics of different landing sites were studied in this paper in order to analyze the load of the main landing gear on different types of grounds. Based on this analysis, the structural design optimization along with the strength and stiffness characteristics of the main landing gear has been done, which enables it to have good takeoff and landing performance on different types of grounds given the relevant regulations and standards. Additionally, the impact of the skidding on the aircraft during the flight was also taken into consideration. Finally, a universal multi-function leaf spring type of the main landing gear suitable for light aircraft has been developed.

Keywords: Landing gear, multi-function, leaf spring, skidding.

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Authors: Ahmad Rouhani

Abstract:

Iran has several potential for using renewable energies, so use them could significantly contribute to energy supply. The purpose of this paper is to identify the potential of the country and select the appropriate DG technologies with consideration the potential and primary energy resources in the regions. In this context, hybrid energy systems proportionate with the potential of different regions will be determined based on technical, economic, and environmental aspect. In the following the proposed structure will be optimized in terms of size and cost. DG technologies used in this project include photovoltaic system, wind turbine, diesel generator and battery bank. The HOMER software is applied for choosing the appropriate structure and the optimization of system sizing. The results have been analyzed in terms of technical and economic. The performance and the cost of each project demonstrate the appropriate structure of hybrid energy system in that region.

Keywords: Feasibility, Hybrid Energy System, Iran, Renewable Energy.

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Authors: Nur Syibrah Muhamad Naim, Mohd Lazim Abdullah, Che Mohd Imran Che Taib, Abu OsmanMd. Tap

Abstract:

Decision making preferences to certain criteria usually focus on positive degrees without considering the negative degrees. However, in real life situation, evaluation becomes more comprehensive if negative degrees are considered concurrently. Preference is expected to be more effective when considering both positive and negative degrees of preference to evaluate the best selection. Therefore, the aim of this paper is to propose the conflicting bifuzzy preference relations in group decision making by utilization of a novel score function. The conflicting bifuzzy preference relation is obtained by introducing some modifications on intuitionistic fuzzy preference relations. Releasing the intuitionistic condition by taking into account positive and negative degrees simultaneously and utilizing the novel score function are the main modifications to establish the proposed preference model. The proposed model is tested with a numerical example and proved to be simple and practical. The four-step decision model shows the efficiency of obtaining preference in group decision making.

Keywords: Fuzzy preference relations, score function, conflicting bifuzzy, decision making.

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Authors: C. Ardil

Abstract:

Aircraft supplier selection process, which is considered as a fundamental supply chain problem, is a multi-criteria group decision problem that has a significant impact on the performance of the entire supply chain. In practical situations are frequently incomplete and uncertain information, making it difficult for decision-makers to communicate their opinions on candidates with precise and definite values. To solve the aircraft supplier selection problem in an environment of incomplete and uncertain information, proximity measure method is proposed. It uses determinate fuzzy numbers. The weights of each decision maker are equally predetermined and the entropic criteria weights are calculated using each decision maker's decision matrix. Additionally, determinate fuzzy numbers, it is proposed to use the weighted normalized Minkowski distance function and Hausdorff distance function to determine the ranking order patterns of alternatives. A numerical example for aircraft supplier selection is provided to further demonstrate the applicability, effectiveness, validity and rationality of the proposed method.

Keywords: Aircraft supplier selection, multiple criteria decision making, fuzzy sets, determinate fuzzy sets, intuitionistic fuzzy sets, proximity measure method, Minkowski distance function, Hausdorff distance function, PMM, MCDM

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Authors: Y. T. Boon, M. N. Naim, R. Zakaria, N. F. Abu Bakar, N. Ahmad, I. W. Lenggoro

Abstract:

In this study, encapsulation of agarwood oil with non-ionic surfactant, Tween 80 was prepared at critical micelle concentration of 0.0167 % v/v to produce the most stable nano-emulsion in aqueous. The encapsulation has minimized the bioactive compounds degradation in various pH conditions thus prolong their shelf life and maintained its initial oil grade. The oil grading of the prepared samples were conducted using the gel electrophoresis instead of using common analytical industrial grading such as gas chromatography- mass spectrometry (GC- MS). The grading method was chosen due to their unique zeta potential value after the encapsulation process. This paper demonstrates the feasibility of applying the electrophoresis principles to separate the encapsulated agarwood oil or grading of the emulsified agarwood oil. The results indicated that the grading process are potential to be further investigate based on their droplet size and zeta potential value at various pH condition when the droplet were migrate through polyacrylamide gel.

Keywords: Electrophoretic mobility, essential oil, nanoemulsion, polyacrylamide gel electrophoresis, Tween 80, zeta potential.

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Authors: Jagannath Aryal, Don Kulasiri, Dishi Liu

Abstract:

This paper describes the optimization of a complex dairy farm simulation model using two quite different methods of optimization, the Genetic algorithm (GA) and the Lipschitz Branch-and-Bound (LBB) algorithm. These techniques have been used to improve an agricultural system model developed by Dexcel Limited, New Zealand, which describes a detailed representation of pastoral dairying scenarios and contains an 8-dimensional parameter space. The model incorporates the sub-models of pasture growth and animal metabolism, which are themselves complex in many cases. Each evaluation of the objective function, a composite 'Farm Performance Index (FPI)', requires simulation of at least a one-year period of farm operation with a daily time-step, and is therefore computationally expensive. The problem of visualization of the objective function (response surface) in high-dimensional spaces is also considered in the context of the farm optimization problem. Adaptations of the sammon mapping and parallel coordinates visualization are described which help visualize some important properties of the model-s output topography. From this study, it is found that GA requires fewer function evaluations in optimization than the LBB algorithm.

Keywords: Genetic Algorithm, Linux Cluster, LipschitzBranch-and-Bound, Optimization

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Authors: N. Sridee, S. Boonanuntanasarn

Abstract:

Oxyleotris marmorata is considered as undomesticated fish, and its culture occasionally faces a problem of food deprivation. The present study aims to evaluate alteration of hematological indices, blood chemical associated with liver function during 4 weeks of fasting. A non-linear relationships between fasting days and hematological parameters (red blood cell number; y = - 0.002x2 + 0.041x + 1.249; R2=0.915, P<0.05, hemoglobin; y = - 0.002x2 + 0.030x + 3.470; R2=0.460, P>0.05), mean corpuscular volume; y = -0.180x2 + 2.183x + 149.61; R2=0.732, P>0.05, mean corpuscular hemoglobin; y = -0.041x2 + 0.862x + 29.864; R2=0.818, P>0.05 and mean corpuscular hemoglobin concentration; y = - 0.044x2 + 0.711x + 21.580; R2=0.730, P>0.05) were demonstrated. Significant change in hematocrit (Ht) during fasting period was observed. Ht elevated sharply increase at the first weeks of fasting period. Higher Ht also was detected during week 2-4 of fasting time. The significant reduction of hepatosomatic index was observed (y = - 0.007x2 - 0.096x + 1.414; R2=0.968, P<0.05). Moreover, alteration of enzyme associated with liver function was evaluated during 4 weeks of fasting (alkalin phosphatase; y = -0.026x2 - 0.935x + 12.188; R2=0.737, P>0.05, serum glutamic oxaloacetic transaminase; y = 0.005x2 – 0.201x2 + 1.297x + 33.256; R2=1, P<0.01, serum glutamic pyruvic transaminase; y = 0.007x2 – 0.274x2 + 2.277x + 25.257; R2=0.807, P>0.05). Taken together, prolonged fasting has deleterious effects on hematological indices, liver mass and enzyme associated in liver function. The marked adverse effects occurred after the first week of fasting state.

Keywords: food deprivation, Oxyleotris marmorata, hematology, alkaline phosphatase, SGOT, SGPT

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Authors: Muhammad Aqil, Ichiro Kita, Moses Macalinao

Abstract:

Reliable water level forecasts are particularly important for warning against dangerous flood and inundation. The current study aims at investigating the suitability of the adaptive network based fuzzy inference system for continuous water level modeling. A hybrid learning algorithm, which combines the least square method and the back propagation algorithm, is used to identify the parameters of the network. For this study, water levels data are available for a hydrological year of 2002 with a sampling interval of 1-hour. The number of antecedent water level that should be included in the input variables is determined by two statistical methods, i.e. autocorrelation function and partial autocorrelation function between the variables. Forecasting was done for 1-hour until 12-hour ahead in order to compare the models generalization at higher horizons. The results demonstrate that the adaptive networkbased fuzzy inference system model can be applied successfully and provide high accuracy and reliability for river water level estimation. In general, the adaptive network-based fuzzy inference system provides accurate and reliable water level prediction for 1-hour ahead where the MAPE=1.15% and correlation=0.98 was achieved. Up to 12-hour ahead prediction, the model still shows relatively good performance where the error of prediction resulted was less than 9.65%. The information gathered from the preliminary results provide a useful guidance or reference for flood early warning system design in which the magnitude and the timing of a potential extreme flood are indicated.

Keywords: Neural Network, Fuzzy, River, Forecasting

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Authors: Randle O. A., Olugbara, O. O., Lall M.

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In this paper we describe a hybrid technique of Minimax search and aggregate Mahalanobis distance function synthesis to evolve Awale game player. The hybrid technique helps to suggest a move in a short amount of time without looking into endgame database. However, the effectiveness of the technique is heavily dependent on the training dataset of the Awale strategies utilized. The evolved player was tested against Awale shareware program and the result is appealing.

Keywords: Minimax Search, Mahalanobis Distance, Strategic Game, Awale

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Authors: F. Bayatbabolghani, K. Parand

Abstract:

In this paper, we propose Hermite collocation method for solving Thomas-Fermi equation that is nonlinear ordinary differential equation on semi-infinite interval. This method reduces the solution of this problem to the solution of a system of algebraic equations. We also present the comparison of this work with solution of other methods that shows the present solution is more accurate and faster convergence in this problem.

Keywords: Collocation method, Hermite function, Semi-infinite, Thomas-Fermi equation.

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Authors: Ricardo C. Silva, Luiza A. P. Cantao, Akebo Yamakami

Abstract:

Based on the fuzzy set theory this work develops two adaptations of iterative methods that solve mathematical programming problems with uncertainties in the objective function and in the set of constraints. The first one uses the approach proposed by Zimmermann to fuzzy linear programming problems as a basis and the second one obtains cut levels and later maximizes the membership function of fuzzy decision making using the bound search method. We outline similarities between the two iterative methods studied. Selected examples from the literature are presented to validate the efficiency of the methods addressed.

Keywords: Fuzzy Theory, Nonlinear Optimization, Fuzzy Mathematics Programming.

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Authors: Young-Seok Choi

Abstract:

This work presents a new type of the affine projection (AP) algorithms which incorporate the sparsity condition of a system. To exploit the sparsity of the system, a weighted l1-norm regularization is imposed on the cost function of the AP algorithm. Minimizing the cost function with a subgradient calculus and choosing two distinct weighting for l1-norm, two stochastic gradient based sparsity regularized AP (SR-AP) algorithms are developed. Experimental results exhibit that the SR-AP algorithms outperform the typical AP counterparts for identifying sparse systems.

Keywords: System identification, adaptive filter, affine projection, sparsity, sparse system.

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Authors: Saif Ul Haq

Abstract:

The current study intends to examine the safety and quality considerations of clients of housing projects and their impact on the adoption of Quality Function Deployment (QFD) by the construction firm. Mixed method research technique has been used to collect and analyze the data wherein a survey was conducted to collect the data from 220 clients of housing projects in Saudi Arabia. Then, the telephonic and Skype interviews were conducted to collect data of 15 professionals working in the top ten real estate companies of Saudi Arabia. Data were analyzed by using partial least square (PLS) and thematic analysis techniques. Findings reveal that today’s customer prioritizes the safety and quality requirements of their houses and as a result, construction firms adopt QFD to address the needs of customers. The findings are of great importance for the clients of housing projects as well as for the construction firms as they could apply QFD in housing projects to address the safety and quality concerns of their clients.

Keywords: Construction industry, quality considerations, quality function deployment, safety considerations.

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Authors: Wanhyun Cho, Soonja Kang, Sangkyoon Kim, Soonyoung Park

Abstract:

In this paper, we propose the variational EM inference algorithm for the multi-class Gaussian process classification model that can be used in the field of human behavior recognition. This algorithm can drive simultaneously both a posterior distribution of a latent function and estimators of hyper-parameters in a Gaussian process classification model with multiclass. Our algorithm is based on the Laplace approximation (LA) technique and variational EM framework. This is performed in two steps: called expectation and maximization steps. First, in the expectation step, using the Bayesian formula and LA technique, we derive approximately the posterior distribution of the latent function indicating the possibility that each observation belongs to a certain class in the Gaussian process classification model. Second, in the maximization step, using a derived posterior distribution of latent function, we compute the maximum likelihood estimator for hyper-parameters of a covariance matrix necessary to define prior distribution for latent function. These two steps iteratively repeat until a convergence condition satisfies. Moreover, we apply the proposed algorithm with human action classification problem using a public database, namely, the KTH human action data set. Experimental results reveal that the proposed algorithm shows good performance on this data set.

Keywords: Bayesian rule, Gaussian process classification model with multiclass, Gaussian process prior, human action classification, laplace approximation, variational EM algorithm.

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Authors: G. C. Mahata, A. Goswami

Abstract:

This paper deals with infinite time horizon fuzzy Economic Order Quantity (EOQ) models for deteriorating items with  stock dependent demand rate and nonlinear holding costs by taking deterioration rate θ0 as a triangular fuzzy number  (θ0 −δ 1, θ0, θ0 +δ 2), where 1 2 0 0 <δ ,δ <θ are fixed real numbers. The traditional parameters such as unit cost and ordering  cost have been kept constant but holding cost is considered to vary. Two possibilities of variations in the holding cost function namely, a non-linear function of the length of time for which the item is held in stock and a non-linear function of the amount of on-hand inventory have been used in the models. The approximate optimal solution for the fuzzy cost functions in both these cases have been obtained and the effect of non-linearity in holding costs is studied with the help of a numerical example.

Keywords: Inventory Model, Deterioration, Holding Cost, Fuzzy Total Cost, Extension Principle.

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Authors: Emad K. Jaradat, Ala’a Al-Faqih

Abstract:

Nonlinear Schrödinger equations are regularly experienced in numerous parts of science and designing. Varieties of analytical methods have been proposed for solving these equations. In this work, we construct an approximate solution for the nonlinear Schrodinger equations, with harmonic oscillator potential, by Elzaki Decomposition Method (EDM). To illustrate the effects of harmonic oscillator on the behavior wave function, nonlinear Schrodinger equation in one and two dimensions is provided. The results show that, it is more perfectly convenient and easy to apply the EDM in one- and two-dimensional Schrodinger equation.

Keywords: Non-linear Schrodinger equation, Elzaki decomposition method, harmonic oscillator, one and two- dimensional Schrodinger equation.

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Authors: Zhizhong Jiang, Peter Naudé, Binghua Jiang

Abstract:

Effective evaluation of software development effort is an important issue during project plan. This study provides a model to predict development effort based on the software size estimated with function points. We generalize the average amount of effort spent on each phase of the development, and give the estimates for the effort used in software building, testing, and implementation. Finally, this paper finds a strong correlation between software defects and software size. As the size of software constantly increases, the quality remains to be a matter which requires major concern.

Keywords: Development effort, function points, software quality, software size.

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Authors: Sadia Idrees, Gianpaolo Vignali, Simeon Gill

Abstract:

The study aims to establish the virtual size and fit technology features to enhance fashion online retailing platforms, utilising digital human measurements to provide customised style and function to consumers. A few firms in the UK have launched advanced interactive fashion shopping domains for personalised shopping globally, aided by the latest internet technology. Virtual size and fit interfaces have a great potential to provide a personalised better-fitted garment to promote mass customisation globally. Made-to-measure clothing, consuming unstitched fabric is a common practice offered by fashion brands in Pakistan. This product is regarded as economical and sustainable to be utilised by consumers in Pakistan. Although the manual sizing system is practiced to sell garments online, virtual size and fit visualisation and recommendation technologies are uncommon in Pakistani fashion interfaces. A comparative assessment of Pakistani fashion brand websites and UK technology-driven fashion interfaces was conducted to highlight the vast potential of the virtual size and fit technology. The results indicated that web 2.0 technology adopted by Pakistani apparel brands has limited features, whereas companies practicing web 3.0 technology provide interactive online real-store shopping experience leading to enhanced customer satisfaction and globalisation of brands.

Keywords: E-commerce, mass customization, virtual size and fit, web 3.0 technology.

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Authors: Chun-Yao Lee, Yi-Xing Shen

Abstract:

This paper presents an application of particle swarm optimization (PSO) to the grounding grid planning which compares to the application of genetic algorithm (GA). Firstly, based on IEEE Std.80, the cost function of the grounding grid and the constraints of ground potential rise, step voltage and touch voltage are constructed for formulating the optimization problem of grounding grid planning. Secondly, GA and PSO algorithms for obtaining optimal solution of grounding grid are developed. Finally, a case of grounding grid planning is shown the superiority and availability of the PSO algorithm and proposal planning results of grounding grid in cost and computational time.

Keywords: Genetic algorithm, particle swarm optimization, grounding grid.

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Authors: Ram Kumar Soni, Alok Jain, Rajiv Saxena

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This paper proposes an efficient method for the design of two channel quadrature mirror filter (QMF) bank. To achieve minimum value of reconstruction error near to perfect reconstruction, a linear optimization process has been proposed. Prototype low pass filter has been designed using Kaiser window function. The modified algorithm has been developed to optimize the reconstruction error using linear objective function through iteration method. The result obtained, show that the performance of the proposed algorithm is better than that of the already exists methods.

Keywords: Filterbank, near perfect reconstruction, Kaiserwindow, QMF.

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Authors: Fathi Taibi

Abstract:

The abnormal increase in the number of applications available for download in Android markets is a good indication that they are being reused. However, little is known about their real reusability potential. A considerable amount of these applications is reported as having a poor quality or being malicious. Hence, in this paper, an approach to measure the reusability potential of classes in Android applications is proposed. The approach is not meant specifically for this particular type of applications. Rather, it is intended for Object-Oriented (OO) software systems in general and aims also to provide means to discard the classes of low quality and defect prone applications from being reused directly through inheritance and instantiation. An empirical investigation is conducted to measure and rank the reusability potential of the classes of randomly selected Android applications. The results obtained are thoroughly analyzed in order to understand the extent of this potential and the factors influencing it.

Keywords: Reusability, Software Quality Factors, Software Metrics, Empirical Investigation, Object-Oriented Software, Android Applications.

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Authors: Randhir Singh Baghel, Govind Shay Sharma

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In this paper, we explore an ecosystem that contains a three-species food chain. The first and second species are in competition with one another for resources. However, the third species plays an important role in providing non-linear Crowley-Martin functional support for the first species. Additionally, the third species consumes the second species in a linear fashion, taking advantage of the available resources. This intricate balance ensures the survival of all three species in the ecosystem. A set of non-linear isolated first-order differential equations establish this model. We examine the system's stability at all potential equilibrium locations using the perturbed technique. Furthermore, by spending a lot of time observing the species in their natural habitat, the numerical illustrations at suitable parameter values for the model are shown.

Keywords: Competition, predator, response function, local stability, numerical simulations.

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Authors: F. Pourhasanzade, S. H. Sabzpoushan

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The heart tissue is an excitable media. A Cellular Automata is a type of model that can be used to model cardiac action potential propagation. One of the advantages of this approach against the methods based on differential equations is its high speed in large scale simulations. Recent cellular automata models are not able to avoid flat edges in the result patterns or have large neighborhoods. In this paper, we present a new model to eliminate flat edges by minimum number of neighbors.

Keywords: Cellular Automata, Action Potential Simulation, Isotropic Pattern.

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Authors: J. J. Peña, J. Morales, J. García-Ravelo, L. Arcos-Díaz

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The Point canonical transformation method is applied for solving the Schrödinger equation with position-dependent mass. This class of problem has been solved for continuous mass distributions. In this work, a staggered mass distribution for the case of a free particle in an infinite square well potential has been proposed. The continuity conditions as well as normalization for the wave function are also considered. The proposal can be used for dealing with other kind of staggered mass distributions in the Schrödinger equation with different quantum potentials.

Keywords: Free particle, point canonical transformation method, position-dependent mass, staggered mass distribution.

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Authors: Jatinderdeep Kaur

Abstract:

In this paper, the results of Kano from one dimensional cosine and sine series are extended to two dimensional cosine and sine series. To extend these results, some classes of coefficient sequences such as class of semi convexity and class R are extended from one dimension to two dimensions. Further, the function f(x, y) is two dimensional Fourier Cosine and Sine series or equivalently it represents an integrable function or not, has been studied. Moreover, some results are obtained which are generalization of Moricz’s results.

Keywords: Conjugate Dirichlet kernel, conjugate Fejer kernel, Fourier series, Semi-convexity.

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