Search results for: lexical and numerical error-recognition tasks

Authors: Essam Al-Daoud

Abstract:

Several combinations of the preprocessing algorithms, feature selection techniques and classifiers can be applied to the data classification tasks. This study introduces a new accurate classifier, the proposed classifier consist from four components: Signal-to- Noise as a feature selection technique, support vector machine, Bayesian neural network and AdaBoost as an ensemble algorithm. To verify the effectiveness of the proposed classifier, seven well known classifiers are applied to four datasets. The experiments show that using the suggested classifier enhances the classification rates for all datasets.

Keywords: AdaBoost, Bayesian neural network, Signal-to-Noise, support vector machine, MCMC.

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Authors: Behzad Khademian, Mohammad Haeri

Abstract:

In this paper, an effective sliding mode design is applied to chaos synchronization. The proposed controller can make the states of two identical modified Chua-s circuits globally asymptotically synchronized. Numerical results are provided to show the effectiveness and robustness of the proposed method.

Keywords: Sliding mode, Chaos synchronization, Modified Chua's circuit.

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Authors: A. Pajaziti, H. Cana

Abstract:

In this paper, the structural genetic algorithm is used to optimize the neural network to control the joint movements of robotic arm. The robotic arm has also been modeled in 3D and simulated in real-time in MATLAB. It is found that Neural Networks provide a simple and effective way to control the robot tasks. Computer simulation examples are given to illustrate the significance of this method. By combining Genetic Algorithm optimization method and Neural Networks for the given robotic arm with 5 D.O.F. the obtained the results shown that the base joint movements overshooting time without controller was about 0.5 seconds, while with Neural Network controller (optimized with Genetic Algorithm) was about 0.2 seconds, and the population size of 150 gave best results.

Keywords: Robotic Arm, Neural Network, Genetic Algorithm, Optimization.

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Authors: Katarzyna Antosz, DorotaStadnicka

Abstract:

Having regard to the necessity of maintaining the technical infrastructure in a proper condition that ensures production continuity, companies decide to implement modern methods of technological machines park management. These methods include TPM, RCM and outsourcing. Large companies, in particular, are ready to invest in the implementation of these methods because of a great number of machines and a wide range of tasks of their technical service. Methodology of implementing these methods is well known. The aim of the studies, of which the results are presented in this publication, was the identification of real actions that are conducted in enterprises within the application of the TPM method. The studies were carried out in large manufacturing companies of different industries located on a certain area. The study’s results point to the actions actually performed within TPM as well as to the effects of those actions achieved by the studied enterprises.

Keywords: Infrastructure management, modern methods, technical infrastructure, TPM.

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Authors: Qianhong Zhang, Wenzhuan Zhang

Abstract:

This paper is concerned with the global asymptotic behavior of positive solution for a system of two nonlinear rational difference equations. Moreover, some numerical examples are given to illustrate results obtained.

Keywords: Difference equations, stability, unstable, global asymptotic behavior.

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Authors: Mohammed A. Abutheraa, David Lester

Abstract:

We show that Chebyshev Polynomials are a practical representation of computable functions on the computable reals. The paper presents error estimates for common operations and demonstrates that Chebyshev Polynomial methods would be more efficient than Taylor Series methods for evaluation of transcendental functions.

Keywords: Approximation Theory, Chebyshev Polynomial, Computable Functions, Computable Real Arithmetic, Integration, Numerical Analysis.

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Authors: Anastasia Katsamaki, Nikolaos Bilalis, Vassilis Dedoussis

Abstract:

This work proposes a set of actions to assist redesign procedure in existing products of Electric and Electronic Equipment (EEE). The aim is to improve their environmental behavior after their withdrawal in the End-of-Life (EOL) phase. In the beginning data collection takes place. Then follows selection and implementation of the optimal EOL Treatment Strategy (EOL_TS) and its results- evaluation concerning the environment. In parallel, product design characteristics that can be altered are selected based on their significance for the environment in the EOL stage. All results from the previous stages are combined and possible redesign actions are formulated for further examination and afterwards configuration in the design stage. The applied method to perform these tasks is Lean Thinking (LT). At the end, results concerning the application of the proposed method on a distribution transformer are presented.

Keywords: End-of-life treatment, Lean thinking, WEEE

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Authors: Mohammed A. Elhaj, Jamal S. Yassin

Abstract:

Owing to the lack of synchronization between the solar energy availability and the heat demands in a specific application, the energy storing sub-system is necessary to maintain the continuity of thermal process. The present work is dealing with an active solar heating storing system in which an air solar collector is connected to storing unit where this energy is distributed and provided to the heated space in a controlled manner. The solar collector is a box type absorber where the air flows between a number of vanes attached between the collector absorber and the bottom plate. This design can improve the efficiency due to increasing the heat transfer area exposed to the flowing air, as well as the heat conduction through the metal vanes from the top absorbing surface. The storing unit is a packed bed type where the air is coming from the air collector and circulated through the bed in order to add/remove the energy through the charging / discharging processes, respectively. The major advantage of the packed bed storage is its high degree of thermal stratification. Numerical solution of the packed bed energy storage is considered through dividing the bed into a number of equal segments for the bed particles and solved the energy equation for each segment depending on the neighbor ones. The studied design and performance parameters in the developed simulation model including, particle size, void fraction, etc. The final results showed that the collector efficiency was fluctuated between 55%-61% in winter season (January) under the climatic conditions of Misurata in Libya. Maximum temperature of 52ºC is attained at the top of the bed while the lower one is 25ºC at the end of the charging process of hot air into the bed. This distribution can satisfy the required load for the most house heating in Libya.

Keywords: Solar energy, thermal process, performance, collector, packed bed, numerical analysis, simulation.

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Authors: C. Temaneh Nyah

Abstract:

The analysis of electromagnetic environment using deterministic mathematical models is characterized by the impossibility of analyzing a large number of interacting network stations with a priori unknown parameters, and this is characteristic, for example, of mobile wireless communication networks. One of the tasks of the tools used in designing, planning and optimization of mobile wireless network is to carry out simulation of electromagnetic environment based on mathematical modelling methods, including computer experiment, and to estimate its effect on radio communication devices. This paper proposes the development of a statistical model of electromagnetic environment of a mobile wireless communication network by describing the parameters and factors affecting it including the propagation channel and their statistical models.

Keywords: Electromagnetic Environment, Statistical model, Wireless communication network.

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Authors: Delowar Hossain, Genci Capi

Abstract:

This paper concerns with the problem of deep learning parameters tuning using a genetic algorithm (GA) in order to improve the performance of deep learning (DL) method. We present a GA based DL method for robot object recognition and grasping. GA is used to optimize the DL parameters in learning procedure in term of the fitness function that is good enough. After finishing the evolution process, we receive the optimal number of DL parameters. To evaluate the performance of our method, we consider the object recognition and robot grasping tasks. Experimental results show that our method is efficient for robot object recognition and grasping.

Keywords: Deep learning, genetic algorithm, object recognition, robot grasping.

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Authors: Zachariah Sinkala

Abstract:

A systems approach model for prostate cancer in prostate duct, as a sub-system of the organism is developed. It is accomplished in two steps. First this research work starts with a nonlinear system of coupled Fokker-Plank equations which models continuous process of the system like motion of cells. Then extended to PDEs that include discontinuous processes like cell mutations, proliferation and deaths. The discontinuous processes is modeled by using intensity poisson processes. The model incorporates the features of the prostate duct. The system of PDEs spatial coordinate is along the proximal distal axis. Its parameters depend on features of the prostate duct. The movement of cells is biased towards distal region and mutations of prostate cancer cells is localized in the proximal region. Numerical solutions of the full system of equations are provided, and are exhibit traveling wave fronts phenomena. This motivates the use of the standard transformation to derive a canonically related system of ODEs for traveling wave solutions. The results obtained show persistence of prostate cancer by showing that the non-negative cone for the traveling wave system is time invariant. The traveling waves have a unique global attractor is proved also. Biologically, the global attractor verifies that evolution of prostate cancer stem cells exhibit the avascular tumor growth. These numerical solutions show that altering prostate stem cell movement or mutation of prostate cancer cells lead to avascular tumor. Conclusion with comments on clinical implications of the model is discussed.

Keywords: Fokker-Plank equations, global attractor, stem cell.

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Authors: C. Malça, P. Gonçalves, N. Alves, A. Mateus

Abstract:

Regardless of the manufacturing process used, subtractive or additive, material, purpose and application, produced components are conventionally solid mass with more or less complex shape depending on the production technology selected. Aspects such as reducing the weight of components, associated with the low volume of material required and the almost non-existent material waste, speed and flexibility of production and, primarily, a high mechanical strength combined with high structural performance, are competitive advantages in any industrial sector, from automotive, molds, aviation, aerospace, construction, pharmaceuticals, medicine and more recently in human tissue engineering. Such features, properties and functionalities are attained in metal components produced using the additive technique of Rapid Prototyping from metal powders commonly known as Selective Laser Melting (SLM), with optimized internal topologies and varying densities. In order to produce components with high strength and high structural and functional performance, regardless of the type of application, three different internal topologies were developed and analyzed using numerical computational tools. The developed topologies were numerically submitted to mechanical compression and four point bending testing. Finite Element Analysis results demonstrate how different internal topologies can contribute to improve mechanical properties, even with a high degree of porosity relatively to fully dense components. Results are very promising not only from the point of view of mechanical resistance, but especially through the achievement of considerable variation in density without loss of structural and functional high performance.

Keywords: Additive Manufacturing, Internal topologies, Porosity, Rapid Prototyping, Selective Laser Melting.

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Authors: M. Adamski, J. Cwiklak

Abstract:

The contemporary battlefield creates a demand for more costly and highly advanced munitions. Training personnel responsible for operations as well as immediate execution of combat tasks which engage real asset is unrealistic and economically not feasible. Owing to a wide array of exploited simulators and various types of imitators, it is possible to reduce the costs. One of the effective elements of training, which can be applied in the training of all service branches, is imitator of aerial targets. This research serves as an introduction to the commencement of design analysis over a real aerial target imitator. Within the project, the basic aerodynamic calculations were made, which enabled to determine its geometry, design layout, performance as well as mass balance of individual components. The conducted calculations of the parameters of flight characteristics come closer to the real performance of such Unmanned Aerial Vehicles.

Keywords: Aerial target, aerodynamics, imitator, performance.

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Authors: S. Liepina, A. Jemeljanovs

Abstract:

Tasks of the work were study the possible E.coli contamination in red deer meat, identify pathogenic strains from isolated E.coli, determine their incidence in red deer meat and determine the presence of VT1, VT2 and eaeA genes for the pathogenic E.coli. 8 (10%) samples were randomly selected from 80 analysed isolates of E.coli and PCR reaction was performed on them. PCR was done both on initial materials – samples of red deer meat - and for already isolated liqueurs. Two of analysed venison samples contain verotoxin-producing strains of E. coli. It means that this meat is not safe to consumer. It was proven by the sequestration reaction of E. coli and by comparison of the obtained results with the database of microorganism genome available on the internet that the isolated culture corresponds to region 16S rDNS of E. coli thus presenting correctness of the microbiological methods.

Keywords: Deer meat, pathogenic Escherichia coli

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Authors: Nara Guimarães, Marcelo Aquino Martorano, Douglas Gouvêa

Abstract:

An investigation into Cahn-Hilliard equation was carried out through numerical simulation to identify a possible phase separation for one and two dimensional domains. It was observed that this equation can reproduce important mass fluxes necessary for phase separation within the miscibility gap and for coalescence of particles.

Keywords: Cahn-Hilliard equation, miscibility gap, phase separation.

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Authors: Foad Hassaninejadafarahani, Scott Ormiston

Abstract:

Reflux condensation occurs in vertical channels and tubes when there is an upward core flow of vapour (or gas-vapour mixture) and a downward flow of the liquid film. The understanding of this condensation configuration is crucial in the design of reflux condensers, distillation columns, and in loss-of-coolant safety analyses in nuclear power plant steam generators. The unique feature of this flow is the upward flow of the vapour-gas mixture (or pure vapour) that retards the liquid flow via shear at the liquid-mixture interface. The present model solves the full, elliptic governing equations in both the film and the gas-vapour core flow. The computational mesh is non-orthogonal and adapts dynamically the phase interface, thus produces a sharp and accurate interface. Shear forces and heat and mass transfer at the interface are accounted for fundamentally. This modeling is a big step ahead of current capabilities by removing the limitations of previous reflux condensation models which inherently cannot account for the detailed local balances of shear, mass, and heat transfer at the interface. Discretisation has been done based on finite volume method and co-located variable storage scheme. An in-house computer code was developed to implement the numerical solution scheme. Detailed results are presented for laminar reflux condensation from steam-air mixtures flowing in vertical parallel plate channels. The results include velocity and gas mass fraction profiles, as well as axial variations of film thickness.

Keywords: Reflux Condensation, Heat Transfer, Channel, Laminar Flow

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Authors: Maassoumeh Bemani Naeini

Abstract:

Studies on interlanguage have long been engaged in describing the phenomenon of variation in SLA. Pursuing the same goal and particularly addressing the role of linguistic features, this study describes the use of Persian morphology in the interlanguage of two adult English-speaking learners of Persian L2. Taking the general approach of a combination of contrastive analysis, error analysis and interlanguage analysis, this study focuses on the identification and prediction of some possible instances of transfer from English L1 to Persian L2 across six elicitation tasks aiming to investigate whether any of contextual features may variably influence the learners’ order of morpheme accuracy in the areas of copula, possessives, articles, demonstratives, plural form, personal pronouns, and genitive cases.  Results describe the existence of task variation in the interlanguage system of Persian L2 learners.

Keywords: English L1, Interlanguage Analysis, Persian L2, SLA variation.

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Authors: Samee Ullah Khan, C. Ardil

Abstract:

We model the process of a data center as a multi- objective problem of mapping independent tasks onto a set of data center machines that simultaneously minimizes the energy consump¬tion and response time (makespan) subject to the constraints of deadlines and architectural requirements. A simple technique based on multi-objective goal programming is proposed that guarantees Pareto optimal solution with excellence in convergence process. The proposed technique also is compared with other traditional approach. The simulation results show that the proposed technique achieves superior performance compared to the min-min heuristics, and com¬petitive performance relative to the optimal solution implemented in UNDO for small-scale problems.

Keywords: Energy-efficient computing, distributed systems, multi-objective optimization.

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Authors: Andrzej Śluzek

Abstract:

To illustrate diversity of methods used to extract relevant (where the concept of relevance can be differently defined for different applications) visual data, the paper discusses three groups of such methods. They have been selected from a range of alternatives to highlight how hardware and software tools can be complementarily used in order to achieve various functionalities in case of different specifications of “relevant data". First, principles of gated imaging are presented (where relevance is determined by the range). The second methodology is intended for intelligent intrusion detection, while the last one is used for content-based image matching and retrieval. All methods have been developed within projects supervised by the author.

Keywords: Relevant visual data, gated imaging, intrusion detection, image matching.

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Authors: Bin Yu, Minghui Wang, Juntao Zhang

Abstract:

By the real representation of the quaternionic matrix, an iterative method for quaternionic linear equations Ax = b is proposed. Then the convergence conditions are obtained. At last, a numerical example is given to illustrate the efficiency of this method.

Keywords: Quaternionic linear equations, Real representation, Iterative algorithm.

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Authors: Kejun Zhuang

Abstract:

In this paper, a three dimensional autonomous chaotic system is considered. The existence of Hopf bifurcation is investigated by choosing the appropriate bifurcation parameter. Furthermore, formulas for determining the direction of the Hopf bifurcation and the stability of bifurcating periodic solutions are derived with the help of normal form theory. Finally, a numerical example is given.

Keywords: Chaotic system, Hopf bifurcation, normal form theory.

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Authors: Xingyu Pan, Laure Tougne

Abstract:

For recognizing coins, the graved release date is important information to identify precisely its monetary type. However, reading characters in coins meets much more obstacles than traditional character recognition tasks in the other fields, such as reading scanned documents or license plates. To address this challenging issue in a numismatic context, we propose a training-free approach dedicated to detection and recognition of the release date of the coin. In the first step, the date zone is detected by comparing histogram features; in the second step, a topology-based algorithm is introduced to recognize coin numbers with various font types represented by binary gradient map. Our method obtained a recognition rate of 92% on synthetic data and of 44% on real noised data.

Keywords: Coin, detection, character recognition, topology.

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Authors: M. K. Zholdassova, G. Matthews, A. M. Kustubayeva, S. M. Jakupov

Abstract:

The aim of this study was to test whether the Attention Networks Test (ANT) showed temporal decrements in performance. Vigilance tasks typically show such decrements, which may reflect impairments in executive control resulting from cognitive fatigue. The ANT assesses executive control, as well as alerting and orienting. Thus, it was hypothesized that ANT executive control would deteriorate over time. Manipulations including task condition (trial composition) and masking were included in the experimental design in an attempt to increase performance decrements. However, results showed that there is no temporal decrement on the ANT. The roles of task demands, cognitive fatigue and participant motivation in producing this result are discussed. The ANT may not be an effective tool for investigating temporal decrement in attention.

Keywords: ANT, executive control, task engagement, vigilancedecrement

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Authors: A. Javed, K. Djidjeli, J. T. Xing, S. J. Cox

Abstract:

A method for simulating flow around the solid bodies has been presented using hybrid meshfree and mesh-based schemes. The presented scheme optimizes the computational efficiency by combining the advantages of both meshfree and mesh-based methods. In this approach, a cloud of meshfree nodes has been used in the domain around the solid body. These meshfree nodes have the ability to efficiently adapt to complex geometrical shapes. In the rest of the domain, conventional Cartesian grid has been used beyond the meshfree cloud. Complex geometrical shapes can therefore be dealt efficiently by using meshfree nodal cloud and computational efficiency is maintained through the use of conventional mesh-based scheme on Cartesian grid in the larger part of the domain. Spatial discretization of meshfree nodes has been achieved through local radial basis functions in finite difference mode (RBF-FD). Conventional finite difference scheme has been used in the Cartesian ‘meshed’ domain. Accuracy tests of the hybrid scheme have been conducted to establish the order of accuracy. Numerical tests have been performed by simulating two dimensional steady and unsteady incompressible flows around cylindrical object. Steady flow cases have been run at Reynolds numbers of 10, 20 and 40 and unsteady flow problems have been studied at Reynolds numbers of 100 and 200. Flow Parameters including lift, drag, vortex shedding, and vorticity contours are calculated. Numerical results have been found to be in good agreement with computational and experimental results available in the literature.

Keywords: CFD, Meshfree particle methods, Hybrid grid, Incompressible Navier Strokes equations, RBF-FD.

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Authors: Roberto Sabatini, Celia Bartel, Anish Kaharkar, Tesheen Shaid, Subramanian Ramasamy

Abstract:

Two multisensor system architectures for navigation and guidance of small Unmanned Aircraft (UA) are presented and compared. The main objective of our research is to design a compact, light and relatively inexpensive system capable of providing the required navigation performance in all phases of flight of small UA, with a special focus on precision approach and landing, where Vision Based Navigation (VBN) techniques can be fully exploited in a multisensor integrated architecture. Various existing techniques for VBN are compared and the Appearance-Based Navigation (ABN) approach is selected for implementation. Feature extraction and optical flow techniques are employed to estimate flight parameters such as roll angle, pitch angle, deviation from the runway centreline and body rates. Additionally, we address the possible synergies of VBN, Global Navigation Satellite System (GNSS) and MEMS-IMU (Micro-Electromechanical System Inertial Measurement Unit) sensors, and the use of Aircraft Dynamics Model (ADM) to provide additional information suitable to compensate for the shortcomings of VBN and MEMS-IMU sensors in high-dynamics attitude determination tasks. An Extended Kalman Filter (EKF) is developed to fuse the information provided by the different sensors and to provide estimates of position, velocity and attitude of the UA platform in real-time. The key mathematical models describing the two architectures i.e., VBN-IMU-GNSS (VIG) system and VIGADM (VIGA) system are introduced. The first architecture uses VBN and GNSS to augment the MEMS-IMU. The second mode also includes the ADM to provide augmentation of the attitude channel. Simulation of these two modes is carried out and the performances of the two schemes are compared in a small UA integration scheme (i.e., AEROSONDE UA platform) exploring a representative cross-section of this UA operational flight envelope, including high dynamics manoeuvres and CAT-I to CAT-III precision approach tasks. Simulation of the first system architecture (i.e., VIG system) shows that the integrated system can reach position, velocity and attitude accuracies compatible with the Required Navigation Performance (RNP) requirements. Simulation of the VIGA system also shows promising results since the achieved attitude accuracy is higher using the VBN-IMU-ADM than using VBN-IMU only. A comparison of VIG and VIGA system is also performed and it shows that the position and attitude accuracy of the proposed VIG and VIGA systems are both compatible with the RNP specified in the various UA flight phases, including precision approach down to CAT-II.

Keywords: Global Navigation Satellite System (GNSS), Lowcost Navigation Sensors, MEMS Inertial Measurement Unit (IMU), Unmanned Aerial Vehicle, Vision Based Navigation.

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Authors: Shidvash Vakilipour, Scott Ormiston, Masoud Mohammadi, Rouzbeh Riazi, Kimia Amiri, Sahar Barati

Abstract:

Two-phase and multi-phase flows are common flow types in fluid mechanics engineering. Among the basic and applied problems of these flow types, two-phase parallel flow is the one that two immiscible fluids flow in the vicinity of each other. In this type of flow, fluid properties (e.g. density, viscosity, and temperature) are different at the two sides of the interface of the two fluids. The most challenging part of the numerical simulation of two-phase flow is to determine the location of interface accurately. In the present work, a coupled interface tracking algorithm is developed based on Arbitrary Lagrangian-Eulerian (ALE) approach using a cell-centered, pressure-based, coupled solver. To validate this algorithm, an analytical solution for fully developed two-phase flow in presence of gravity is derived, and then, the results of the numerical simulation of this flow are compared with analytical solution at various flow conditions. The results of the simulations show good accuracy of the algorithm despite using a nearly coarse and uniform grid. Temporal variations of interface profile toward the steady-state solution show that a greater difference between fluids properties (especially dynamic viscosity) will result in larger traveling waves. Gravity effect studies also show that favorable gravity will result in a reduction of heavier fluid thickness and adverse gravity leads to increasing it with respect to the zero gravity condition. However, the magnitude of variation in favorable gravity is much more than adverse gravity.

Keywords: Coupled solver, gravitational force, interface tracking, Reynolds number to Froude number, two-phase flow.

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Authors: B. Chandra, P. Paul Varghese

Abstract:

Crypto System Identification is one of the challenging tasks in Crypt analysis. The paper discusses the possibility of employing Neural Networks for identification of Cipher Systems from cipher texts. Cascade Correlation Neural Network and Back Propagation Network have been employed for identification of Cipher Systems. Very large collection of cipher texts were generated using a Block Cipher (Enhanced RC6) and a Stream Cipher (SEAL). Promising results were obtained in terms of accuracy using both the Neural Network models but it was observed that the Cascade Correlation Neural Network Model performed better compared to Back Propagation Network.

Keywords: Back Propagation Neural Networks, CascadeCorrelation Neural Network, Crypto systems, Block Cipher, StreamCipher.

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Authors: Ilya Kavalchuk, Hayrettin Arisoy, Alex Stojcevski, Aman Maun Than Oo

Abstract:

Electric vehicles are one of the most complicated electric devices to simulate due to the significant number of different processes involved in electrical structure of it. There are concurrent processes of energy consumption and generation with different onboard systems, which make simulation tasks more complicated to perform. More accurate simulation on energy consumption can provide a better understanding of all energy management for electric transport. As a result of all those processes, electric transport can allow for a more sustainable future and become more convenient in relation to the distance range and recharging time. This paper discusses the problems of energy consumption simulations for electric vehicles using different software packages to provide ideas on how to make this process more precise, which can help engineers create better energy management strategies for electric vehicles.

Keywords: Electric Vehicles, EV, Power Consumption, Power Management, Simulation.

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Authors: Bella Llego

Abstract:

This study aims to investigate the motivating and de-motivating factors that affect the learning ability of students attending the English Learning Center in Thailand. The subjects of this research were 20 students from the Hana Semiconductor Co., Limited. The data were collected by using questionnaire and analyzed using the SPSS program for the percentage, mean and standard deviation. The research results show that the main motivating factor in learning English at Hana Semiconductor Co., Ltd. is that it would help the employees to communicate with foreign customers and managers. Other reasons include the need to read and write e-mails, and reports in English, as well as to increase overall general knowledge. The main de-motivating factor is that there is a lot of vocabulary to remember when learning English. Another de-motivating factor is that when homework is given, the students have no time to complete the tasks required of them at the end of the working day.

Keywords: Motivating, demotivating, English learning center, student communicate.

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Authors: N. Khelil. L. Djerou , A. Zerarka, M. Batouche

Abstract:

Consider the Gregory integration (G) formula with end corrections where h Δ is the forward difference operator with step size h. In this study we prove that can be optimized by minimizing some of the coefficient k a in the remainder term by particle swarm optimization. Experimental tests prove that can be rendered a powerful formula for library use.

Keywords: Numerical integration, Gregory Formula, Particle Swarm optimization.

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