Search results for: prediction equations

Authors: Yacine Arioua

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In this paper, we investigate the existence and uniqueness of solutions for a coupled system of nonlinear Caputo-type Katugampola fractional differential equations with integral boundary conditions. Based upon a contraction mapping principle, Schauders fixed point theorems, some new existence and uniqueness results of solutions for the given problems are obtained. For application, some examples are given to illustrate the usefulness of our main results.

Keywords: fractional differential equations, coupled system, Caputo-Katugampola derivative, fixed point theorems, existence, uniqueness

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Authors: Jeff Clarine, Chang-Shyh Peng, Daisy Sang

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Bioassay is the measurement of the potency of a chemical substance by its effect on a living animal or plant tissue. Bioassay data and chemical structures from pharmacokinetic and drug metabolism screening are mined from and housed in multiple databases. Bioassay prediction is calculated accordingly to determine further advancement. This paper proposes a four-step preprocessing of datasets for improving the bioassay predictions. The first step is instance selection in which dataset is categorized into training, testing, and validation sets. The second step is discretization that partitions the data in consideration of accuracy vs. precision. The third step is normalization where data are normalized between 0 and 1 for subsequent machine learning processing. The fourth step is feature selection where key chemical properties and attributes are generated. The streamlined results are then analyzed for the prediction of effectiveness by various machine learning algorithms including Pipeline Pilot, R, Weka, and Excel. Experiments and evaluations reveal the effectiveness of various combination of preprocessing steps and machine learning algorithms in more consistent and accurate prediction.

Keywords: bioassay, machine learning, preprocessing, virtual screen

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Authors: Anne-Lena Kampen, Øivind Kure

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Machine learning (ML) can be implemented in Wireless Sensor Networks (WSNs) as a central solution or distributed solution where the ML is embedded in the nodes. Embedding improves privacy and may reduce prediction delay. In addition, the number of transmissions is reduced. However, quality factors such as prediction accuracy, fault detection efficiency and coordinated control of the overall system suffer. Here, we discuss and highlight the trade-offs that should be considered when choosing between embedding and centralized ML, especially for multihop networks. In addition, we present estimations that demonstrate the energy trade-offs between embedded and centralized ML. Although the total network energy consumption is lower with central prediction, it makes the network more prone for partitioning due to the high forwarding load on the one-hop nodes. Moreover, the continuous improvements in the number of operations per joule for embedded devices will move the energy balance toward embedded prediction.

Keywords: central machine learning, embedded machine learning, energy consumption, local machine learning, wireless sensor networks, WSN

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Authors: Manop Aorpimai, Ponthep Navakitkanok

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In this paper, the development of the ephemeris generation module used for the Thaichote satellite operations is presented. It is a vital part of the flight dynamics system, which comprises, the orbit determination, orbit propagation, event prediction and station-keeping maneuver modules. In the generation of the spacecraft ephemeris data, the estimated orbital state vector from the orbit determination module is used as an initial condition. The equations of motion are then integrated forward in time to predict the satellite states. The higher geopotential harmonics, as well as other disturbing forces, are taken into account to resemble the environment in low-earth orbit. Using a highly accurate numerical integrator based on the Burlish-Stoer algorithm the ephemeris data can be generated for long-term predictions, by using a relatively small computation burden and short calculation time. Some events occurring during the prediction course that are related to the mission operations, such as the satellite’s rise/set viewed from the ground station, Earth and Moon eclipses, the drift in ground track as well as the drift in the local solar time of the orbital plane are all detected and reported. When combined with other modules to form a flight dynamics system, this application is aimed to be applied for the Thaichote satellite and successive Thailand’s Earth-observation missions.

Keywords: flight dynamics system, orbit propagation, satellite ephemeris, Thailand’s Earth Observation Satellite

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Authors: Mansoureh Naderipour, Susan Bastani, Mohammad Fazel Zarandi

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Predicting links that may occur in the future and missing links in social networks is an attractive problem in social network analysis. Granular computing can help us to model the relationships between human-based system and social sciences in this field. In this paper, we present a model based on granular computing approach and Type-2 fuzzy logic to predict links regarding nodes’ activity and the relationship between two nodes. Our model is tested on collaboration networks. It is found that the accuracy of prediction is significantly higher than the Type-1 fuzzy and crisp approach.

Keywords: social network, link prediction, granular computing, type-2 fuzzy sets

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Authors: Mezghiche Kamel

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We present solitary wave solutions for the perturbed nonlinear Schrodinger (PNLS) equation describing propagation of femtosecond light pulses through the fiber Bragg grating structure where the pulse dynamics is governed by the nonlinear-coupled mode (NLCM) equations. Using the multiple scale analysis, we reduce the NLCM equations into the perturbed nonlinear Schrodinger (PNLS) type equation. Unlike the reported solitary wave solutions of the PNLS equation, the novel ones can describe W shaped of solitons and their properties.

Keywords: fiber bragg grating, nonlinear-coupled mode equations, w shaped of solitons, PNLS

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Authors: Gunasekaran Raja, Rajakumar Arul, Kottilingam Kottursamy, Ramkumar Jayaraman, Sathya Pavithra, Swaminathan Venkatraman

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Wireless Interoperability for Microwave Access (WiMAX) utilizes the IEEE 802.1X mechanism for authentication. However, this mechanism incurs considerable delay during handoffs. This delay during handoffs results in service disruption which becomes a severe bottleneck. To overcome this delay, our article proposes a key caching mechanism based on user path prediction. If the user mobility follows that path, the user bypasses the normal IEEE 802.1X mechanism and establishes the necessary authentication keys directly. Through analytical and simulation modeling, we have proved that our mechanism effectively decreases the handoff delay thereby achieving fast authentication.

Keywords: authentication, authorization, and accounting (AAA), handoff, mobile, user path prediction (UPP) and user pattern

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Authors: Anurag Tripathi, Sanad Khandelwal

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Age and gender determination are required in forensic for victim identification. There is secondary dentine deposition throughout life, resulting in decreased pulp volume and size. Evaluation of pulp volume using Cone Beam Computed Tomography (CBCT)is a noninvasive method to evaluate the age and gender of an individual. The study was done to evaluate the efficacy of pulp volume method in the determination of age and gender.Aims/Objectives: The study was conducted to estimate age and determine sex by measuring tooth pulp volume with the help of CBCT. An observational study of one year duration on CBCT data of individuals was conducted in Lucknow. Maxillary central incisors (CI) and maxillary canine (C) of the randomly selected samples were assessed for measurement of pulp volume using a software. Statistical analysis: Chi Square Test, Arithmetic Mean, Standard deviation, Pearson’s Correlation, Linear & Logistic regression analysis. Results: The CBCT data of Ninety individuals with age range between 18-70 years was evaluated for pulp volume of central incisor and canine (CI & C). The Pearson correlation coefficient between the tooth pulp volume (CI & C) and chronological age suggested that pulp volume decreased with age. The validation of the equations for sex determination showed higher prediction accuracy for CI (56.70%) and lower for C (53.30%).Conclusion: Pulp volume obtained from CBCT is a reliable indicator for age estimation and gender prediction.

Keywords: forensic, dental age, pulp volume, cone beam computed tomography

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Authors: O. Acan, Y. Keskin

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In this study, we will carry out a comparative study between the reduced differential transform method, the adomian decomposition method, the variational iteration method and the homotopy analysis method. These methods are used in many fields of engineering. This is been achieved by handling a kind of 2-Dimensional and forth-order partial differential equations called the Kuramoto–Sivashinsky equations. Three numerical examples have also been carried out to validate and demonstrate efficiency of the four methods. Furthermost, it is shown that the reduced differential transform method has advantage over other methods. This method is very effective and simple and could be applied for nonlinear problems which used in engineering.

Keywords: reduced differential transform method, adomian decomposition method, variational iteration method, homotopy analysis method

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Authors: Kiyoumars Roushangar, Saeid Sadaghian

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Although accurate sediment load prediction is very important in planning, designing, operating and maintenance of water resources structures, the transport mechanism is complex, and the deterministic transport models are based on simplifying assumptions often lead to large prediction errors. In this research, firstly, two intelligent ANN methods, Radial Basis and General Regression Neural Networks, are adopted to model of total sediment load transport into Madani Dam reservoir (north of Iran) using the measured data and then applicability of the sediment transport methods developed by Engelund and Hansen, Ackers and White, Yang, and Toffaleti for predicting of sediment load discharge are evaluated. Based on comparison of the results, it is found that the GRNN model gives better estimates than the sediment rating curve and mentioned classic methods.

Keywords: sediment transport, dam reservoir, RBF, GRNN, prediction

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Authors: Alexandre Barbosa de Almeida, Telma Woerle de Lima Soares

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Protein structure prediction is a challenging task in the bioinformatics field. The biological function of all proteins majorly relies on the shape of their three-dimensional conformational structure, but less than 1% of all known proteins in the world have their structure solved. This work proposes a deep learning model to address this problem, attempting to predict some aspects of the protein conformations. Throughout a process of multiobjective dominance, a recurrent neural network was trained to abstract the particular bias of each individual multiobjective algorithm, generating a heuristic that could be useful to predict some of the relevant aspects of the three-dimensional conformation process formation, known as protein folding.

Keywords: Ab initio heuristic modeling, multiobjective optimization, protein structure prediction, recurrent neural network

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Authors: Danladi Ali, Abdullahi Mukaila

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In this work, GSM signal strength (power) was monitored in an indoor environment. Samples of the GSM signal strength was measured on mobile equipment (ME). One-dimensional multilevel wavelet is used to predict the fading phenomenon of the GSM signal measured and neural network clustering to determine the average power received in the study area. The wavelet prediction revealed that the GSM signal is attenuated due to the fast fading phenomenon which fades about 7 times faster than the radio wavelength while the neural network clustering determined that -75dBm appeared more frequently followed by -85dBm. The work revealed that significant part of the signal measured is dominated by weak signal and the signal followed more of Rayleigh than Gaussian distribution. This confirmed the wavelet prediction.

Keywords: decomposition, clustering, propagation, model, wavelet, signal strength and spectral efficiency

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Authors: Ciro Cursio, Giulia Cursio, Pio Luigi Cursio, Luigi Cursio

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Communication between practitioner and patient is of the utmost importance in aesthetic medicine: as of today, images of previous treatments are the most common tool used by doctors to describe and anticipate future results for their patients. However, using photos of other people often reduces the engagement of the prospective patient and is further limited by the number and quality of pictures available to the practitioner. Pre-existing work solves this issue in two ways: 3D scanning of the area with manual editing of the 3D model by the doctor or automatic prediction of the treatment by warping the image with hand-written parameters. The first approach requires the manual intervention of the doctor, while the second approach always generates results that aren’t always realistic. Thus, in one case, there is significant manual work required by the doctor, and in the other case, the prediction looks artificial. We propose an AI-based algorithm that autonomously generates a realistic prediction of treatment results. For the purpose of this study, we focus on hyaluronic acid treatments in the facial area. Our approach takes into account the individual characteristics of each face, and furthermore, the prediction system allows the patient to decide which area of the face she wants to modify. We show that the predictions generated by our system are realistic: first, the quality of the generated images is on par with real images; second, the prediction matches the actual results obtained after the treatment is completed. In conclusion, the proposed approach provides a valid tool for doctors to show patients what they will look like before deciding on the treatment.

Keywords: prediction, hyaluronic acid, treatment, artificial intelligence

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Authors: Etienne Alain Feukeu, L. W. Snyman

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Water scarcity is becoming a real issue nowadays. Most countries in the world are facing it in their own way based on their own geographical coordinate and condition. Many countries are facing a challenge of a growing water demand as a result of not only an increased population, economic growth, but also as a pressure of the population dynamic and urbanization. In view to mitigate some of this related problem, an accurate method of water estimation and future prediction, forecast is essential to guarantee not only the sufficient quantity, but also a good water distribution and management system. Beside the fact that several works have been undertaken to address this concern, there is still a considerable disparity between different methods and standard used for water prediction and estimation. Hence this work contrast and compare two well-defined and established methods from two countries (USA and South Africa) to demonstrate the inconsistency when different method and standards are used interchangeably.

Keywords: water scarcity, water estimation, water prediction, water forecast.

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Authors: M. Pienaar, J. W. Odendaal, J. C. Smit, J. Joubert

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Simulations are commonly used to predict the bistatic radar cross section (RCS) of military targets since characterization measurements can be expensive and time consuming. It is thus important to accurately predict the bistatic RCS of targets. Computational electromagnetic (CEM) methods can be used for bistatic RCS prediction. CEM methods are divided into full-wave and asymptotic methods. Full-wave methods are numerical approximations to the exact solution of Maxwell’s equations. These methods are very accurate but are computationally very intensive and time consuming. Asymptotic techniques make simplifying assumptions in solving Maxwell's equations and are thus less accurate but require less computational resources and time. Asymptotic techniques can thus be very valuable for the prediction of bistatic RCS of electrically large targets, due to the decreased computational requirements. This study extends previous work by validating the accuracy of asymptotic techniques to predict bistatic RCS through comparison with full-wave simulations as well as measurements. Validation is done with canonical structures as well as complex realistic aircraft models instead of only looking at a complex slicy structure. The slicy structure is a combination of canonical structures, including cylinders, corner reflectors and cubes. Validation is done over large bistatic angles and at different polarizations. Bistatic RCS measurements were conducted in a compact range, at the University of Pretoria, South Africa. The measurements were performed at different polarizations from 2 GHz to 6 GHz. Fixed bistatic angles of β = 30.8°, 45° and 90° were used. The measurements were calibrated with an active calibration target. The EM simulation tool FEKO was used to generate simulated results. The full-wave multi-level fast multipole method (MLFMM) simulated results together with the measured data were used as reference for validation. The accuracy of physical optics (PO) and geometrical optics (GO) was investigated. Differences relating to amplitude, lobing structure and null positions were observed between the asymptotic, full-wave and measured data. PO and GO were more accurate at angles close to the specular scattering directions and the accuracy seemed to decrease as the bistatic angle increased. At large bistatic angles PO did not perform well due to the shadow regions not being treated appropriately. PO also did not perform well for canonical structures where multi-bounce was the main scattering mechanism. PO and GO do not account for diffraction but these inaccuracies tended to decrease as the electrical size of objects increased. It was evident that both asymptotic techniques do not properly account for bistatic structural shadowing. Specular scattering was calculated accurately even if targets did not meet the electrically large criteria. It was evident that the bistatic RCS prediction performance of PO and GO depends on incident angle, frequency, target shape and observation angle. The improved computational efficiency of the asymptotic solvers yields a major advantage over full-wave solvers and measurements; however, there is still much room for improvement of the accuracy of these asymptotic techniques.

Keywords: asymptotic techniques, bistatic RCS, geometrical optics, physical optics

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Authors: Francis Mark A. Fernandez, Chelca Ubay, Armithan Suguitan

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Regions or provinces in a definite state certainly contribute to the economy of their mainland. These regions or provinces are the ones supplying the mainland with different resources and assets. Thus, with a certain region separating from the mainland would indeed impinge the heart of an entire state to develop and expand. With these, the researchers decided to study on the effects of the separation of one’s region to its mainland and the consequences that will take place if the mainland would rule out the region to separate from them. The researchers wrote this paper to present the causes of the separation of Catalonia from Spain and the prediction regarding the pursuance of this region to revolt from its mainland, Spain. In conducting this research, the researchers utilized two analyses, namely: qualitative and quantitative. In qualitative, numerous of information regarding the existing experiences of the citizens of Catalonia were gathered by the authors to give certainty to the prediction of the researchers. Besides this undertaking, the researchers will also gather needed information and figures through books, journals and the published news and reports. In addition, to further support this prediction under qualitative analysis, the researchers intended to operate the Phenomenological research in which the examiners will exemplify the lived experiences of each citizen in Catalonia. Moreover, the researchers will utilize one of the types of Phenomenological research which is hermeneutical phenomenology by Van Manen. In quantitative analysis, the researchers utilized the regression analysis in which it will ascertain the causality in an underlying theory in understanding the relationship of the variables. The researchers assigned and identified different variables, wherein the dependent variable or the y which represents the prediction of the researchers, the independent variable however or the x represents the arising problems that grounds the partition of the region, the summation of the independent variable or the ∑x represents the sum of the problem and finally the summation of the dependent variable or the ∑y is the result of the prediction. With these variables, using the regression analysis, the researchers will be able to show the connections and how a single variable could affect the other variables. From these approaches, the prediction of the researchers will be specified. This research could help different states dealing with this kind of problem. It will further help certain states undergoing this problem by analyzing the causes of these insurgencies and the effects on it if it will obstruct its region to consign their full-pledge autonomy.

Keywords: autonomy, liberty, prediction, separation

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Authors: Amal A. Mashali, Omar Eltaweel, Elerian Ekladious

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Stature of an individual has an important role in identification, which is often required in medico-legal practice. The estimation of stature is an important step in the identification of dismembered remains or when only a part of a skeleton is only available as in major disasters or with mutilation. There is no published data on anthropological data among Jordanian population. The present study was designed in order to find out relationship of stature to some anthropometric measures among a sample of Jordanian population and to determine the most accurate and reliable one in predicting the stature of an individual. A cross sectional study was conducted on 336 adult healthy volunteers , free of bone diseases, nutritional diseases and abnormalities in the extremities after taking their consent. Students of Faculty of Medicine, Mutah University helped in collecting the data. The anthropometric measurements (anatomically defined) were stature, humerus length, hand length and breadth, foot length and breadth, foot index and knee height on both right and left sides of the body. The measurements were typical on both sides of the bodies of the studied samples. All the anthropologic data showed significant relation with age except the knee height. There was a significant difference between male and female measurements except for the foot index where F= 0.269. There was a significant positive correlation between the different measures and the stature of the individuals. Three equations were developed for estimation of stature. The most sensitive measure for prediction of a stature was found to be the humerus length.

Keywords: foot index, foot length, hand length, humerus length, stature

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Authors: Jaan Lellep, Shahid Mubasshar

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A numerical solution is developed for simply supported nanoarches based on the non-local theory of elasticity. The nanoarch under consideration has a step-wise variable cross-section and is weakened by crack-like defects. It is assumed that the cracks are stationary and the mechanical behaviour of the nanoarch can be modeled by Eringen’s non-local theory of elasticity. The physical and thermal properties are sensitive with respect to changes of dimensions in the nano level. The classical theory of elasticity is unable to describe such changes in material properties. This is because, during the development of the classical theory of elasticity, the speculation of molecular objects was avoided. Therefore, the non-local theory of elasticity is applied to study the vibration of nanostructures and it has been accepted by many researchers. In the non-local theory of elasticity, it is assumed that the stress state of the body at a given point depends on the stress state of each point of the structure. However, within the classical theory of elasticity, the stress state of the body depends only on the given point. The system of main equations consists of equilibrium equations, geometrical relations and constitutive equations with boundary and intermediate conditions. The system of equations is solved by using the method of separation of variables. Consequently, the governing differential equations are converted into a system of algebraic equations whose solution exists if the determinant of the coefficients of the matrix vanishes. The influence of cracks and steps on the natural vibration of the nanoarches is prescribed with the aid of additional local compliance at the weakened cross-section. An algorithm to determine the eigenfrequencies of the nanoarches is developed with the help of computer software. The effects of various physical and geometrical parameters are recorded and drawn graphically.

Keywords: crack, nanoarches, natural frequency, step

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Authors: H. D. Ibrahim, H. C. Chinwenyi, T. Danjuma

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An option is defined as a financial contract that provides the holder the right but not the obligation to buy or sell a specified quantity of an underlying asset in the future at a fixed price (called a strike price) on or before the expiration date of the option. This paper examined two approaches for derivation of Partial Differential Equation (PDE) options price valuation formula for the Heston stochastic volatility model. We obtained various PDE option price valuation formulas using the riskless portfolio method and the application of Feynman-Kac theorem respectively. From the results obtained, we see that the two derived PDEs for Heston model are distinct and non-unique. This establishes the fact of incompleteness in the model for option price valuation.

Keywords: Black-Scholes partial differential equations, Ito process, option price valuation, partial differential equations

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Authors: Jorge Gonzalez-Camus

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In this work is proved the existence of at least one minimal and maximal mild solutions to the Cauchy problem, for fractional evolution equation of neutral type, involving a general kernel. An operator A generating a resolvent family and integral resolvent family on a Banach space X and a kernel belonging to a large class appears in the equation, which covers many relevant cases from physics applications, in particular, the important case of time - fractional evolution equations of neutral type. The main tool used in this work was the Kuratowski measure of noncompactness and fixed point theorems, specifically Darbo-type, and an iterative method of lower and upper solutions, based in an order in X induced by a normal cone P. Initially, the equation is a Cauchy problem, involving a fractional derivate in Caputo sense. Then, is formulated the equivalent integral version, and defining a convenient functional, using the theory of resolvent families, and verifying the hypothesis of the fixed point theorem of Darbo type, give us the existence of mild solution for the initial problem. Furthermore, the existence of minimal and maximal mild solutions was proved through in an iterative method of lower and upper solutions, using the Azcoli-Arzela Theorem, and the Gronwall’s inequality. Finally, we recovered the case derivate in Caputo sense.

Keywords: fractional evolution equations, Volterra integral equations, minimal and maximal mild solutions, neutral type equations, non-local in time equations

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Authors: Nilubon Kurubanjerdjit, Nattakarn Iam-On, Ka-Lok Ng

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MicroRNAs are small non-coding RNA found in many different species. They play crucial roles in cancer such as biological processes of apoptosis and proliferation. The identification of microRNA-target genes can be an essential first step towards to reveal the role of microRNA in various cancer types. In this paper, we predict miRNA-target genes for lung cancer by integrating prediction scores from miRanda and PITA algorithms used as a feature vector of miRNA-target interaction. Then, machine-learning algorithms were implemented for making a final prediction. The approach developed in this study should be of value for future studies into understanding the role of miRNAs in molecular mechanisms enabling lung cancer formation.

Keywords: microRNA, miRNAs, lung cancer, machine learning, Naïve Bayes, SVM

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Authors: Dong Wu, Michael Grenn

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Managing software projects effectively is crucial for meeting deadlines, ensuring quality, and managing resources well. Traditional methods often struggle with predicting project timelines accurately due to uncertain schedules and complex data. This study addresses these challenges by combining time prediction algorithms with Large Language Models (LLMs). It makes use of real-world software project data to construct and validate a model. The model takes detailed project progress data such as task completion dynamic, team Interaction and development metrics as its input and outputs predictions of project timelines. To evaluate the effectiveness of this model, a comprehensive methodology is employed, involving simulations and practical applications in a variety of real-world software project scenarios. This multifaceted evaluation strategy is designed to validate the model's significant role in enhancing forecast accuracy and elevating overall management efficiency, particularly in complex software project environments. The results indicate that the integration of time prediction algorithms with LLMs has the potential to optimize software project progress management. These quantitative results suggest the effectiveness of the method in practical applications. In conclusion, this study demonstrates that integrating time prediction algorithms with LLMs can significantly improve the predictive accuracy and efficiency of software project management. This offers an advanced project management tool for the industry, with the potential to improve operational efficiency, optimize resource allocation, and ensure timely project completion.

Keywords: software project management, time prediction algorithms, large language models (LLMS), forecast accuracy, project progress prediction

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Authors: Arcady Ponosov

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Many well-known age-structured population models are derived from the celebrated McKendrick-von Foerster equation (MFE), also called the biological conservation law. A similar technique is suggested for the stochastically perturbed MFE. This technique is shown to produce stochastic versions of the deterministic population models, which appear to be very different from those one can construct by simply appending additive stochasticity to deterministic equations. In particular, it is shown that stochastic Nicholson’s blowflies model should contain both additive and multiplicative stochastic noises. The suggested transformation technique is similar to that used in the deterministic case. The difference is hidden in the formulas for the exact solutions of the simplified boundary value problem for the stochastically perturbed MFE. The analysis is also based on the theory of stochastic delay differential equations.

Keywords: boundary value problems, population models, stochastic delay differential equations, stochastic partial differential equation

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Authors: Xiaogang Li, Jieqiong Miao

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As for the problem of the grey forecasting model prediction accuracy is low, an improved grey prediction model is put forward. Firstly, use trigonometric function transform the original data sequence in order to improve the smoothness of data , this model called SGM( smoothness of grey prediction model), then combine the improved grey model with support vector machine , and put forward the grey support vector machine model (SGM - SVM).Before the establishment of the model, we use trigonometric functions and accumulation generation operation preprocessing data in order to enhance the smoothness of the data and weaken the randomness of the data, then use support vector machine (SVM) to establish a prediction model for pre-processed data and select model parameters using genetic algorithms to obtain the optimum value of the global search. Finally, restore data through the "regressive generate" operation to get forecasting data. In order to prove that the SGM-SVM model is superior to other models, we select the battery life data from calce. The presented model is used to predict life of battery and the predicted result was compared with that of grey model and support vector machines．For a more intuitive comparison of the three models, this paper presents root mean square error of this three different models .The results show that the effect of grey support vector machine (SGM-SVM) to predict life is optimal, and the root mean square error is only 3.18%. Keywords: grey forecasting model, trigonometric function, support vector machine, genetic algorithms, root mean square error

Keywords: Grey prediction model, trigonometric functions, support vector machines, genetic algorithms, root mean square error

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Authors: Sufyan Muhammad

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Recently, in achieving highly efficient but at the same time highly accurate solutions has become the major target of numerical analyst community. The concept is termed as compact schemes and has gained great popularity and consequently, we construct compact schemes for fourth order parabolic differential equations used to study vibrations in structures. For the superiority of newly constructed schemes, we consider range of examples. We have achieved followings i.e. (a) numerical scheme utilizes minimum number of stencil points (which means new scheme is compact); (b) numerical scheme is highly accurate (which means new scheme is reliable) and (c) numerical scheme is highly efficient (which means new scheme is fast).

Keywords: central finite differences, compact schemes, Bernoulli's equations, finite differences

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Authors: R. A. Petre, S. E. Nichifor, A. Craifaleanu, I. Stroe

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The relative motion of a robotic arm formed by homogeneous bars of different lengths and masses, hinged to each other is investigated. The first bar of the mechanism is articulated on a platform, considered initially fixed on the surface of the Earth, while for the second case the platform is considered to be in rotation with respect to the Earth. For both analyzed cases the motion equations are determined using the Lagrangian formalism, applied in its traditional form, valid with respect to an inertial reference system, conventionally considered as fixed. However, in the second case, a generalized form of the formalism valid with respect to a non-inertial reference frame will also be applied. The numerical calculations were performed using a MATLAB program.

Keywords: Lagrange equations, relative motion, inertial reference frame, non-inertial reference frame

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Authors: Yenni Kurniawati

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Students Prediction Skill in chemistry experiments is an important skill for pre-service chemistry students to stimulate students reflective thinking at each stage of many chemistry experiments, qualitatively and quantitatively. A Virtual Chemistry Laboratory was designed to give students opportunities and times to practicing many kinds of chemistry experiments repeatedly, everywhere and anytime, before they do a real experiment. The Virtual Chemistry Laboratory content was constructed using the Model of Educational Reconstruction and developed to enhance students ability to predicted the experiment results and analyzed the cause of error, calculating the accuracy and precision with carefully in using chemicals. This research showed students changing in making a decision and extremely beware with accuracy, but still had a low concern in precision. It enhancing students level of reflective thinking skill related to their prediction skill 1 until 2 stage in average. Most of them could predict the characteristics of the product in experiment, and even the result will going to be an error. In addition, they take experiments more seriously and curiously about the experiment results. This study recommends for a different subject matter to provide more opportunities for students to learn about other kinds of chemistry experiments design.

Keywords: virtual chemistry laboratory, chemistry experiments, prediction skill, pre-lab experiences

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Authors: Mina Jafari, Kobra Hamraee, Saied Hossein Hosseini

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The prediction of breast cancer disease is one of the challenges in medicine. In this paper we collected 528 records of women’s information who live in Kabul including demographic, life style, diet and pregnancy data. There are many classification algorithm in breast cancer prediction and tried to find the best model with most accurate result and lowest error rate. We evaluated some other common supervised algorithms in data mining to find the best model in prediction of breast cancer disease among afghan women living in Kabul regarding to momography result as target variable. For evaluating these algorithms we used Cross Validation which is an assured method for measuring the performance of models. After comparing error rate and accuracy of three models: Decision Tree, Naive Bays and Rule Induction, Decision Tree with accuracy of 94.06% and error rate of %15 is found the best model to predicting breast cancer disease based on the health care records.

Keywords: decision tree, breast cancer, probability, data mining

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Authors: Syed M. Jawwad Riaz

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There has been a lot of interest in exploring the thermodynamic properties at the horizon of a black hole geometry. Earlier, it has been shown, for different spacetimes, that the Einstein field equations at the horizon can be expressed as a first law of black hole thermodynamics. In this paper, considering r = constant slices, for the Kerr-Newman black hole, shown that the Einstein field equations for the induced 3-metric of the hypersurface is expressed in thermodynamic quantities under the virtual displacements of the hypersurfaces. As expected, it is found that the field equations of the induced metric corresponding to the horizon can only be written as a first law of black hole thermodynamics. It is to be mentioned here that the procedure adopted is much easier, to obtain such results, as here one has to essentially deal with (n - 1)-dimensional induced metric for an n-dimensional spacetime.

Keywords: black hole space-times, Einstein's field equation, foliation, hyper-surfaces

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Authors: Davit Shahnazaryan, Diogo Gomes, Mher Safaryan

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Many symbolic computations and manipulations required in the analysis of partial differential equations (PDE) or systems of PDEs are tedious and error-prone. These computations arise when determining conservation laws, entropies or integral identities, which are essential tools for the study of PDEs. Here, we discuss a new Mathematica package for the symbolic analysis of PDEs that automate multiple tasks, saving time and effort. Methodologies: During the research, we have used concepts of linear algebra and partial differential equations. We have been working on creating algorithms based on theoretical mathematics to find results mentioned below. Major Findings: Our package provides the following functionalities; finding symmetry group of different PDE systems, generation of polynomials invariant with respect to different symmetry groups; simplification of integral quantities by integration by parts and null Lagrangian cleaning, computing general forms of expressions by integration by parts; finding equivalent forms of an integral expression that are simpler or more symmetric form; determining necessary and sufficient conditions on the coefficients for the positivity of a given symbolic expression. Conclusion: Using this package, we can simplify integral identities, find conserved and dissipated quantities of time-dependent PDE or system of PDEs. Some examples in the theory of mean-field games and semiconductor equations are discussed.

Keywords: partial differential equations, symbolic computation, conserved and dissipated quantities, mathematica

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