Search results for: generalized pair correlation method

Authors: Lidija R. Jevrić, Sanja O. Podunavac-Kuzmanović, Strahinja Z. Kovačević

Abstract:

In this paper, quantitative structure-retention relationships (QSRR) analysis was applied in order to correlate in silico biological and lipophilicity molecular descriptors with retention values for the set of selected s-triazine herbicides. In silico generated biological and lipophilicity descriptors were discriminated using generalized pair correlation method (GPCM). According to this method, the significant difference between independent variables can be noticed regardless almost equal correlation with dependent variable. Using established multiple linear regression (MLR) models some biological characteristics could be predicted. Established MLR models were evaluated statistically and the most suitable models were selected and ranked using sum of ranking differences (SRD) method. In this method, as reference values, average experimentally obtained values are used. Additionally, using SRD method, similarities among investigated s-triazine herbicides can be noticed. These analysis were conducted in order to characterize selected s-triazine herbicides for future investigations regarding their biodegradability. This study is financially supported by COST action TD1305.

Keywords: descriptors, generalized pair correlation method, pesticides, sum of ranking differences

Procedia PDF Downloads 270

Authors: Milica Karadzic, Lidija Jevric, Sanja Podunavac-Kuzmanovic, Strahinja Kovacevic, Aleksandra Tepic-Horecki, Zdravko Sumic

Abstract:

In this paper, the influence of six different phytochemical content (phenols, carotenoids, chlorophyll a, chlorophyll b, chlorophyll a + b and vitamin C) on antioxidant potential of Murai and Levistro lettuce varieties was evaluated. Variable selection was made by generalized pair correlation method (GPCM) as a novel ranking method. This method is used for the discrimination between two variables that almost equal correlate to a dependent variable. Fisher’s conditional exact and McNemar’s test were carried out. Established multiple linear (MLR) models were statistically evaluated. As the best phytochemicals for the antioxidant potential prediction, chlorophyll a, chlorophyll a + b and total carotenoids content stand out. This was confirmed through both GPCM and MLR, predictive ability of obtained MLR can be used for antioxidant potential estimation for similar lettuce samples. This article is based upon work from the project of the Provincial Secretariat for Science and Technological Development of Vojvodina (No. 114-451-347/2015-02).

Keywords: antioxidant activity, generalized pair correlation method, lettuce, regression analysis

Procedia PDF Downloads 361

Authors: Milica Ž. Karadžić, Lidija R. Jevrić, Sanja Podunavac-Kuzmanović, Strahinja Z. Kovačević, Anamarija I. Mandić, Katarina Penov-Gaši, Andrea R. Nikolić, Aleksandar M. Oklješa

Abstract:

This study considered selection of the in silico molecular descriptors and the models for newly synthesized steroid derivatives description and their characterization using chemometric techniques. Multiple linear regression (MLR) models were established and gave the best molecular descriptors for quantitative structure-retention relationship (QSRR) modeling of the retention of the investigated molecules. MLR models were without multicollinearity among the selected molecular descriptors according to the variance inflation factor (VIF) values. Used molecular descriptors were ranked using generalized pair correlation method (GPCM). In this method, the significant difference between independent variables can be noticed regardless almost equal correlation between dependent variable. Generated MLR models were statistically and cross-validated and the best models were kept. Models were ranked using sum of ranking differences (SRD) method. According to this method, the most consistent QSRR model can be found and similarity or dissimilarity between the models could be noticed. In this study, SRD was performed using average values of experimentally observed data as a golden standard. Chemometric analysis was conducted in order to characterize newly synthesized steroid derivatives for further investigation regarding their potential biological activity and further synthesis. This article is based upon work from COST Action (CM1105), supported by COST (European Cooperation in Science and Technology).

Keywords: generalized pair correlation method, molecular descriptors, regression analysis, steroids, sum of ranking differences

Procedia PDF Downloads 314

Authors: Zubdahe Noor, Haseeb Athar

Abstract:

In this article, first a relation for conditional expectation is developed and then is used to characterize a general class of distributions F(x) = 1-e^(-ah(x)) through conditional expectation of difference of pair of generalized order statistics. Some results are reduced for particular cases. In the end, a list of distributions is presented in the form of table that are compatible with the given general class.

Keywords: generalized order statistics, order statistics, record values, conditional expectation, characterization

Procedia PDF Downloads 437

Authors: A. Ishag Mohamed, A. A. Rabah

Abstract:

The objective of this research is to develop a generalized correlation for the prediction of thermal conductivity of n-Alkanes and Alkenes. There is a minority of research and lack of correlation for thermal conductivity of liquids in the open literature. The available experimental data are collected covering the groups of n-Alkanes and Alkenes.The data were assumed to correlate to temperature using Filippov correlation. Nonparametric regression of Grace Algorithm was used to develop the generalized correlation model. A spread sheet program based on Microsoft Excel was used to plot and calculate the value of the coefficients. The results obtained were compared with the data that found in Perry's Chemical Engineering Hand Book. The experimental data correlated to the temperature ranged "between" 273.15 to 673.15 K, with R2 = 0.99.The developed correlation reproduced experimental data that which were not included in regression with absolute average percent deviation (AAPD) of less than 7 %. Thus the spread sheet was quite accurate which produces reliable data.

Keywords: N-Alkanes, N-Alkenes, nonparametric, regression

Procedia PDF Downloads 629

Authors: Weizhi Zhong, Xiaoyi Lu, Lei Xu

Abstract:

In order to solve the problem of inaccurate synchronization for distributed multiple-input multiple-output (MIMO) system in multipath environment, a golay pair aided timing synchronization method is proposed in this paper. A new synchronous training sequence based on golay pair is designed. By utilizing the aperiodic auto-correlation complementary property of the new training sequence, the fine timing point is obtained at the receiver. Simulation results show that, compared with the tradition timing synchronization approaches, the proposed algorithm can provide high accuracy in synchronization, especially under multipath condition.

Keywords: distributed MIMO system, golay pair, multipath, synchronization

Procedia PDF Downloads 219

Authors: Li-Zhi Liao

Abstract:

The central path has played the key role in the interior point method. However, the convergence of the central path may not be true even in some convex programming problems with linear constraints. In this paper, the generalized central paths are introduced for convex programming. One advantage of the generalized central paths is that the paths will always converge to some optimal solutions of the convex programming problem for any initial interior point. Some additional theoretical properties for the generalized central paths will be also reported.

Keywords: central path, convex programming, generalized central path, interior point method

Procedia PDF Downloads 290

Authors: Hubert Klar

Abstract:

High double excitation of two-electron atoms has been investigated using hyperpherical coordinates within a modified adiabatic expansion technique. This modification creates a novel fictitious force leading to a spontaneous exchange symmetry breaking at high double excitation. The Pauli principle must therefore be regarded as approximation valid only at low excitation energy. Threshold electron scattering from high Rydberg states shows an unexpected time reversal symmetry breaking. At threshold for double escape we discover a broad (few eV) Cooper pair.

Keywords: correlation, resonances, threshold ionization, Cooper pair

Procedia PDF Downloads 317

Authors: Vijay Kumar Singh, Pooja Kushwaha, Prabhat Ranjan, Krishna Kumar Ojha, Jitendra Kumar

Abstract:

Present day high-throughput genomic technologies, NGS/microarrays, are producing large volume of data that require improved analysis methods to make sense of the data. The correlation between genes and samples has been regularly used to gain insight into many biological phenomena including, but not limited to, co-expression/co-regulation, gene regulatory networks, clustering and pattern identification. However, presence of outliers and violation of assumptions underlying Pearson correlation is frequent and may distort the actual correlation between the genes and lead to spurious conclusions. Here, we report a method to measure the strength of association between genes. The method assumes that the expression values of a gene are Bernoulli random variables whose outcome depends on the sample being probed. The method considers the two genes as uncorrelated if the number of sample with same outcome for both the genes (Ns) is equal to certainly expected number (Es). The extent of correlation depends on how far Ns can deviate from the Es. The method does not assume normality for the parent population, fairly unaffected by the presence of outliers, can be applied to qualitative data and it uses the binomial distribution to assess the significance of association. At this stage, we would not claim about the superiority of the method over other existing correlation methods, but our method could be another way of calculating correlation in addition to existing methods. The method uses binomial distribution, which has not been used until yet, to assess the significance of association between two variables. We are evaluating the performance of our method on NGS/microarray data, which is noisy and pierce by the outliers, to see if our method can differentiate between spurious and actual correlation. While working with the method, it has not escaped our notice that the method could also be generalized to measure the association of more than two variables which has been proven difficult with the existing methods.

Keywords: binomial distribution, correlation, microarray, outliers, transcriptome

Procedia PDF Downloads 382

Authors: Luh Eka Suryani, Purhadi

Abstract:

Poisson regression is a non-linear regression model with response variable in the form of count data that follows Poisson distribution. Modeling for a pair of count data that show high correlation can be analyzed by Poisson Bivariate Regression. Data, the number of infant mortality and maternal mortality, are count data that can be analyzed by Poisson Bivariate Regression. The Poisson regression assumption is an equidispersion where the mean and variance values are equal. However, the actual count data has a variance value which can be greater or less than the mean value (overdispersion and underdispersion). Violations of this assumption can be overcome by applying Generalized Poisson Regression. Characteristics of each regency can affect the number of cases occurred. This issue can be overcome by spatial analysis called geographically weighted regression. This study analyzes the number of infant mortality and maternal mortality based on conditions in East Java in 2016 using Geographically Weighted Bivariate Generalized Poisson Regression (GWBGPR) method. Modeling is done with adaptive bisquare Kernel weighting which produces 3 regency groups based on infant mortality rate and 5 regency groups based on maternal mortality rate. Variables that significantly influence the number of infant and maternal mortality are the percentages of pregnant women visit health workers at least 4 times during pregnancy, pregnant women get Fe3 tablets, obstetric complication handled, clean household and healthy behavior, and married women with the first marriage age under 18 years.

Keywords: adaptive bisquare kernel, GWBGPR, infant mortality, maternal mortality, overdispersion

Procedia PDF Downloads 133

Authors: Igor Filikhin, Vladimir M. Suslov, Roman Ya. Kezerashvili, Branislav Vlahivic

Abstract:

The mass-polarization term of the three-body kinetic energy operator is evaluated for different systems which include two identical particles: A+A+B. The term has to be taken into account for the analysis of AB- and AA-interactions based on experimental data for two- and three-body ground state energies. In this study, we present three-body calculations within the framework of a potential model for the kaonic clusters K−K−p and ppK−, nucleus 3H and hypernucleus 6 ΛΛHe. The systems are well clustering as A+ (A+B) with a ground state energy E2 for the pair A+B. The calculations are performed using the method of the Faddeev equations in configuration space. The phenomenological pair potentials were used. We show a correlation between the mass ratio mA/mB and the value δB of the mass-polarization term. For bosonic-like systems, this value is defined as δB = 2E2 − E3, where E3 is three-body energy when VAA = 0. For the systems including three particles with spin(isospin), the models with average AB-potentials are used. In this case, the Faddeev equations become a scalar one like for the bosonic-like system αΛΛ. We show that the additional energy conected with the mass-polarization term can be decomposite to a sum of the two parts: exchenge related and reduced mass related. The state of the system can be described as the following: the particle A1 is bound within the A + B pair with the energy E2, and the second particle A2 is bound with the pair with the energy E3 − E2. Due to the identity of A particles, the particles A1 and A2 are interchangeable in the pair A + B. We shown that the mass polarization δB correlates with a type of AB potential using the system αΛΛ as an example.

Keywords: three-body systems, mass polarization, Faddeev equations, nuclear interactions

Procedia PDF Downloads 327

Authors: Manideepa Saha, Jahnavi Chakrabarty

Abstract:

Generalized Jacobi (GJ) and Generalized Gauss-Seidel (GGS) methods are most effective than conventional Jacobi and Gauss-Seidel methods for solving linear system of equations. It is known that GJ and GGS methods converge for strictly diagonally dominant (SDD) and for M-matrices. In this paper, we study the convergence of GJ and GGS converge for symmetric positive definite (SPD) matrices, L-matrices and H-matrices. We introduce a generalization of successive overrelaxation (SOR) method for solving linear systems and discuss its convergence for the classes of SDD matrices, SPD matrices, M-matrices, L-matrices and for H-matrices. Advantages of generalized SOR method are established through numerical experiments over GJ, GGS, and SOR methods.

Keywords: convergence, Gauss-Seidel, iterative method, Jacobi, SOR

Procedia PDF Downloads 156

Authors: Christian Lavault

Abstract:

In this paper, the generalized fractional integral operators of two generalized Mittag-Leffler type functions are investigated. The special cases of interest involve the generalized M-series and K-function, both introduced by Sharma. The two pairs of theorems established herein generalize recent results about left- and right-sided generalized fractional integration operators applied here to the M-series and the K-function. The note also results in important applications in physics and mathematical engineering.

Keywords: Fox–Wright Psi function, generalized hypergeometric function, generalized Riemann– Liouville and Erdélyi–Kober fractional integral operators, Saigo's generalized fractional calculus, Sharma's M-series and K-function

Procedia PDF Downloads 405

Authors: Wikanda Phaphan

Abstract:

Mixture generalized gamma distribution is a combination of two distributions: generalized gamma distribution and length biased generalized gamma distribution. These two distributions were presented by Suksaengrakcharoen and Bodhisuwan in 2014. The findings showed that probability density function (pdf) had fairly complexities, so it made problems in estimating parameters. The problem occurred in parameter estimation was that we were unable to calculate estimators in the form of critical expression. Thus, we will use numerical estimation to find the estimators. In this study, we presented a new method of the parameter estimation by using the expectation – maximization algorithm (EM), the conjugate gradient method, and the quasi-Newton method. The data was generated by acceptance-rejection method which is used for estimating α, β, λ and p. λ is the scale parameter, p is the weight parameter, α and β are the shape parameters. We will use Monte Carlo technique to find the estimator's performance. Determining the size of sample equals 10, 30, 100; the simulations were repeated 20 times in each case. We evaluated the effectiveness of the estimators which was introduced by considering values of the mean squared errors and the bias. The findings revealed that the EM-algorithm had proximity to the actual values determined. Also, the maximum likelihood estimators via the conjugate gradient and the quasi-Newton method are less precision than the maximum likelihood estimators via the EM-algorithm.

Keywords: conjugate gradient method, quasi-Newton method, EM-algorithm, generalized gamma distribution, length biased generalized gamma distribution, maximum likelihood method

Procedia PDF Downloads 198

Authors: Tokuei Sako

Abstract:

The ground and low-lying singly-excited states of He and He-like atomic ions have been studied by the Full Configuration Interaction (FCI) method focusing on the angular correlation between two electrons in the studied systems. The two-electron angle density distribution obtained by integrating the square-modulus of the FCI wave function over the coordinates other than the interelectronic angle shows a distinct trend between the singlet-triplet pair of states for different values of the nuclear charge Zn. Further, both of these singlet and triplet distributions tend to show an increasingly stronger dependence on the interelectronic angle as Zn increases, in contrast to the well-known fact that the correlation energy approaches towards zero for increasing Zn. This controversial observation has been rationalized on the basis of the recently introduced concept of so-called conjugate Fermi holes.

Keywords: He-like systems, angular correlation, configuration interaction wave function, conjugate Fermi hole

Procedia PDF Downloads 385

Authors: Nikolay E. Dubinin

Abstract:

Pair-interaction approximations allow to consider a different states of condensed matter from a single position. At the same time, description of an effective pair interaction in transition metal is a hard task since the d-electron contribution to the potential energy in this case is non-pairwise in principle. There are a number of models for transition-metal effective pair potentials. Here we use the Wills-Harrison (WH) approach to calculate pair potentials for Fe, Co, and Ni in crystalline, liquid, and nano states. Last is especially interesting since nano particles of pure transition metals immobilized on the dielectric matrices are widely used in different fields of advanced technologies: as carriers and transmitters of information, as an effective catalytic materials, etc. It is found that the minimum of the pair potential is deeper and oscillations are stronger in nano crystalline state in comparison with the liquid and crystalline states for all metals under consideration.

Keywords: effective pair potential, nanocrystalline state, transition metal, Wills-Harrison approach

Procedia PDF Downloads 361

Authors: Ines Elouedi, Atef Hammouda

Abstract:

This paper presents a new fast version of the generalized Multi-Directional Radon Transform method. The new method uses the inverse Fast Fourier Transform to lead to a faster Generalized Radon projections. We prove in this paper that the fast algorithm leads to almost the same results of the eldest one but with a considerable lower time computation cost. The projection end result of the fast method is a parameterized Radon space where a high valued pixel allows the detection of a curve from the original image. The proposed fast inversion algorithm leads to an exact reconstruction of the initial image from the Radon space. We show examples of the impact of this algorithm on the pattern recognition domain.

Keywords: fast generalized multi-directional Radon transform, curve, exact reconstruction, pattern recognition

Procedia PDF Downloads 249

Authors: Malay Bhattacharyya, Saparya Suresh

Abstract:

The Correlation Structure associated with a portfolio is subjected to vary across time. Studying the structural breaks in the time-dependent Correlation matrix associated with a collection had been a subject of interest for a better understanding of the market movements, portfolio selection, etc. The current paper proposes a methodology for testing the change in the time-dependent correlation structure of a portfolio in the high dimensional data using the techniques of generalized inverse, singular valued decomposition and multivariate distribution theory which has not been addressed so far. The asymptotic properties of the proposed test are derived. Also, the performance and the validity of the method is tested on a real data set. The proposed test performs well for detecting the change in the dependence of global markets in the context of high dimensional data.

Keywords: correlation structure, high dimensional data, multivariate distribution theory, singular valued decomposition

Procedia PDF Downloads 101

Authors: M. O. Olayiwola

Abstract:

Numerical solutions of the generalized Burger-Fisher are obtained using a Modified Variational Iteration Method (MVIM) with minimal computational efforts. The computed results with this technique have been compared with other results. The present method is seen to be a very reliable alternative method to some existing techniques for such nonlinear problems.

Keywords: burger-fisher, modified variational iteration method, lagrange multiplier, Taylor’s series, partial differential equation

Procedia PDF Downloads 403

Authors: Boukari Nassim

Abstract:

This paper describes the use of odd pair autoregressive coefficients (Yule _Walker and Burg) for the feature extraction of electroencephalogram (EEG) signals. In the classification: the radial basis function neural network neural network (RBFNN) is employed. The RBFNN is described by his architecture and his characteristics: as the RBF is defined by the spread which is modified for improving the results of the classification. Five types of EEG signals are defined for this work: Set A, Set B for normal signals, Set C, Set D for interictal signals, set E for ictal signal (we can found that in Bonn university). In outputs, two classes are given (AC, AD, AE, BC, BD, BE, CE, DE), the best accuracy is calculated at 99% for the combined odd pair autoregressive coefficients. Our method is very effective for the diagnosis of epileptic EEG signals.

Keywords: epilepsy, EEG signals classification, combined odd pair autoregressive coefficients, radial basis function neural network

Procedia PDF Downloads 322

Authors: Wei Feilong

Abstract:

In this study, an local invariant generalized Houghtransform (LI-GHT) method is proposed for integrated circuit (IC) visual positioning. The original generalized Hough transform (GHT) is robust to external noise; however, it is not suitable for visual positioning of IC chips due to the four-dimensionality (4D) of parameter space which leads to the substantial storage requirement and high computational complexity. The proposed LI-GHT method can reduce the dimensionality of parameter space to 2D thanks to the rotational invariance of local invariant geometric feature and it can estimate the accuracy position and rotation angle of IC chips in real-time under noise and blur influence. The experiment results show that the proposed LI-GHT can estimate position and rotation angle of IC chips with high accuracy and fast speed. The proposed LI-GHT algorithm was implemented in IC visual positioning system of radio frequency identification (RFID) packaging equipment.

Keywords: Integrated Circuit Visual Positioning, Generalized Hough Transform, Local invariant Generalized Hough Transform, ICpacking equipment

Procedia PDF Downloads 244

Authors: Youngji Lee, Yonghyeon Jeon, Sunyoung Bu, Philsu Kim

Abstract:

The aim of this paper is to construct an algorithm of time step control for the error correction method most recently developed by one of the authors for solving stiff initial value problems. It is achieved with the generalized Chebyshev polynomial and the corresponding error correction method. The main idea of the proposed scheme is in the usage of the duplicated node points in the generalized Chebyshev polynomials of two different degrees by adding necessary sample points instead of re-sampling all points. At each integration step, the proposed method is comprised of two equations for the solution and the error, respectively. The constructed algorithm controls both the error and the time step size simultaneously and possesses a good performance in the computational cost compared to the original method. Two stiff problems are numerically solved to assess the effectiveness of the proposed scheme.

Keywords: stiff initial value problem, error correction method, generalized Chebyshev polynomial, node points

Procedia PDF Downloads 538

Authors: Serge Provost, Abdous Saboor

Abstract:

A q-analogue of the generalized extreme value distribution which includes the Gumbel distribution is introduced. The additional parameter q allows for increased modeling flexibility. The resulting distribution can have a finite, semi-infinite or infinite support. It can also produce several types of hazard rate functions. The model parameters are determined by making use of the method of maximum likelihood. It will be shown that it compares favourably to three related distributions in connection with the modeling of a certain hydrological data set.

Keywords: extreme value theory, generalized extreme value distribution, goodness-of-fit statistics, Gumbel distribution

Procedia PDF Downloads 314

Authors: Hudson Akewe

Abstract:

In this study, we introduce a modified Jungck (Dual Jungck) iterative scheme and use the scheme to approximate the unique common fixed point of a pair of generalized contractive-like operators in a Banach space. The iterative scheme is also shown to be stable with respect to the maps (S,T). An example is taken to justify the convergence of the scheme. Our result is a generalization and improvement of several results in the literature on single map T.

Keywords: generalized contractive-like operators, modified Jungck iterative scheme, stability results, weakly compatible maps, unique common fixed point

Procedia PDF Downloads 318

Authors: Wided Bakari, Patrce Bellot, Mahmoud Neji

Abstract:

With the development of electronic media and the heterogeneity of Arabic data on the Web, the idea of building a clean corpus for certain applications of natural language processing, including machine translation, information retrieval, question answer, become more and more pressing. In this manuscript, we seek to create and develop our own corpus of pair’s questions-texts. This constitution then will provide a better base for our experimentation step. Thus, we try to model this constitution by a method for Arabic insofar as it recovers texts from the web that could prove to be answers to our factual questions. To do this, we had to develop a java script that can extract from a given query a list of html pages. Then clean these pages to the extent of having a database of texts and a corpus of pair’s question-texts. In addition, we give preliminary results of our proposal method. Some investigations for the construction of Arabic corpus are also presented in this document.

Keywords: Arabic, web, corpus, search engine, URL, question, corpus building, script, Google, html, txt

Procedia PDF Downloads 296

Authors: Menghzheng Yao

Abstract:

Generalized social trust among Chinese has been declining in the past few decades, making the search for its causes necessary. Drawing on the symbolic interaction theory and the 2012 Chinese General Social Survey data, this research investigated the impact of people’s socialization preferences and frequencies on their perceptions of generalized social trust in China. This research also took a preliminary step towards understanding the spatial differences of the generalized social trust using the ArcGIS software. The results show that respondents who interacted with their neighbors more frequently were more likely to have higher levels of perceptions of generalized social trust. Several demographics were also significantly related to perception of generalized social trust. Elderly and better educated Chinese and people with higher self-perceived social status were associated with greater levels of generalized social trust perception, while urban dwellers and religious respondents expressed lower levels of such perception. Implications for future research and policy are discussed.

Keywords: China, generalized social trust, symbolic interaction, ArcGIS

Procedia PDF Downloads 343

Authors: Mohammad Farid

Abstract:

In this paper, we introduce and study an explicit iterative method based on hybrid extragradient method to approximate a common solution of generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup in Hilbert space. Further, we prove that the sequence generated by the proposed iterative scheme converge strongly to the common solution of generalized mixed equilibrium problem and fixed point problem for a nonexpansive semigroup. This common solution is the unique solution of a variational inequality problem and is the optimality condition for a minimization problem. The results presented in this paper are the supplement, extension and generalization of the previously known results in this area.

Keywords: generalized mixed equilibrium problem, fixed-point problem, nonexpansive semigroup, variational inequality problem, iterative algorithms, hybrid extragradient method

Procedia PDF Downloads 447

Authors: M. Y. Bakeir

Abstract:

Rough set theory is a recent approach for reasoning about data. It has achieved a large amount of applications in various real-life fields. The main idea of rough sets corresponds to the lower and upper set approximations. These two approximations are exactly the interior and the closure of the set with respect to a certain topology on a collection U of imprecise data acquired from any real-life field. The base of the topology is formed by equivalence classes of an equivalence relation E defined on U using the available information about data. The theory of generalized topology was studied by Cs´asz´ar. It is well known that generalized topology in the sense of Cs´asz´ar is a generalization of the topology on a set. On the other hand, many important collections of sets related with the topology on a set form a generalized topology. The notion of Nano topology was introduced by Lellis Thivagar, which was defined in terms of approximations and boundary region of a subset of an universe using an equivalence relation on it. The purpose of this paper is to introduce a new generalized topology in terms of rough set called nano generalized topology

Keywords: rough sets, topological space, generalized topology, nano topology

Procedia PDF Downloads 407

Authors: Abdel-Maksoud Abdel-Kader Soliman

Abstract:

The General Regularized Long Wave (GRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the Fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm.

Keywords: generalized RLW equation, solitons, quartic b-spline, nonlinear partial differential equations, difference equations

Procedia PDF Downloads 465

Authors: Hamdy M. Youssef, Eman A. Al-Lehaibi

Abstract:

This paper presents an iteration method for the numerical solutions of a one-dimensional problem of generalized thermoelasticity with one relaxation time under given initial and boundary conditions. The thermoelastic material with variable properties as a power functional graded has been considered. Adomian’s decomposition techniques have been applied to the governing equations. The numerical results have been calculated by using the iterations method with a certain algorithm. The numerical results have been represented in figures, and the figures affirm that Adomian’s decomposition method is a successful method for modeling thermoelastic problems. Moreover, the empirical parameter of the functional graded, and the lattice design parameter have significant effects on the temperature increment, the strain, the stress, the displacement.

Keywords: Adomian, decomposition method, generalized thermoelasticity, algorithm

Procedia PDF Downloads 113