Search results for: generalized linear regression

Authors: S. Deswal, M. Pal

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The paper aims to compare the performance of vertical and inclined multiple plunging jets and to model and predict their mass transfer capacity by multi-linear regression based approach. The multiple vertical plunging jets have jet impact angle of θ = 90O; whereas, multiple inclined plunging jets have jet impact angle of θ = 600. The results of the study suggests that mass transfer is higher for multiple jets, and inclined multiple plunging jets have up to 1.6 times higher mass transfer than vertical multiple plunging jets under similar conditions. The derived relationship, based on multi-linear regression approach, has successfully predicted the volumetric mass transfer coefficient (KLa) from operational parameters of multiple plunging jets with a correlation coefficient of 0.973, root mean square error of 0.002 and coefficient of determination of 0.946. The results suggests that predicted overall mass transfer coefficient is in good agreement with actual experimental values; thereby suggesting the utility of derived relationship based on multi-linear regression based approach and can be successfully employed in modelling mass transfer by multiple plunging jets.

Keywords: mass transfer, multiple plunging jets, multi-linear regression, earth sciences

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Authors: Christian Lavault

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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

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Authors: Kornelius Ronald Demu, Dewi Retno Sari Saputro, Purnami Widyaningsih

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Human Development Index (HDI) is a standard measurement for a country's human development. Several factors may have influenced it, such as life expectancy, gross domestic product (GDP) based on the province's annual expenditure, the number of poor people, and the percentage of an illiterate people. The scatter plot between HDI and the influenced factors show that the plot does not follow a specific pattern or form. Therefore, the HDI's data in Indonesia can be applied with a nonparametric regression model. The estimation of the regression curve in the nonparametric regression model is flexible because it follows the shape of the data pattern. One of the nonparametric regression's method is a truncated spline. Truncated spline regression is one of the nonparametric approach, which is a modification of the segmented polynomial functions. The estimator of a truncated spline regression model was affected by the selection of the optimal knots point. Knot points is a focus point of spline truncated functions. The optimal knots point was determined by the minimum value of generalized cross validation (GCV). In this article were applied the data of Human Development Index with a truncated spline nonparametric regression model. The results of this research were obtained the best-truncated spline regression model to the HDI's data in Indonesia with the combination of optimal knots point 5-5-5-4. Life expectancy and the percentage of an illiterate people were the significant factors depend to the HDI in Indonesia. The coefficient of determination is 94.54%. This means the regression model is good enough to applied on the data of HDI in Indonesia.

Keywords: generalized cross validation (GCV), Human Development Index (HDI), knots point, nonparametric regression, truncated spline

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Authors: Hyon I. Paek, Sang Rim Kim, Hyon A. Ryu

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In functional linear regression, one typical problem is to reduce dimension. Compared with multivariate linear regression, functional linear regression is regarded as an infinite-dimensional case, and the main task is to reduce dimensions of functional response and functional predictors. One common approach is to adapt functional principal component analysis (FPCA) on functional predictors and then use a few leading functional principal components (FPC) to predict the functional model. The leading FPCs estimated by the typical FPCA explain a major variation of the functional predictor, but these leading FPCs may not be mostly correlated with the functional response, so they may not be significant in the prediction for response. In this paper, we propose a supervised functional principal component analysis method for a functional response model with FPCs obtained by considering the correlation of the functional response. Our method would have a better prediction accuracy than the typical FPCA method.

Keywords: supervised, functional principal component analysis, functional response, functional linear regression

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Authors: Galal Elkobrosy, Amr M. Abdelrazek, Bassuny M. Elsouhily, Mohamed E. Khidr

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Crank shaft length, connecting rod length, crank angle, engine rpm, cylinder bore, mass of piston and compression ratio are the inputs that can control the performance of the slider crank mechanism and then its efficiency. Several combinations of these seven inputs are used and compared. The throughput engine torque predicted by the simulation is analyzed through two different regression models, with and without interaction terms, developed according to multi-linear regression using LU decomposition to solve system of algebraic equations. These models are validated. A regression model in seven inputs including their interaction terms lowered the polynomial degree from 3^rd degree to 1^st degree and suggested valid predictions and stable explanations.

Keywords: design of experiments, regression analysis, SI engine, statistical modeling

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Authors: Weiwen Li, Hao Huang, Chengmao You, Jianji Liao, Lei Wang, Lina An

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Zooplankton are a central issue in the ecology which makes a great contribution to maintaining the balance of an ecosystem. It is critical in promoting the material cycle and energy flow within the ecosystems. A generalized additive model (GAM) was applied to analyze the relationships between the density (individuals per m³) of zooplankton and other variables in West Daya Bay. All data used in this analysis (the survey month, survey station (longitude and latitude), the depth of the water column, the superficial concentration of chlorophyll a, the benthonic concentration of chlorophyll a, the number of zooplankton species and the number of zooplankton species) were collected through monthly scientific surveys during January to December 2016. GLM model (generalized linear model) was used to choose the significant variables’ impact on the density of zooplankton, and the GAM was employed to analyze the relationship between the density of zooplankton and the significant variables. The results showed that the density of zooplankton increased with an increase of the benthonic concentration of chlorophyll a, but decreased with a decrease in the depth of the water column. Both high numbers of zooplankton species and the overall total number of zooplankton individuals led to a higher density of zooplankton.

Keywords: density, generalized linear model, generalized additive model, the West Daya Bay, zooplankton

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Authors: Rana Rimawi, Ayman Baklizi

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Skewed distributions are important models that are frequently used in applications. Generalized distributions form a class of skewed distributions and gain widespread use in applications because of their flexibility in data analysis. More specifically, the Generalized Logistic Distribution with its different types has received considerable attention recently. In this study, based on progressively type-II censored data, we will consider point estimation in type II Generalized Logistic Distribution (Type II GLD). We will develop several estimators for its unknown parameters, including maximum likelihood estimators (MLE), Bayes estimators and linear estimators (BLUE). The estimators will be compared using simulation based on the criteria of bias and Mean square error (MSE). An illustrative example of a real data set will be given.

Keywords: point estimation, type II generalized logistic distribution, progressive censoring, maximum likelihood estimation

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Authors: Jan Henrik Wosnitza

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The logistic regression has developed into a standard approach for estimating conditional probabilities in a wide range of applications including credit risk prediction. The article at hand contributes to the current literature on logistic regression fourfold: First, it is demonstrated that the binary logistic regression automatically meets its model assumptions under very general conditions. This result explains, at least in part, the logistic regression's popularity. Second, the requirement of homoscedasticity in the context of binary logistic regression is theoretically substantiated. The variances among the groups of defaulted and non-defaulted obligors have to be the same across the level of the aggregated default indicators in order to achieve linear logits. Third, this article sheds some light on the question why nonlinear logits might be superior to linear logits in case of a small amount of data. Fourth, an innovative methodology for estimating correlations between obligor-specific log-odds is proposed. In order to crystallize the key ideas, this paper focuses on the example of credit risk prediction. However, the results presented in this paper can easily be transferred to any other field of application.

Keywords: correlation, credit risk estimation, default correlation, homoscedasticity, logistic regression, nonlinear logistic regression

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Authors: Altaf H. Khan, Frank Stenger, Mohammed A. Hussein, Reaz A. Chaudhuri, Sameera Asif

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This paper discusses a novel approach to approximate quadrature integrals that arise in the estimation of likelihood parameters for the generalized linear mixed models (GLMM) as well as Bayesian methodology also requires computation of multidimensional integrals with respect to the posterior distributions in which computation are not only tedious and cumbersome rather in some situations impossible to find solutions because of singularities, irregular domains, etc. An attempt has been made in this work to apply Sinc function based quadrature rules to approximate intractable integrals, as there are several advantages of using Sinc based methods, for example: order of convergence is exponential, works very well in the neighborhood of singularities, in general quite stable and provide high accurate and double precisions estimates. The Sinc function based approach seems to be utilized first time in statistical domain to our knowledge, and it's viability and future scopes have been discussed to apply in the estimation of parameters for GLMM models as well as some other statistical areas.

Keywords: generalized linear mixed model, likelihood parameters, qudarature, Sinc function

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Authors: L. Q. Yuan, J. Yang, A. Siddiqui

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A new regression uncertainty analysis methodology was applied to determine the uncertainties of the critical heat flux (CHF) power correlation for an advanced 43-element bundle design, which was developed by Canadian Nuclear Laboratories (CNL) to achieve improved economics, resource utilization and energy sustainability. The new methodology is considered more appropriate than the traditional methodology in the assessment of the experimental uncertainty associated with regressions. The methodology was first assessed using both the Monte Carlo Method (MCM) and the Taylor Series Method (TSM) for a simple linear regression model, and then extended successfully to a non-linear CHF power regression model (CHF power as a function of inlet temperature, outlet pressure and mass flow rate). The regression uncertainty assessed by MCM agrees well with that by TSM. An equation to evaluate the CHF power regression uncertainty was developed and expressed as a function of independent variables that determine the CHF power.

Keywords: CHF experiment, CHF correlation, regression uncertainty, Monte Carlo Method, Taylor Series Method

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Authors: Bader Alkandari, Jamal Y. Madouh, Ahmad M. Alkandari, Anwar A. Alnaqi

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A new formulation of fuzzy linear estimation problem is presented. It is formulated as a linear programming problem. The objective is to minimize the spread of the data points, taking into consideration the type of the membership function of the fuzzy parameters to satisfy the constraints on each measurement point and to insure that the original membership is included in the estimated membership. Different models are developed for a fuzzy triangular membership. The proposed models are applied to different examples from the area of fuzzy linear regression and finally to different examples for estimating the electrical load on a busbar. It had been found that the proposed technique is more suited for electrical load estimation, since the nature of the load is characterized by the uncertainty and vagueness.

Keywords: fuzzy regression, load estimation, fuzzy linear parameters, electrical load estimation

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Authors: Ishapathik Das

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The purpose of this article is to find a method of comparing designs for ordinal regression models using quantile dispersion graphs in the presence of linear predictor misspecification. The true relationship between response variable and the corresponding control variables are usually unknown. Experimenter assumes certain form of the linear predictor of the ordinal regression models. The assumed form of the linear predictor may not be correct always. Thus, the maximum likelihood estimates (MLE) of the unknown parameters of the model may be biased due to misspecification of the linear predictor. In this article, the uncertainty in the linear predictor is represented by an unknown function. An algorithm is provided to estimate the unknown function at the design points where observations are available. The unknown function is estimated at all points in the design region using multivariate parametric kriging. The comparison of the designs are based on a scalar valued function of the mean squared error of prediction (MSEP) matrix, which incorporates both variance and bias of the prediction caused by the misspecification in the linear predictor. The designs are compared using quantile dispersion graphs approach. The graphs also visually depict the robustness of the designs on the changes in the parameter values. Numerical examples are presented to illustrate the proposed methodology.

Keywords: model misspecification, multivariate kriging, multivariate logistic link, ordinal response models, quantile dispersion graphs

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Authors: Mehdi Jafari Matehkolaee

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In this paper, we have obtained the adjoint of an arbitrary operator (linear and nonlinear) in Hilbert space by introducing an n-dimensional Riemannian manifold. This general formalism covers every linear operator (non – differential) in Hilbert space. In fact, our approach shows that instead of using the adjoint definition of an operator directly, it can be obtained directly by relying on a suitable generalized space according to the action of the operator in question. For the case of nonlinear operators, we have to change the definition of the linear operator adjoint. But here, we have obtained an adjoint of these operators with respect to the definition of the derivative of the operator. As a matter of fact, we have shown one of the straight applications of the ''Frechet derivative'' in the algebra of the operators.

Keywords: adjoint operator, non-linear operator, differentiable operator, manifold

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Authors: Muqaddas Javed, Muhammad Hanif

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The generalized multivariate ratio and regression type estimators for population mean are suggested under multi-phase stratified systematic sampling (MPSSS) using multi auxiliary information. Estimators are developed under the two different situations of availability of auxiliary information. The expressions of bias and mean square error (MSE) are developed. Special cases of suggested estimators are also discussed and simulation study is conducted to observe the performance of estimators.

Keywords: generalized estimators, multi-phase sampling, stratified random sampling, systematic sampling

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Authors: Filippo Portera

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Usually standard algorithms employ a loss where each error is the mere absolute difference between the true value and the prediction, in case of a regression task. In the present, we present several error weighting schemes that are a generalization of the consolidated routine. We study both a binary classification model for Support Vextor Classification and a regression net for Multylayer Perceptron. Results proves that the error is never worse than the standard procedure and several times it is better.

Keywords: loss, binary-classification, MLP, weights, regression

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Authors: Abhijith Asok

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This paper presents a generalized approach for the simple linear data transformation, Y=bX, through an integration of multidimensional coordinate geometry, vector space theory and polygonal geometry. The scaling is performed by adding an additional ’Dummy Dimension’ to the n-dimensional data, which helps plot two dimensional component-wise straight lines on pairs of dimensions. The end result is a set of scaled extensions of observations in any of the 2n spatial divisions, where n is the total number of applicable dimensions/dataset variables, created by shifting the n-dimensional plane along the ’Dummy Axis’. The derived scaling factor was found to be dependent on the coordinates of the common point of origin for diverging straight lines and the plane of extension, chosen on and perpendicular to the ’Dummy Axis’, respectively. This result indicates the geometrical interpretation of a linear data transformation and hence, opportunities for a more informed choice of the factor ’b’, based on a better choice of these coordinate values. The paper follows on to identify the effect of this transformation on certain popular distance metrics, wherein for many, the distance metric retained the same scaling factor as that of the features.

Keywords: data transformation, dummy dimension, linear transformation, scaling

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Authors: Shokrya Saleh A. Alshqaq, Abdullah Ali H. Ahmadini

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The Schwarz information criterion (SIC) is a popular tool for selecting the best variables in regression datasets. However, SIC is defined using an unbounded estimator, namely, the least-squares (LS), which is highly sensitive to outlying observations, especially bad leverage points. A method for robust variable selection based on SIC for linear regression models is thus needed. This study investigates the robustness properties of SIC by deriving its influence function and proposes a robust SIC based on the MM-estimation scale. The aim of this study is to produce a criterion that can effectively select accurate models in the presence of vertical outliers and high leverage points. The advantages of the proposed robust SIC is demonstrated through a simulation study and an analysis of a real dataset.

Keywords: influence function, robust variable selection, robust regression, Schwarz information criterion

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Authors: Saba Riaz, Syed A. Hussain

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This paper is addressing the estimation method of the unknown population variance of the variable of interest. A new generalized class of estimators of the finite population variance has been suggested using the auxiliary information. To improve the precision of the proposed class, known population variance of the auxiliary variable has been used. Mathematical expressions for the biases and the asymptotic variances of the suggested class are derived under large sample approximation. Theoretical and numerical comparisons are made to investigate the performances of the proposed class of estimators. The empirical study reveals that the suggested class of estimators performs better than the usual estimator, classical ratio estimator, classical product estimator and classical linear regression estimator. It has also been found that the suggested class of estimators is also more efficient than some recently published estimators.

Keywords: study variable, auxiliary variable, finite population variance, bias, asymptotic variance, percent relative efficiency

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Authors: Kiurski S. Jelena, Aksentijević M. Snežana, Oros B. Ivana, Kecić S. Vesna, Djogo Z. Maja

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The paper investigates the effect of light intensity on the formation of two ketones, acetone and methyl ethyl ketone, in working premises of five pad printing departments in Novi Sad, Serbia. Multiple linear regression analysis examined the form of interdependency concentrations of methyl ethyl ketone, acetone and light intensity in five printing presses at seven sampling points, using Statistica software package version 10th. The results show an average stacking variation investigated variable and can be presented by the general regression model: y = b0 + b1xi1 + b2xi2.

Keywords: acetone, methyl ethyl ketone, multiple linear regression analysis, pad printing

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Authors: Raya Al Khayari, Rasha Al Jassim, Muna Al Balushi, Fatma Al Moqbali, Said El Hajjar

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This study utilizes linear regression analysis to investigate the correlation between user account passwords and the probability of civil ID exposure, offering statistical insights into civil ID security. The study employs multiple linear regression (MLR) analysis to further investigate the elements that influence consumers’ views of civil ID security. This aims to increase awareness and improve preventive measures. The results obtained from the MLR analysis provide a thorough comprehension and can guide specific educational and awareness campaigns aimed at promoting improved security procedures. In summary, the study’s results offer significant insights for improving existing security measures and developing more efficient tactics to reduce risks related to civil ID security in Oman. By identifying key factors that impact consumers’ perceptions, organizations can tailor their strategies to address vulnerabilities effectively. Additionally, the findings can inform policymakers on potential regulatory changes to enhance civil ID security in the country.

Keywords: civil-id disclosure, awareness, linear regression, multiple regression

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Authors: Arun Goel

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Prediction of maximum local scour is necessary for the safety and economical design of the bridges. A number of equations have been developed over the years to predict local scour depth using laboratory data and a few pier equations have also been proposed using field data. Most of these equations are empirical in nature as indicated by the past publications. In this paper, attempts have been made to compute local depth of scour around bridge pier in dimensional and non-dimensional form by using linear regression, simple regression and SVM (Poly and Rbf) techniques along with few conventional empirical equations. The outcome of this study suggests that the SVM (Poly and Rbf) based modeling can be employed as an alternate to linear regression, simple regression and the conventional empirical equations in predicting scour depth of bridge piers. The results of present study on the basis of non-dimensional form of bridge pier scour indicates the improvement in the performance of SVM (Poly and Rbf) in comparison to dimensional form of scour.

Keywords: modeling, pier scour, regression, prediction, SVM (Poly and Rbf kernels)

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Authors: Tahani Salman Alangari

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Student success can be impacted by internal factors such as their emotional well-being and external factors such as organizational support and instructional support in the classroom. This study is to identify at least one factor that forecasts student engagement. It is a cross-sectional, conducted on 6206 teachers and encompassed three years of data collection and observations of math instruction in approximately 50 schools and 300 classrooms. A multiple linear regression revealed that a model predicting student engagement from emotional support, classroom organization, and instructional support was significant. Four linear regression models were tested using hierarchical regression to examine the effects of independent variables: emotional support was the highest predictor of student engagement while instructional support was the lowest.

Keywords: student engagement, emotional support, organizational support, instructional support, well-being

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Authors: Navab Karimi, Tohid Alizadeh

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An intelligent vision-based system was designed to measure the quality and purity of raisins. A machine vision setup was utilized to capture the images of bulk raisins in ranges of 5-50% mixed pure-impure berries. The textural features of bulk raisins were extracted using Grey-level Histograms, Co-occurrence Matrix, and Local Binary Pattern (a total of 108 features). Genetic Algorithm and neural network regression were used for selecting and ranking the best features (21 features). As a result, the GLCM features set was found to have the highest accuracy (92.4%) among the other sets. Followingly, multiple feature combinations of the previous stage were fed into the second regression (linear regression) to increase accuracy, wherein a combination of 16 features was found to be the optimum. Finally, a Support Vector Machine (SVM) classifier was used to differentiate the mixtures, producing the best efficiency and accuracy of 96.2% and 97.35%, respectively.

Keywords: sun-dried organic raisin, genetic algorithm, feature extraction, ann regression, linear regression, support vector machine, south azerbaijan.

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Authors: M. S. Wickramarachchi, L. S. Nawarathna, C. M. B. Dematawewa

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Hatchery performance is critical for the profitability of poultry breeder operations. Some extrinsic parameters of eggs and breeders cause to increase or decrease the hatchability. This study aims to identify the affecting extrinsic parameters on the commercial hatchability of local chicken's eggs and determine the most efficient classification model with a hatchability rate greater than 90%. In this study, seven extrinsic parameters were considered: egg weight, moisture loss, breeders age, number of fertilised eggs, shell width, shell length, and shell thickness. Multiple linear regression was performed to determine the most influencing variable on hatchability. First, the correlation between each parameter and hatchability were checked. Then a multiple regression model was developed, and the accuracy of the fitted model was evaluated. Linear Discriminant Analysis (LDA), Classification and Regression Trees (CART), k-Nearest Neighbors (kNN), Support Vector Machines (SVM) with a linear kernel, and Random Forest (RF) algorithms were applied to classify the hatchability. This grouping process was conducted using binary classification techniques. Hatchability was negatively correlated with egg weight, breeders' age, shell width, shell length, and positive correlations were identified with moisture loss, number of fertilised eggs, and shell thickness. Multiple linear regression models were more accurate than single linear models regarding the highest coefficient of determination (R²) with 94% and minimum AIC and BIC values. According to the classification results, RF, CART, and kNN had performed the highest accuracy values 0.99, 0.975, and 0.972, respectively, for the commercial hatchery process. Therefore, the RF is the most appropriate machine learning algorithm for classifying the breeder outcomes, which are economically profitable or not, in a commercial hatchery.

Keywords: classification models, egg weight, fertilised eggs, multiple linear regression

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

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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

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Authors: Riadh Zorgati, Thomas Triboulet

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In quite diverse application areas such as astronomy, medical imaging, geophysics or nondestructive evaluation, many problems related to calibration, fitting or estimation of a large number of input parameters of a model from a small amount of output noisy data, can be cast as inverse problems. Due to noisy data corruption, insufficient data and model errors, most inverse problems are ill-posed in a Hadamard sense, i.e. existence, uniqueness and stability of the solution are not guaranteed. A wide class of inverse problems in physics relates to the Fredholm equation of the first kind. The ill-posedness of such inverse problem results, after discretization, in a very ill-conditioned linear system of equations, the condition number of the associated matrix can typically range from 109 to 1018. This condition number plays the role of an amplifier of uncertainties on data during inversion and then, renders the inverse problem difficult to handle numerically. Similar problems appear in other areas such as numerical optimization when using interior points algorithms for solving linear programs leads to face ill-conditioned systems of linear equations. Devising efficient solution approaches for such system of equations is therefore of great practical interest. Efficient iterative algorithms are proposed for solving a system of linear equations. The approach is based on a preconditioning of the initial matrix of the system with an approximation of a generalized inverse leading to a stochastic preconditioned matrix. This approach, valid for non-negative matrices, is first extended to hermitian, semi-definite positive matrices and then generalized to any complex rectangular matrices. The main results obtained are as follows: 1) We are able to build a generalized inverse of any complex rectangular matrix which satisfies the convergence condition requested in iterative algorithms for solving a system of linear equations. This completes the (short) list of generalized inverse having this property, after Kaczmarz and Cimmino matrices. Theoretical results on both the characterization of the type of generalized inverse obtained and the convergence are derived. 2) Thanks to its properties, this matrix can be efficiently used in different solving schemes as Richardson-Tanabe or preconditioned conjugate gradients. 3) By using Lp norms, we propose generalized Kaczmarz’s type matrices. We also show how Cimmino's matrix can be considered as a particular case consisting in choosing the Euclidian norm in an asymmetrical structure. 4) Regarding numerical results obtained on some pathological well-known test-cases (Hilbert, Nakasaka, …), some of the proposed algorithms are empirically shown to be more efficient on ill-conditioned problems and more robust to error propagation than the known classical techniques we have tested (Gauss, Moore-Penrose inverse, minimum residue, conjugate gradients, Kaczmarz, Cimmino). We end on a very early prospective application of our approach based on stochastic matrices aiming at computing some parameters (such as the extreme values, the mean, the variance, …) of the solution of a linear system prior to its resolution. Such an approach, if it were to be efficient, would be a source of information on the solution of a system of linear equations.

Keywords: conditioning, generalized inverse, linear system, norms, stochastic matrix

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Authors: Menghzheng Yao

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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

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Authors: R. Vigneswaran, S. Thilakanathan

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Variable time-stepping algorithms for solving dynamical systems performed poorly for long time computations which pass close to a fixed point. To overcome this difficulty, several authors considered phase space error controls for numerical simulation of dynamical systems. In one generalized phase space error control, a step-size selection scheme was proposed, which allows this error control to be incorporated into the standard adaptive algorithm as an extra constraint at negligible extra computational cost. For this generalized error control, it was already analyzed the forward Euler method applied to the linear system whose coefficient matrix has real and negative eigenvalues. In this paper, this result was extended to the linear system whose coefficient matrix has complex eigenvalues with negative real parts. Some theoretical results were obtained and numerical experiments were carried out to support the theoretical results.

Keywords: adaptivity, fixed point, long time simulations, stability, linear system

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Authors: M. Y. Bakeir

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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

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Authors: Arun Goel

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The present paper attempts to investigate the prediction of air entrainment rate and aeration efficiency of a free over-fall jets issuing from a triangular sharp crested weir by using regression based modelling. The empirical equations, support vector machine (polynomial and radial basis function) models and the linear regression techniques were applied on the triangular sharp crested weirs relating the air entrainment rate and the aeration efficiency to the input parameters namely drop height, discharge, and vertex angle. It was observed that there exists a good agreement between the measured values and the values obtained using empirical equations, support vector machine (Polynomial and rbf) models, and the linear regression techniques. The test results demonstrated that the SVM based (Poly & rbf) model also provided acceptable prediction of the measured values with reasonable accuracy along with empirical equations and linear regression techniques in modelling the air entrainment rate and the aeration efficiency of a free over-fall jets issuing from triangular sharp crested weir. Further sensitivity analysis has also been performed to study the impact of input parameter on the output in terms of air entrainment rate and aeration efficiency.

Keywords: air entrainment rate, dissolved oxygen, weir, SVM, regression

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