Search results for: positive definite

Authors: Ahmet Tekcan

Abstract:

Let F(x, y) = ax2 + bxy + cy2 be a positive definite binary quadratic form with discriminant Δ whose base points lie on the line x = -1/m for an integer m ≥ 2, let p be a prime number and let Fp be a finite field. Let EF : y2 = ax3 + bx2 + cx be an elliptic curve over Fp and let CF : ax3 + bx2 + cx ≡ 0(mod p) be the cubic congruence corresponding to F. In this work we consider some properties of positive definite quadratic forms, elliptic curves and cubic congruences.

Keywords: Binary quadratic form, elliptic curves, cubic congruence.

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Authors: Minghui Wang

Abstract:

The real representation of the quaternionic matrix is definited and studied. The relations between the positive (semi)define quaternionic matrix and its real representation matrix are presented. By means of the real representation, the relation between the positive (semi)definite solutions of quaternionic matrix equations and those of corresponding real matrix equations is established.

Keywords: Matrix equation, Quaternionic matrix, Real representation, positive (semi)definite solutions.

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Authors: Tian Baoguang, Liang Chunyan, Chen Nan

Abstract:

In this paper, the nonlinear matrix equation is investigated. Based on the fixed-point theory, the boundary and the existence of the solution with the case r>-δ_i are discussed. An algorithm that avoids matrix inversion with the case -1<-δ_i<0 is proposed.

Keywords: Nonlinear matrix equation, Positive definite solution, The maximal-minimal solution, Iterative method, Free-inversion

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Authors: Minghui Wang, Juntao Zhang

Abstract:

An inversion-free iterative algorithm is presented for solving nonlinear matrix equation with a stepsize parameter t. The existence of the maximal solution is discussed in detail, and the method for finding it is proposed. Finally, two numerical examples are reported that show the efficiency of the method.

Keywords: Inversion-free method, Hermitian positive definite solution, Maximal solution, Convergence.

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Authors: H. D. Ibrahim, H. C. Chinwenyi, H. N. Ude

Abstract:

In this paper, efforts were made to examine and compare the algorithmic iterative solutions of conjugate gradient method as against other methods such as Gauss-Seidel and Jacobi approaches for solving systems of linear equations of the form Ax = b, where A is a real n x n symmetric and positive definite matrix. We performed algorithmic iterative steps and obtained analytical solutions of a typical 3 x 3 symmetric and positive definite matrix using the three methods described in this paper (Gauss-Seidel, Jacobi and Conjugate Gradient methods) respectively. From the results obtained, we discovered that the Conjugate Gradient method converges faster to exact solutions in fewer iterative steps than the two other methods which took much iteration, much time and kept tending to the exact solutions.

Keywords: conjugate gradient, linear equations, symmetric and positive definite matrix, Gauss-Seidel, Jacobi, algorithm

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Authors: Qian-Ping Guo, Hou-Biao Li

Abstract:

The generalized Higham matrix is a complex symmetric matrix A = B + iC, where both B ∈ Cn×n and C ∈ Cn×n are Hermitian positive definite, and i = √−1 is the imaginary unit. The growth factor in Gaussian elimination is less than 3√2 for this kind of matrices. In this paper, we give a new brief proof on this result by different techniques, which can be understood very easily, and obtain some new findings.

Keywords: CSPD matrix, positive definite, Schur complement, Higham matrix, Gaussian elimination, Growth factor.

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Authors: Chen Wu, Jingyu Yang

Abstract:

Using maximal consistent blocks of tolerance relation on the universe in incomplete decision table, the concepts of join block and meet block are introduced and studied. Including tolerance class, other blocks such as tolerant kernel and compatible kernel of an object are also discussed at the same time. Upper and lower approximations based on those blocks are also defined. Default definite decision rules acquired from incomplete decision table are proposed in the paper. An incremental algorithm to update default definite decision rules is suggested for effective mining tasks from incomplete decision table into which data is appended. Through an example, we demonstrate how default definite decision rules based on maximal consistent blocks, join blocks and meet blocks are acquired and how optimization is done in support of discernibility matrix and discernibility function in the incomplete decision table.

Keywords: rough set, incomplete decision table, maximalconsistent block, default definite decision rule, join and meet block.

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Authors: M. T. Sichani, B. J. Pedersen, S. R. K. Nielsen

Abstract:

Turbulence of the incoming wind field is of paramount importance to the dynamic response of civil engineering structures. Hence reliable stochastic models of the turbulence should be available from which time series can be generated for dynamic response and structural safety analysis. In the paper an empirical cross spectral density function for the along-wind turbulence component over the wind field area is taken as the starting point. The spectrum is spatially discretized in terms of a Hermitian cross-spectral density matrix for the turbulence state vector which turns out not to be positive definite. Since the succeeding state space and ARMA modelling of the turbulence rely on the positive definiteness of the cross-spectral density matrix, the problem with the non-positive definiteness of such matrices is at first addressed and suitable treatments regarding it are proposed. From the adjusted positive definite cross-spectral density matrix a frequency response matrix is constructed which determines the turbulence vector as a linear filtration of Gaussian white noise. Finally, an accurate state space modelling method is proposed which allows selection of an appropriate model order, and estimation of a state space model for the vector turbulence process incorporating its phase spectrum in one stage, and its results are compared with a conventional ARMA modelling method.

Keywords: Turbulence, wind turbine, complex coherence, state space modelling, ARMA modelling.

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Authors: Ranajay Bhowmick

Abstract:

Analysis of stresses for an infinitesimal tetrahedron leads to a situation where we obtain a cubic equation consisting of three stress invariants. This cubic equation, when solved for a definite condition, gives the principal stresses directly without requiring any cumbersome and time-consuming trial and error methods or iterative numerical procedures. Since the failure criterion of different materials are generally expressed as functions of principal stresses, an attempt has been made in this study to incorporate the solutions of the cubic equation in the form of principal stresses, obtained for a definite condition, into some of the established failure theories to determine their modified descriptions. It has been observed that the failure theories can be represented using the quadratic stress invariant and the orientation of the principal plane.

Keywords: Cubic equation, stress invariant, trigonometric, explicit solution, principal stress, failure criterion.

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Authors: Hidemi Ogasawara, Kiyoshi Akama, Hiroshi Mabuchi

Abstract:

The purpose of this paper is to propose a framework for constructing correct parallel processing programs based on Equivalent Transformation Framework (ETF). ETF regards computation as In the framework, a problem-s domain knowledge and a query are described in definite clauses, and computation is regarded as transformation of the definite clauses. Its meaning is defined by a model of the set of definite clauses, and the transformation rules generated must preserve meaning. We have proposed a parallel processing method based on “specialization", a part of operation in the transformations, which resembles substitution in logic programming. The method requires “Memo-tree", a history of specialization to maintain correctness. In this paper we proposes the new method for the specialization-base parallel processing without Memo-tree.

Keywords: Parallel processing, Program correctness, Equivalent transformation, Specializer generation rule

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Authors: Guangbin Wang, Xue Li

Abstract:

In this paper, we present parallel alternating two-stage methods for solving linear system Ax=b, where A is a symmetric positive definite matrix. And we give some convergence results of these methods for nonsingular linear system.

Keywords: alternating two-stage, convergence, linear system, parallel.

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Authors: Win Win Tun, Han Su Yin, Ohn Zin Lin

Abstract:

Transmission networks are an important part of an electric power system. The transmission lines not only have high power transmission capacity but also they are prone of larger magnitudes. Different types of faults occur in transmission lines such as single line to ground (L-G) fault, double line to ground (L-L-G) fault, line to line (L-L) fault and three phases (L-L-L) fault. These faults are needed to be cleared quickly in order to reduce damage caused to the system and they have high impact on the electrical power system equipment’s which are connected in transmission line. The main fault in transmission line is L-G fault. Therefore, protection relays are needed to protect transmission line. Overcurrent and earth fault relay is an important relay used to protect transmission lines, distribution feeders, transformers and bus couplers etc. Sometimes these relays can be used as main protection or backup protection. The modeling of protection relays is important to indicate the effects of network parameters and configurations on the operation of relays. Therefore, the modeling of overcurrent and earth fault relay is described in this paper. The overcurrent and earth fault relays with standard inverse definite minimum time are modeled and simulated by using MATLAB/Simulink software. The developed model was tested with L-G, L-L-G, L-L and L-L-L faults with various fault locations and fault resistance (0.001Ω). The simulation results are obtained by MATLAB software which shows the feasibility of analysis of transmission line protection with overcurrent and earth fault relay.

Keywords: Transmission line, overcurrent and earth fault relay, standard inverse definite minimum time, various faults, MATLAB Software.

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Authors: Elragig Aiman, Dreiwi Hanan, Townley Stuart, Elmabrook Idriss

Abstract:

In this paper, we reconsider the analysis of the Oregonator model. We highlight an error in this analysis which leads to an incorrect depiction of the parameter region in which diffusion driven instability is possible. We believe that the cause of the oversight is the complexity of stability analyses based on eigenvalues and the dependence on parameters of matrix minors appearing in stability calculations. We regenerate the parameter space where Turing patterns can be seen, and we use the common Lyapunov function (CLF) approach, which is numerically reliable, to further confirm the dependence of the results on diffusion coefficients intensities.

Keywords: Diffusion driven instability, common Lyapunov function (CLF), turing pattern, positive-definite matrix.

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Authors: Mojtaba Hakimi-Moghaddam

Abstract:

Positive real and strictly positive real transfer functions are important concepts in the control theory. In this paper, the results of researches in these areas are summarized. Definitions together with their graphical interpretations are mentioned. The equivalent conditions in the frequency domain and state space representations are reviewed. Their equivalent electrical networks are explained. Also, a comprehensive discussion about a difference between behavior of real part of positive real and strictly positive real transfer functions in high frequencies is presented. Furthermore, several illustrative examples are given.

Keywords: Real rational transfer functions, positive realness property, strictly positive realness property, equivalent conditions.

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Authors: Xueting Liu, Daojin Song, Chuandai Dong, Hongkui Li

Abstract:

From a set of shifted, blurred, and decimated image , super-resolution image reconstruction can get a high-resolution image. So it has become an active research branch in the field of image restoration. In general, super-resolution image restoration is an ill-posed problem. Prior knowledge about the image can be combined to make the problem well-posed, which contributes to some regularization methods. In the regularization methods at present, however, regularization parameter was selected by experience in some cases and other techniques have too heavy computation cost for computing the parameter. In this paper, we construct a new super-resolution algorithm by transforming the solving of the System stem Є=An into the solving of the equations X+A*X-1A=I , and propose an inverse iterative method.

Keywords: High-resolution MAP image, Reconstruction, Image interpolation, Motion Estimation, Hermitian positive definite solutions.

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Authors: Marque Adrien, Delahaye Daniel, Marechal Pierre, Berry Isabelle

Abstract:

Wind direction and uncertainty are crucial in aircraft or unmanned aerial vehicle trajectories. By computing wind covariance matrices on each spatial grid point, these spatial grids can be defined as images with symmetric positive definite matrix elements. A data pre-processing step, a specific convolution, a specific max-pooling, and specific flatten layers are implemented to process such images. Then, the neural network is applied to spatial grids, whose elements are wind covariance matrices, to solve classification problems related to the feasibility of unmanned aerial vehicles based on wind direction and wind uncertainty.

Keywords: Wind direction, uncertainty level, Unmanned Aerial Vehicle, convolution neural network, SPD matrices.

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Authors: Ber-Lin Yu, Jie Cui, Hong Cheng, Zhengfeng Yu

Abstract:

A sign pattern is a matrix whose entries belong to the set {+,−, 0}. An n-by-n sign pattern A is said to allow an eventually positive matrix if there exist some real matrices A with the same sign pattern as A and a positive integer k0 such that Ak > 0 for all k ≥ k0. It is well known that identifying and classifying the n-by-n sign patterns that allow an eventually positive matrix are posed as two open problems. In this article, the tree sign patterns of small order that allow an eventually positive matrix are classified completely.

Keywords: Eventually positive matrix, sign pattern, tree.

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Authors: K. Ramash Kumar, S. Jeevananthan

Abstract:

The object of this paper is to design and analyze a proportional – integral (PI) control for positive output elementary super lift Luo converter (POESLLC), which is the start-of-the-art DC-DC converter. The positive output elementary super lift Luo converter performs the voltage conversion from positive source voltage to positive load voltage. This paper proposes a development of PI control capable of providing the good static and dynamic performance compared to proportional – integralderivative (PID) controller. Using state space average method derives the dynamic equations describing the positive output elementary super lift luo converter and PI control is designed. The simulation model of the positive output elementary super lift Luo converter with its control circuit is implemented in Matlab/Simulink. The PI control for positive output elementary super lift Luo converter is tested for transient region, line changes, load changes, steady state region and also for components variations.

Keywords: DC-DC converter, Positive output elementarysuper lift Luo converter (POESLLC), Proportional – Integral (PI)control.

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Authors: Thanin Sitthiwirattham, Jiraporn Reunsumrit

Abstract:

We study the existence of positive solutions to the three points difference-summation boundary value problem. We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem due to Krasnoselskii in cones.

Keywords: Positive solution, Boundary value problem, Fixed point theorem, Cone.

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Authors: Ebregbe David, Deng Weibo

Abstract:

The traditional second order statistics approach of using only the hermitian covariance for non circular signals, does not take advantage of the information contained in the complementary covariance of these signals. Radar systems often use non circular signals such as Binary Phase Shift Keying (BPSK) signals. Their noncicular property can be exploited together with the dual centrosymmetry of the bistatic MIMO radar system to improve angle estimation performance. We construct an augmented matrix from the received data vectors using both the positive definite hermitian covariance matrix and the complementary covariance matrix. The Unitary ESPRIT technique is then applied to the signal subspace of the augmented covariance matrix for automatically paired Direction-of-arrival (DOA) and Direction-of-Departure (DOD) angle estimates. The number of targets that can be detected is twice that obtainable with the conventional ESPRIT approach. Simulation results show the effectiveness of this method in terms of increase in resolution and the number of targets that can be detected.

Keywords: Bistatic MIMO Radar, Unitary Esprit, Non circular signals.

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Authors: K. Ramash Kumar, S. Jeevananthan

Abstract:

The Object of this paper is to design and analyze a Hysteresis modulation based sliding mode control (HMSMC) for positive output elementary super lift Luo converter (POESLLC), which is the start-of-the-art DC-DC converter. The positive output elementary super lift Luo converter performs the voltage conversion from positive source voltage to positive load voltage. This paper proposes a HMSMC capable of providing the good steady state and dynamic performance compared to conventional controllers. Dynamic equations describing the positive output elementary super lift luo converter are derived by using state space average method. The simulation model of the positive output elementary super lift Luo converter with its control circuit is implemented in Matlab/Simulink. The HMSMC for positive output elementary super lift Luo converter is tested for line changes, load changes and also for components variations.

Keywords: DC-DC converter, Positive output elementarysuper lift Luo converter (POESLLC), Hysteresis modulation basedsliding mode control (HMSMC).

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Authors: Z. Zainuddin, W. D. Wan Rosli, R. Lanouette, S. Sathasivam

Abstract:

This paper reports work done to improve the modeling of complex processes when only small experimental data sets are available. Neural networks are used to capture the nonlinear underlying phenomena contained in the data set and to partly eliminate the burden of having to specify completely the structure of the model. Two different types of neural networks were used for the application of pulping problem. A three layer feed forward neural networks, using the Preconditioned Conjugate Gradient (PCG) methods were used in this investigation. Preconditioning is a method to improve convergence by lowering the condition number and increasing the eigenvalues clustering. The idea is to solve the modified odified problem M-1 Ax= M-1b where M is a positive-definite preconditioner that is closely related to A. We mainly focused on Preconditioned Conjugate Gradient- based training methods which originated from optimization theory, namely Preconditioned Conjugate Gradient with Fletcher-Reeves Update (PCGF), Preconditioned Conjugate Gradient with Polak-Ribiere Update (PCGP) and Preconditioned Conjugate Gradient with Powell-Beale Restarts (PCGB). The behavior of the PCG methods in the simulations proved to be robust against phenomenon such as oscillations due to large step size.

Keywords: Convergence, pulping modeling, neural networks, preconditioned conjugate gradient.

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Authors: Syed Dawood Md. Taimur, Saidur Rahman Khan, Farzana Islam

Abstract:

To evaluate the factors which predetermine the coronary artery disease in patients having positive Exercise Tolerance Test (ETT) that is treadmill results and coronary artery findings. This descriptive study was conducted at Department of Cardiology, Ibrahim Cardiac Hospital & Research Institute, Dhaka, Bangladesh from 1st January, 2014 to 31st August, 2014. All patients who had done ETT (treadmill) for chest pain diagnosis were studied. One hundred and four patients underwent coronary angiogram after positive treadmill result. Patients were divided into two groups depending upon the angiographic findings, i.e. true positive and false positive. Positive treadmill test patients who have coronary artery involvement these are called true positive and who have no involvement they are called false positive group. Both groups were compared with each other. Out of 104 patients, 81 (77.9%) patients had true positive ETT and 23 (22.1%) patients had false positive ETT. The mean age of patients in positive ETT was 53.46± 8.06 years and male mean age was 53.63±8.36 years and female was 52.87±7.0 years. Sixty nine (85.19%) male patients and twelve (14.81%) female patients had true positive ETT, whereas 15 (65.21%) males and 8 (34.79%) females had false positive ETT, this was statistically significant (p<0.032) in the two groups (sex) in comparison of true and false positive ETT. The risk factors of these patients like diabetes mellitus, hypertension, dyslipidemia, family history and smoking were seen among these patients. Hypertensive patients having true positive which were statistically significant (p<0.004) and diabetic, dyslipidemic patients having true positive which were statistically significant (p<0.032 & 0.030).True positive patients had family history were 68(83.95%) and smoking were 52 (64.20%), where family history patients had statistically significant (p<0.017) between two groups of patients and smokers were significant (p<0.012). 46 true positive patients achieved THR which was not statistically significant (P<0.138) and 79 true patients had abnormal resting ECG whether it was significant (p<0.036). Amongst the vessels involvement the most common was LAD 55 (67.90 %) followed by LCX 42 (51.85%), RCA 36 (44.44%), and the LMCA was 9 (11.11%). 40 patients (49.38%) had SVD, 26 (30.10%) had DVD, 15(18.52%) had TVD and 23 had normal coronary arteries. It can be concluded that among the female patients who have positive ETT with normal resting ECG, who had achieved target heart rate are likely to have a false positive test result. Conversely male patients, resting abnormal ECG who had not achieved THR, symptom limited ETT, have a hypertension, diabetes, dyslipidemia, family history and smoking are likely to have a true positive treadmill test result.

Keywords: Exercise tolerance test, Coronary artery disease, Coronary angiography, True positive, False positive.

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Authors: W. D. Wan Rosli, Z. Zainuddin, R. Lanouette, S. Sathasivam

Abstract:

This paper reports work done to improve the modeling of complex processes when only small experimental data sets are available. Neural networks are used to capture the nonlinear underlying phenomena contained in the data set and to partly eliminate the burden of having to specify completely the structure of the model. Two different types of neural networks were used for the application of Pulping of Sugar Maple problem. A three layer feed forward neural networks, using the Preconditioned Conjugate Gradient (PCG) methods were used in this investigation. Preconditioning is a method to improve convergence by lowering the condition number and increasing the eigenvalues clustering. The idea is to solve the modified problem where M is a positive-definite preconditioner that is closely related to A. We mainly focused on Preconditioned Conjugate Gradient- based training methods which originated from optimization theory, namely Preconditioned Conjugate Gradient with Fletcher-Reeves Update (PCGF), Preconditioned Conjugate Gradient with Polak-Ribiere Update (PCGP) and Preconditioned Conjugate Gradient with Powell-Beale Restarts (PCGB). The behavior of the PCG methods in the simulations proved to be robust against phenomenon such as oscillations due to large step size.

Keywords: Convergence, Modeling, Neural Networks, Preconditioned Conjugate Gradient.

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Authors: Xiuyong Ding, Lan Shu, Xiu Liu

Abstract:

This paper is concerned with the existence of a linear copositive Lyapunov function(LCLF) for a special class of switched positive linear systems(SPLSs) composed of continuousand discrete-time subsystems. Firstly, by using system matrices, we construct a special kind of matrices in appropriate manner. Secondly, our results reveal that the Hurwitz stability of these matrices is equivalent to the existence of a common LCLF for arbitrary finite sets composed of continuous- and discrete-time positive linear timeinvariant( LTI) systems. Finally, a simple example is provided to illustrate the implication of our results.

Keywords: Linear co-positive Lyapunov functions, positive systems, switched systems.

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Authors: Mustafa Jahanara

Abstract:

The aim of present research was to study of the relationship between emotional intelligence, perceived stress, positive religious coping with psychological distress to in a sample of undergraduate students in Polytechnic University in Kabul. One hundred and fifty-tow students (102 male, 50 female) were included in this study. All participants completed the Emotional Intelligence Scale (EIS), General Health Questionnaire (GHQ 12), Perceived Stress Scale (PSS-10), and the Brief RCOPE. The results revealed that EI was negatively associated with perceived stress and psychological distress. Also emotional intelligence was positively correlated with positive religious coping. Perceived stress was positive related with psychological distress and negatively correlated with positive religious coping. Eventually positive religious coping was significantly and negatively correlated with psychological distress. However, emotional intelligence and positive religious coping could influence on mental health.

Keywords: Emotional intelligence, perceived stress, positive religious coping, psychological distress.

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Authors: Na Cheng, Zi-li Chen

Abstract:

We investigate the sufficient condition under which each positive b-weakly compact operator is Dunford-Pettis. We also investigate the necessary condition on which each positive b-weakly compact operator is Dunford-Pettis. Necessary condition on which each positive b-weakly compact operator is weakly compact is also considered. We give the operator that is semi-compact, but it is not bweakly. We present a necessary and sufficient condition under which each positive semi-compact operator is b-weakly compact.

Keywords: b-weakly compact, Dunford-Pettis operator, M-weakly compact operator, L-weakly compact operator, semi-compact operator, weakly sequentially continuous lattice operations, order continuous norm, positive Schur property.

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Authors: A. K. M. Rezaul Karim, Abu Yusuf Mahmud, S. H. Mahmud

Abstract:

The study aimed to investigate whether the affect (experience of feeling or emotion) of ethnic minority people can be predicted by gender and marital status. Toward this end, positive affect and negative affect of 103 adult indigenous persons were measured. Analysis of data in multiple regressions demonstrated that both gender and marital status are significantly associated with positive affect (Gender: β=.318, p<.001; Marital status: β=.201, p<.05), but not with negative affect. Results indicated that the indigenous males have 0.32 standard deviations increased positive affect as compared to the indigenous females and that married individuals have 0.20 standard deviations increased positive affect as compared to their unmarried counterparts. These findings advance our understanding that gender and marital status inequalities in the experience of emotion are not specific to the mainstream society; rather it is a generalized picture of all societies. In general, men possess more positive affect than females; married persons possess more positive affect than the unmarried persons.

Keywords: Positive Affect, Negative Affect, Ethnic Minority, Gender, Marital Status.

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Authors: Hyeondal Jeong, Yoonjung Baek

Abstract:

This research examines the effects of positive psychological capital (or PsyCap) on employee’s outcomes (satisfaction, commitment, organizational citizenship behavior, innovation behavior and individual creativity). This study conducted a meta-analysis of articles published in the Republic of Korea. As a result, positive psychological capital has a positive effect on the behavior of employees. Heterogeneity was identified among the studies included in the analysis and the context factors were analyzed; the study proposes contextual factors such as team tenure. The moderating effect of team tenure was not statistically significant. The implications were discussed based on the analysis results.

Keywords: Positive psychological capital, satisfaction, commitment, OCB, creativity, meta-analysis.

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Authors: Wongvisarut Khuangsatung, Pakkinee Chitsakul

Abstract:

In this paper, we studied some properties of geodesic on some open surfaces: Hyperboloid, Paraboloid and Funnel Surface. Geodesic equation in the v-Clairaut parameterization was calculated and reduced to definite integral. Some geodesics on some open surfaces as mention above were classified by Clairaut's relation.

Keywords: Geodesic, Surface of revolution, Clairaut's relation, Clairaut parameterization.

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