Search results for: Linear discrimination

Authors: M. Benbrahim, K. Benjelloun, A. Ibenbrahim, M. Kasmi, E. Ardil

Abstract:

The automatic discrimination of seismic signals is an important practical goal for the earth-science observatories due to the large amount of information that they receive continuously. An essential discrimination task is to allocate the incoming signal to a group associated with the kind of physical phenomena producing it. In this paper, we present new techniques for seismic signals classification: local, regional and global discrimination. These techniques were tested on seismic signals from the data base of the National Geophysical Institute of the Centre National pour la Recherche Scientifique et Technique (Morocco) by using the Moroccan software for seismic signals analysis.

Keywords: Seismic signals, local discrimination, regionaldiscrimination, global discrimination, Moroccan software for seismicsignals analysis.

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Authors: Ramaswamy Palaniappan

Abstract:

In this paper, a second order autoregressive (AR) model is proposed to discriminate alcoholics using single trial gamma band Visual Evoked Potential (VEP) signals using 3 different classifiers: Simplified Fuzzy ARTMAP (SFA) neural network (NN), Multilayer-perceptron-backpropagation (MLP-BP) NN and Linear Discriminant (LD). Electroencephalogram (EEG) signals were recorded from alcoholic and control subjects during the presentation of visuals from Snodgrass and Vanderwart picture set. Single trial VEP signals were extracted from EEG signals using Elliptic filtering in the gamma band spectral range. A second order AR model was used as gamma band VEP exhibits pseudo-periodic behaviour and second order AR is optimal to represent this behaviour. This circumvents the requirement of having to use some criteria to choose the correct order. The averaged discrimination errors of 2.6%, 2.8% and 11.9% were given by LD, MLP-BP and SFA classifiers. The high LD discrimination results show the validity of the proposed method to discriminate between alcoholic subjects.

Keywords: Linear Discriminant, Neural Network, VisualEvoked Potential.

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Authors: Li Lei, Jia Jidong

Abstract:

Employment right is linked to the people’s livelihood in our society. As a most important and representative part in the labor market, the employment of public servants is always taking much attention. But the discrimination in the employment of public servants has always existed and, to become a controversy in our society. The paper try to discuss this problem from four parts as follows: First, the employment of public servants has a representative status in our labor market. The second part is about the discrimination in the employment of public servants. The third part is about the right of equality and its significance. The last part is to analysis the legal predicament about discrimination in the employment of public servants in China.

Keywords: Discrimination, Employment of public servants, Right of labor.

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Authors: Harlida Abdul Wahab

Abstract:

Discrimination in employment has its wider social and economic consequences other than mere violating a basic human right. Discrimination involves treating people differently because of certain grounds such as race, color, or sex, which results in the impairment of equality of opportunity and treatment. As an essential part of promoting decent work, combating discrimination through the principle of non-discrimination has been established by the International Labor Organization (ILO) through the Declaration on Fundamental Principles and Rights at Work 1998. Considering elimination of discrimination in employment as a core labor standard, member states are expected to respect, promote and implement it to their national laws and policies. Being a member state, Malaysia has to position herself align with this international requirement. The author discusses the related convention together with Malaysia-s responses on the matter. At the closing stage, the prospect of Malaysia is presumed taking into account of the current positions and reports submitted to the ILO.

Keywords: Discrimination, employment, international labor standard, Malaysia.

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Authors: Soungwan Kim

Abstract:

The present study analyzed the effect of discrimination experience on the life satisfaction in women with severe disabilities and the mediating effect of disability acceptance. In verifying this mediating effect of disability acceptance between discrimination experience and life satisfaction, both discrimination experience and disability acceptance were found to be statistically significant in the first and second phases. Disability acceptance was found to have a mediating effect on the relationship between discrimination experience and life satisfaction. Based on this finding, measures for enhancing the quality of life in individuals with disabilities that experience low levels of life satisfaction were proposed.

Keywords: Disability Discrimination, Disability Acceptance, Life Satisfaction, Mediating Effect.

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Authors: Delaram Jarchi, Reza Boostani

Abstract:

Linear Discrimination Analysis (LDA) is a linear solution for classification of two classes. In this paper, we propose a variant LDA method for multi-class problem which redefines the between class and within class scatter matrices by incorporating a weight function into each of them. The aim is to separate classes as much as possible in a situation that one class is well separated from other classes, incidentally, that class must have a little influence on classification. It has been suggested to alleviate influence of classes that are well separated by adding a weight into between class scatter matrix and within class scatter matrix. To obtain a simple and effective weight function, ordinary LDA between every two classes has been used in order to find Fisher discrimination value and passed it as an input into two weight functions and redefined between class and within class scatter matrices. Experimental results showed that our new LDA method improved classification rate, on glass, iris and wine datasets, in comparison to different versions of LDA.

Keywords: Discriminant vectors, weighted LDA, uncorrelation, principle components, Fisher-face method, Bootstarp method.

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Authors: Daniel E. Gberevbie, Adewale O. Osibanjo, Anthonia A. Adeniji, Olumuyiwa A. Oludayo

Abstract:

Research has shown that a recruitment policy devoid of gender discrimination enhances employee performance in an organization. Previous studies in Nigeria show that gender discrimination against men and women based on their ethnic, religious and geographical identity is common. This survey, however, focuses on discrimination against women on the basis of gender and performance in government universities in Lagos State, Nigeria. The model used for this study was developed and tested in which one hundred and eighty seven copies of the questionnaire that were administered to respondents as completed by the academic staff of government universities in Lagos State were retrieved. Pearson correlation and regression were utilized for the analysis of the study, and the result showed that managerial roles based on gender discrimination against women in government universities in Lagos State have affected employee job performance negatively. The study concludes that for as long as gender discrimination rather than merit remains the basis for staff employment into positions of authority in Nigerian Universities, enhanced performance is more likely to elude employees and the educational sector in general. 

Keywords: Academic staff, Employee performance, Gender discrimination, Nigeria, Universities.

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Authors: Ramaswamy Palaniappan

Abstract:

This paper reports a new approach on identifying the individuality of persons by using parametric classification of multiple mental thoughts. In the approach, electroencephalogram (EEG) signals were recorded when the subjects were thinking of one or more (up to five) mental thoughts. Autoregressive features were computed from these EEG signals and classified by Linear Discriminant classifier. The results here indicate that near perfect identification of 400 test EEG patterns from four subjects was possible, thereby opening up a new avenue in biometrics.

Keywords: Autoregressive, Biometrics, Electroencephalogram, Linear discrimination, Mental thoughts.

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Authors: Dursun Aydın

Abstract:

In this paper, estimation of the linear regression model is made by ordinary least squares method and the partially linear regression model is estimated by penalized least squares method using smoothing spline. Then, it is investigated that differences and similarity in the sum of squares related for linear regression and partial linear regression models (semi-parametric regression models). It is denoted that the sum of squares in linear regression is reduced to sum of squares in partial linear regression models. Furthermore, we indicated that various sums of squares in the linear regression are similar to different deviance statements in partial linear regression. In addition to, coefficient of the determination derived in linear regression model is easily generalized to coefficient of the determination of the partial linear regression model. For this aim, it is made two different applications. A simulated and a real data set are considered to prove the claim mentioned here. In this way, this study is supported with a simulation and a real data example.

Keywords: Partial Linear Regression Model, Linear RegressionModel, Residuals, Deviance, Smoothing Spline.

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Authors: Ivana Šalinović

Abstract:

The term gender emerged in the second half of the last century and since then a growing body of research dealing with the topic demonstrates its importance. Primarily, the research and the theories that were addressing the topic were focused on stating the differences between the terms sex and gender, where sex refers to the biological aspect of a person, while gender refers to the socially ascribed roles, attitudes, behaviors, and etc., and on gender discrimination whose visible and invisible repercussions are harming society and one of the agents of change should be educators on all educational levels since they are emotionally sculpting their students, that is why considerable effort should be put into implementing education about this topic into the standard curriculum. Not only educators, but it is also necessary to change the mindset of the younger generations because they will be important agents in the further elimination of gender discrimination, thus causing societal changes. Therefore, it is very important to hear their voices and their experiences and for these reasons, this research has been done, to see what the students of the second year at a private college university Aspira in Croatia have gone through in their educational ladder. The hypothesis was that the findings would most certainly show a huge difference between female and male students’ experiences and effects of gender discrimination, but the results have actually shown a very mixed picture and the original hypothesis was somewhat disapproved. Instead of finding out that girls experienced a lot of gender discrimination, it turned out that it was the boys who believed that in their previous and current education, there was no equal time distribution between genders, they noticed that the language was not gender-sensitive, teaching aids were not adopted to the genders. They were also the ones that pointed out that the discipline path was not the same for everyone, and they were the ones that the teacher’s gender had more influence on and were also the ones that experienced more gender discrimination.

Keywords: Gender, discrimination, elementary school, high school.

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Authors: Chua Bee Seok, Shamsul Amri Baharuddin, Rosnah Ismail, Ferlis Bahari, Jasmine Adela Mutang, Lailawati Madlan, Asong Joseph

Abstract:

The aims of this study were to determine the factor structure and psychometric properties (i.e., reliability and convergent validity) of the Malaysian Multi-Ethnic Discrimination Scale (MMEDS). It consists of 71-items measure experience, strategies used and consequences of ethnic discrimination. A sample of 649 university students from one of the higher education institution in Malaysia was asked to complete MMEDS, as well as Perceived Ethnic and Racial Discrimination. The exploratory factor analysis on ethnic discrimination experience extracted two factors labeled ‘unfair treatment’ (15 items) and ‘Denial of the ethnic right’ (12 items) which accounted for 60.92% of the total variance. The two sub scales demonstrated clear reliability with internal consistency above .70. The convergent validity of the Scale was supported by an expected pattern of correlations (positive and significant correlation) between the score of unfair treatment and denial of the ethnic right and the score of Perceived Ethnic and Racial Discrimination by Peers Scale. The results suggest that the MMEDS is a reliable and valid measure. However, further studies need to be carried out in other groups of sample as to validate the Scale.

Keywords: Factor structure, psychometric properties, exploratory factor analysis.

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Authors: Soo-young Ye, Jun-mo Park, Jae-hyung Kim, Jae-hee Jung, Ah-young Jeon, In-cheol Kim, Jung-man Son, Ki-gon Nam, Seong-wan Baik, Jung-hoon Ro, Gye-rok Jeon

Abstract:

The linear SEF (Spectral Edge Frequency) parameter and spectrum analysis method can not reflect the non-linear of EEG. This method can not contribute to acquire real time analysis and obtain a high confidence in the clinic due to low discrimination. To solve the problems, the development of a new index is carried out using the bispectrum analyzing the EEG(electroencephalogram) including the non-linear characteristic. After analyzing the bispectrum of the 2 dimension, the most significant power spectrum density peaks appeared abundantly at the specific area in awakening and anesthesia state. These points are utilized to create the new index since many peaks appeared at the specific area in the frequency coordinate. The measured range of an index was 0-100. An index is 20-50 at an anesthesia, while the index is 90-60 at the awake. New index could afford to effectively discriminate the awake and anesthesia state.

Keywords: Bispectrum, anesthesia depth, EEG, SEF.

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Authors: Keun Woo Lee, Minky Son, Chanin Park, Ayoung Baek

Abstract:

Certain tRNA synthetases have developed highly accurate molecular machinery to discriminate their cognate amino acids. Those aaRSs achieve their goal via editing reaction in the Connective Polypeptide 1 (CP1). Recently mutagenesis studies have revealed the critical importance of residues in the CP1 domain for editing activity and X-ray structures have shown binding mode of noncognate amino acids in the editing domain. To pursue molecular mechanism for amino acid discrimination, molecular modeling studies were performed. Our results suggest that aaRS bind the noncognate amino acid more tightly than the cognate one. Finally, by comparing binding conformations of the amino acids in three systems, the amino acid binding mode was elucidated and a discrimination mechanism proposed. The results strongly reveal that the conserved threonines are responsible for amino acid discrimination. This is achieved through side chain interactions between T252 and T247/T248 as well as between those threonines and the incoming amino acids.

Keywords: Amino acid discrimination, Binding free energy Leucyl-tRNAsynthetase, Molecular dynamics.

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Authors: S.H. Nasseri, E. Ardil

Abstract:

Fuzzy linear programming is an application of fuzzy set theory in linear decision making problems and most of these problems are related to linear programming with fuzzy variables. A convenient method for solving these problems is based on using of auxiliary problem. In this paper a new method for solving fuzzy variable linear programming problems directly using linear ranking functions is proposed. This method uses simplex tableau which is used for solving linear programming problems in crisp environment before.

Keywords: Fuzzy variable linear programming, fuzzy number, ranking function, simplex method.

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Authors: K.M. Faraoun, A. Boukelif

Abstract:

This paper describes a new approach of classification using genetic programming. The proposed technique consists of genetically coevolving a population of non-linear transformations on the input data to be classified, and map them to a new space with a reduced dimension, in order to get a maximum inter-classes discrimination. The classification of new samples is then performed on the transformed data, and so become much easier. Contrary to the existing GP-classification techniques, the proposed one use a dynamic repartition of the transformed data in separated intervals, the efficacy of a given intervals repartition is handled by the fitness criterion, with a maximum classes discrimination. Experiments were first performed using the Fisher-s Iris dataset, and then, the KDD-99 Cup dataset was used to study the intrusion detection and classification problem. Obtained results demonstrate that the proposed genetic approach outperform the existing GP-classification methods [1],[2] and [3], and give a very accepted results compared to other existing techniques proposed in [4],[5],[6],[7] and [8].

Keywords: Genetic programming, patterns classification, intrusion detection

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Authors: Mohammed Benbrahim, Adil Daoudi, Khalid Benjelloun, Aomar Ibenbrahim

Abstract:

The automatic discrimination of seismic signals is an important practical goal for earth-science observatories due to the large amount of information that they receive continuously. An essential discrimination task is to allocate the incoming signal to a group associated with the kind of physical phenomena producing it. In this paper, two classes of seismic signals recorded routinely in geophysical laboratory of the National Center for Scientific and Technical Research in Morocco are considered. They correspond to signals associated to local earthquakes and chemical explosions. The approach adopted for the development of an automatic discrimination system is a modular system composed by three blocs: 1) Representation, 2) Dimensionality reduction and 3) Classification. The originality of our work consists in the use of a new wavelet called "modified Mexican hat wavelet" in the representation stage. For the dimensionality reduction, we propose a new algorithm based on the random projection and the principal component analysis.

Keywords: Seismic signals, Wavelets, Dimensionality reduction, Artificial neural networks, Classification.

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Authors: Chao Wang, Ting-Zhu Huang Chen Jia

Abstract:

In this paper, we propose a new linear complementarity problem named as bi-linear complementarity problem (BLCP) and the method for solving BLCP. In addition, the algorithm for error estimation of BLCP is also given. Numerical experiments show that the algorithm is efficient.

Keywords: Bi-linear complementarity problem, Linear complementarity problem, Extended linear complementarity problem, Error estimation, P-matrix, M-matrix.

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Authors: Chia-Hung Lin, Mei-Sung Kang, Cong-Hui Huang, Chao-Lin Kuo

Abstract:

This paper proposes fractal patterns for power quality (PQ) detection using color relational analysis (CRA) based classifier. Iterated function system (IFS) uses the non-linear interpolation in the map and uses similarity maps to construct various fractal patterns of power quality disturbances, including harmonics, voltage sag, voltage swell, voltage sag involving harmonics, voltage swell involving harmonics, and voltage interruption. The non-linear interpolation functions (NIFs) with fractal dimension (FD) make fractal patterns more distinguishing between normal and abnormal voltage signals. The classifier based on CRA discriminates the disturbance events in a power system. Compared with the wavelet neural networks, the test results will show accurate discrimination, good robustness, and faster processing time for detecting disturbing events.

Keywords: Power Quality (PQ), Color Relational Analysis(CRA), Iterated Function System (IFS), Non-linear InterpolationFunction (NIF), Fractal Dimension (FD).

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Authors: H. Taghvafard, G. H. Erjaee

Abstract:

A method for solving linear and non-linear Goursat problem is given by using the two-dimensional differential transform method. The approximate solution of this problem is calculated in the form of a series with easily computable terms and also the exact solutions can be achieved by the known forms of the series solutions. The method can easily be applied to many linear and non-linear problems and is capable of reducing the size of computational work. Several examples are given to demonstrate the reliability and the performance of the presented method.

Keywords: Quadrature, Spline interpolation, Trapezoidal rule, Numericalintegration, Error analysis.

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Authors: I Made Darmayuda, Chai Tshun Chuan Kevin, Je Minkyu

Abstract:

Plenty researches have reported techniques to harvest energy from piezoelectric transducer. In the earlier years, the researches mainly report linear energy harvesting techniques whereby interface circuitry is designed to have input impedance that match with the impedance of the piezoelectric transducer. In recent years non-linear techniques become more popular. The non-linear technique employs voltage waveform manipulation to boost the available-for-extraction energy at the time of energy transfer.  The fact that non-linear energy extraction provides larger available-for-extraction energy doesn’t mean the linear energy extraction is completely obsolete. In some scenarios, such as where initial power is not available, linear energy extraction is still preferred. A modified Buck Boost circuit which is capable of harvesting piezoelectric energy using both linear and non-linear techniques is reported in this paper. Efficiency of at least 64% can be achieved using this circuit. For linear extraction, the modified Buck Boost circuit is controlled using a fix frequency and duty cycle clock. A voltage sensor and a pulse generator are added as the controller for the non-linear extraction technique. 

Keywords: Buck boost, energy harvester, linear energy harvester, non-linear energy harvester, piezoelectric, synchronized charge extraction.

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Authors: Baoguang Tian, Nan Chen

Abstract:

A new relative efficiency in linear model in reference is instructed into the linear weighted regression, and its upper and lower bound are proposed. In the linear weighted regression model, for the best linear unbiased estimation of mean matrix respect to the least-squares estimation, two new relative efficiencies are given, and their upper and lower bounds are also studied.

Keywords: Linear weighted regression, Relative efficiency, Mean matrix, Trace.

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Authors: Alireza Dadkhah, Mahmoud Ghorbanzadeh- Neghab

Abstract:

This study carried out in order to investigate the effects of salinity on carbon isotope discrimination (Δ) of shoots and roots of four sugar beet cultivars (cv) including Madison (British origin) and three Iranian culivars (7233-P12, 7233-P21 and 7233-P29). Plants were grown in sand culture medium in greenhouse conditions. Plants irrigated with saline water (tap water as control, 50 mM, 150 mM, 250 mM and 350 mM of NaCl + CaCl2 in 5 to 1 molar ratio) from 4 leaves stage for 16 weeks. Carbon isotope discrimination significantly decreased with increasing salinity. Significant differences of Δ between shoot and root were observed in all cvs and all levels of salinity. Madison cv showed lower Δ in shoot and root than other three cvs at all levels of salinity expect control, but cv 7233-P29 had significantly higher Δ values at saline conditions of 150 mM and above. Therefore, Δ might be applicable, as a useful tool, for study of salinity tolerance of sugar beet genotypes.

Keywords: Carbon isotope discrimination, Photosynthesis, Salt stress, Sugar beet

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Authors: Nagwa Soliman

Abstract:

Women for centuries have undergone gender discrimination under the pretext of patriarchy which is engraved in the culture and tradition of some societies. It is important to highlight that this condition has been encoded by the male gender to dominate and manipulate women. It is therefore necessary to draw attention to this important obstacle that stands in the way of women’s achievement of their full potential and humanity in the face of these cultural traditions. The appropriate style that was chosen for this literary analysis is a qualitative research method that relies on the feminist technique using Freud’s psychological theories. This article explores patriarchy and gender discrimination as portrayed in Ahdaf Soueif’s In The Eye of the Sun (1992) and Pramoedya Ananta Toer’s The Girl from the Coast (2002). It could be argued that those two novels describe a society that is feminist, patriarchal, and gender discriminatory. Moreover, it is important to assert that patriarchy and gender discrimination are part of the system’s social order which compels the female characters to adjust to society’s norms and conventions. This social order is supported by traditional and cultural masculine attitudes and results in sustaining gender inequality, female stereo typing and patriarchy which suppress women’s beliefs and dreams.

Keywords: Gender discrimination, Patriarchy, Feminism, Stereotype.

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Authors: Alka Obadić

Abstract:

The research concentrates on the role of tourism in generating female employment and on impact of gender discrimination in tourism sector. Unfortunately, in many countries there are still some barriers to the inclusion of women at all hierarchical levels of tourism labor market. Research analysis focuses on EU countries where tourism is a main employer of women. The analysis shows that women represent over third persons employed in the non-financial business economy and almost two thirds in core tourism activities. Women's gross hourly earnings in accommodation and food services were below those of men in the European Union and only countries who recorded increase of gender pay gap from the beginning of crisis are Bulgaria and Croatia. Women in tourism industry are still overrepresented in lower status jobs with fewer opportunities for career progression and are often treated unequally.

Keywords: Employment, gender discrimination, tourism, women’s participation.

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Authors: Boukhzer Abdenbi, El Bikri Khalid, Benamar Rhali

Abstract:

In the present study, the problem of geometrically non-linear free vibrations of functionally graded rectangular plates (FGRP) is studied. The theoretical model, previously developed and based on Hamilton’s principle, is adapted here to determine the fundamental non-linear mode shape of these plates. Frequency parameters, displacements and stress are given for various power-law distributions of the volume fractions of the constituents and various aspect ratios. Good agreement with previous published results is obtained in the case of linear and non-linear analyses.

Keywords: Non-linear vibration, functionally graded materials, rectangular plates.

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Authors: Khaled Harrar, Rachid Jennane

Abstract:

The purpose of this study is the discrimination of 28 postmenopausal with osteoporotic femoral fractures from an agematched control group of 28 women using texture analysis based on fractals. Two pre-processing approaches are applied on radiographic images; these techniques are compared to highlight the choice of the pre-processing method. Furthermore, the values of the fractal dimension are compared to those of the fractal signature in terms of the classification of the two populations. In a second analysis, the BMD measure at proximal femur was compared to the fractal analysis, the latter, which is a non-invasive technique, allowed a better discrimination; the results confirm that the fractal analysis of texture on calcaneus radiographs is able to discriminate osteoporotic patients with femoral fracture from controls. This discrimination was efficient compared to that obtained by BMD alone. It was also present in comparing subgroups with overlapping values of BMD.

Keywords: Osteoporosis, fractal dimension, fractal signature, bone mineral density.

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Authors: S. H. Nasseri, E. Ardil, A. Yazdani, R. Zaefarian

Abstract:

The fuzzy set theory has been applied in many fields, such as operations research, control theory, and management sciences, etc. In particular, an application of this theory in decision making problems is linear programming problems with fuzzy numbers. In this study, we present a new method for solving fuzzy number linear programming problems, by use of linear ranking function. In fact, our method is similar to simplex method that was used for solving linear programming problems in crisp environment before.

Keywords: Fuzzy number linear programming, rankingfunction, simplex method.

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Authors: Triyanto

Abstract:

The purposes of the paper are to know and improve the legal awareness of Surakarta local government officer to Law No.12/2006 on Citizenship in vanishing civic discrimination to Chinese Indonesians. Some issues of the Chinese Indonesian are the definitions of Indonesian citizens and native Indonesian people or “warga negara Indonesia (WNI) asli" and their obligation to show Indonesian Citizenship Certificate (SBKRI) in processing civil documents. Legal awareness of Surakarta local government officer can be categorized as “legal knowledge" only. They know the laws but they do not implement it yet. Nevertheless, at least this research has given the new awareness in citizenship law for the officers.

Keywords: Legal Awareness, Government Officer, Civic Discrimination, Chinese Indonesians

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Authors: Mounir Sayadi, Farhat Fnaiech

Abstract:

In the framework of adaptive parametric modelling of images, we propose in this paper a new technique based on the Chandrasekhar fast adaptive filter for texture characterization. An Auto-Regressive (AR) linear model of texture is obtained by scanning the image row by row and modelling this data with an adaptive Chandrasekhar linear filter. The characterization efficiency of the obtained model is compared with the model adapted with the Least Mean Square (LMS) 2-D adaptive algorithm and with the cooccurrence method features. The comparison criteria is based on the computation of a characterization degree using the ratio of "betweenclass" variances with respect to "within-class" variances of the estimated coefficients. Extensive experiments show that the coefficients estimated by the use of Chandrasekhar adaptive filter give better results in texture discrimination than those estimated by other algorithms, even in a noisy context.

Keywords: Texture analysis, statistical features, adaptive filters, Chandrasekhar algorithm.

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Authors: R. B. Ogunrinde, C. C. Jibunoh

Abstract:

In this paper, a spectral decomposition method is developed for the direct integration of stiff and nonstiff homogeneous linear (ODE) systems with linear, constant, or zero right hand sides (RHSs). The method does not require iteration but obtains solutions at any random points of t, by direct evaluation, in the interval of integration. All the numerical solutions obtained for the class of systems coincide with the exact theoretical solutions. In particular, solutions of homogeneous linear systems, i.e. with zero RHS, conform to the exact analytical solutions of the systems in terms of t.

Keywords: Spectral decomposition, eigenvalues of the Jacobian, linear RHS, homogeneous linear systems.

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