Search results for: quaternion distance functions

Authors: Michael Torggler

Abstract:

Modern information and communication technologies offer a variety of support options for the efficient handling of customer relationships. CRM systems have been developed, which are designed to support the processes in the areas of marketing, sales and service. Along with technological progress, CRM systems are constantly changing, i.e. the systems are continually enhanced by new functions. However, not all functions are suitable for every company because of different frameworks and business processes. In this context the question arises whether or not CRM systems are widely used in Austrian companies and which business processes are most frequently supported by CRM systems. This paper aims to shed light on the popularity of CRM systems in Austrian companies in general and the use of different functions to support their daily business. First of all, the paper provides a theoretical overview of the structure of modern CRM systems and proposes a categorization of currently available software functionality for collaborative, operational and analytical CRM processes, which provides the theoretical background for the empirical study. Apart from these theoretical considerations, the paper presents the empirical results of a field survey on the use of CRM systems in Austrian companies and analyzes its findings.

Keywords: CRM systems, CRM system adoption, CRM system diffusion, CRM functionality, Market study.

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Authors: Mahdad M’hamed, Belaidi Idir

Abstract:

This paper develops a meshless approach, called Element Free Galerkin (EFG) method, which is based on the weak form Moving Least Squares (MLS) of the partial differential governing equations and employs the interpolation to construct the meshless shape functions. The variation weak form is used in the EFG where the trial and test functions are approximated bye the MLS approximation. Since the shape functions constructed by this discretization have the weight function property based on the randomly distributed points, the essential boundary conditions can be implemented easily. The local weak form of the partial differential governing equations is obtained by the weighted residual method within the simple local quadrature domain. The spline function with high continuity is used as the weight function. The presently developed EFG method is a truly meshless method, as it does not require the mesh, either for the construction of the shape functions, or for the integration of the local weak form. Several numerical examples of two-dimensional static structural analysis are presented to illustrate the performance of the present EFG method. They show that the EFG method is highly efficient for the implementation and highly accurate for the computation. The present method is used to analyze the static deflection of beams and plate hole

Keywords: Numerical computation, element-free Galerkin, moving least squares, meshless methods.

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Authors: C. Ardil

Abstract:

Aircraft supplier selection process, which is considered as a fundamental supply chain problem, is a multi-criteria group decision problem that has a significant impact on the performance of the entire supply chain. In practical situations are frequently incomplete and uncertain information, making it difficult for decision-makers to communicate their opinions on candidates with precise and definite values. To solve the aircraft supplier selection problem in an environment of incomplete and uncertain information, proximity measure method is proposed. It uses determinate fuzzy numbers. The weights of each decision maker are equally predetermined and the entropic criteria weights are calculated using each decision maker's decision matrix. Additionally, determinate fuzzy numbers, it is proposed to use the weighted normalized Minkowski distance function and Hausdorff distance function to determine the ranking order patterns of alternatives. A numerical example for aircraft supplier selection is provided to further demonstrate the applicability, effectiveness, validity and rationality of the proposed method.

Keywords: Aircraft supplier selection, multiple criteria decision making, fuzzy sets, determinate fuzzy sets, intuitionistic fuzzy sets, proximity measure method, Minkowski distance function, Hausdorff distance function, PMM, MCDM

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Authors: Moulay A. Akhloufi, Abdelhakim Bendada

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In this work we present an efficient approach for face recognition in the infrared spectrum. In the proposed approach physiological features are extracted from thermal images in order to build a unique thermal faceprint. Then, a distance transform is used to get an invariant representation for face recognition. The obtained physiological features are related to the distribution of blood vessels under the face skin. This blood network is unique to each individual and can be used in infrared face recognition. The obtained results are promising and show the effectiveness of the proposed scheme.

Keywords: Face recognition, biometrics, infrared imaging.

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Authors: K. V. Geetha, N. R. Mangalambal

Abstract:

Aim. We have introduced the notion of order to multinormed spaces and countable union spaces and their duals. The topology of bounded convergence is assigned to the dual spaces. The aim of this paper is to develop the theory of ordered topological linear spaces La,b, L(w, z), the dual spaces of ordered multinormed spaces La,b, ordered countable union spaces L(w, z), with the topology of bounded convergence assigned to the dual spaces. We apply Laplace transformation to the ordered linear space of Laplace transformable generalized functions. We ultimately aim at finding solutions to nonhomogeneous nth order linear differential equations with constant coefficients in terms of generalized functions and comparing different solutions evolved out of different initial conditions. Method. The above aim is achieved by • Defining the spaces La,b, L(w, z). • Assigning an order relation on these spaces by identifying a positive cone on them and studying the properties of the cone. • Defining an order relation on the dual spaces La,b, L(w, z) of La,b, L(w, z) and assigning a topology to these dual spaces which makes the order dual and the topological dual the same. • Defining the adjoint of a continuous map on these spaces and studying its behaviour when the topology of bounded convergence is assigned to the dual spaces. • Applying the two-sided Laplace Transformation on the ordered linear space of generalized functions W and studying some properties of the transformation which are used in solving differential equations. Result. The above techniques are applied to solve non-homogeneous n-th order linear differential equations with constant coefficients in terms of generalized functions and to compare different solutions of the differential equation.

Keywords: Laplace transformable generalized function, positive cone, topology of bounded convergence

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Authors: S. Dorbani, M. Badaoui, D. Benouar

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The aim of this paper is to investigate the effect of the building fundamental period of reinforced concrete buildings of (6, 9, and 12-storey), with different floor plans: Symmetric, mono-symmetric, and unsymmetric. These structures are erected at different epicentral distances. Using the Boumerdes, Algeria (2003) earthquake data, we focused primarily on the establishment of the deterministic formulation linking the base shear force to two parameters: The first one is the fundamental period that represents the numerical fingerprint of the structure, and the second one is the epicentral distance used to represent the impact of the earthquake on this force. In a second step, with a view to highlight the effect of uncertainty in these parameters on the analyzed response, these parameters are modeled as random variables with a log-normal distribution. The variability of the coefficients of variation of the chosen uncertain parameters, on the statistics on the seismic base shear force, showed that the effect of uncertainty on fundamental period on this force statistics is low compared to the epicentral distance uncertainty influence.

Keywords: Base shear force, fundamental period, epicentral distance, uncertainty, lognormal variable, statistics.

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Authors: Zhanar Kozhabekova

Abstract:

There are many demonstrations of political interrelation of Turk kaganate and Mongol empire. The article deals with one of the points of Turk-Mongol interrelation as the ceremony of ascending the khan to the throne. It is historically proved that the ascending to the throne ceremony takes origin from Turk kaganate period by comparing the materials, concerning the facts of the history of both states. The function of Turk-Mongol kaganates remained unchangeable for ages.

Keywords: Enthronement, kagan functions, Mongol empire, Turk kaganate.

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Authors: Nakhoon Baek

Abstract:

Stipples are desired for pattern fillings and transparency effects. In contrast, some graphics standards, including OpenGL ES 1.1 and 2.0, omitted this feature. We represent details of providing line stipples and polygon stipples, through combining texture mapping and alpha blending functions. We start from the OpenGL-specified stipple-related API functions. The details of mathematical transformations are explained to get the correct texture coordinates. Then, the overall algorithm is represented, and its implementation results are followed. We accomplished both of line and polygon stipples, and verified its result with conformance test routines.

Keywords: Stipple operation, OpenGL ES, Implementation.

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Authors: Tudor Barbu

Abstract:

We provide a supervised speech-independent voice recognition technique in this paper. In the feature extraction stage we propose a mel-cepstral based approach. Our feature vector classification method uses a special nonlinear metric, derived from the Hausdorff distance for sets, and a minimum mean distance classifier.

Keywords: Text-independent speaker recognition, mel cepstral analysis, speech feature vector, Hausdorff-based metric, supervised classification.

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Authors: Barenten Suciu, Yuya Nakamoto

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Power generation effect, obtained by inserting a piezo- electric sheet in the backlash clearance of a circular arc helical gear, is evaluated. Such type of screw gear is preferred since, in comparison with the involute tooth profile, the circular arc profile leads to reduced stress-concentration effects, and improved life of the piezoelectric film. Firstly, geometry of the circular arc helical gear, and properties of the piezoelectric sheet are presented. Then, description of the test-rig, consisted of a right-hand thread gear meshing with a left-hand thread gear, and the voltage measurement procedure are given. After creating the tridimensional (3D) model of the meshing gears in SolidWorks, they are 3D-printed in acrylonitrile butadiene styrene (ABS) resin. Variation of the generated voltage versus time, during a meshing cycle of the circular arc helical gear, is measured for various values of the center distance. Then, the change of the maximal, minimal, and peak-to-peak voltage versus the center distance is illustrated. Optimal center distance of the gear, to achieve voltage maximization, is found and its significance is discussed. Such results prove that the contact pressure of the meshing gears can be measured, and also, the electrical power can be generated by employing the proposed technique.

Keywords: Power generation, circular arc helical gear, piezo- electric sheet, contact problem, optimal center distance.

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Authors: T. N. Sindhu, M. Aslam

Abstract:

A comprehensive Bayesian analysis has been carried out in the context of informative and non-informative priors for the shape parameter of the Burr type X distribution under different symmetric and asymmetric loss functions. Elicitation of hyperparameter through prior predictive approach is also discussed. Also we derive the expression for posterior predictive distributions, predictive intervals and the credible Intervals. As an illustration, comparisons of these estimators are made through simulation study.

Keywords: Credible Intervals, Loss Functions, Posterior Predictive Distributions, Predictive Intervals.

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Authors: K. Bommanna Raja, M.Madheswaran, K.Thyagarajah

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A higher order spline interpolated contour obtained with up-sampling of homogenously distributed coordinates for segmentation of kidney region in different classes of ultrasound kidney images has been developed and presented in this paper. The performance of the proposed method is measured and compared with modified snake model contour, Markov random field contour and expert outlined contour. The validation of the method is made in correspondence with expert outlined contour using maximum coordinate distance, Hausdorff distance and mean radial distance metrics. The results obtained reveal that proposed scheme provides optimum contour that agrees well with expert outlined contour. Moreover this technique helps to preserve the pixels-of-interest which in specific defines the functional characteristic of kidney. This explores various possibilities in implementing computer-aided diagnosis system exclusively for US kidney images.

Keywords: Ultrasound Kidney Image – Kidney Segmentation –Active Contour – Markov Random Field – Higher Order SplineInterpolation

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Authors: Robert Gold

Abstract:

Control flow graphs are a well-known representation of the sequential control flow structure of programs with a multitude of applications. Not only single functions but also sets of functions or complete programs can be modeled by control flow graphs. In this case the size of the graphs can grow considerably and thus makes it difficult for software engineers to analyze the control flow. Graph reductions are helpful in this situation. In this paper we define reductions to subsets of nodes. Since executions of programs are represented by paths through the control flow graphs, paths should be preserved. Furthermore, the composition of reductions makes a stepwise analysis approach possible.

Keywords: Control flow graph, graph reduction.

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Authors: Mehmet Bozca

Abstract:

Singular value decomposition based optimisation of geometric design parameters of a 5-speed gearbox is studied. During the optimisation, a four-degree-of freedom torsional vibration model of the pinion gear-wheel gear system is obtained and the minimum singular value of the transfer matrix is considered as the objective functions. The computational cost of the associated singular value problems is quite low for the objective function, because it is only necessary to compute the largest and smallest singular values (μmax and μmin) that can be achieved by using selective eigenvalue solvers; the other singular values are not needed. The design parameters are optimised under several constraints that include bending stress, contact stress and constant distance between gear centres. Thus, by optimising the geometric parameters of the gearbox such as, the module, number of teeth and face width it is possible to obtain a light-weight-gearbox structure. It is concluded that the all optimised geometric design parameters also satisfy all constraints.

Keywords: Singular value, optimisation, gearbox, torsional vibration.

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Authors: Marios Poulos, Sozon Papavlasopoulos, V. S. Belesiotis

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In the proposed method for Web page-ranking, a novel theoretic model is introduced and tested by examples of order relationships among IP addresses. Ranking is induced using a convexity feature, which is learned according to these examples using a self-organizing procedure. We consider the problem of selforganizing learning from IP data to be represented by a semi-random convex polygon procedure, in which the vertices correspond to IP addresses. Based on recent developments in our regularization theory for convex polygons and corresponding Euclidean distance based methods for classification, we develop an algorithmic framework for learning ranking functions based on a Computational Geometric Theory. We show that our algorithm is generic, and present experimental results explaining the potential of our approach. In addition, we explain the generality of our approach by showing its possible use as a visualization tool for data obtained from diverse domains, such as Public Administration and Education.

Keywords: Computational Geometry, Education, e-Governance, Semantic Web.

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Authors: Photjanat Phimnom, Haruetai Lohasiriwat

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In today’s world, the LED display has been used for presenting visual information under various circumstances. Such information is an important intermediary in the human information processing. Researchers have been investigated diverse factors that influence this process effectiveness. The letter size is undoubtedly one major factor that has been tested and recommended by many standards and guidelines. However, viewing information on the display from direct perpendicular position is a typical assumption whereas many actual events are required viewing from the angles. This current research aims to study the effect of oblique viewing angle and viewing distance on ability to recognize alphabet, number, and English word. The total of ten participants was volunteered to our 3 x 4 x 4 within subject study. Independent variables include three distance levels (2, 6, and 12 m), four oblique angles (0, 45, 60, 75 degree), and four target types (alphabet, number, short word, and long word). Following the method of constant stimuli our study suggests that the larger oblique angle, ranging from 0 to 75 degree from the line of sight, results in significant higher legibility threshold or larger font size required (p-value < 0.05). Viewing distance factor also shows to have significant effect on the threshold (p-value < 0.05). However, the effect from distance factor is expected to be confounded by the quality of the screen used in our experiment. Lastly, our results show that single alphabet as well as single number are recognized at significant lower threshold (smaller font size) as compared to both short and long words (p-value < 0.05). Therefore, it is recommended that when designs information to be presented on LED display, understanding of all possible ranges of oblique angle should be taken into account in order to specify the preferred letter size. Additionally, the recommendation of letter size for 100% legibility in our tested conditions is provided in the paper.

Keywords: Letter Size, Oblique Angle, Viewing Distance, Legibility Threshold.

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Authors: Soon-Hyun Park, Takami Matsuo

Abstract:

This paper presents an adaptive differentiator of sequential data based on the adaptive control theory. The algorithm is applied to detect moving objects by estimating a temporal gradient of sequential data at a specified pixel. We adopt two nonlinear intensity functions to reduce the influence of noises. The derivatives of the nonlinear intensity functions are estimated by an adaptive observer with σ-modification update law.

Keywords: Adaptive estimation, parameter adjustmentlaw, motion detection, temporal gradient, differential filter.

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Authors: Sheila R. Bonito

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This study describes the relationship between motivation factors and academic performance among distance education students enrolled in a postgraduate nursing course. Students (n=96) participated in a survey that assesses student's motivational orientations from a cognitive perspective using a selfadministered questionnaire based on Pintrich-s Motivation Strategies for Learning Questionnaire (MLSQ). Results showed students- motivational factors are highest on task value (6.44, 0.71); followed by intrinsic goal orientation (6.20, 0.76), control beliefs (6.02, 0.89); extrinsic goal orientation (5.85, 1.13); self-efficacy for learning and performance (5.62, 0.84), and finally, test anxiety (4.21, 1.37). Weak positive correlations were found between academic performance and intrinsic goal orientation (r=0.13), extrinsic goal orientation (r=0.04), task value (r=0.09), control beliefs (r=0.02), and self-efficacy (r=0.05), while there was weak negative correlation with test anxiety (r=-0.04). Conclusions from the study indicate the need to focus on improving tasks and targeting intrinsic goal orientations of students to courses since these were positively correlated with academic performance and downplay the use of tests since these were negatively correlated with academic performance.

Keywords: Motivation factors, academic performance, distance education

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Authors: Mark Kaahwa, Chang Zhu, Moses Muhumuza

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This study investigates the satisfaction of distance education university students (DEUS) with the use of audio media as a medium of instruction. Studying students’ satisfaction is vital because it shows whether learners are comfortable with a certain instructional strategy or not. Although previous studies have investigated the use of audio media, the satisfaction of students with an instructional strategy that combines radio teaching and podcasts as an independent teaching strategy has not been fully investigated. In this study, all lectures were delivered through the radio and students had no direct contact with their instructors. No modules or any other material in form of text were given to the students. They instead, revised the taught content by listening to podcasts saved on their mobile electronic gadgets. Prior to data collection, DEUS received orientation through workshops on how to use audio media in distance education. To achieve objectives of the study, a survey, naturalistic observations and face-to-face interviews were used to collect data from a sample of 211 undergraduate and graduate students. Findings indicate that there was no statistically significant difference in the levels of satisfaction between male and female students. The results from post hoc analysis show that there is a statistically significant difference in the levels of satisfaction regarding the use of audio media between diploma and graduate students. Diploma students are more satisfied compared to their graduate counterparts. T-test results reveal that there was no statistically significant difference in the general satisfaction with audio media between rural and urban-based students. And ANOVA results indicate that there is no statistically significant difference in the levels of satisfaction with the use of audio media across age groups. Furthermore, results from observations and interviews reveal that DEUS found learning using audio media a pleasurable medium of instruction. This is an indication that audio media can be considered as an instructional strategy on its own merit.

Keywords: Audio media, distance education, distance education university students, medium of instruction, satisfaction.

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Authors: Salah Gariani, Islam Shyha, Osama Elgadi, Khaled Jegandi

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In this work, a cooling coherent round nozzle was developed and the impact of nozzle placement (i.e. nozzle angle and stand-off/impinging distance) on the machinability of Ti-6Al-4V was evaluated. Key process measures were cutting force, workpiece temperature, tool wear, burr formation and average surface roughness (Ra). Experimental results showed that nozzle position at a 15° angle in the feed direction and 45°/60° against feed direction assisted in minimising workpiece temperature. A stand-off distance of 55 and 75 mm is also necessary to control burr formation, workpiece temperature and Ra, but coherent nozzle orientation has no statistically significant impact on the mean values of cutting force and tool wear. It can be concluded that stand-off distance is more substantially significant than nozzle angles when step shoulder milling Ti-6Al- 4V using vegetable oil-based cutting fluid.

Keywords: Coherent round nozzle, step shoulder milling, Ti-6Al-4V, vegetable oil-based cutting fluid.

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Authors: Zelalem Teshome Wale

Abstract:

The notions of I-vague groups with membership and non-membership functions taking values in an involutary dually residuated lattice ordered semigroup are introduced which generalize the notions with truth values in a Boolean algebra as well as those usual vague sets whose membership and non-membership functions taking values in the unit interval [0, 1]. Moreover, various operations and properties are established.

Keywords: Involutary dually residuated lattice ordered semigroup, I-vague set and I-vague group.

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Authors: Mário C. Ricci

Abstract:

An alternative iterative computational procedure is proposed for internal normal ball loads calculation in statically loaded single-row, angular-contact ball bearings, subjected to a known thrust load, which is applied in the inner ring at the geometric bearing center line. An accurate method for curvature radii at contacts with inner and outer raceways in the direction of the motion is used. Numerical aspects of the iterative procedure are discussed. Numerical examples results for a 218 angular-contact ball bearing have been compared with those from the literature. Twenty figures are presented showing the geometrical features, the behavior of the convergence variables and the following parameters as functions of the thrust load: normal ball loads, contact angle, distance between curvature centers, and normal ball and axial deflections.

Keywords: Ball, Bearing, Static, Load, Iterative, Numerical, Method.

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Authors: Panikos Heracleous

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In this study, the use of silicon NAM (Non-Audible Murmur) microphone in automatic speech recognition is presented. NAM microphones are special acoustic sensors, which are attached behind the talker-s ear and can capture not only normal (audible) speech, but also very quietly uttered speech (non-audible murmur). As a result, NAM microphones can be applied in automatic speech recognition systems when privacy is desired in human-machine communication. Moreover, NAM microphones show robustness against noise and they might be used in special systems (speech recognition, speech conversion etc.) for sound-impaired people. Using a small amount of training data and adaptation approaches, 93.9% word accuracy was achieved for a 20k Japanese vocabulary dictation task. Non-audible murmur recognition in noisy environments is also investigated. In this study, further analysis of the NAM speech has been made using distance measures between hidden Markov model (HMM) pairs. It has been shown the reduced spectral space of NAM speech using a metric distance, however the location of the different phonemes of NAM are similar to the location of the phonemes of normal speech, and the NAM sounds are well discriminated. Promising results in using nonlinear features are also introduced, especially under noisy conditions.

Keywords: Speech recognition, unvoiced speech, nonlinear features, HMM distance measures

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Authors: Ru-Shuo Sheu, Han-Hsin Chou, Te-Shyang Tan

Abstract:

Considering a reservoir with periodic states and different cost functions with penalty, its release rules can be modeled as a periodic Markov decision process (PMDP). First, we prove that policy- iteration algorithm also works for the PMDP. Then, with policy- iteration algorithm, we obtain the optimal policies for a special aperiodic reservoir model with two cost functions under large penalty and give a discussion when the penalty is small.

Keywords: periodic Markov decision process, periodic state, policy-iteration algorithm.

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Authors: Chih-Cheng Kao, Hsin- Hua Chu

Abstract:

This paper mainly proposes an efficient modified particle swarm optimization (MPSO) method, to identify a slidercrank mechanism driven by a field-oriented PM synchronous motor. In system identification, we adopt the MPSO method to find parameters of the slider-crank mechanism. This new algorithm is added with “distance" term in the traditional PSO-s fitness function to avoid converging to a local optimum. It is found that the comparisons of numerical simulations and experimental results prove that the MPSO identification method for the slider-crank mechanism is feasible.

Keywords: Slider-crank mechanism, distance, systemidentification, modified particle swarm optimization.

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Authors: Yao-Hong Tsai

Abstract:

This paper presents a weighted approach to unconstrained iris recognition. In nowadays, commercial systems are usually characterized by strong acquisition constraints based on the subject’s cooperation. However, it is not always achievable for real scenarios in our daily life. Researchers have been focused on reducing these constraints and maintaining the performance of the system by new techniques at the same time. With large variation in the environment, there are two main improvements to develop the proposed iris recognition system. For solving extremely uneven lighting condition, statistic based illumination normalization is first used on eye region to increase the accuracy of iris feature. The detection of the iris image is based on Adaboost algorithm. Secondly, the weighted approach is designed by Gaussian functions according to the distance to the center of the iris. Furthermore, local binary pattern (LBP) histogram is then applied to texture classification with the weight. Experiment showed that the proposed system provided users a more flexible and feasible way to interact with the verification system through iris recognition.

Keywords: Authentication, iris recognition, Adaboost, local binary pattern.

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Authors: Padmanabhan Balasubramanian, C. Hari Narayanan

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This paper discusses a new, systematic approach to the synthesis of a NP-hard class of non-regenerative Boolean networks, described by FON[FOFF]={mi}[{Mi}], where for every mj[Mj]∈{mi}[{Mi}], there exists another mk[Mk]∈{mi}[{Mi}], such that their Hamming distance HD(mj, mk)=HD(Mj, Mk)=O(n), (where 'n' represents the number of distinct primary inputs). The method automatically ensures exact minimization for certain important selfdual functions with 2n-1 points in its one-set. The elements meant for grouping are determined from a newly proposed weighted incidence matrix. Then the binary value corresponding to the candidate pair is correlated with the proposed binary value matrix to enable direct synthesis. We recommend algebraic factorization operations as a post processing step to enable reduction in literal count. The algorithm can be implemented in any high level language and achieves best cost optimization for the problem dealt with, irrespective of the number of inputs. For other cases, the method is iterated to subsequently reduce it to a problem of O(n-1), O(n-2),.... and then solved. In addition, it leads to optimal results for problems exhibiting higher degree of adjacency, with a different interpretation of the heuristic, and the results are comparable with other methods. In terms of literal cost, at the technology independent stage, the circuits synthesized using our algorithm enabled net savings over AOI (AND-OR-Invert) logic, AND-EXOR logic (EXOR Sum-of- Products or ESOP forms) and AND-OR-EXOR logic by 45.57%, 41.78% and 41.78% respectively for the various problems. Circuit level simulations were performed for a wide variety of case studies at 3.3V and 2.5V supply to validate the performance of the proposed method and the quality of the resulting synthesized circuits at two different voltage corners. Power estimation was carried out for a 0.35micron TSMC CMOS process technology. In comparison with AOI logic, the proposed method enabled mean savings in power by 42.46%. With respect to AND-EXOR logic, the proposed method yielded power savings to the tune of 31.88%, while in comparison with AND-OR-EXOR level networks; average power savings of 33.23% was obtained.

Keywords: AOI logic, ESOP, AND-OR-EXOR, Incidencematrix, Hamming distance.

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Authors: Satyendra Nath Mandal, J. Pal Choudhury, Dilip De, S. R. Bhadra Chaudhuri

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The selection for plantation of a particular type of mustard plant depending on its productivity (pod yield) at the stage of maturity. The growth of mustard plant dependent on some parameters of that plant, these are shoot length, number of leaves, number of roots and roots length etc. As the plant is growing, some leaves may be fall down and some new leaves may come, so it can not gives the idea to develop the relationship with the seeds weight at mature stage of that plant. It is not possible to find the number of roots and root length of mustard plant at growing stage that will be harmful of this plant as roots goes deeper to deeper inside the land. Only the value of shoot length which increases in course of time can be measured at different time instances. Weather parameters are maximum and minimum humidity, rain fall, maximum and minimum temperature may effect the growth of the plant. The parameters of pollution, water, soil, distance and crop management may be dominant factors of growth of plant and its productivity. Considering all parameters, the growth of the plant is very uncertain, fuzzy environment can be considered for the prediction of shoot length at maturity of the plant. Fuzzification plays a greater role for fuzzification of data, which is based on certain membership functions. Here an effort has been made to fuzzify the original data based on gaussian function, triangular function, s-function, Trapezoidal and L –function. After that all fuzzified data are defuzzified to get normal form. Finally the error analysis (calculation of forecasting error and average error) indicates the membership function appropriate for fuzzification of data and use to predict the shoot length at maturity. The result is also verified using residual (Absolute Residual, Maximum of Absolute Residual, Mean Absolute Residual, Mean of Mean Absolute Residual, Median of Absolute Residual and Standard Deviation) analysis.

Keywords: Fuzzification, defuzzification, gaussian function, triangular function, trapezoidal function, s-function, , membership function, residual analysis.

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Authors: M. Reni Sagayaraj, S. Anand Gnana Selvam, R. Reynald Susainathan

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We analyze stochastic integrals associated with a mutation process. To be specific, we describe the cell population process and derive the differential equations for the joint generating functions for the number of mutants and their integrals in generating functions and their applications. We obtain first-order moments of the processes of the two-way mutation process in first-order moment structure of X (t) and Y (t) and the second-order moments of a one-way mutation process. In this paper, we obtain the limiting behaviour of the integrals in limiting distributions of X (t) and Y (t).

Keywords: Stochastic integrals, single–server queue model, catastrophes, busy period.

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Authors: Khalid Minaoui, Thierry Chonavel, Benayad Nsiri, Driss Aboutajdine

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This paper deals with efficient quadrature formulas involving functions that are observed only at fixed sampling points. The approach that we develop is derived from efficient continuous quadrature formulas, such as Gauss-Legendre or Clenshaw-Curtis quadrature. We select nodes at sampling positions that are as close as possible to those of the associated classical quadrature and we update quadrature weights accordingly. We supply the theoretical quadrature error formula for this new approach. We show on examples the potential gain of this approach.

Keywords: Gauss-Legendre, Clenshaw-Curtis, quadrature, Peano kernel, irregular sampling.

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