Search results for: the theory of fuzzy sets.

Authors: Guoyuan Qi , Yskandar Hamam, Barend Jacobus van Wyk, Shengzhi Du

Abstract:

The majority of existing predictors for time series are model-dependent and therefore require some prior knowledge for the identification of complex systems, usually involving system identification, extensive training, or online adaptation in the case of time-varying systems. Additionally, since a time series is usually generated by complex processes such as the stock market or other chaotic systems, identification, modeling or the online updating of parameters can be problematic. In this paper a model-free predictor (MFP) for a time series produced by an unknown nonlinear system or process is derived using tracking theory. An identical derivation of the MFP using the property of the Newton form of the interpolating polynomial is also presented. The MFP is able to accurately predict future values of a time series, is stable, has few tuning parameters and is desirable for engineering applications due to its simplicity, fast prediction speed and extremely low computational load. The performance of the proposed MFP is demonstrated using the prediction of the Dow Jones Industrial Average stock index.

Keywords: Forecast, model-free predictor, prediction, time series

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Authors: M.R. Isvandzibaei, M.R. Alinaghizadeh, A.H. Zaman

Abstract:

In the present work, study of the vibration of thin cylindrical shells made of a functionally gradient material (FGM) composed of stainless steel and nickel is presented. Material properties are graded in the thickness direction of the shell according to volume fraction power law distribution. The objective is to study the natural frequencies, the influence of constituent volume fractions and the effects of boundary conditions on the natural frequencies of the FG cylindrical shell. The study is carried out using third order shear deformation shell theory. The analysis is carried out using Hamilton's principle. The governing equations of motion of FG cylindrical shells are derived based on shear deformation theory. Results are presented on the frequency characteristics, influence of constituent volume fractions and the effects of clamped-free boundary conditions

Keywords: Vibration, FGM, cylindrical shell, Hamilton's principle, clamped supported.

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Authors: M. R. Aghaebrahimi, S. H. Zahiri, M. Amiri

Abstract:

In this paper a data miner based on the learning automata is proposed and is called LA-miner. The LA-miner extracts classification rules from data sets automatically. The proposed algorithm is established based on the function optimization using learning automata. The experimental results on three benchmarks indicate that the performance of the proposed LA-miner is comparable with (sometimes better than) the Ant-miner (a data miner algorithm based on the Ant Colony optimization algorithm) and CNZ (a well-known data mining algorithm for classification).

Keywords: Data mining, Learning automata, Classification rules, Knowledge discovery.

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Authors: Omid Mirmotahari, Yngvar Berg, Ahmad Habibizad Navin

Abstract:

Reversible logic is becoming more and more prominent as the technology sets higher demands on heat, power, scaling and stability. Reversible gates are able at any time to "undo" the current step or function. Multiple-valued logic has the advantage of transporting and evaluating higher bits each clock cycle than binary. Moreover, we demonstrate in this paper, combining these disciplines we can construct powerful multiple-valued reversible logic structures. In this paper a reversible block implemented by pseudo floatinggate can perform AD-function and a DA-function as its reverse application.

Keywords: Reversible logic, bi-directional, Pseudo floating-gate(PFG), multiple-valued logic (MVL).

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Authors: M. R.Isvandzibaei, A.Jahani

Abstract:

In the present work, study of the vibration of thin cylindrical shells made of a functionally gradient material (FGM) composed of stainless steel and nickel is presented. Material properties are graded in the thickness direction of the shell according to volume fraction power law distribution. The objective is to study the natural frequencies, the influence of constituent volume fractions and the effects of boundary conditions on the natural frequencies of the FG cylindrical shell. The study is carried out using third order shear deformation shell theory. The analysis is carried out using Hamilton's principle. The governing equations of motion of FG cylindrical shells are derived based on shear deformation theory. Results are presented on the frequency characteristics, influence of constituent volume fractions and the effects of free-free and clamped-clamped boundary conditions.

Keywords: Vibration, FGM, cylindrical shell, Hamilton's principle.

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Authors: T. Zalabsky, P. Bezousek, T. Shejbal

Abstract:

The paper describes new concept of the ribbon beam antenna for RFID technology. Antenna is located near to railway lines to monitor tags situated on trains. Antenna works at 2.45 GHz and it is fabricated by microstrip technology. Antenna contains two same mirrored parts having the same radiation patterns. Each part consists of three dielectric layers. The first layer has on one side radiation elements. The second layer is only for mechanical construction and it sets optimal electromagnetic field for each radiating elements. The third layer has on its top side a ground plane and on the bottom side a microstrip circuit used for individual radiation elements feeding.

Keywords: RFID, cosecant radiation pattern, ribbon beam, patch antenna, microstrip.

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Authors: K. N. Penna, J. P. English

Abstract:

The destruction of the Juukan Gorge rock shelters in 2020 has catalysed impetus within Australian society for a significant change in engagement with Indigenous Peoples, and the approach to Indigenous cultural heritage, both within the Pilbara region and more broadly across Australia. Culture-based and people-centred approaches are inherent to inclusive sustainable development and Free, Prior, Informed Consent, outcomes encouraged by international and local recommendations on the human rights and cultural heritage preservation of Indigenous peoples. In this paper, we present an interpretive model of an evolved process for mining project development, incorporating culture-based and people-centred approaches, based on the Theory U system change method. The evolved process advocates a change in organisational mindset and culture, and a comprehensive understanding of Indigenous Peoples’ culture and values, as the foundations for increasing their influence and achieving mutually beneficial developments.

Keywords: Indigenous Engagement, mining industry, culture-based approach, people-centred approach, Theory U.

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Authors: E. K. A. Ogunshile

Abstract:

This paper is aimed at creating an Automatic Java X-Machine testing tool for software development. The nature of software development is changing; thus, the type of software testing tools required is also changing. Software is growing increasingly complex and, in part due to commercial impetus for faster software releases with new features and value, increasingly in danger of containing faults. These faults can incur huge cost for software development organisations and users; Cambridge Judge Business School’s research estimated the cost of software bugs to the global economy is $312 billion. Beyond the cost, faster software development methodologies and increasing expectations on developers to become testers is driving demand for faster, automated, and effective tools to prevent potential faults as early as possible in the software development lifecycle. Using X-Machine theory, this paper will explore a new tool to address software complexity, changing expectations on developers, faster development pressures and methodologies, with a view to reducing the huge cost of fixing software bugs.

Keywords: Conformance testing, finite state machine, software testing, X-Machine.

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Authors: Sylvia Encheva

Abstract:

Students in high education are presented with new terms and concepts in nearly every lecture they attend. Many of them prefer Web-based self-tests for evaluation of their concepts understanding since they can use those tests independently of tutors- working hours and thus avoid the necessity of being in a particular place at a particular time. There is a large number of multiple-choice tests in almost every subject designed to contribute to higher level learning or discover misconceptions. Every single test provides immediate feedback to a student about the outcome of that test. In some cases a supporting system displays an overall score in case a test is taken several times by a student. What we still find missing is how to secure delivering of personalized feedback to a user while taking into consideration the user-s progress. The present work is motivated to throw some light on that question.

Keywords: Clustering, rough sets, many valued logic, predictions

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Authors: Al-Amin Bhuiyan, Chang Hong Liu

Abstract:

This paper addresses the development of an intelligent vision system for human-robot interaction. The two novel contributions of this paper are 1) Detection of human faces and 2) Localizing the eye. The method is based on visual attributes of human skin colors and geometrical analysis of face skeleton. This paper introduces a spatial domain filtering method named ?Fuzzily skewed filter' which incorporates Fuzzy rules for deciding the gray level of pixels in the image in their neighborhoods and takes advantages of both the median and averaging filters. The effectiveness of the method has been justified over implementing the eye tracking commands to an entertainment robot, named ''AIBO''.

Keywords: Fuzzily skewed filter, human-robot interface, rmscontrast, skin color segmentation.

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Authors: Zhifeng Kong

Abstract:

Over-parameterized neural networks have attracted a great deal of attention in recent deep learning theory research, as they challenge the classic perspective of over-fitting when the model has excessive parameters and have gained empirical success in various settings. While a number of theoretical works have been presented to demystify properties of such models, the convergence properties of such models are still far from being thoroughly understood. In this work, we study the convergence properties of training two-hidden-layer partially over-parameterized fully connected networks with the Rectified Linear Unit activation via gradient descent. To our knowledge, this is the first theoretical work to understand convergence properties of deep over-parameterized networks without the equally-wide-hidden-layer assumption and other unrealistic assumptions. We provide a probabilistic lower bound of the widths of hidden layers and proved linear convergence rate of gradient descent. We also conducted experiments on synthetic and real-world datasets to validate our theory.

Keywords: Over-parameterization, Rectified Linear Units (ReLU), convergence, gradient descent, neural networks.

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Authors: Morteza Moazami-Goudarzi, Mohammad. H. Moradi

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In this paper we are to find the optimum multiwavelet for compression of electrocardiogram (ECG) signals. At present, it is not well known which multiwavelet is the best choice for optimum compression of ECG. In this work, we examine different multiwavelets on 24 sets of ECG data with entirely different characteristics, selected from MITBIH database. For assessing the functionality of the different multiwavelets in compressing ECG signals, in addition to known factors such as Compression Ratio (CR), Percent Root Difference (PRD), Distortion (D), Root Mean Square Error (RMSE) in compression literature, we also employed the Cross Correlation (CC) criterion for studying the morphological relations between the reconstructed and the original ECG signal and Signal to reconstruction Noise Ratio (SNR). The simulation results show that the cardbal2 by the means of identity (Id) prefiltering method to be the best effective transformation.

Keywords: ECG compression, Multiwavelet, Prefiltering.

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Authors: Ayman M. Mansour

Abstract:

In this paper, we propose an intelligent system that is used for monitoring the health conditions of patients. Monitoring the health condition of patients is a complex problem that involves different medical units and requires continuous monitoring especially in rural areas because of inadequate number of available specialized physicians. The proposed system will improve patient care and drive costs down comparing to the existing system in Jordan. The proposed system will be the start point to faster and improve the communication between different units in the health system in Jordan. Connecting patients and their physicians beyond hospital doors regarding their geographical area is an important issue in developing the health system in Jordan. The ability of making medical decisions, the quality of medical is expected to be improved.

Keywords: GSM, SMS, Patient, Monitoring system, Fuzzy Logic, Multi-agent system.

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Authors: C. C. D. Kulathilake, M. Jayatilake, T. Takahashi

Abstract:

The myocardium is composed of specialized muscle which relies mainly on fatty acid and sugar metabolism and it is widely contribute to the heart functioning. The changes of the cardiac energy-producing system during heart failure have been proved using autoradiography techniques. This study focused on evaluating sugar and fatty acid metabolism in myocardium as cardiac energy getting system using heart-accumulated radiopharmaceuticals. Two sets of autoradiographs of heart cross sections of Lewis male rats were analyzed and the time- accumulation curve obtained with use of the MATLAB image processing software to evaluate fatty acid and sugar metabolic functions.

Keywords: Autoradiographs, fatty acid, radiopharmaceuticals and sugar.

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Authors: XhevrieMamaqi

Abstract:

Organization capacity learning is a process referring to the sum total of individual and collective learning through training programs, experience and experimentation, among others. Today, in-business ongoing training is one of the most important strategies for human capital development and it is crucial to sustain and improve workers’ knowledge and skills. Many organizations, firms and business are adopting a strategy of continuous learning, encouraging employees to learn new skills continually to be innovative and to try new processes and work in order to achieve a competitive advantage and superior business results. This paper uses the Resource Based View and Capacities (RBV) approach to construct a hypothetical relationships model between training and business results. The test of the model is applied on transversal data. A sample of 266 business of Spanish sector service has been selected. A Structural Equation Model (SEM) is used to estimate the relationship between ongoing training, represented by two latent dimension denominated Human and Social Capital resources and economic business results. The coefficients estimated have shown the efficient of some training aspectsexplaining the variation in business results.

Keywords: Business results, Human and Social Capital resources, training, RBV Theory, SEM.

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Authors: Varun Joshi, Manish K. Rathod

Abstract:

The latent heat thermal energy storage system is a thrust area of research due to exuberant thermal energy storage potential. The thermal performance of PCM is significantly augmented by installation of the high thermal conductivity fins. The objective of the present study is to obtain optimum size and location of the fins to enhance diffusion heat transfer without altering overall melting time. Hence, the constructal theory is employed to eliminate, resize, and re-position the fins. A numerical code based on conjugate heat transfer coupled enthalpy porosity approached is developed to solve Navier-Stoke and energy equation.The numerical results show that the constructal fin design has enhanced the thermal performance along with the increase in the overall volume of PCM when compared to conventional. The overall volume of PCM is found to be increased by half of total of volume of fins. The elimination and repositioning the fins at high temperature gradient from low temperature gradient is found to be vital.

Keywords: Constructal theory, enthalpy porosity approach, phase change materials, fins.

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Authors: I. Khutsishvili, G. Sirbiladze, B. Ghvaberidze

Abstract:

This work proposes a fuzzy methodology to support the investment decisions. While choosing among competitive investment projects, the methodology makes ranking of projects using the new aggregation OWA operator – AsPOWA, presented in the environment of possibility uncertainty. For numerical evaluation of the weighting vector associated with the AsPOWA operator the mathematical programming problem is constructed. On the basis of the AsPOWA operator the projects’ group ranking maximum criteria is constructed. The methodology also allows making the most profitable investments into several of the project using the method developed by the authors for discrete possibilistic bicriteria problems. The article provides an example of the investment decision-making that explains the work of the proposed methodology.

Keywords: Expert evaluations, investment decision making, OWA operator, possibility uncertainty.

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Authors: I. Bikit, S. Forkapic, J. Nikolov, N. Todorovic, D. Mrdja

Abstract:

During the year 1999, Serbia (ex Yugoslavia) and their northern province, Vojvodina, has been bombarded. Because of that general public believe is that this region was contaminated by depleted uranium and that there is a potential contaminant of agricultural products due to soil radioactivity. This paper presents the repeated analysis of agricultural soil samples in Vojvodina. The same investigation was carried out during the year 2001, and it was concluded that, based on the gamma-spectrometric analysis of 50 soil samples taken from the region of Vojvodina, there haven-t been registered any increase of radioactivity that could endanger the food production. We continue with the monitoring of this region. The comparison between those two sets of results is presented.

Keywords: gamma spectrometry analysis, radioactivity of theagricultural soil.

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Authors: K.L. Verma

Abstract:

Analysis for the generalized thermoelastic Lamb waves, which propagates in anisotropic thin plates in generalized thermoelasticity, is presented employing normal mode expansion method. The displacement and temperature fields are expressed by a summation of the symmetric and antisymmetric thermoelastic modes in the surface thermal stresses and thermal gradient free orthotropic plate, therefore the theory is particularly appropriate for waveform analyses of Lamb waves in thin anisotropic plates. The transient waveforms excited by the thermoelastic expansion are analyzed for an orthotropic thin plate. The obtained results show that the theory provides a quantitative analysis to characterize anisotropic thermoelastic stiffness properties of plates by wave detection. Finally numerical calculations have been presented for a NaF crystal, and the dispersion curves for the lowest modes of the symmetric and antisymmetric vibrations are represented graphically at different values of thermal relaxation time. However, the methods can be used for other materials as well

Keywords: Anisotropic, dispersion, frequency, normal, thermoelasticity, wave modes.

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Authors: A. Abdikian

Abstract:

Propagation of nonlinear acoustic wave in dense electron-positron (e-p) plasmas in the presence of an external magnetic field and stationary ions (to neutralize the plasma background) is studied. By means of the quantum hydrodynamics model and applying the reductive perturbation method, the Zakharov-Kuznetsov equation is derived. Using the bifurcation theory of planar dynamical systems, the compressive structure of electrostatic solitary wave and periodic travelling waves is found. The numerical results show how the ion density ratio, the ion cyclotron frequency, and the direction cosines of the wave vector affect the nonlinear electrostatic travelling waves. The obtained results may be useful to better understand the obliquely nonlinear electrostatic travelling wave of small amplitude localized structures in dense magnetized quantum e-p plasmas and may be applicable to study the particle and energy transport mechanism in compact stars such as the interior of massive white dwarfs etc.

Keywords: Bifurcation theory, magnetized electron-positron plasma, phase portrait, the Zakharov-Kuznetsov equation.

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Authors: H. P. Kerry

Abstract:

Drone technology has become a significant discourse in a nation’s national security, while this technology could constitute a danger to national security on the one hand, on the other hand, it is used in developed and developing countries for border security, and in some cases, for protection of security agents and migrants. In the case of Nigeria, drones are used by the military to monitor and tighten security around the borders. However, terrorist groups have devised a means to utilize the technology to their advantage. Therefore, the potential danger in the widespread proliferation of this technology has become a myriad of risks. The research on the effects of cross-border use of drones in Nigerian national security looks at the negative and positive consequences of using drone technology. The study employs the use of interviews and relevant documents to obtain data while the study applied the Just War theory to justify the reason why countries use force; it further buttresses the points with what the realist theory thinks about the use of force. In conclusion, the paper recommends that the Nigerian government through the National Assembly should pass a bill for the establishment of a law that will guide the use of armed and unarmed drones in Nigeria enforced by the Nigeria Civil Aviation Authority and the office of the National Security Adviser.

Keywords: Armed drones, cross-border, drones, national security.

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Authors: Serge B. Provost, Min Jiang

Abstract:

The density estimates considered in this paper comprise a base density and an adjustment component consisting of a linear combination of orthogonal polynomials. It is shown that, in the context of density approximation, the coefficients of the linear combination can be determined either from a moment-matching technique or a weighted least-squares approach. A kernel representation of the corresponding density estimates is obtained. Additionally, two refinements of the Kronmal-Tarter stopping criterion are proposed for determining the degree of the polynomial adjustment. By way of illustration, the density estimation methodology advocated herein is applied to two data sets.

Keywords: kernel density estimation, orthogonal polynomials, moment-based methodologies, density approximation.

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Authors: Encarnación Álvarez, Rosa M. García-Fernández, Francisco J. Blanco-Encomienda, Juan F. Muñoz

Abstract:

The European Union Survey on Income and Living Conditions (EU-SILC) is a popular survey which provides information on income, poverty, social exclusion and living conditions of households and individuals in the European Union. The EU-SILC contains variables which may contain outliers. The presence of outliers can have an impact on the measures and indicators used by the EU-SILC. In this paper, we used data sets from various countries to analyze the presence of outliers. In addition, we obtain some indicators after removing these outliers, and a comparison between both situations can be observed. Finally, some conclusions are obtained.

Keywords: Headcount index, poverty line, risk of poverty, skewness coefficient.

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Authors: D. K. Tiwari, Mukesh Kumar Awasthi, G. S. Agrawal

Abstract:

The effect of an axial electric field on the capillary instability of a cylindrical interface in the presence of heat and mass transfer has been investigated using viscous potential flow theory. In viscous potential flow, the viscous term in Navier-Stokes equation vanishes as vorticity is zero but viscosity is not zero. Viscosity enters through normal stress balance in the viscous potential flow theory and tangential stresses are not considered. A dispersion relation that accounts for the growth of axisymmetric waves is derived and stability is discussed theoretically as well as numerically. Stability criterion is given by critical value of applied electric field as well as critical wave number. Various graphs have been drawn to show the effect of various physical parameters such as electric field, heat transfer capillary number, conductivity ratio, permittivity ratio on the stability of the system. It has been observed that the axial electric field and heat and mass transfer both have stabilizing effect on the stability of the system.

Keywords: Capillary instability, Viscous potential flow, Heat and mass transfer, Axial electric field.

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Authors: Chanchai Supaartagorn

Abstract:

Structured Query Language (SQL) is the standard de facto language to access and manipulate data in a relational database. Although SQL is a language that is simple and powerful, most novice users will have trouble with SQL syntax. Thus, we are presenting SQL generator tool which is capable of translating actions and displaying SQL commands and data sets simultaneously. The tool was developed based on Model-View-Controller (MVC) pattern. The MVC pattern is a widely used software design pattern that enforces the separation between the input, processing, and output of an application. Developers take full advantage of it to reduce the complexity in architectural design and to increase flexibility and reuse of code. In addition, we use White-Box testing for the code verification in the Model module.

Keywords: MVC, relational database, SQL, White-Box testing.

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Authors: Djamal Hamadi, Sifeddine Abderrahmani, Toufik Maalem, Oussama Temami

Abstract:

In recent years many finite elements have been developed for plate bending analysis. The formulated elements are based on the strain based approach. This approach leads to the representation of the displacements by higher order polynomial terms without the need for the introduction of additional internal and unnecessary degrees of freedom. Good convergence can also be obtained when the results are compared with those obtained from the corresponding displacement based elements, having the same total number of degrees of freedom. Furthermore, the plate bending elements are free from any shear locking since they converge to the Kirchhoff solution for thin plates contrarily for the corresponding displacement based elements. In this paper the efficiency of the strain based approach compared to well known displacement formulation is presented. The results obtained by a new formulated plate bending element based on the strain approach and Kirchhoff theory are compared with some others elements. The good convergence of the new formulated element is confirmed.

Keywords: Displacement fields, finite elements, plate bending, Kirchhoff theory, strain based approach.

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Authors: M. Reza Bagerzadeh Karimi, M. Mahdi Bagerzadeh Karimi

Abstract:

In the present paper, active control system is used in different heights of the building and the most effective part was studied where the active control system is applied. The mathematical model of the building is established in MATLAB and in order to active control the system FLC method was used. Three different locations of the building are chosen to apply active control system, namely at the lowest story, the middle height of the building, and at the highest point of the building with TMD system. The equation of motion was written for high rise building and it was solved by statespace method. Also passive control was used with Tuned Mass Damper (TMD) at the top floor of the building to show the robustness of FLC method when compared with passive control system.

Keywords: Fuzzy Logic Controller (FLC), Tuned Mass Damper(TMD), Active control, passive control

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Authors: R. K. Saxena, Ravi Saxena

Abstract:

In view of their importance and usefulness in reliability theory and probability distributions, several generalizations of the inverse Gaussian distribution and the Krtzel function are investigated in recent years. This has motivated the authors to introduce and study a new generalization of the inverse Gaussian distribution and the Krtzel function associated with a product of a Bessel function of the third kind )(zKQ and a Z - Fox-Wright generalized hyper geometric function introduced in this paper. The introduced function turns out to be a unified gamma-type function. Its incomplete forms are also discussed. Several properties of this gamma-type function are obtained. By means of this generalized function, we introduce a generalization of inverse Gaussian distribution, which is useful in reliability analysis, diffusion processes, and radio techniques etc. The inverse Gaussian distribution thus introduced also provides a generalization of the Krtzel function. Some basic statistical functions associated with this probability density function, such as moments, the Mellin transform, the moment generating function, the hazard rate function, and the mean residue life function are also obtained.KeywordsFox-Wright function, Inverse Gaussian distribution, Krtzel function & Bessel function of the third kind.

Keywords: Fox-Wright function, Inverse Gaussian distribution, Krtzel function & Bessel function of the third kind.

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Authors: Israa Sh. Tawfic, Sema Koc Kayhan

Abstract:

Given a large sparse signal, great wishes are to reconstruct the signal precisely and accurately from lease number of measurements as possible as it could. Although this seems possible by theory, the difficulty is in built an algorithm to perform the accuracy and efficiency of reconstructing. This paper proposes a new proved method to reconstruct sparse signal depend on using new method called Least Support Matching Pursuit (LS-OMP) merge it with the theory of Partial Knowing Support (PSK) given new method called Partially Knowing of Least Support Orthogonal Matching Pursuit (PKLS-OMP). The new methods depend on the greedy algorithm to compute the support which depends on the number of iterations. So to make it faster, the PKLS-OMP adds the idea of partial knowing support of its algorithm. It shows the efficiency, simplicity, and accuracy to get back the original signal if the sampling matrix satisfies the Restricted Isometry Property (RIP). Simulation results also show that it outperforms many algorithms especially for compressible signals.

Keywords: Compressed sensing, Lest Support Orthogonal Matching Pursuit, Partial Knowing Support, Restricted isometry property, signal reconstruction.

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Authors: Mohammad Jafarifar

Abstract:

This paper presents a speed estimation scheme based on second-order sliding-mode Super Twisting Algorithm (STA) and Model Reference Adaptive System (MRAS) estimation theory for Sensorless control of multiphase induction machine. A stator current observer is designed based on the STA, which is utilized to take the place of the reference voltage model of the standard MRAS algorithm. The observer is insensitive to the variation of rotor resistance and magnetizing inductance when the states arrive at the sliding mode. Derivatives of rotor flux are obtained and designed as the state of MRAS, thus eliminating the integration. Compared with the first-order sliding-mode speed estimator, the proposed scheme makes full use of the auxiliary sliding-mode surface, thus alleviating the chattering behavior without increasing the complexity. Simulation results show the robustness and effectiveness of the proposed scheme.

Keywords: Multiphase induction machine, field oriented control, sliding mode, super twisting algorithm, MRAS algorithm.

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