Search results for: spectra graph theory.

Authors: Malika Yaici, Kamel Hariche, Tim Clarke

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The relationship between eigenstructure (eigenvalues and eigenvectors) and latent structure (latent roots and latent vectors) is established. In control theory eigenstructure is associated with the state space description of a dynamic multi-variable system and a latent structure is associated with its matrix fraction description. Beginning with block controller and block observer state space forms and moving on to any general state space form, we develop the identities that relate eigenvectors and latent vectors in either direction. Numerical examples illustrate this result. A brief discussion of the potential of these identities in linear control system design follows. Additionally, we present a consequent result: a quick and easy method to solve the polynomial eigenvalue problem for regular matrix polynomials.

Keywords: Eigenvalues/Eigenvectors, Latent values/vectors, Matrix fraction description, State space description.

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Authors: E. Zippelius

Abstract:

Urban design aims to provide a stage for public life that, when once brought to life, is right away subject to subtle but continuous transformation. This paper explores such transformations and searches for ways how public life can be reinforced in the case of a housing settlement for the displaced in Nicosia, Cyprus. First, a sound basis of theoretical knowledge is established through literature review, notably the theory of the Production of Space by Henri Lefebvre, exploring its potential and defining key criteria for the following empirical analysis. The analysis is pinpointing the differences between spatial practice, representation of space and spaces of representation as well as their interaction, alliance, or even conflict. In doing so uncertainties, chances and challenges are unraveled that will be consequently linked to practice and action and lead to the formulation of a design strategy. A strategy, though, that does not long for achieving an absolute, finite certainty but understands the three dimensions of space formulated by Lefebvre as equal and space as continuously produced, hence, unfinished.

Keywords: Production of space, public space, urban life, urban transformation.

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Authors: Yoojin Chung

Abstract:

Compare to western cultures, women who smoke in Korea are not tolerated. Korean people are prejudiced against women smoking. In spite of the relative prevalence of sexual equality in South Korea, women too often feel obliged to confine their smoking to only a few public spaces, such as designated smoking rooms, coffee shops or pubs. Korean Confucianism classifies people according to gender and social status. According to Confucian culture, cigarettes convey clear social meanings as well as reinforcing status, age and gender, beyond personal preferences. For these reasons, the significant of people smoking in Korea varies according to their gender. This study will determine reasons for the ongoing sexual discrimination against female Korean smokers thorough analyzing Korean films. Since film is a medium reflects social phenomenon. Roland Barthes- Mythology Theory will be used to analyze films.

Keywords: Korean films, Mythology, Sexual discrimination, Women Smoking

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Authors: Elizabeth Simão Carvalho, Marcirio Silveira Chaves

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The information visualization is still a knowledge field that lacks from a solid theory to support it and there is a myriad of existing methodologies and taxonomies that can be combined and adopted as guidelines. In this context, it is necessary to pre-evaluate as much as possible all the assumptions that are considered for its design and development. We present an exploratory study (n = 123) to detect the graphical preferences of travelers using accommodation portals of Web 2.0 (e.g. tripadvisor.com). We took into account some of the most relevant ground rules applied in the field to map visually data and design end-user interaction. Moreover, the evaluation process was completely data visualization oriented. We found out that people tend to refuse more advanced types of visualization and that a hybrid combination between radial graphs and stacked bars should be explored. In sum, this paper introduces new findings about the visual model and the cognitive response of users of accommodation booking websites.

Keywords: Information visualization, Data visualization, Visualization evaluation, Online reviews, Booking portal, Hotel booking.

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Authors: Yingyi Zhou, Tohru Kawabe

Abstract:

With the spread of EVs (electric Vehicles), the ride comfort has been gaining a lot of attention. The influence of the lateral acceleration is important for the improvement of ride comfort of EVs as well as the longitudinal acceleration, especially upon turning of the vehicle. Therefore, this paper proposes a practical optimal speed control method to greatly improve the ride comfort in the vehicle turning situation. For consturcting this method, effective criteria that can appropriately evaluate deterioration of ride comfort is derived. The method can reduce the influence of both the longitudinal and the lateral speed changes for providing a confortable ride. From several simulation results, we can see the fact that the method can prevent aggravation of the ride comfort by suppressing the influence of longitudinal speed change in the turning situation. Hence, the effectiveness of the method is recognized.

Keywords: Electric vehicle, speed control, ride comfort, optimal control theory, driving support system.

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Authors: Anmari H. Viljamaa, Elina M. Varamäki

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In this study, we compare the profiles of transitory hybrid entrepreneurs and persistent hybrid entrepreneurs to determine how they differ. Hybrid entrepreneurs (HEs) represent a significant share of entrepreneurial activity yet little is known about them. We define HEs as individuals who are active as entrepreneurs but do no support themselves primarily by their enterprise. Persistent HEs (PHEs) are not planning to transition to fulltime entrepreneurship whereas transitory HEs (THEs) consider it probable. Our results show that THEs and PHEs are quite similar in background. THEs are more interested in increasing their turnover than PHEs, as expected, but also emphasize self-fulfillment as a motive for entrepreneurship more than PHEs. The clearest differences between THEs and PHEs are found in their views on how well their immediate circle supports full-time entrepreneurship, and their views of their own entrepreneurial abilities and the market potential of their firm. Our results support earlier arguments that hybrids should be considered separately in research on entrepreneurial entry and self-employment.

Keywords: Hybrid entrepreneurship, part-time entrepreneurship, self-employment, Theory of Planned Behavior.

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Authors: A. Puras Trueba, J. R. Llata García

Abstract:

A nonlinear optimal controller with a fuzzy gain scheduler has been designed and applied to a Line-Of-Sight (LOS) stabilization system. Use of Linear Quadratic Regulator (LQR) theory is an optimal and simple manner of solving many control engineering problems. However, this method cannot be utilized directly for multigimbal LOS systems since they are nonlinear in nature. To adapt LQ controllers to nonlinear systems at least a linearization of the model plant is required. When the linearized model is only valid within the vicinity of an operating point a gain scheduler is required. Therefore, a Takagi-Sugeno Fuzzy Inference System gain scheduler has been implemented, which keeps the asymptotic stability performance provided by the optimal feedback gain approach. The simulation results illustrate that the proposed controller is capable of overcoming disturbances and maintaining a satisfactory tracking performance.

Keywords: Fuzzy Gain-Scheduling, Gimbal, Line-Of-SightStabilization, LQR, Optimal Control

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Authors: Ümit Morsünbül

Abstract:

Attachment theory focuses on the bond that develops between child and caretaker and the consequences that this bond has on the childs future relationships. Adolescents attempt to define their identity by experiencing various risky behaviors. The first aim of the study was whether risk taking behavior differs according to attachment styles. The second was to examine risk taking behavior differences according to gender. The third aim of this study was to examine attachment X gender interaction effect for risk taking behavior. And final was to investigate attachment styles differences according to gender. Data were collected from 218 participants (114 female and 104 male) who are university students. The results of this study showed that attachment styles differentiated by risk taking behavior and males had higher risk taking score than females. It was also found out that there was significant attachment X gender interaction effect for risk taking behavior. And finally, the results showed that attachment styles differentiated according to gender.KeywordsAttachment style, risk taking

Keywords: Attachment style, risk taking

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Authors: Miyoun Won, Youngkyung Choi

Abstract:

In the meantime, there were lots of hardware solutions like products or urban facilities for crime prevention in the public design area. Meanwhile, people have growing interest in public design so by making a village; community design in public design is getting active by the society. The system for crime prevention is actively done by the citizens who created the community. Regarding the social situation, in this project, we saw it as a kind of community design practices and researched about 'how does community design influence Crime prevention?' The purpose of this study is to propose the community design as a way of preventing the crime in the city. First, we found out about the definition, elements and methods of community design by reviewing the theory. And then, this study analyzed the case that was enforced in Seoul and organize the elements and methods of community design. This study can be refer to Public Design based on civil participation and make the community design area contribute to expand the way of solving social problems.

Keywords: Public Design, Sustainable Community Design, Crime Prevention, Participatory Design.

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Authors: M. Asato, C. Liu, N. Fujima, T. Hoshino, Y. Chen, T. Mohri

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We study the temperature dependence of the interaction energies (IEs) of X (=Ru, Rh) impurities in Pd, due to the Fermi-Dirac (FD) distribution and the thermal vibration effect by the Debye-Grüneisen model. The n-body (n=2~4) IEs among X impurities in Pd, being used to calculate the internal energies in the free energies of the Pd-rich PdX alloys, are determined uniquely and successively from the lower-order to higher-order, by the full-potential Korringa-Kohn-Rostoker Green’s function method (FPKKR), combined with the generalized gradient approximation in the density functional theory. We found that the temperature dependence of IEs due to the FD distribution, being usually neglected, is very important to reproduce the X-concentration dependence of the observed solvus temperatures of the Pd-rich PdX (X=Ru, Rh) alloys.

Keywords: Full-potential KKR-Green’s function method, Fermi-Dirac distribution, GGA, phase diagram of Pd-rich PdX (X=Ru, Rh) alloys, thermal vibration effect.

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Authors: Ena Bhattacharyya

Abstract:

The notion of communicative competence has been deemed fuzzy in communication studies. This fuzziness has led to tensions among engineers across tenures in interpreting what constitutes communicative competence. The study seeks to investigate novice and professional engineers- understanding of the said notion in terms of two main elements of communicative competence: linguistic and rhetorical competence. Novice engineers are final year engineering students, whilst professional engineers represent engineers who have at least 5 years working experience. Novice and professional engineers were interviewed to gauge their perceptions on linguistic and rhetorical features deemed necessary to enhance communicative competence for the profession. Both groups indicated awareness and differences on the importance of the sub-sets of communicative competence, namely, rhetorical explanatory competence, linguistic oral immediacy competence, technical competence and meta-cognitive competence. Such differences, a possible attribute of the learning theory, inadvertently indicate sublime differences in the way novice and professional engineers perceive communicative competence.

Keywords: Communicative competence, technical oral presentation, linguistic competence, rhetorical competence.

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Authors: Mahmoud Zarrini, R. N. Pralhad

Abstract:

We estimate snow velocity and snow drift density on hilly terrain under the assumption that the drifting snow mass can be represented using a micro-continuum approach (i.e. using a nonclassical mechanics approach assuming a class of fluids for which basic equations of mass, momentum and energy have been derived). In our model, the theory of coupled stress fluids proposed by Stokes [1] has been employed for the computation of flow parameters. Analyses of bulk drift velocity, drift density, drift transport and mass transport of snow particles have been carried out and computations made, considering various parametric effects. Results are compared with those of classical mechanics (logarithmic wind profile). The results indicate that particle size affects the flow characteristics significantly.

Keywords: Snow velocity, snow drift density, mass transport of snow particles, snow avalanche.

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Authors: Sung-Hun Lee, Yun-Seong Lee, Jin-O Kim

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Reliability Centered Maintenance(RCM) is one of most widely used methods in the modern power system to schedule a maintenance cycle and determine the priority of inspection. In order to apply the RCM method to the Smart Grid, a precedence study for the new structure of rearranged system should be performed due to introduction of additional installation such as renewable and sustainable energy resources, energy storage devices and advanced metering infrastructure. This paper proposes a new method to evaluate the priority of maintenance and inspection of the power system facilities in the Smart Grid using the Risk Priority Number. In order to calculate that risk index, it is required that the reliability block diagram should be analyzed for the Smart Grid system. Finally, the feasible technical method is discussed to estimate the risk potential as part of the RCM procedure.

Keywords: Expert System, FMECA, Fuzzy Theory, Reliability Centered Maintenance, Risk Priority Number

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Authors: Defne Akay, Bekir S. Kandemir

Abstract:

In this paper, we investigate the low-lying energy levels of the two-dimensional parabolic graphene quantum dots (GQDs) in the presence of topological defects with long range Coulomb impurity and subjected to an external uniform magnetic field. The low-lying energy levels of the system are obtained within the framework of the perturbation theory. We theoretically demonstrate that a valley splitting can be controlled by geometrical parameters of the graphene quantum dots and/or by tuning a uniform magnetic field, as well as topological defects. It is found that, for parabolic graphene dots, the valley splitting occurs due to the introduction of spatial confinement. The corresponding splitting is enhanced by the introduction of a uniform magnetic field and it increases by increasing the angle of the cone in subcritical regime.

Keywords: Coulomb impurity, graphene cones, graphene quantum dots, topological defects.

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Authors: Ju-Hong Lee, Yi-Lin Shieh

Abstract:

The paper deals with the minimax design of two-channel linear-phase (LP) quadrature mirror filter (QMF) banks using infinite impulse response (IIR) digital all-pass filters (DAFs). Based on the theory of two-channel QMF banks using two IIR DAFs, the design problem is appropriately formulated to result in an appropriate Chebyshev approximation for the desired group delay responses of the IIR DAFs and the magnitude response of the low-pass analysis filter. Through a frequency sampling and iterative approximation method, the design problem can be solved by utilizing a weighted least squares approach. The resulting two-channel QMF banks can possess approximately LP response without magnitude distortion. Simulation results are presented for illustration and comparison.

Keywords: Chebyshev approximation, Digital All-Pass Filter, Quadrature Mirror Filter, Weighted Least Squares.

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Authors: M. R. Aghaebrahimi, H. Khorashadi Zadeh

Abstract:

This paper presents a new approach for busbar protection with stable operation of current transformer during saturation, using fuzzy neuro and symmetrical components theory. This technique uses symmetrical components of current signals to learn the hidden relationship existing in the input patterns. Simulation studies are preformed and the influence of changing system parameters such as inception fault and source impedance is studied. Details of the design procedure and the results of performance studies with the proposed relay are given in the paper. An analysis of the performance of the proposed technique during ct saturation conditions is presented. The performance of the technique was investigated for a variety of operating conditions and for several busbar configurations. Data generated by EMTDC simulations of model power systems were used in the investigations. The results indicate that the proposed technique is stable during ct saturation conditions.

Keywords: Busbar protection, fuzzy neuro, Ct saturation.

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Authors: A.R.Tahmasebi Birgani, M.Hosseinjani Zamenjani, M.R.Isvandzibaei

Abstract:

Study is on the vibration of thin cylindrical shells made of a functionally gradient material (FGM) composed of stainless steel and nickel is presented. The effects of the FGM configuration are studied by studying the frequencies of FG cylindrical shells. In this case FG cylindrical shell has Nickel on its inner surface and stainless steel on its outer surface. The study is carried out based on third order shear deformation shell theory. The objective is to study the natural frequencies, the influence of constituent volume fractions and the effects of configurations of the constituent materials on the frequencies. The properties are graded in the thickness direction according to the volume fraction power-law distribution. Results are presented on the frequency characteristics, the influence of the constituent various volume fractions on the frequencies.

Keywords: Nickel, Stainless Steel, Cylindrical shell.

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Authors: M. Linek, P. Nita

Abstract:

In the previous airfield construction industry, pavements made of reinforced concrete have been used very rarely; however, the necessity to use this type of pavements in an emergency situations justifies the need reference to this issue. The paper concerns the problem of airfield pavement dimensioning made of reinforced concrete and the evaluation of selected dimensioning methods of reinforced concrete slabs intended for airfield pavements. Analysis of slabs dimensioning, according to classical method of limit states has been performed and it has been compared to results obtained in case of methods complying with Eurocode 2 guidelines. Basis of an analysis was a concrete slab of class C35/45 with reinforcement, located in tension zone. Steel bars of 16.0 mm have been used as slab reinforcement. According to comparative analysis of obtained results, conclusions were reached regarding application legitimacy of the discussed methods and their design advantages.

Keywords: Reinforced concrete, cement concrete, airport pavements.

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Authors: Guangyu Liu

Abstract:

In the last decade, energy based control theory has undergone a significant breakthrough in dealing with underactated mechanical systems with two successful and similar tools, controlled Lagrangians and controlled Hamiltanians (IDA-PBC). However, because of the complexity of these tools, successful case studies are lacking, in particular, MIMO cases. The seminal theoretical paper of controlled Lagrangians proposed by Bloch and his colleagues presented a benchmark example–a 4 d.o.f underactuated pendulum on a cart but a detailed and completed design is neglected. To compensate this ignorance, the note revisit their design idea by addressing explicit control functions for a similar device motivated by a vector thrust body hovering in the air. To the best of our knowledge, this system is the first MIMO, underactuated example that is stabilized by using energy based tools at the courtesy of the original design idea. Some observations are given based on computer simulation.

Keywords: Controlled Lagrangian, Energy Shaping, Spherical Inverted Pendulum, Controlled Hamiltonian.

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Authors: Tinatin Kurdghelashvili

Abstract:

The paper deals with the usage of speech acts and politeness strategies in an EFL classroom in Georgia (Rep of). It explores the students’ and the teachers’ practice of the politeness strategies and the speech acts of apology, thanking, request, compliment / encouragement, command, agreeing / disagreeing, addressing and code switching. The research method includes observation as well as a questionnaire. The target group involves the students from Georgian public schools and two certified, experienced local English teachers. The analysis is based on Searle’s Speech Act Theory and Brown and Levinson’s politeness strategies. The findings show that the students have certain knowledge regarding politeness yet they fail to apply them in English communication. In addition, most of the speech acts from the classroom interaction are used by the teachers and not the students. Thereby, it is suggested that teachers should cultivate the students’ communicative competence and attempt to give them opportunities to practise more English speech acts than they do today.

Keywords: English as a foreign language, Georgia, politeness principles, speech acts.

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Authors: S. C. Kattimani

Abstract:

This article deals with the analysis of active constrained layer damping (ACLD) of smart multiferroic or magneto-electro-elastic doubly curved shells. The kinematics of deformations of the multiferroic doubly curved shell is described by a layer-wise shear deformation theory. A three-dimensional finite element model of multiferroic shells has been developed taking into account the electro-elastic and magneto-elastic couplings. A simple velocity feedback control law is employed to incorporate the active damping. Influence of layer stacking sequence and boundary conditions on the response of the multiferroic doubly curved shell has been studied. In addition, for the different orientation of the fibers of the constraining layer, the performance of the ACLD treatment has been studied.

Keywords: Active constrained layer damping, doubly curved shells, magneto-electro-elastic, multiferroic composite, smart structures.

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Authors: Panagiotis Pentaris

Abstract:

The issue of social and legal recognition of LGBTQ families is of high importance when exploring the possibility of a family. Of equal importance is the fact that both society and the individual contribute to the overall recognition of LGBTQ families. This paper is a conceptual discussion, by methodology, of both sides; it uses a method of constructive analysis to expound on this issue. This method’s aim is to broaden conceptual theory, and introduce a new relationship between concepts that were previously not associated by evidence. This exploration has found that LGBTQ realities from an international perspective may differ and both legal and social rights are critical toward self-consciousness and the formation of a family. This paper asserts that internalised and historic oppression of LGBTQ individuals, places them, not always and not in all places, in a disadvantageous position as far as engaging with the potential of forming a family goes. The paper concludes that lack of social recognition and internalised oppression are key barriers regarding LGBTQ families.

Keywords: Family, gay, LGBTQ, self-worth, social rights.

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Authors: Hossein Shahinzadeh, Ladan Darougaran, Ebrahim Jalili Sani, Hamed Yavari, Mahdi Mozaffari Legha

Abstract:

This paper present a new method for design of power system stabilizer (PSS) based on sliding mode control (SMC) technique. The control objective is to enhance stability and improve the dynamic response of the multi-machine power system. In order to test effectiveness of the proposed scheme, simulation will be carried out to analyze the small signal stability characteristics of the system about the steady state operating condition following the change in reference mechanical torque and also parameters uncertainties. For comparison, simulation of a conventional control PSS (lead-lag compensation type) will be carried out. The main approach is focusing on the control performance which later proven to have the degree of shorter reaching time and lower spike.

Keywords: Power system stabilizer (PSS), multi-machine power system, sliding mode control

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Authors: Raouf Fareh, Maarouf Saad, Sofiane Khadraoui, Tamer Rabie

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This paper presents a tracking control strategy based on Lyapunov approach for nonholonomic wheeled mobile robot. This control strategy consists of two levels. First, a kinematic controller is developed to adjust the right and left wheel velocities. Using this velocity control law, the stability of the tracking error is guaranteed using Lyapunov approach. This kinematic controller cannot be generated directly by the motors. To overcome this problem, the second level of the controllers, dynamic control, is designed. This dynamic control law is developed based on Lyapunov theory in order to track the desired trajectories of the mobile robot. The stability of the tracking error is proved using Lupunov and Barbalat approaches. Simulation results on a nonholonomic wheeled mobile robot are given to demonstrate the feasibility and effectiveness of the presented approach.

Keywords: Mobile robot, trajectory tracking, Lyapunov, stability.

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Authors: Tariq T. Darabseh

Abstract:

The transient thermoelastic response of thick hollow cylinder made of functionally graded material under thermal loading is studied. The generalized coupled thermoelasticity based on the Green-Lindsay model is used. The thermal and mechanical properties of the functionally graded material are assumed to be varied in the radial direction according to a power law variation as a function of the volume fractions of the constituents. The thermal and elastic governing equations are solved by using Galerkin finite element method. All the finite element calculations were done by using commercial finite element program FlexPDE. The transient temperature, radial displacement, and thermal stresses distribution through the radial direction of the cylinder are plotted.

Keywords: Finite element method, thermal stresses, Green-Lindsay theory, functionally graded material.

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Authors: Denis Trcek

Abstract:

Trust is essential for further and wider acceptance of contemporary e-services. It was first addressed almost thirty years ago in Trusted Computer System Evaluation Criteria standard by the US DoD. But this and other proposed approaches of that period were actually solving security. Roughly some ten years ago, methodologies followed that addressed trust phenomenon at its core, and they were based on Bayesian statistics and its derivatives, while some approaches were based on game theory. However, trust is a manifestation of judgment and reasoning processes. It has to be dealt with in accordance with this fact and adequately supported in cyber environment. On the basis of the results in the field of psychology and our own findings, a methodology called qualitative algebra has been developed, which deals with so far overlooked elements of trust phenomenon. It complements existing methodologies and provides a basis for a practical technical solution that supports management of trust in contemporary computing environments. Such solution is also presented at the end of this paper.

Keywords: internet security, trust management, multi-agent systems, reasoning and judgment, modeling and simulation, qualitativealgebra

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Authors: Kazuo Komatsu, Hitoshi Takata

Abstract:

The objective of this study is to propose an observer design for nonlinear systems by using an augmented linear system derived by application of a formal linearization method. A given nonlinear differential equation is linearized by the formal linearization method which is based on Taylor expansion considering up to the higher order terms, and a measurement equation is transformed into an augmented linear one. To this augmented dimensional linear system, a linear estimation theory is applied and a nonlinear observer is derived. As an application of this method, an estimation problem of transient state of electric power systems is studied, and its numerical experiments indicate that this observer design shows remarkable performances for nonlinear systems.

Keywords: nonlinear system, augmented linear system, nonlinear observer, formal linearization, electric power system.

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Authors: Ifere, Eugene Okoi, Eko, Eko Omini

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Taxation as a potent fiscal policy instrument through which infrastructures and social services that drive the development process of any society has been ineffective in Nigeria. The adoption of appropriate measures is, however, a requirement for the generation of adequate tax revenue. This study set out to investigates efficiency and effectiveness in the administration of tax in Nigeria, using Cross River State as a case-study. The methodology to achieve this objective is a qualitative technique using structured questionnaires to survey the three senatorial districts in the state; the central limit theory is adopted as our analytical technique. Result showed a significant degree of inefficiency in the administration of taxes. It is recommended that periodic review and update of tax policy will bring innovation and effectiveness in the administration of taxes. Also proper appropriation of tax revenue will drive development in needed infrastructural and social services.

Keywords: Administration, Efficiency, Effectiveness, Taxation

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Authors: Y. Z. Zhu, S. P. Meng, W. W. Sun

Abstract:

The influence of eccentric discharge of stored solids in squat silos has been highly valued by many researchers. However, calculation method of lateral pressure under eccentric flowing still needs to be deeply studied. In particular, the lateral pressure distribution on vertical wall could not be accurately recognized mainly because of its asymmetry. In order to build mechanical model of lateral pressure, flow channel and flow pattern of stored solids in squat silo are studied. In this passage, based on Janssen-s theory, the method for calculating lateral static pressure in squat silos after eccentric discharge is proposed. Calculative formulae are deduced for each of three possible cases. This method is also focusing on unsymmetrical distribution characteristic of silo wall normal pressure. Finite element model is used to analysis and compare the results of lateral pressure and the numerical results illustrate the practicability of the theoretical method.

Keywords: Squat silo, eccentric discharge, lateral pressure, asymmetric distribution

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Authors: Yi Xu, Zexiang Li

Abstract:

In inspection and workpiece localization, sampling point data is an important issue. Since the devices for sampling only sample discrete points, not the completely surface, sampling size and location of the points will be taken into consideration. In this paper a method is presented for determining the sampled points size and location for achieving efficient sampling. Firstly, uncertainty analysis of the localization parameters is investigated. A localization uncertainty model is developed to predict the uncertainty of the localization process. Using this model the minimum size of the sampled points is predicted. Secondly, based on the algebra theory an eigenvalue-optimal optimization is proposed. Then a freeform surface is used in the simulation. The proposed optimization is implemented. The simulation result shows its effectivity.

Keywords: eigenvalue-optimal optimization, freeform surface inspection, sampling size and location, sampled points.

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