Search results for: dropping point

Authors: Heungsu Lee, Youngseok Kim, Jonghwa Yi, Chul Park

Abstract:

A landing pier is subjected to safety assessment by visual inspection and design data, but it is difficult to check the damage in real-time. In this study, real - time damage detection and safety evaluation methods were studied. As a result of structural analysis of the arbitrary landing pier structure, the inflection point of deformation and moment occurred at 10%, 50%, and 90% of pile length. The critical value of Fiber Bragg Grating (FBG) sensor was set according to the safety factor, and the FBG sensor application method for real - time safety evaluation was derived.

Keywords: FBG sensor, harbor structure, maintenance, safety evaluation system.

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Authors: Raheleh Hedayati, Sanaz Haddadian, Hooman Nabovati

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A 2.4GHz (RF) down conversion Gilbert Cell mixer, implemented in a 0.18-μm CMOS technology with a 1.8V supply, is presented. Current bleeding (charge injection) technique has been used to increase the conversion gain and the linearity of the mixer. The proposed mixer provides 10.75 dB conversion gain ( C G ) with 14.3mw total power consumption. The IIP3 and 1-dB compression point of the mixer are 8dbm and -4.6dbm respectively, at 300 MHz IF frequencies. Comparing the current design against the conventional mixer design, demonstrates better performance in the conversion gain, linearity, noise figure and port-to-port isolation.

Keywords: Mixer, Gilbert Cell, Charge Injection, RFIC, CMOSTechnology.

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Authors: A. Darvizeh, H. Rajabi, S. Fatahtooei Nejad, A. Khaheshi, P. Haghdoust

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In this article, biomechanical aspects of hen-s eggshell as a natural ceramic structure are studied. The images, taken by a scanning electron microscope (SEM), are used to investigate the microscopic aspects of the egg. It is observed that eggshell has a three-layered microstructure with different morphological and structural characteristics. Studies on the eggshell membrane (ESM) as a prosperous tissue suggest that it is placed to prevent the penetration of microorganisms into the egg. Finally, numerical models of the egg are presented to study the stress distribution and its deformation under different loading conditions. The effects of two different types of loading (hydrostatic and point loadings) on two different shell models (with constant and variable thicknesses) are investigated in detail.

Keywords: Eggshell, biomechanical properties, Scanning electron microscope, Numerical Modeling.

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Authors: Guelfo Carbone

Abstract:

The paper focuses on Heidegger’s 1919-1920 early research in order to point out his hermeneutical phenomenology of the life-world, arguing that the concept of world (Welt) is the main philosophical trigger for the phenomenology of factical life. Accordingly, the argument of the paper is twofold: First, the phenomenological hermeneutics of facticity is preceded both chronologically and philosophically by an original phenomenological investigation of life-world, in which the world is construed as the context of the givenness of life. Second, the phenomenology of life-world anticipates the question of being (Seinsfrage), but it also follows it, once this latter is shattered, the question of world as event remaining at the very core of Heidegger’s last meditations on the dominion of technology and the post-metaphysical abode of human beings on earth.

Keywords: Life-world, Heidegger, phenomenology, hermeneutics.

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Authors: Ozlem Bozok, Yusuf Bozok

Abstract:

The importance of using mother tongue and translation in foreign language classrooms cannot be ignored and translation can be utilized as a method in English Language Teaching courses. There exist researches advocating or objecting to the use of translation in foreign language learning but they all have a point in common: Translation should be used as an aid to teaching, not an end in itself. In this research, prospective English language teachers’ opinions about translation use and use of mother tongue in foreign language teaching are investigated and according to the findings, some explanations and recommendations are made.

Keywords: Exposure to foreign language, translation, foreign language learning, prospective teachers’ opinions, use of L1.

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Authors: Siddhartha Bhattacharyya, Paramartha Dutta, Ujjwal Maulik, Prashanta Kumar Nandi

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A multilayer self organizing neural neural network (MLSONN) architecture for binary object extraction, guided by a beta activation function and characterized by backpropagation of errors estimated from the linear indices of fuzziness of the network output states, is discussed. Since the MLSONN architecture is designed to operate in a single point fixed/uniform thresholding scenario, it does not take into cognizance the heterogeneity of image information in the extraction process. The performance of the MLSONN architecture with representative values of the threshold parameters of the beta activation function employed is also studied. A three layer bidirectional self organizing neural network (BDSONN) architecture comprising fully connected neurons, for the extraction of objects from a noisy background and capable of incorporating the underlying image context heterogeneity through variable and adaptive thresholding, is proposed in this article. The input layer of the network architecture represents the fuzzy membership information of the image scene to be extracted. The second layer (the intermediate layer) and the final layer (the output layer) of the network architecture deal with the self supervised object extraction task by bi-directional propagation of the network states. Each layer except the output layer is connected to the next layer following a neighborhood based topology. The output layer neurons are in turn, connected to the intermediate layer following similar topology, thus forming a counter-propagating architecture with the intermediate layer. The novelty of the proposed architecture is that the assignment/updating of the inter-layer connection weights are done using the relative fuzzy membership values at the constituent neurons in the different network layers. Another interesting feature of the network lies in the fact that the processing capabilities of the intermediate and the output layer neurons are guided by a beta activation function, which uses image context sensitive adaptive thresholding arising out of the fuzzy cardinality estimates of the different network neighborhood fuzzy subsets, rather than resorting to fixed and single point thresholding. An application of the proposed architecture for object extraction is demonstrated using a synthetic and a real life image. The extraction efficiency of the proposed network architecture is evaluated by a proposed system transfer index characteristic of the network.

Keywords: Beta activation function, fuzzy cardinality, multilayer self organizing neural network, object extraction,

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Authors: Melisa Yazdan Panahi

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Since, today in most countries around the world much attention is paid to planning the smallest unit in the city i.e. the residential neighborhoods to achieve sustainable urban development goals, a variety of assessment tools have been developed to assess and monitor the sustainability of new developments. One of the most reliable and widely used assessment tools is LEED-ND rating system. This paper whit the aim of assessing sustainability level of Roshdieh neighborhood in Tabriz, has introduced this rating system and applied it in the study area. The results indicate that Roshdieh has the potential of achieving the standards of sustainable neighborhoods, but the present situation is far from the ideal point.

Keywords: LEED-ND, Sustainable Neighborhood, New Developments, Tabriz.

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Authors: Lenka Ševelová, Aleš Florian

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Appropriate and progressive tool for analyzing behavior of low volume roads are probabilistic models used in reliability analyses. The necessary part of the probabilistic model is the deterministic model of structural behavior. The FE model of low volume roads is created in the ANSYS software. It is able to determine the state of stress and deformation in any point of the structure and thus generate data required for the reliability analysis. The paper compares two material constitutive models used for modeling of unbound non-homogenous materials used in low volume roads. The first model is linear elastic model according to Hook theory (H model), the second one is nonlinear elastic-plastic Drucker-Prager model (D-P model).

Keywords: FEA, FEM, geotechnical materials, low volume roads, material constitutive models, pavement.

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Authors: Young-Lim Choi, Nak-Yun Choi, Jae-Yong Seo, Sang-Il Park, Jong-Wook Kim

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This paper proposes a prototype of a lower-limb rehabilitation system for recovering and strengthening patients- injured lower limbs. The system is composed of traction motors for each leg position, a treadmill as a walking base, tension sensors, microcontrollers controlling motor functions and a main system with graphic user interface. For derivation of reference or normal velocity profiles of the body segment point, kinematic method is applied based on the humanoid robot model using the reference joint angle data of normal walking.

Keywords: Rehabilitation, lower limb, treadmill, humanoid robot.

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Authors: A. Youseef

Abstract:

IEEE 802.16 (WiMAX) aims to present high speed wireless access to cover wide range coverage. The base station (BS) and the subscriber station (SS) are the main parts of WiMAX. WiMAX uses either Point-to-Multipoint (PMP) or mesh topologies. In the PMP mode, the SSs connect to the BS to gain access to the network. However, in the mesh mode, the SSs connect to each other to gain access to the BS. The main components of QoS management in the 802.16 standard are the admission control, buffer management and packet scheduling. In this paper, we use QualNet 5.0.2 to study the performance of different scheduling schemes, such as WFQ, SCFQ, RR and SP when the numbers of SSs increase. We find that when the number of SSs increases, the average jitter and average end-to-end delay is increased and the throughput is reduced.

Keywords: WiMAX, Scheduling Scheme, QoS, QualNet.

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Authors: N. Feroze, M. Aslam

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The paper deals with the maximum likelihood estimation of the parameters of the Burr type V distribution based on left censored samples. The maximum likelihood estimators (MLE) of the parameters have been derived and the Fisher information matrix for the parameters of the said distribution has been obtained explicitly. The confidence intervals for the parameters have also been discussed. A simulation study has been conducted to investigate the performance of the point and interval estimates.

Keywords: Fisher information matrix, confidence intervals, censoring.

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Authors: Trung-Kien Pham, Yoonsu Nam, Hyungun Kim, Jaehoon Son

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This paper addresses linear quadratic regulation (LQR) for variable speed variable pitch wind turbines. Because of the inherent nonlinearity of wind turbine, a set of operating conditions is identified and then a LQR controller is designed for each operating point. The feedback controller gains are then interpolated linearly to get control law for the entire operating region. Besides, the aerodynamic torque and effective wind speed are estimated online to get the gain-scheduling variable for implementing the controller. The potential of the method is verified through simulation with the help of MATLAB/Simulink and GH Bladed. The performance and mechanical load when using LQR are also compared with that when using PI controller.

Keywords: variable speed variable pitch wind turbine, multi-MW size wind turbine, wind energy conversion system, LQR control.

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Authors: Guruprasad Khataniar, Hitesh Tahbildar, Prakriti Prava Das

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There are various overlay structures that provide efficient and scalable solutions for point and range query in a peer-topeer network. Overlay structure based on m-Binary Search Tree (BST) is one such popular technique. It deals with the division of the tree into different key intervals and then assigning the key intervals to a BST. The popularity of the BST makes this overlay structure vulnerable to different kinds of attacks. Here we present four such possible attacks namely index poisoning attack, eclipse attack, pollution attack and syn flooding attack. The functionality of BST is affected by these attacks. We also provide different security techniques that can be applied against these attacks.

Keywords: BST, eclipse attack, index poisoning attack, pollution attack, syn flooding attack.

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Authors: Yanping Liao, Zenan Wu, Ruigang Zhao

Abstract:

Frequency diverse array (FDA) beamforming is a technology developed in recent years, and its antenna pattern has a unique angle-distance-dependent characteristic. However, the beam is always required to have strong concentration, high resolution and low sidelobe level to form the point-to-point interference in the concentrated set. In order to eliminate the angle-distance coupling of the traditional FDA and to make the beam energy more concentrated, this paper adopts a multi-carrier FDA structure based on proposed power exponential frequency offset to improve the array structure and frequency offset of the traditional FDA. The simulation results show that the beam pattern of the array can form a dot-shape beam with more concentrated energy, and its resolution and sidelobe level performance are improved. However, the covariance matrix of the signal in the traditional adaptive beamforming algorithm is estimated by the finite-time snapshot data. When the number of snapshots is limited, the algorithm has an underestimation problem, which leads to the estimation error of the covariance matrix to cause beam distortion, so that the output pattern cannot form a dot-shape beam. And it also has main lobe deviation and high sidelobe level problems in the case of limited snapshot. Aiming at these problems, an adaptive beamforming technique based on exponential correction for multi-carrier FDA is proposed to improve beamforming robustness. The steps are as follows: first, the beamforming of the multi-carrier FDA is formed under linear constrained minimum variance (LCMV) criteria. Then the eigenvalue decomposition of the covariance matrix is ​​performed to obtain the diagonal matrix composed of the interference subspace, the noise subspace and the corresponding eigenvalues. Finally, the correction index is introduced to exponentially correct the small eigenvalues ​​of the noise subspace, improve the divergence of small eigenvalues ​​in the noise subspace, and improve the performance of beamforming. The theoretical analysis and simulation results show that the proposed algorithm can make the multi-carrier FDA form a dot-shape beam at limited snapshots, reduce the sidelobe level, improve the robustness of beamforming, and have better performance.

Keywords: Multi-carrier frequency diverse array, adaptive beamforming, correction index, limited snapshot, robust.

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Authors: E. Taslak, C. Kocatepe, O. Arıkan, C. F. Kumru

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In insulation and cooling of power transformers various liquids are used. Mineral oils have wide availability and low cost. However, they have a poor biodegradability potential and lower fire point in comparison with other insulating liquids. Use of a liquid having high biodegradability is important due to environmental consideration. This paper investigates edible corn oil as an alternative to mineral oil. Various properties of mineral and corn oil like breakdown voltage, dissipation factor, relative dielectric constant, power loss and resistivity were measured according to different standards.

Keywords: Breakdown voltage, corn oil, dissipation factor, mineral oil, power loss, relative dielectric constant, resistivity.

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Authors: Mehrdad Ahmadi Kamarposhti, Mostafa Alinezhad

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One of the major causes of voltage instability is the reactive power limit of the system. Improving the system's reactive power handling capacity via Flexible AC transmission System (FACTS) devices is a remedy for prevention of voltage instability and hence voltage collapse. In this paper, the effects of SVC and STATCOM in Static Voltage Stability Margin Enhancement will be studied. AC and DC representations of SVC and STATCOM are used in the continuation power flow process in static voltage stability study. The IEEE-14 bus system is simulated to test the increasing loadability. It is found that these controllers significantly increase the loadability margin of power systems.

Keywords: SVC, STATCOM, Voltage Collapse, Maximum Loading Point.

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Authors: Shunsuke Miyoshi, Yasuyuki Nogami, Takuya Kusaka, Nariyoshi Yamai

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Elliptic curve discrete logarithm problem(ECDLP) is one of problems on which the security of pairing-based cryptography is based. This paper considers Pollard’s rho method to evaluate the security of ECDLP on Barreto-Naehrig(BN) curve that is an efficient pairing-friendly curve. Some techniques are proposed to make the rho method efficient. Especially, the group structure on BN curve, distinguished point method, and Montgomery trick are well-known techniques. This paper applies these techniques and shows its optimization. According to the experimental results for which a large-scale parallel system with MySQL is applied, 94-bit ECDLP was solved about 28 hours by parallelizing 71 computers.

Keywords: Pollard’s rho method, BN curve, Montgomery multiplication.

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Authors: Thomas Kampke

Abstract:

Equations with differentials relating to the inverse of an unknown function rather than to the unknown function itself are solved exactly for some special cases and numerically for the general case. Invertibility combined with differentiability over connected domains forces solutions always to be monotone. Numerical function inversion is key to all solution algorithms which either are of a forward type or a fixed point type considering whole approximate solution functions in each iteration. The given considerations are restricted to ordinary differential equations with inverted functions (ODEIs) of first order. Forward type computations, if applicable, admit consistency of order one and, under an additional accuracy condition, convergence of order one.

Keywords: Euler method, fixed points, golden section, multi-step procedures, Runge Kutta methods.

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Authors: Felicitas Pielsticker, Christoph Pielsticker, Ingo Witzke

Abstract:

Many people know ‘Mathematics needs practice!’ statement or similar ones from their mathematics lessons. It seems important to practice when learning mathematics. At the same time, it also seems important to practice how to learn mathematics. This paper places neuroscientific-radiological findings on “practicing” while learning mathematics in a context of mathematics education. To accomplish this, we use a literature-based discussion of our case study on practice. We want to describe neuroscientific-radiological findings in the context of mathematics education and point out stimulating connections between both perspectives. From a connective perspective we expect incentives that lead discussions in future research in the field of mathematics education.

Keywords: fMRI, education, mathematics learning, practicing.

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Authors: A. Harifi, A. Aghagolzadeh

Abstract:

The main problem for recognition of handwritten Persian digits using Neural Network is to extract an appropriate feature vector from image matrix. In this research an asymmetrical segmentation pattern is proposed to obtain the feature vector. This pattern can be adjusted as an optimum model thanks to its one degree of freedom as a control point. Since any chosen algorithm depends on digit identity, a Neural Network is used to prevail over this dependence. Inputs of this Network are the moment of inertia and the center of gravity which do not depend on digit identity. Recognizing the digit is carried out using another Neural Network. Simulation results indicate the high recognition rate of 97.6% for new introduced pattern in comparison to the previous models for recognition of digits.

Keywords: Pattern recognition, Persian digits, NeuralNetwork.

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Authors: Theodosia Prodromou

Abstract:

The article investigates how 14- to 15- year-olds build informal conceptions of inferential statistics as they engage in a modelling process and build their own computer simulations with dynamic statistical software. This study proposes four primary phases of informal inferential reasoning for the students in the statistical modeling and simulation process. Findings show shifts in the conceptual structures across the four phases and point to the potential of all of these phases for fostering the development of students- robust knowledge of the logic of inference when using computer based simulations to model and investigate statistical questions.

Keywords: Inferential reasoning, learning, modelling, statistical inference, simulation.

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Authors: Georgia C. Kosta, Christos S. Nicolaidis

Abstract:

The present paper discusses the role of teams’ climate in the intrapreneurial process. Intrapreneurship, which corresponds for entrepreneurship in existing organizations, puts special emphasis on climate as an influential factor of the intrapreneurial behavior. Although climate exists at every level and in every subgroup of the organizational structure, research focuses mainly on the study of climate that characterizes organization as a whole. However, the climate of a work team may differ radically from the organizational climate, and in fact it can be far more influential. The paper provides a conceptual analysis of organizational climate from the intrapreneurial point of view, and sheds light upon teams’ climate role in the intrapreneurial posture.

Keywords: Entrepreneurship, innovation, intrapreneurship, organizational climate, teams’ climate.

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Authors: Marco Hemmerling

Abstract:

The paper outlines the relevance of computational geometry within the design and production process of architecture. Based on two case studies, the digital chain - from the initial formfinding to the final realization of spatial concepts - is discussed in relation to geometric principles. The association with the fascinating complexity that can be found in nature and its underlying geometry was the starting point for both projects presented in the paper. The translation of abstract geometric principles into a three-dimensional digital design model – realized in Rhinoceros – was followed by a process of transformation and optimization of the initial shape that integrated aesthetic, spatial and structural qualities as well as aspects of material properties and conditions of production.

Keywords: Architecture, Computer Aided Architectural Design, 3D-Modeling, Rapid Prototyping, CAD/CAM.

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Authors: M.Somjarod, V. Tanawat, l. Weerawat

Abstract:

The understanding of knee movement during swing importance for golf swing improving and preventing injury. Thirty male professional and amateur golfers were assigned to swing time by time for 3 times. Data from a vedio-based motion capture were used to compute knee joint movement variables. The results showed that professional and amateur golfers were significantly in left knee flexion angle at the impact point and mid follow through phase. Nevertheless, left knee external rotation in both groups was also significant. The right knee were no significant different in all variable. However, pattern of knee joint movement are also likely between professional and amateur golfers.

Keywords: Golfer, Knee joint, Movement, Swing

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Authors: Safeer Hussain Khan

Abstract:

In this paper, we use a one-step iteration scheme to approximate common fixed points of two quasi-asymptotically nonexpansive mappings. We prove weak and strong convergence theorems in a uniformly convex Banach space. Our results generalize the corresponding results of Yao and Chen [15] to a wider class of mappings while extend those of Khan, Abbas and Khan [4] to an improved one-step iteration scheme without any condition and improve upon many others in the literature.

Keywords: One-step iteration scheme, asymptotically quasi non expansive mapping, common fixed point, condition (a'), weak and strong convergence.

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Authors: N. Kekelidze, B. Kvirkvelia, E. Khutsishvili, T. Qamushadze, D. Kekelidze, R. Kobaidze, Z. Chubinishvili, N. Qobulashvili, G. Kekelidze

Abstract:

On the basis of InAs, InP and their InP_xAs_1-x solid solutions, the technologies were developed and materials were created where the electron concentration and optical and thermoelectric properties do not change under the irradiation with Ф = 2∙10¹⁸ n/cm² fluences of fast neutrons high-energy electrons (50 MeV, Ф = 6·10¹⁷ e/cm²) and 3 MeV electrons with fluence Ф = 3∙10¹⁸ e/cm². The problem of obtaining such material has been solved, in which under hard irradiation the mobility of the electrons does not decrease, but increases. This material is characterized by high thermal stability up to T = 700 °C. The complex process of defects formation has been analyzed and shown that, despite of hard irradiation, the essential properties of investigated materials are mainly determined by point type defects.

Keywords: InAs, InP, solid solutions, irradiation.

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Authors: M. Garcia-Alsina, J. Cobarsí

Abstract:

The role of controlled vocabularies in information retrieval is broadly recognized as a relevant feature. Besides, there is a standing demand that editors and databases should consider the effective introduction of controlled vocabularies in their procedures to index scientific literature. That is especially important because information retrieval is pointed out as a significant point to drive systematic literature review. Hence, a first question emerges: Are the controlled vocabularies at this moment considered? On the other hand, subject searching in the catalogs is complex mainly due to the dichotomy between keywords from authors versus keywords based on controlled vocabularies. Finally, there is some demand to unify the terminology related to health to make easier the medical history exploitation and research. Considering these features, this paper focuses on controlled vocabularies related to the health field and their role for storing, classifying, and retrieving relevant literature. The objective is knowing which role plays the controlled vocabularies related to the health field to index and retrieve research literature in data bases such as Web of Science (WoS) and Scopus. So, this exploratory research is grounded over two research questions: 1) Which are the terms considered in specific controlled vocabularies of the health field; and 2) How papers are indexed in relevant databases to be easily retrieved, considering keywords vs specific health’ controlled vocabularies? This research takes as fieldwork the controlled vocabularies related to health and the scientific interest for 1918 flu pandemic, also known equivocally as ‘Spanish flu’. This interest has been fostered by the emergence in the early 21st of epidemics of pneumonic diseases caused by virus. Searches about and with controlled vocabularies on WoS and Scopus databases are conducted. First results of this work in progress are surprising. There are different controlled vocabularies for the health field, into which the terms collected and preferred related to ‘1918 pandemic’ are identified. To summarize, ‘Spanish influenza epidemic’ or ‘Spanish flu’ are collected as not preferred terms. The preferred terms are: ‘influenza’ or ‘influenza pandemic, 1918-1919’. Although the controlled vocabularies are clear in their election, most of the literature about ‘1918 pandemic’ is retrievable either by ‘Spanish’ or by ‘1918’ disjunct, and the dominant word to retrieve literature is ‘Spanish’ rather than ‘1918’. This is surprising considering the existence of suitable controlled vocabularies related to health topics, and the modern guidelines of World Health Organization concerning naming of diseases that point out to other preferred terms. A first conclusion is the failure of using controlled vocabularies for a field such as health, and in consequence for WoS and Scopus. This research opens further research questions about which is the role that controlled vocabularies play in the instructions to authors that journals deliver to documents’ authors.

Keywords: Controlled vocabularies, indexing, 1918 influenza, information retrieval, keywords, 1918 pandemic, scientific databases.

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Authors: Guang Zhou, Shouming Zhong

Abstract:

In this paper, we investigate the problem of the existence, uniqueness and global asymptotic stability of the equilibrium point for a class of neural networks, the neutral system has mixed time delays and parameter uncertainties. Under the assumption that the activation functions are globally Lipschitz continuous, we drive a new criterion for the robust stability of a class of neural networks with time delays by utilizing the Lyapunov stability theorems and the Homomorphic mapping theorem. Numerical examples are given to illustrate the effectiveness and the advantage of the proposed main results.

Keywords: Neural networks, Delayed systems, Lyapunov function, Stability analysis.

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Authors: Nafise Fareghzadeh

Abstract:

Service identification is one of the main activities in the modeling of a service-oriented solution, and therefore errors made during identification can flow down through detailed design and implementation activities that may necessitate multiple iterations, especially in building composite applications. Different strategies exist for how to identify candidate services that each of them has its own benefits and trade offs. The approach presented in this paper proposes a selective identification of services approach, based on in depth business process analysis coupled with use cases and existing assets analysis and goal service modeling. This article clearly emphasizes the key activities need for the analysis and service identification to build a optimized service oriented architecture. In contrast to other approaches this article mentions some best practices and steps, wherever appropriate, to point out the vagueness involved in service identification.

Keywords: SOA, service identification, service taxonomy, service layer.

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Authors: Aarthi Chandramohan, M. V. C. Rao

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This paper presents three new methodologies for the basic operations, which aim at finding new ways of computing union (maximum) and intersection (minimum) membership values by taking into effect the entire membership values in a fuzzy set. The new methodologies are conceptually simple and easy from the application point of view and are illustrated with a variety of problems such as Cartesian product of two fuzzy sets, max –min composition of two fuzzy sets in different product spaces and an application of an inverted pendulum to determine the impact of the new methodologies. The results clearly indicate a difference based on the nature of the fuzzy sets under consideration and hence will be highly useful in quite a few applications where different values have significant impact on the behavior of the system.

Keywords: Centroid, fuzzy set operations, intersection, triangular norms , triangular S-norms, union.

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