Search results for: Volume Determination.
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 33100

Search results for: Volume Determination.

31600 The Distance between a Point and a Bezier Curveon a Bezier Surface

Authors: Wen-Haw Chen, Sheng-Gwo Chen

Abstract:

The distance between two objects is an important problem in CAGD, CAD and CG etc. It will be presented in this paper that a simple and quick method to estimate the distance between a point and a Bezier curve on a Bezier surface.

Keywords: Geodesic-like curve, distance, projection, Bezier.

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31599 LOWL: Logic and OWL, an Extension

Authors: M. Mohsenzadeh, F. Shams, M. Teshnehlab

Abstract:

Current research on semantic web aims at making intelligent web pages meaningful for machines. In this way, ontology plays a primary role. We believe that logic can help ontology languages (such as OWL) to be more fluent and efficient. In this paper we try to combine logic with OWL to reduce some disadvantages of this language. Therefore we extend OWL by logic and also show how logic can satisfy our future expectations of an ontology language.

Keywords: Logical Programming, OWL, Language Extension.

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31598 Reputation and Transparency of Cooperative Movement in Malaysia

Authors: Maslinawati Mohamad, Intan Waheedah Othman

Abstract:

This paper studies the reputation and transparency of cooperative movement in Malaysia.

Keywords: Cooperative movement, reputation, transparency, web presence.

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31597 Molecular Dynamics Simulation of the Effect of the Solid Gas Interface Nanolayer on Enhanced Thermal Conductivity of Copper-CO2 Nanofluid

Authors: Zeeshan Ahmed, Ajinkya Sarode, Pratik Basarkar, Atul Bhargav, Debjyoti Banerjee

Abstract:

The use of CO2 in oil recovery and in CO2 capture and storage is gaining traction in recent years. These applications involve heat transfer between CO2 and the base fluid, and hence, there arises a need to improve the thermal conductivity of CO2 to increase the process efficiency and reduce cost. One way to improve the thermal conductivity is through nanoparticle addition in the base fluid. The nanofluid model in this study consisted of copper (Cu) nanoparticles in varying concentrations with CO2 as a base fluid. No experimental data are available on thermal conductivity of CO2 based nanofluid. Molecular dynamics (MD) simulations are an increasingly adopted tool to perform preliminary assessments of nanoparticle (NP) fluid interactions. In this study, the effect of the formation of a nanolayer (or molecular layering) at the gas-solid interface on thermal conductivity is investigated using equilibrium MD simulations by varying NP diameter and keeping the volume fraction (1.413%) of nanofluid constant to check the diameter effect of NP on the nanolayer and thermal conductivity. A dense semi-solid fluid layer was seen to be formed at the NP-gas interface, and the thickness increases with increase in particle diameter, which also moves with the NP Brownian motion. Density distribution has been done to see the effect of nanolayer, and its thickness around the NP. These findings are extremely beneficial, especially to industries employed in oil recovery as increased thermal conductivity of CO2 will lead to enhanced oil recovery and thermal energy storage.

Keywords: Copper-CO2 nanofluid, molecular interfacial layer, thermal conductivity, molecular dynamic simulation.

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31596 Urban Air Pollution – Trend and Forecasting of Major Pollutants by Timeseries Analysis

Authors: A.L. Seetharam, B.L. Udaya Simha

Abstract:

The Bangalore City is facing the acute problem of pollution in the atmosphere due to the heavy increase in the traffic and developmental activities in recent years. The present study is an attempt in the direction to assess trend of the ambient air quality status of three stations, viz., AMCO Batteries Factory, Mysore Road, GRAPHITE INDIA FACTORY, KHB Industrial Area, Whitefield and Ananda Rao Circle, Gandhinagar with respect to some of the major criteria pollutants such as Total Suspended particular matter (SPM), Oxides of nitrogen (NOx), and Oxides of sulphur (SO2). The sites are representative of various kinds of growths viz., commercial, residential and industrial, prevailing in Bangalore, which are contributing to air pollution. The concentration of Sulphur Dioxide (SO2) at all locations showed a falling trend due to use of refined petrol and diesel in the recent years. The concentration of Oxides of nitrogen (NOx) showed an increasing trend but was within the permissible limits. The concentration of the Suspended particular matter (SPM) showed the mixed trend. The correlation between model and observed values is found to vary from 0.4 to 0.7 for SO2, 0.45 to 0.65 for NOx and 0.4 to 0.6 for SPM. About 80% of data is observed to fall within the error band of ±50%. Forecast test for the best fit models showed the same trend as actual values in most of the cases. However, the deviation observed in few cases could be attributed to change in quality of petro products, increase in the volume of traffic, introduction of LPG as fuel in many types of automobiles, poor condition of roads, prevailing meteorological conditions, etc.

Keywords: Bangalore, urban air pollution, time series analysis.

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31595 Design and Performance Comparison of Metamaterial Based Antenna for 4G/5G Mobile Devices

Authors: Jalal Khan, Daniyal Ali Sehrai, Shakeel Ahmad

Abstract:

This paper presents the design and performance evaluation of multiband metamaterial based antenna operating in the 3.6 GHz (4G), 14.33 GHz, and 28.86 GHz (5G) frequency bands, for future mobile and handheld devices. The radiating element of the proposed design is made up of a conductive material supported by a 1.524 mm thicker Rogers-4003 substrate, having a relative dielectric constant and loss tangent of 3.55 and 0.0027, respectively. The substrate is backed by truncated ground plane. The future mobile communication system is based on higher frequencies, which are highly affected by the atmospheric conditions. Therefore, to overcome the path loss problem, essential enhancements and improvements must be made in the overall performance of the antenna. The traditional ground plane does not provide the in-phase reflection and surface wave suppression due to which side and back lobes are produced. This will affect the antenna performance in terms of gain and efficiency. To enhance the overall performance of the antenna, a metamaterial acting as a high impedance surface (HIS) is used as a reflector in the proposed design. The simulated gain of the metamaterial based antenna is enhanced from {2.76-6.47, 4.83-6.71 and 7.52-7.73} dB at 3.6, 14.33 and 28.89 GHz, respectively relative to the gain of the antenna backed by a traditional ground plane. The proposed antenna radiated efficiently with a radiated efficiency (>85 %) in all the three frequency bands with and without metamaterial surface. The total volume of the antenna is (L x W x h=45 x 40 x 1.524) mm3. The antenna can be potentially used for wireless handheld devices and mobile terminal. All the simulations have been performed using the Computer Simulation Technology (CST) software.

Keywords: Multiband, fourth generation (4G), fifth generation (5G), metamaterial, CST MWS.

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31594 Miniaturization of a Rectangular Microstrip Patch Antenna Loaded with Metamaterial

Authors: Anahita Ghaznavi Jahromi, Farzad Mohajeri, Nooshin Feiz

Abstract:

In this paper a novel structure of metamaterial is proposed in order to miniaturize a rectangular microstrip patch antenna. The metamaterial is composed of two nested split octagons which are located on a 10 mm

Keywords: Metamaterial, miniaturization, patch antenna, sub- wavelength resonance.

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31593 Solving Linear Matrix Equations by Matrix Decompositions

Authors: Yongxin Yuan, Kezheng Zuo

Abstract:

In this paper, a system of linear matrix equations is considered. A new necessary and sufficient condition for the consistency of the equations is derived by means of the generalized singular-value decomposition, and the explicit representation of the general solution is provided.

Keywords: Matrix equation, Generalized inverse, Generalized singular-value decomposition.

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31592 Influence of Sr(BO2)2 Doping on Superconducting Properties of (Bi,Pb)-2223 Phase

Authors: N. G. Margiani, I. G. Kvartskhava, G. A. Mumladze, Z. A. Adamia

Abstract:

Chemical doping with different elements and compounds at various amounts represents the most suitable approach to improve the superconducting properties of bismuth-based superconductors for technological applications. In this paper, the influence of partial substitution of Sr(BO2)2 for SrO on the phase formation kinetics and transport properties of (Bi,Pb)-2223 HTS has been studied for the first time. Samples with nominal composition Bi1.7Pb0.3Sr2-xCa2Cu3Oy[Sr(BO2)2]x, x=0, 0.0375, 0.075, 0.15, 0.25, were prepared by the standard solid state processing. The appropriate mixtures were calcined at 845 oC for 40 h. The resulting materials were pressed into pellets and annealed at 837 oC for 30 h in air. Superconducting properties of undoped (reference) and Sr(BO2)2-doped (Bi,Pb)-2223 compounds were investigated through X-ray diffraction (XRD), resistivity (ρ) and transport critical current density (Jc) measurements. The surface morphology changes in the prepared samples were examined by scanning electron microscope (SEM). XRD and Jc studies have shown that the low level Sr(BO2)2 doping (x=0.0375-0.075) to the Sr-site promotes the formation of high-Tc phase and leads to the enhancement of current carrying capacity in (Bi,Pb)-2223 HTS. The doped sample with x=0.0375 has the best performance compared to other prepared samples. The estimated volume fraction of (Bi,Pb)-2223 phase increases from ~25 % for reference specimen to ~70 % for x=0.0375. Moreover, strong increase in the self-field Jc value was observed for this dopant amount (Jc=340 A/cm2), compared to an undoped sample (Jc=110 A/cm2). Pronounced enhancement of superconducting properties of (Bi,Pb)-2223 superconductor can be attributed to the acceleration of high-Tc phase formation as well as the improvement of inter-grain connectivity by small amounts of Sr(BO2)2 dopant.

Keywords: Bismuth-based superconductor, critical current density, phase formation, Sr(BO2)2 doping.

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31591 The Role of Ideophones: Phonological and Morphological Characteristics in Literature

Authors: Cristina Bahón Arnaiz

Abstract:

Many Asian languages, such as Korean and Japanese, are well-known for their wide use of sound symbolic words or ideophones. This is a very particular characteristic which enriches its lexicon hugely. Ideophones are a class of sound symbolic words that utilize sound symbolism to express aspects, states, emotions, or conditions that can be experienced through the senses, such as shape, color, smell, action or movement. Ideophones have very particular characteristics in terms of sound symbolism and morphology, which distinguish them from other words. The phonological characteristics of ideophones are vowel ablaut or vowel gradation and consonant mutation. In the case of Korean, there are light vowels and dark vowels. Depending on the type of vowel that is used, the meaning will slightly change. Consonant mutation, also known as consonant ablaut, contributes to the level of intensity, emphasis, and volume of an expression. In addition to these phonological characteristics, there is one main morphological singularity, which is reduplication and it carries the meaning of continuity, repetition, intensity, emphasis, and plurality. All these characteristics play an important role in both linguistics and literature as they enhance the meaning of what is trying to be expressed with incredible semantic detail, expressiveness, and rhythm. The following study will analyze the ideophones used in a single paragraph of a Korean novel, which add incredible yet subtle detail to the meaning of the words, and advance the expressiveness and rhythm of the text. The results from analyzing one paragraph from a novel, after presenting the phonological and morphological characteristics of Korean ideophones, will evidence the important role that ideophones play in literature. 

Keywords: Ideophones, mimetic words, phonomimes, phenomimes, psychomimes, sound symbolism.

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31590 OSGi in Cloud Environments

Authors: Irina Astrova, Arne Koschel, Björn Siekmann, Mark Starrach, Christopher Tebbe, StefanWolf, Marc Schaaf

Abstract:

This paper deals with the combination of OSGi and cloud computing. Both technologies are mainly placed in the field of distributed computing. Therefore, it is discussed how different approaches from different institutions work. In addition, the approaches are compared to each other.

Keywords: Cloud computing, OSGi, distributed environments.

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31589 On 6-Figures in Finite Klingenberg Planes of Parameters (p2k-1, p)

Authors: Atilla Akpinar, Basri Celik, Suleyman Ciftci

Abstract:

In this paper, we deal with finite projective Klingenberg plane M (A) coordinatized by local ring A := Zq+Zq E (where prime power q = p', e0 Z q and 62 = 0). So, we get some combinatorical results on 6-figures. For example, we show that there exist p — 1 6-figure classes in M(A).

Keywords: finite Klingenberg plane, 6-figure, ratio of 6-figure, cross-ratio.

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31588 On the Solution of the Towers of Hanoi Problem

Authors: Hayedeh Ahrabian, Comfar Badamchi, Abbass Nowzari-Dalini

Abstract:

In this paper, two versions of an iterative loopless algorithm for the classical towers of Hanoi problem with O(1) storage complexity and O(2n) time complexity are presented. Based on this algorithm the number of different moves in each of pegs with its direction is formulated.

Keywords: Loopless algorithm, Binary tree, Towers of Hanoi.

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31587 A Concept of Rational Water Management at Local Utilities – The Use of RO for Water Supply and Wastewater Treatment/Reuse

Authors: N. Matveev, A. Pervov

Abstract:

Local utilities often face problems of local industrial wastes, storm water disposal due to existing strict regulations. For many local industries, the problem of wastewater treatment and discharge into surface reservoirs can’t be solved through the use of conventional biological treatment techniques. Current discharge standards require very strict removal of a number of impurities such as ammonia, nitrates, phosphate, etc. To reach this level of removal, expensive reagents and sorbents are used. The modern concept of rational water resources management requires the development of new efficient techniques that provide wastewater treatment and reuse. As RO membranes simultaneously reject all dissolved impurities such as BOD, TDS, ammonia, phosphates etc., they become very attractive for the direct treatment of wastewater without biological stage. To treat wastewater, specially designed membrane "open channel" modules are used that do not possess "dead areas" that cause fouling or require pretreatment. A solution to RO concentrate disposal problem is presented that consists of reducing of initial wastewater volume by 100 times. Concentrate is withdrawn from membrane unit as sludge moisture. The efficient use of membrane RO techniques is connected with a salt balance in water system. Thus, to provide high ecological efficiency of developed techniques, all components of water supply and wastewater discharge systems should be accounted for.

Keywords: Reverse osmosis, stormwater treatment, openchannel module, wastewater reuse.

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31586 Sediment Transport Experiments: The Influence of the Furrow Geometry

Authors: S. Haddad, M. Bouhadef

Abstract:

In this experimental work, we have shown that the geometric shape of the grooves (furrows) plays an important role in sediment dynamics. In addition, the rheological behaviour of solid discharge does not depend only on the velocity discharge but also on the geometric shape.

Keywords: Laboratory experiments, soil erosion, groove, furrow, sediment transport

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31585 Group of Square Roots of Unity Modulo n

Authors: Rochdi Omami, Mohamed Omami, Raouf Ouni

Abstract:

Let n ≥ 3 be an integer and G2(n) be the subgroup of square roots of 1 in (Z/nZ)*. In this paper, we give an algorithm that computes a generating set of this subgroup.

Keywords: Group, modulo, square roots, unity.

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31584 Intelligent Solutions for Umbrella Systems in Telecommunication Supervision Systems

Authors: K. P. Csányi, L. T. Kóczy, D. Tikk

Abstract:

This paper indicate the importance of telecommunications supervision systems (TSS), integrating heterogeneous TSS into single system thru umbrella systems, introduces the structure, features, requirements of TSS and TSS related intelligent solutions.

Keywords: Telecommunication, telecommunication supervisionsystems, umbrella systems

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31583 Iterative Methods for An Inverse Problem

Authors: Minghui Wang, Shanrui Hu

Abstract:

An inverse problem of doubly center matrices is discussed. By translating the constrained problem into unconstrained problem, two iterative methods are proposed. A numerical example illustrate our algorithms.

Keywords: doubly center matrix, electric network theory, iterative methods, least-square problem.

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31582 The Number of Rational Points on Singular Curvesy 2 = x(x - a)2 over Finite Fields Fp

Authors: Ahmet Tekcan

Abstract:

Let p ≥ 5 be a prime number and let Fp be a finite field. In this work, we determine the number of rational points on singular curves Ea : y2 = x(x - a)2 over Fp for some specific values of a.

Keywords: Singular curve, elliptic curve, rational points.

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31581 On the Fp-Normal Subgroups of Finite Groups

Authors: Shitian Liu, Deqin Chen

Abstract:

Let G be a finite group, and let F be a formation of finite group. We say that a subgroup H of G is p F -normal in G if there exists a normal subgroup T of G such that HT is a permutable Hall subgroup of G and G G (H

Keywords: Finite group, Fp -normal subgroup, Sylowsubgroup, Maximal subgroup

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31580 The Design of a Vehicle Traffic Flow Prediction Model for a Gauteng Freeway Based on an Ensemble of Multi-Layer Perceptron

Authors: Tebogo Emma Makaba, Barnabas Ndlovu Gatsheni

Abstract:

The cities of Johannesburg and Pretoria both located in the Gauteng province are separated by a distance of 58 km. The traffic queues on the Ben Schoeman freeway which connects these two cities can stretch for almost 1.5 km. Vehicle traffic congestion impacts negatively on the business and the commuter’s quality of life. The goal of this paper is to identify variables that influence the flow of traffic and to design a vehicle traffic prediction model, which will predict the traffic flow pattern in advance. The model will unable motorist to be able to make appropriate travel decisions ahead of time. The data used was collected by Mikro’s Traffic Monitoring (MTM). Multi-Layer perceptron (MLP) was used individually to construct the model and the MLP was also combined with Bagging ensemble method to training the data. The cross—validation method was used for evaluating the models. The results obtained from the techniques were compared using predictive and prediction costs. The cost was computed using combination of the loss matrix and the confusion matrix. The predicted models designed shows that the status of the traffic flow on the freeway can be predicted using the following parameters travel time, average speed, traffic volume and day of month. The implications of this work is that commuters will be able to spend less time travelling on the route and spend time with their families. The logistics industry will save more than twice what they are currently spending.

Keywords: Bagging ensemble methods, confusion matrix, multi-layer perceptron, vehicle traffic flow.

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31579 Blood Lymphocyte and Neutrophil Response of Cultured Rainbow Trout, Oncorhynchus mykiss, Administered Varying Dosages of an Oral Immunomodulator – ‘Fin-Immune™’

Authors: Duane Barker, John Holliday

Abstract:

In a 10-week (May – August, 2008) Phase I trial, 840, 1+ rainbow trout, Oncorhynchus mykiss, received a commercial oral immunomodulator, Fin Immune™, at four different dosages (0, 10, 20 and 30 mg g-1) to evaluate immune response and growth. The overall objective of was to determine an optimal dosage of this product for rainbow trout that provides enhanced immunity with maximal growth and health. Biweekly blood samples were taken from 10 randomly selected fish in each tank (30 samples per treatment) to evaluate the duration of enhanced immunity conferred by Fin-Immune™. The immunological assessment included serum white blood cell (lymphocyte, neutrophil) densities and blood hematocrit (packed cell volume %). Of these three variables, only lymphocyte density increased significantly among trout fed Fin- Immune™ at 20 and 30 mg g-1 which peaked at week 6. At week 7, all trout were switched to regular feed (lacking Fin-Immune™) and by week 10, lymphocyte levels decreased among all levels but were still greater than at week 0. There was growth impairment at the highest dose of Fin-Immune™ tested (30 mg g-1) which can be associated with a physiological compensatory mechanism due to a dose-specific threshold level. Thus, our main objective of this Phase I study was achieved, the 20 mg g-1 dose of Fin-Immune™ should be the most efficacious (of those we tested) to use for a Phase II disease challenge trial.

Keywords: Blood Lymphocyte, Neutrophil Response of Cultured Rainbow Trout, Oncorhynchus mykiss, Oral Immunomodulator – 'Fin-ImmuneTM'.

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31578 The Reliability of Wireless Sensor Network

Authors: B. Juhasova, I. Halenar, M. Juhas

Abstract:

The wireless communication is one of the widely used methods of data transfer at the present days. The benefit of this communication method is the partial independence of the infrastructure and the possibility of mobility. In some special applications it is the only way how to connect. This paper presents some problems in the implementation of a sensor network connection for measuring environmental parameters in the area of manufacturing plants.

Keywords: Network, communication, reliability, sensors.

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31577 Catalytic Decomposition of Potassium Monopersulfate. The Kinetics

Authors: Olga Gimeno, Javier Rivas, Maria Carbajo, Teresa Borralho

Abstract:

Potassium monopersulfate has been decomposed in aqueous solution in the presence of Co(II). The process has been simulated by means of a mechanism based on elementary reactions. Rate constants have been taken from literature reports or, alternatively, assimilated to analogous reactions occurring in Fenton's chemistry. Several operating conditions have been successfully applied.

Keywords: Monopersulfate, Oxone®, Sulfate radicals, Water treatment

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31576 Using Recyclable Steel Material in Tall Buildings

Authors: O. Eren, L. Zakar

Abstract:

Recycling steel building components is key to the sustainability of a structure’s end-of-life, as it is the most economical solution. In this paper the effects of usage of recycled steel material in tall buildings aspects are investigated.

Keywords: Building, recycled material, steel, structure.

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31575 Weakly Generalized Closed Map

Authors: R. Parimelazhagan, N. Nagaveni

Abstract:

In this paper we introduce a new class of mg-continuous mapping and studied some of its basic properties.We obtain some characterizations of such functions. Moreover we define sub minimal structure and further study certain properties of mg-closed sets.

Keywords: M-structure, mg-continuous mapping, minimal structure, mg T2 space, sub minimal structure, T12 space, mg-compact set.

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31574 A Hybrid Ontology Based Approach for Ranking Documents

Authors: Sarah Motiee, Azadeh Nematzadeh, Mehrnoush Shamsfard

Abstract:

Increasing growth of information volume in the internet causes an increasing need to develop new (semi)automatic methods for retrieval of documents and ranking them according to their relevance to the user query. In this paper, after a brief review on ranking models, a new ontology based approach for ranking HTML documents is proposed and evaluated in various circumstances. Our approach is a combination of conceptual, statistical and linguistic methods. This combination reserves the precision of ranking without loosing the speed. Our approach exploits natural language processing techniques to extract phrases from documents and the query and doing stemming on words. Then an ontology based conceptual method will be used to annotate documents and expand the query. To expand a query the spread activation algorithm is improved so that the expansion can be done flexible and in various aspects. The annotated documents and the expanded query will be processed to compute the relevance degree exploiting statistical methods. The outstanding features of our approach are (1) combining conceptual, statistical and linguistic features of documents, (2) expanding the query with its related concepts before comparing to documents, (3) extracting and using both words and phrases to compute relevance degree, (4) improving the spread activation algorithm to do the expansion based on weighted combination of different conceptual relationships and (5) allowing variable document vector dimensions. A ranking system called ORank is developed to implement and test the proposed model. The test results will be included at the end of the paper.

Keywords: Document ranking, Ontology, Spread activation algorithm, Annotation.

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31573 WiMAX RoF Design for Cost Effective Access Points

Authors: Haruka Mikamori, Koyu Chinen

Abstract:

An optimized design of E/O and O/E for access points of WiMAX RoF was carried out by evaluating RCE. The use of the DFB-LD, a low input-impedance driving, a low distortion PIN-PD, and a high gain EPHEMT amplifier is promising the cost-effective design. For the uplink RoF design, the use of EDFA and EP-HEMT amplifiers is necessity.

Keywords: WiMAX, RoF, RCE, RAU, Access Point

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31572 Numerical Investigation of Pressure Drop and Erosion Wear by Computational Fluid Dynamics Simulation

Authors: Praveen Kumar, Nitin Kumar, Hemant Kumar

Abstract:

The modernization of computer technology and commercial computational fluid dynamic (CFD) simulation has given better detailed results as compared to experimental investigation techniques. CFD techniques are widely used in different field due to its flexibility and performance. Evaluation of pipeline erosion is complex phenomenon to solve by numerical arithmetic technique, whereas CFD simulation is an easy tool to resolve that type of problem. Erosion wear behaviour due to solid–liquid mixture in the slurry pipeline has been investigated using commercial CFD code in FLUENT. Multi-phase Euler-Lagrange model was adopted to predict the solid particle erosion wear in 22.5° pipe bend for the flow of bottom ash-water suspension. The present study addresses erosion prediction in three dimensional 22.5° pipe bend for two-phase (solid and liquid) flow using finite volume method with standard k-ε turbulence, discrete phase model and evaluation of erosion wear rate with varying velocity 2-4 m/s. The result shows that velocity of solid-liquid mixture found to be highly dominating parameter as compared to solid concentration, density, and particle size. At low velocity, settling takes place in the pipe bend due to low inertia and gravitational effect on solid particulate which leads to high erosion at bottom side of pipeline.

Keywords: Computational fluid dynamics, erosion, slurry transportation, k-ε Model.

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31571 Lagrangian Geometrical Model of the Rheonomic Mechanical Systems

Authors: Camelia Frigioiu, Katica (Stevanovic) Hedrih, Iulian Gabriel Birsan

Abstract:

In this paper we study the rheonomic mechanical systems from the point of view of Lagrange geometry, by means of its canonical semispray. We present an example of the constraint motion of a material point, in the rheonomic case.

Keywords: Lagrange's equations, mechanical system, non-linear connection, rheonomic Lagrange space.

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