Search results for: predefined properties
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 2937

Search results for: predefined properties

2937 On Formalizing Predefined OCL Properties

Authors: Meryem Lamrani, Younès El Amrani, Aziz Ettouhami

Abstract:

The ability of UML to handle the modeling process of complex industrial software applications has increased its popularity to the extent of becoming the de-facto language in serving the design purpose. Although, its rich graphical notation naturally oriented towards the object-oriented concept, facilitates the understandability, it hardly successes to report all domainspecific aspects in a satisfactory way. OCL, as the standard language for expressing additional constraints on UML models, has great potential to help improve expressiveness. Unfortunately, it suffers from a weak formalism due to its poor semantic resulting in many obstacles towards the build of tools support and thus its application in the industry field. For this reason, many researches were established to formalize OCL expressions using a more rigorous approach. Our contribution join this work in a complementary way since it focuses specifically on OCL predefined properties which constitute an important part in the construction of OCL expressions. Using formal methods, we mainly succeed in expressing rigorously OCL predefined functions.

Keywords: Formal methods, Z, OCL, predefined properties, metamodel types.

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2936 Investigation of Artificial Neural Networks Performance to Predict Net Heating Value of Crude Oil by Its Properties

Authors: Mousavian, M. Moghimi Mofrad, M. H. Vakili, D. Ashouri, R. Alizadeh

Abstract:

The aim of this research is to use artificial neural networks computing technology for estimating the net heating value (NHV) of crude oil by its Properties. The approach is based on training the neural network simulator uses back-propagation as the learning algorithm for a predefined range of analytically generated well test response. The network with 8 neurons in one hidden layer was selected and prediction of this network has been good agreement with experimental data.

Keywords: Neural Network, Net Heating Value, Crude Oil, Experimental, Modeling.

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2935 Finding Viable Pollution Routes in an Urban Network under a Predefined Cost

Authors: Dimitra Alexiou, Stefanos Katsavounis, Ria Kalfakakou

Abstract:

In an urban area the determination of transportation routes should be planned so as to minimize the provoked pollution taking into account the cost of such routes. In the sequel these routes are cited as pollution routes.

The transportation network is expressed by a weighted graph G=(V,E,D,P) where every vertex represents a location to be served and contains unordered pairs (edges) of elements in V that indicate a simple road. The distances / cost and a weight that depict the provoked air pollution by a vehicle transition at every road are assigned to each road as well. These are the items of set D andrespectively.

Furthermore the investigated pollution routes must not exceed predefined corresponding values concerning the route cost and the route pollution level during the vehicle transition.

In this paper we present an algorithm that generates such routes in order that the decision maker selects the most appropriate one. 

Keywords: bi-criteria, pollution, shortest paths.

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2934 Fabrication of Autonomous Wheeled Mobile Robot for Industrial Applications Using Appropriate Technology

Authors: M. M. Islam, Rajib K. Saha, Abdullah A. Amin, M. Z. Haq

Abstract:

The autonomous mobile robot was designed and implemented which was capable of navigating in the industrial environments and did a job of picking objects from variable height and delivering it to another location following a predefined trajectory. In developing country like Bangladesh industrial robotics is not very prevalent yet, due to the high installation cost. The objective of this project was to develop an autonomous mobile robot for industrial application using the available resources in the local market at lower manufacturing cost. The mechanical system of the robot was comprised of locomotion, gripping and elevation system. Grippers were designed to grip objects of a predefined shape. Cartesian elevation system was designed for vertical movement of the gripper. PIC18F452 microcontroller was the brain of the control system. The prototype autonomous robot was fabricated for relatively lower load than the industry and the performance was tested in a virtual industrial environment created within the laboratory to realize the effectiveness.

Keywords: Industrial application, autonomous mobile robot, appropriate technology.

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2933 Assessment of Analytical Equations for the Derivation of Young’s Modulus of Bonded Rubber Materials

Authors: Z. N. Haji, S. O. Oyadiji, H. Samami, O. Farrell

Abstract:

The prediction of the vibration response of rubber products by analytical or numerical method depends mainly on the predefined intrinsic material properties such as Young’s modulus, damping factor and Poisson’s ratio. Such intrinsic properties are determined experimentally by subjecting a bonded rubber sample to compression tests. The compression tests on such a sample yield an apparent Young’s modulus which is greater in magnitude than the intrinsic Young’s modulus of the rubber. As a result, many analytical equations have been developed to determine Young’s modulus from an apparent Young’s modulus of bonded rubber materials. In this work, the applicability of some of these analytical equations is assessed via experimental testing. The assessment is based on testing of vulcanized nitrile butadiene rubber (NBR70) samples using tensile test and compression test methods. The analytical equations are used to determine the intrinsic Young’s modulus from the apparent modulus that is derived from the compression test data of the bonded rubber samples. Then, these Young’s moduli are compared with the actual Young’s modulus that is derived from the tensile test data. The results show significant discrepancy between the Young’s modulus derived using the analytical equations and the actual Young’s modulus.

Keywords: Bonded rubber, quasi-static test, shape factor, apparent Young’s modulus.

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2932 Component Based Framework for Authoring and Multimedia Training in Mathematics

Authors: Ion Smeureanu, Marian Dardala, Adriana Reveiu

Abstract:

The new programming technologies allow for the creation of components which can be automatically or manually assembled to reach a new experience in knowledge understanding and mastering or in getting skills for a specific knowledge area. The project proposes an interactive framework that permits the creation, combination and utilization of components that are specific to mathematical training in high schools. The main framework-s objectives are: • authoring lessons by the teacher or the students; all they need are simple operating skills for Equation Editor (or something similar, or Latex); the rest are just drag & drop operations, inserting data into a grid, or navigating through menus • allowing sonorous presentations of mathematical texts and solving hints (easier understood by the students) • offering graphical representations of a mathematical function edited in Equation • storing of learning objects in a database • storing of predefined lessons (efficient for expressions and commands, the rest being calculations; allows a high compression) • viewing and/or modifying predefined lessons, according to the curricula The whole thing is focused on a mathematical expressions minicompiler, storing the code that will be later used for different purposes (tables, graphics, and optimisations). Programming technologies used. A Visual C# .NET implementation is proposed. New and innovative digital learning objects for mathematics will be developed; they are capable to interpret, contextualize and react depending on the architecture where they are assembled.

Keywords: Adaptor, automatic assembly learning component and user control.

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2931 The Effect of Styrene-Butadiene-Rubber (SBR) Polymer Modifier on Properties of Bitumen

Authors: Seyed Abbas Tabatabaei, Alireza Kiasat, Ferdows Karimi Alkouhi

Abstract:

In order to use bitumen in hot mix asphalt, it must have specific characteristics. There are some methods to reach these properties. Using polymer modifiers are one of the methods to modify the bitumen properties. In this paper the effect of Styrene- Butadiene-Rubber that is one of the bitumen polymer modifiers on rheology properties of bitumen is studied. In this regard, the rheological properties of base bitumen and the modified bitumen with 3, 4, and 5 percent of Styrene-Butadiene-Rubber (SBR) were analysed. The results show that bitumen modified with 5 percent of SBR has the best performance than the other samples.

Keywords: Bitumen, polymer modifier, styrene-butadienerubber, rheological properties.

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2930 Remarks on Some Properties of Decision Rules

Authors: Songlin Yang, Ying Ge

Abstract:

This paper shows that some properties of the decision rules in the literature do not hold by presenting a counterexample. We give sufficient and necessary conditions under which these properties are valid. These results will be helpful when one tries to choose the right decision rules in the research of rough set theory.

Keywords: set, Decision table, Decision rule, coverage factor.

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2929 Gamma Irradiation Effects on the Magnetic Properties of Hard Ferrites

Authors: F. Abbas Pour Khotbehsara, B. Salehpour, A. Kianvash

Abstract:

Many industrial materials like magnets need to be tested for the radiation environment expected at linear colliders (LC) where the accelerator and detectors will be subjected to large influences of beta, neutron and gamma’s over their life Gamma irradiation of the permanent sample magnets using a 60Co source was investigated up to an absorbed dose of 700Mrad shows a negligible effect on some magnetic properties of Nd-Fe-B. In this work it has been tried to investigate the change of some important properties of Barium hexa ferrite. Results showed little decreases of magnetic properties at doses rang of 0.5 to 2.5 Mrad. But at the gamma irradiation dose up to 10 Mrad it is showed a few increase of properties. Also study of gamma irradiation of Nd-Fe-B showed considerably increase of magnetic properties.

Keywords: Gamma ray irradiation, Hard Ferrite, Magnetic coefficient, Radiation dose.

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2928 Process of Reprivatization of Agricultural Properties in the Selected European Countries

Authors: Adam Niewiadomski

Abstract:

Political transition of agricultural properties in Poland and the former German Democratic Republic (GDR) after 1989 had to include not only Reprivatization but also the issue of returning the properties in kind to their former owners. Restitution in kind applied in GDR to all forms of ownership which were subject to expropriation between 1933 and 1989 except for properties taken over during Soviet occupation in 1945-49. This issue was one of the flashpoints during the process of ownership changes. Privatization, limited as it was, took place in unequal legal environment where only one group of owners was privileged. Executing restitution in kind created a feeling of uncertainty among potential real estate buyers.

Keywords: Reprivatization, agricultural properties, German Democratic Republic, Privatization

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2927 Evaluation of the Elastic Mechanical Properties of a Hybrid Adhesive Material

Authors: Moudar H. A. Zgoul, Amin Al Zamer

Abstract:

Adhesive materials and adhesion have been the focal point of multiple research works related to numerous applications, particularly, aerospace, and aviation industries. To enhance the properties of conventional adhesive materials, additives have been introduced to the mix in order to enhance their mechanical and physical properties by creating a hybrid adhesive material. The evaluation of the mechanical properties of such hybrid adhesive materials is thus of an essential requirement for the purpose of properly modeling their behavior accurately. This paper presents an approach/tool to simulate the behavior such hybrid adhesives in a way that will allow researchers to better understand their behavior while in service.

Keywords: Adhesive materials, analysis, hybrid adhesives, mechanical properties, simulation.

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2926 Mechanical Properties and Microstructural Properties of CrSiN Coating

Authors: Dhiflaoui Hafedh, Khlifi Kaouthar, Ben Cheikh Larbi Ahmed

Abstract:

The present study deals with the characterization of CrSiN coatings obtained by PVD magnetron sputtering systems. CrSiN films were deposited with different Si contents, in order to check the effect of at.% variation on the different properties of the Cr–N system. Coatings were characterized by scanning electron microscopy (SEM) for thickness measurements, X-ray diffraction. Surface morphology and the roughness characteristics were explored using AFM, Mechanicals properties, elastic and plastic deformation resistance of thin films were investigated using nanoindentation test. We observed that the Si addition improved the hardness and the Young’s modulus of the Cr–N system. Indeed, the hardness value is 18,56 GPa for CrSiN coatings. Besides, the Young’s modulus value is 224,22 GPa for CrSiN coatings for Si content of 1.2 at.%.

Keywords: Thin film, mechanicals properties, PVD.

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2925 Effect of 2wt% Cu Addition on the Tensile Properties and Fracture Behavior of Peak Aged Al-6Si-0.5Mg-2Ni Alloy at Various Strain Rates

Authors: A. Hossain, A. S. W. Kurny, M. A. Gafur

Abstract:

Effect of 2wt% Cu addition on tensile properties and fracture behavior of Al-6Si-0.5Mg-2Ni alloy at various strain rates were studied. The solution treated Al-6Si-0.5Mg-2Ni (-2Cu) alloys, were aged isochronally for 1 hour at temperatures up to 300oC. The uniaxial tension test was carried out at strain rate ranging from 10-4s-1 to 10-2s-1 in order to investigate the strain rate dependence of tensile properties. Tensile strengths were found to increase with ageing temperature and the maximum being attained ageing for 1 hr at 225oC (peak aged condition). Addition of 2wt% Cu resulted in an increase in tensile properties at all strain rates. Evaluation of tensile properties at three different strain rates (10-4, 10-3 and 10-2 s-1) showed that strain rates affected the tensile properties significantly. At higher strain rates the strength was better but ductility was poor. Microstructures of broken specimens showed that both the void coalescence and the interface debonding affect the fracture behavior of the alloys

Keywords: Al-Si-Mg-Ni-Cu alloy, tensile properties, strain rate, SEM.

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2924 Experimental Study on Thermomechanical Properties of New-Generation ODS Alloys

Authors: O. Khalaj, B. Mašek, H. Jirková, J. Svoboda

Abstract:

By using a combination of new technologies together with an unconventional use of different types of materials, specific mechanical properties and structures of the material can be achieved. Some possibilities are enabled by a combination of powder metallurgy in the preparation of a metal matrix with dispersed stable particles achieved by mechanical alloying and hot consolidation. This paper explains the thermomechanical properties of new generation of Oxide Dispersion Strengthened alloys (ODS) within three ranges of temperature with specified deformation profiles. The results show that the mechanical properties of new ODS alloys are significantly affected by the thermomechanical treatment.

Keywords: Hot forming, ODS, alloys, thermomechanical, Fe-Al, Al2O3.

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2923 Improvement in Properties of Ni-Cr-Mo-V Steel through Process Control

Authors: Arnab Majumdar, Sanjoy Sadhukhan

Abstract:

Although gun barrel steels are an important variety from defense view point, available literatures are very limited. In the present work, an IF grade Ni-Cr-Mo-V high strength low alloy steel is produced in Electric Earth Furnace-ESR Route. Ingot was hot forged to desired dimension with a reduction ratio of 70-75% followed by homogenization, hardening and tempering treatment. Sample chemistry, NMIR, macro and micro structural analyses were done. Mechanical properties which include tensile, impact, and fracture toughness were studied. Ultrasonic testing was done to identify internal flaws. The existing high strength low alloy Ni-Cr-Mo-V steel shows improved properties in modified processing route and heat treatment schedule in comparison to properties noted earlier for manufacturing of gun barrels. The improvement in properties seems to withstand higher explosive loads with the same amount of steel in gun barrel application.

Keywords: Gun barrel steels, IF grade, physical properties, thermal and mechanical processing, mechanical properties, ultrasonic testing.

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2922 Automatically Generated and Marked E-Learning Exercises for Logistics Cost Accounting

Authors: Markus Siepermann, Christoph Siepermann

Abstract:

This paper presents the concept and realisation of an e-learning tool that provides predefined or automatically generated exercises concerning logistics cost accounting. Students may practise where and whenever they like to via the Internet. Their solutions are marked automatically by the tool while considering consecutive faults and without any intervention of lecturers.

Keywords: Automatic marking, e-learning environment, onlinepracticing, randomly-generated exercises.

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2921 Possibilities of Utilization Zeolite in Concrete

Authors: M. Sedlmajer, J. Zach, J. Hroudová, P. Rovnaníková

Abstract:

There are several possibilities of reducing the required amount of cement in concrete production. Natural zeolite is one of the raw materials which can partly substitute Portland cement. The effort to reduce the amount of Portland cement used in concrete production is brings both economical as well as ecological benefits. The paper presents the properties of concrete containing natural zeolite as an active admixture in the concrete which partly substitutes Portland cement. The properties discussed here bring information about the basic mechanical properties and frost resistance of concrete containing zeolite. The properties of concretes with the admixture of zeolite are compared with a reference concrete with no content of zeolite. The properties of the individual concretes are observed for 360 days.

Keywords: Concrete, zeolite, compressive strength, modulus of elasticity, durability.

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2920 Effect of Non-Crimp Fabric Structure on Mechanical Properties of Laminates

Authors: Hireni R. Mankodi, D. J. Chudasama

Abstract:

The textile preforms play a key role in providing the mechanical properties and gives the idea about selection parameter of preforms to improve the quality and performance of laminates. The main objectives of this work are to study the effect of non-crimp fabric preform structure in final properties of laminates. It has been observed that the multi-axial preform give better mechanical properties of laminates as compared to woven and biaxial fabrics. This study investigated the effect of different non-crimp glass preform structure on tensile strength, bending and compression properties of glass laminates. The different woven, bi-axial and multi-axial fabrics with similar GSM used to manufacture the laminates using polyester resin. The structural and mechanical properties of preform and laminates were studied using standard methods. It has been observed that the glass fabric geometry, including type of weaves, warps and filling density and number of layer plays significant role in deciding mechanical properties of laminates.

Keywords: Preform, non-crimp, laminates, bi-axial, multiaxial.

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2919 Mechanical and Thermal Properties Characterisation of Vinyl Ester Matrix Nanocomposites Based On Layered Silicate: Effect of Processing Parameters

Authors: A. I. Alateyah, H. N. Dhakal, Z. Y. Zhang

Abstract:

The mechanical properties including flexural and tensile of neat vinyl ester and polymer based on layered silicate nanocomposite materials of two different methodologies are discussed. Methodology 1 revealed that the addition of layered silicate into the polymer matrix increased the mechanical and thermal properties up to 1 wt.% clay loading. The incorporation of more clay resulted in decreasing the properties which was traced to the existence of aggregation layers. The aggregation layers imparted a negative impact on the overall mechanical and thermal properties. On the other hand, methodology 2 increased the mechanical and thermal properties up to 4 wt.% clay loading. The different amounts of improvements were assigned to the various preparation parameters. Wide Angle X-ray Diffraction, Scanning Electron Microscopy and Transmission Electron Microscopy were utilized in order to characterize the interlamellar structure of nanocomposites.

Keywords: Vinyl ester, nanocomposites, layered silicate, mechanical properties, thermal analysis.

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2918 Flow Properties of Commercial Infant Formula Powders

Authors: Maja Benkovic, Ingrid Bauman

Abstract:

The objective of this work was to investigate flow properties of powdered infant formula samples. Samples were purchased at a local pharmacy and differed in composition. Lactose free infant formula, gluten free infant formula and infant formulas containing dietary fibers and probiotics were tested and compared with a regular infant formula sample which did not contain any of these supplements. Particle size and bulk density were determined and their influence on flow properties was discussed. There were no significant differences in bulk densities of the samples, therefore the connection between flow properties and bulk density could not be determined. Lactose free infant formula showed flow properties different to standard supplement-free sample. Gluten free infant formula with addition of probiotic microorganisms and dietary fiber had the narrowest particle size distribution range and exhibited the best flow properties. All the other samples exhibited the same tendency of decreasing compaction coefficient with increasing flow speed, which means they all become freer flowing with higher flow speeds.

Keywords: flow properties, infant formula, powderedmaterial

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2917 Battery/Supercapacitor Emulator for Chargers Functionality Testing

Authors: S. Farag, A. Kupeman

Abstract:

In this paper, design of solid-state battery/supercapacitor emulator based on dc-dc boost converter is described. The emulator mimics charging behavior of any storage device based on a predefined behavior set by the user. The device is operated by a two-level control structure: high-level emulating controller and low- level input voltage controller. Simulation and experimental results are shown to demonstrate the emulator operation.

Keywords: Battery, Charger, Energy, Storage, Supercapacitor.

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2916 Preparation and Characterization of Chitosan / Polyacrylic Acid / Ag-Nanoparticles Composite Membranes

Authors: Abdel-Mohdy, A. Abou-Okeil, S. El-Sabagh, S. M. El-Sawy

Abstract:

Chitosan polyacrylic acid composite membranes were prepared by a bulk polymerization method in presence of N, N'- methylene bisacrylamide (crosslinker) and ammonium persulphate as initiator. Membranes prepared from this copolymer in presence and absence of Ag nanoparticles were characterized by measuring mechanical and physical properties, water up-take and antibacterial properties. The results obtained indicated that the prepared membranes have antibacterial properties which increase with adding Ag nanoparticles.

Keywords: Ag nanoparticles, antimicrobial, composites, Membrane, physical properties.

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2915 Effect of T6 and Re-Aging Heat Treatment on Mechanical Properties of 7055 Aluminum Alloy

Authors: M. Esmailian, M. Shakouri, A. Mottahedi, S. G. Shabestari

Abstract:

Heat treatable aluminum alloys such as 7075 and 7055, because of high strength and low density, are used widely in aircraft industry. For best mechanical properties, T6 heat treatment has recommended for this regards, but this temper treatment is sensitive to corrosion induced and Stress Corrosion Cracking (SCC) damage. For improving this property, the over-aging treatment (T7) applies to this alloy, but it decreases the mechanical properties up to 30 percent. Hence, to increase the mechanical properties, without any remarkable decrease in SCC resistant, Retrogression and Re-Aging (RRA) heat treatment is used. This treatment performs in a relatively short time. In this paper, the RRA heat treatment was applied to 7055 aluminum alloy and then effect of RRA time on the mechanical properties of 7055 has been investigated. The results show that the 40-minute time is suitable time for retrogression of 7055 aluminum alloy and ultimate strength increases up to 625MPa.

Keywords: 7055 Aluminum alloy, Mechanical properties, SCC resistance, Heat Treatment.

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2914 The Use of Information Technologies in Special Education for Preparation of Individual Education Programs

Authors: Yasar Guneri Sahin, Mehmet Cudi Okur

Abstract:

In this presentation, we discuss the use of information technologies in the area of special education for teaching individuals with learning disabilities. Application software which was developed for this purpose is used to demonstrate the applicability of a database integrated information processing system to alleviate the burden of educators. The software allows the preparation of individualized education programs based on the predefined objectives, goals and behaviors.

Keywords: Special education, disabled individual, informationtechnology, individual education programs.

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2913 Effects of Different Drying Methods on the Properties of Viscose Single Jersey Fabrics

Authors: M. Kucukali Ozturk, Y. Beceren, B. Nergis

Abstract:

The study discussed in this paper was conducted in an attempt to investigate effects of different drying methods (line dry and tumble dry) on viscose single jersey fabrics knitted with ring yarn.

Keywords: Color change, dimensional properties, drying method, fabric tightness, physical properties.

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2912 Mechanical Properties of Die-Cast Nonflammable Mg Alloy

Authors: Myoung-Gon Yoon, Jung-Ho Moon, Tae Kwon Ha

Abstract:

Tensile specimens of nonflammable AZ91D Mg alloy were fabricated in this study via cold chamber die-casting process. Dimensions of tensile specimens were 25mm in length, 4mm in width, and 0.8 or 3.0mm in thickness. Microstructure observation was conducted before and after tensile tests at room temperature. In the die casting process, various injection distances from 150 to 260mm were employed to obtain optimum process conditions. Distribution of Al12Mg17 phase was the key factor to determine the mechanical properties of die-cast Mg alloy. Specimens with 3mm of thickness showed superior mechanical properties to those with 0.8mm of thickness. Closed networking of Al12Mg17 phase along grain boundary was found to be detrimental to mechanical properties of die-cast Mg alloy.

Keywords: Non-flammable magnesium alloy, AZ91D, die-casting, microstructure, mechanical properties.

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2911 Effects of Water Content on Dielectric Properties of Mineral Transformer Oil

Authors: Suwarno, M. Helmi Prakoso

Abstract:

Mineral oil is commonly used for high voltage transformer insulation. The insulation quality of mineral oil is affecting the operation process of high voltage transformer. There are many contaminations which could decrease the insulation quality of mineral oil. One of them is water. This research talks about the effect of water content on dielectric properties, physic properties, and partial discharge pattern on mineral oil. Samples were varied with 10 varieties of water content value. And then all samples would be tested to measure the dielectric properties, physic properties, and partial discharge pattern. The result of this research showed that an increment of water content value would decrease the insulation quality of mineral oil.

Keywords: Dielectric properties, high voltage transformer, mineral oil, water content.

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2910 Characteristics of Nanosilica-Geopolymer Nanocomposites and Mixing Effect

Authors: H. Assaedi, F. U. A. Shaikh, I. M. Low

Abstract:

This paper presents the effects of mixing procedures on mechanical properties of flyash-based geopolymer matrices containing nanosilica (NS) at 0.5%, 1.0%, 2.0%, and 3.0% by weight. Comparison is made with conventional mechanical dry-mixing of NS with flyash and wet-mixing of NS in alkaline solutions. Physical and mechanical properties are investigated using X-Ray Diffraction (XRD) and Scanning Electron Microscope (SEM). Results show that generally the addition of NS particles enhanced the microstructure and improved flexural and compressive strengths of geopolymer nanocomposites. However, samples, prepared using dry-mixing approach, demonstrate better physical and mechanical properties comparing to wet-mixing samples.

Keywords: Geopolymer, mechanical properties, nanosilica.

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2909 Lithium Oxide Effect on the Thermal and Physical Properties of the Ternary System Glasses (Li2O3-B2O3-Al2O3)

Authors: D. Aboutaleb, B. Safi

Abstract:

The borate glasses are known by their structural characterized by existence of unit’s structural composed by triangles and tetrahedrons boron in different configurations depending on the percentage of B2O3 in the glass chemical composition. In this paper, effect of lithium oxide addition on the thermal and physical properties of an alumina borate glass, was investigated. It was found that the boron abnormality has a significant effect in the change of glass properties according to the addition rate of lithium oxide.

Keywords: Borate glasses, triangles and tetrahedrons boron, Lithium oxide, Boron anomaly, thermal properties, physical properties.

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2908 Extremal Properties of Generalized Class of Close-to-convex Functions

Authors: Norlyda Mohamed, Daud Mohamad, Shaharuddin Cik Soh

Abstract:

Let Gα ,β (γ ,δ ) denote the class of function f (z), f (0) = f ′(0)−1= 0 which satisfied e δ {αf ′(z)+ βzf ′′(z)}> γ i Re in the open unit disk D = {z ∈ı : z < 1} for some α ∈ı (α ≠ 0) , β ∈ı and γ ∈ı (0 ≤γ <α ) where δ ≤ π and α cosδ −γ > 0 . In this paper, we determine some extremal properties including distortion theorem and argument of f ′( z ) .

Keywords: Argument of f ′(z) , Carathéodory Function, Closeto- convex Function, Distortion Theorem, Extremal Properties

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