Search results for: Mathematical morphology

Authors: O. Sotolongo-Grau, D. Rodriguez-Perez, J. A. Santos-Miranda, M. M. Desco, O. Sotolongo-Costa, J. C. Antoranz

Abstract:

The use of the oncologic index ISTER allows for a more effective planning of the radiotherapic facilities in the hospitals. Any change in the radiotherapy treatment, due to unexpected stops, may be adapted by recalculating the doses to the new treatment duration while keeping the optimal prognosis. The results obtained in a simulation model on millions of patients allow the definition of optimal success probability algorithms.

Keywords: Mathematical model, radiation oncology, dynamical systems applications.

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Authors: R. Bendib, A. Khelassi

Abstract:

In this paper we will consider the most known ratios control schemes ((L/D, V/B),(L/D,V/F), Ryskamp-s, and (D/(L+D),V/B)) for binary distillation column and we compare them in the basis of interactions and disturbance propagation. The models for these configurations are deuced using mathematical transformations taking the energy balance structure (LV) as a base model. The dynamic relative magnitude criterion (DRMC) is used to assess the interactions. The results show that the introduction of ratios in controlling the column tends to minimize the degree of interactions between the loops.

Keywords: Distillation, interaction, DRMC, configurations.

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Authors: Jan Zeman

Abstract:

The paper describes the futures trading and aims to design the speculators trading strategy. The problem is formulated as the decision making task and such as is solved. The solution of the task leads to complex mathematical problems and the approximations of the decision making is demanded. Two kind of approximation are used in the paper: Monte Carlo for the multi-step prediction and iteration spread in time for the optimization. The solution is applied to the real-market data and the results of the off-line experiments are presented.

Keywords: futures trading, decision making

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Authors: Mochamad Chalid, Imam Prabowo

Abstract:

Today, the pollution due to non-degradable material such as plastics, has led to studies about the development of environmental-friendly material. Because of biodegradability obtained from natural sources, polylactid acid (PLA) and ijuk fiber are interesting to modify into a composite. This material is also expected to reduce the impact of environmental pollution. Surface modification of ijuk fiber through alkalinization with 0.25 M NaOH solution for 30 minutes was aimed to enhance its compatibility to PLA, in order to improve properties of the composite such as the mechanical properties. Alkalinization of the ijuk fibers annihilates some surface components such as lignin, wax and hemicelloluse, so the pore on the surface clearly appeared, decreasing of the density and diameter of the ijuk fibers. The change of the ijuk fiber properties leads to increase the mechanical properties of PLA composites reinforced the ijuk fibers through strengthening of the mechanical interlocking with the PLA matrix. An addition to enhance the distribution of the fibers in the PLA matrix, the stirring during DCM solvent evaporation from the mixture of the ijuk fibers and the dissolved-PLA can reduce amount of the trapped-voids and fibers pull-out phenomena, which can decrease the mechanical properties of the composite.

Keywords: Polylactic acid, Arenga pinnata, alkalinization, compatibility, adhesion, morphology, mechanical properties, volume fraction, distributiom.

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Authors: S.Mousavian, D.Ashouri, M.abdolahi, M.H.Vakili, Y.Rahnama

Abstract:

In this study, the dispersed model is used to predict gas phase concentration, liquid drop concentration. The venturi scrubber efficiency is calculated by gas phase concentration. The modified model has been validated with available experimental data of Johnstone, Field and Tasler for a range of throat gas velocities, liquid to gas ratios and particle diameters and is used to study the effect of some design parameters on collection efficiency.

Keywords: Ammonia, Modelling, Purge gas, Removal efficiency, Venturi scrubber

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Authors: Jarno Haapamäki, Juha Röning

Abstract:

Scale defects are common surface defects in hot steel rolling. The modelling of such defects is problematic and their causes are not straightforward. In this study, we investigated genetic algorithms in search for a mathematical solution to scale formation. For this research, a high-dimensional data set from hot steel rolling process was gathered. The synchronisation of the variables as well as the allocation of the measurements made on the steel strip were solved before the modelling phase.

Keywords: Genetic algorithms, hot strip rolling, knowledge discovery, modeling.

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Authors: Hendriëtte van der Walt, Lesley Chown, Richard Harris, Ndabenhle Sosibo, Robert Tshikhudo

Abstract:

The use of magnetic and magnetic/gold core/shell nanoparticles in biotechnology or medicine has shown good promise due to their hybrid nature which possesses superior magnetic and optical properties. Some of these potential applications include hyperthermia treatment, bio-separations, diagnostics, drug delivery and toxin removal. Synthesis refinement to control geometric and magnetic/optical properties, and finding functional surfactants for biomolecular attachment, are requirements to meet application specifics. Various high-temperature preparative methods were used for the synthesis of iron oxide and gold-coated iron oxide nanoparticles. Different surface functionalities, such as 11-aminoundecanoic and 11-mercaptoundecanoic acid, were introduced on the surface of the particles to facilitate further attachment of biomolecular functionality and drug-like molecules. Nanoparticle thermal stability, composition, state of aggregation, size and morphology were investigated and the results from techniques such as Fourier Transform-Infra Red spectroscopy (FT-IR), Ultraviolet visible spectroscopy (UV-vis), Transmission Electron Microscopy (TEM) and thermal analysis are discussed.

Keywords: Core/shell, Iron oxide, Gold coating, Nanoparticles.

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Authors: Francisco Miranda

Abstract:

The optimization problem using time scales is studied. Time scale is a model of time. The language of time scales seems to be an ideal tool to unify the continuous-time and the discrete-time theories. In this work we present necessary conditions for a solution of an optimization problem on time scales. To obtain that result we use properties and results of the partial diamond-alpha derivatives for continuous-multivariable functions. These results are also presented here.

Keywords: Lagrange multipliers, mathematical programming, optimization problem, time scales.

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Authors: Eleni Galiotou, Angela Ralli

Abstract:

In this paper we propose a computational model for the representation and processing of morpho-phonological phenomena in a natural language, like Modern Greek. We aim at a unified treatment of inflection, compounding, and word-internal phonological changes, in a model that is used for both analysis and generation. After discussing certain difficulties cuase by well-known finitestate approaches, such as Koskenniemi-s two-level model [7] when applied to a computational treatment of compounding, we argue that a morphology-based model provides a more adequate account of word-internal phenomena. Contrary to the finite state approaches that cannot handle hierarchical word constituency in a satisfactory way, we propose a unification-based word grammar, as the nucleus of our strategy, which takes into consideration word representations that are based on affixation and [stem stem] or [stem word] compounds. In our formalism, feature-passing operations are formulated with the use of the unification device, and phonological rules modeling the correspondence between lexical and surface forms apply at morpheme boundaries. In the paper, examples from Modern Greek illustrate our approach. Morpheme structures, stress, and morphologically conditioned phoneme changes are analyzed and generated in a principled way.

Keywords: Morpho-Phonology, Natural Language Processing.

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Authors: M. Bahgat, H. Hanafy, H. Al-Tassan

Abstract:

Cluster formation is an essential phenomenon during direct reduction processes at shaft furnaces. Decreasing the reducing temperature to avoid this problem can cause a significant drop in throughput. In order to prevent sticking of pellets, a coating material basically inactive under the reducing conditions prevailing in the shaft furnace, should be applied to cover the outer layer of the pellets. In the present work, steel dust is used as coating material for iron ore pellets to explore dust coating effectiveness and determines the best coating conditions. Steel dust coating is applied for iron ore pellets in various concentrations. Dust slurry concentrations of 5.0-30% were used to have a coated steel dust amount of 1.0-5.0 kg per ton iron ore. Coated pellets with various concentrations were reduced isothermally in weight loss technique with simulated gas mixture to the composition of reducing gases at shaft furnaces. The influences of various coating conditions on the reduction behavior and the morphology were studied. The optimum reduced samples were comparatively applied for sticking index measurement. It was found that the optimized steel dust coating condition that achieve higher reducibility with lower sticking index was 30% steel dust slurry concentration with 3.0 kg steel dust/ton ore.

Keywords: Ironmaking, coating, steel dust, reduction.

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Authors: S. H. Teh, S. Malawaraarachci, W. P. Chan, A. Nassirharand

Abstract:

The purpose of this paper is to present the design and instrumentation of a new benchmark multivariable nonlinear control laboratory. The mathematical model of this system may be used to test the applicability and performance of various nonlinear control procedures. The system is a two degree-of-freedom robotic arm with soft and hard (discontinuous) nonlinear terms. Two novel mechanisms are designed to allow the implementation of adjustable Coulomb friction and backlash.

Keywords: Nonlinear control, describing functions, AdjustableCoulomb friction, Adjustable backlash.

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Authors: Gunawan Nugroho, Ahmed M. S. Ali, Zainal A. Abdul Karim

Abstract:

Incompressible Navier-Stokes equations are reviewed in this work. Three-dimensional Navier-Stokes equations are solved analytically. The Mathematical derivation shows that the solutions for the zero and constant pressure gradients are similar. Descriptions of the proposed formulation and validation against two laminar experiments and three different turbulent flow cases are reported in this paper. Even though, the analytical solution is derived for nonreacting flows, it could reproduce trends for cases including combustion.

Keywords: Navier-Stokes Equations, potential function, turbulent flows.

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Authors: Miroslav Byrtus

Abstract:

Large rotating systems, especially gear drives and gearboxes, occur as parts of many mechanical devices transmitting the torque with relatively small loss of power. With the increased demand for high speed machinery, mathematical modeling and dynamic analysis of gear drives gained importance. Mathematical description of such mechanical systems is a complex task evolving for several decades. In gear drive dynamic models, which include flexible shafts, bearings and gearing and use the finite elements, nonlinear effects due to gear mesh and bearings are usually ignored, for such models have large number of degrees of freedom (DOF) and it is computationally expensive to analyze nonlinear systems with large number of DOF. Therefore, these models are not suitable for simulation of nonlinear behavior with amplitude jumps in frequency response. The contribution uses a methodology of nonlinear large rotating system modeling which is based on degrees of freedom (DOF) number reduction using modal synthesis method (MSM). The MSM enables significant DOF number reduction while keeping the nonlinear behavior of the system in a specific frequency range. Further, the MSM with DOF number reduction is suitable for including detail models of nonlinear couplings (mainly gear and bearing couplings) into the complete gear drive models. Since each subsystem is modeled separately using different FEM systems, it is advantageous to parameterize models of subsystems and to use the parameterization for optimization of chosen design parameters. Final complex model of gear drive is assembled in MATLAB and MATLAB tools are used for dynamical analysis of the nonlinear system. The contribution is further focused on developing of a methodology for investigation of behavior of the system by Nonlinear Normal Modes with combination of the MSM using numerical continuation method. The proposed methodology will be tested using a two-stage gearbox including its housing.

Keywords: Vibro-impact system, rotating system, gear drive, modal synthesis method, numerical continuation method, periodic solution.

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Authors: Hamed Rafiei, Masoud Rabbani

Abstract:

This paper addresses one of the most important issues have been considered in hybrid MTS/MTO production environments. To cope with the problem, a mathematical programming model is applied from a tactical point of view. The model is converted to a fuzzy goal programming model, because a degree of uncertainty is involved in hybrid MTS/MTO context. Finally, application of the proposed model in an industrial center is reported and the results prove the validity of the model.

Keywords: Fuzzy sets theory, Hybrid MTS/MTO, Order penetration point, Quadratic programming.

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Authors: M. Amlie A. Kasim, Ahsana Aqilah, Ahmed Jaffar, Cheng Yee Low, Roseleena Jaafar, M. Saiful Bahari, Armansyah

Abstract:

The study of human hand morphology reveals that developing an artificial hand with the capabilities of human hand is an extremely challenging task. This paper presents the development of a robotic prosthetic hand focusing on the improvement of a tendon driven mechanism towards a biomimetic prosthetic hand. The design of this prosthesis hand is geared towards achieving high level of dexterity and anthropomorphism by means of a new hybrid mechanism that integrates a miniature motor driven actuation mechanism, a Shape Memory Alloy actuated mechanism and a passive mechanical linkage. The synergy of these actuators enables the flexion-extension movement at each of the finger joints within a limited size, shape and weight constraints. Tactile sensors are integrated on the finger tips and the finger phalanges area. This prosthesis hand is developed with an exact size ratio that mimics a biological hand. Its behavior resembles the human counterpart in terms of working envelope, speed and torque, and thus resembles both the key physical features and the grasping functionality of an adult hand.

Keywords: Prosthetic hand, Biomimetic actuation, Shape Memory Alloy, Tactile sensing.

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Authors: M. E. Abalaka, S. Y. Daniyan, S. O. Adeyemo, D. Damisa

Abstract:

Gold nanoparticles (AuNPs) have gained increasing interest in recent times. This is greatly due to their special features, which include unusual optical and electronic properties, high stability and biological compatibility, controllable morphology and size dispersion, and easy surface functionalization. In typical synthesis, AuNPs were produced by reduction of gold salt AuCl4 in an appropriate solvent. A stabilizing agent was added to prevent the particles from aggregating. The antibacterial activity of different sizes of gold nanoparticles was investigated against Staphylococcus aureus, Salmonella typhi and Pseudomonas pneumonia using the disk diffusion method in a Müeller–Hinton Agar. The Au-NPs were effective against all bacteria tested. That the Au-NPs were successfully synthesized in suspension and were used to study the antibacterial activity of the two medicinal plants against some bacterial pathogens suggests that Au-NPs can be employed as an effective bacteria inhibitor and may be an effective tool in medical field. The study clearly showed that the Au-NPs exhibiting inhibition towards the tested pathogenic bacteria in vitro could have the same effects in vivo and thus may be useful in the medical field if well researched into.

Keywords: Gold Nanoparticles, Gomphrena celesioides, Prunus amygdalus, Pathogens.

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Authors: Ashagrie Getnet Flattie

Abstract:

Line-of-sight (LOS) information, data rates, good quality, and flexible network service are limited by the fact that, for the duration of any given connection, they experience severe variation in signal strength due to fading and path loss. Wireless system faces major challenges in achieving wide coverage and capacity without affecting the system performance and to access data everywhere, all the time. In this paper, the cell coverage and edge rate of different Multiple-input multiple-output (MIMO) schemes in 20 MHz Long Term Evolution (LTE) system under Unmanned Air Vehicles (UAV) platform are investigated. After some background on the enormous potential of UAV, MIMO, and LTE in wireless links, the paper highlights the presented system model which attempts to realize the various benefits of MIMO being incorporated into UAV platform. The performances of the three MIMO LTE schemes are compared with the performance of 4x4 MIMO LTE in UAV scheme carried out to evaluate the improvement in cell radius, BER, and data throughput of the system in different morphology. The results show that significant performance gains such as bit error rate (BER), data rate, and coverage can be achieved by using the presented scenario.

Keywords: BER, LTE, MIMO, path loss, UAV.

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Authors: Mohammad Al-Fayoumi, Soumya Banerjee, Jr., P. K. Mahanti

Abstract:

A social network is a set of people or organization or other social entities connected by some form of relationships. Analysis of social network broadly elaborates visual and mathematical representation of that relationship. Web can also be considered as a social network. This paper presents an innovative approach to analyze a social network using a variant of existing ant colony optimization algorithm called as Clever Ant Colony Metaphor. Experiments are performed and interesting findings and observations have been inferred based on the proposed model.

Keywords: Social Network, Ant Colony, Maximum Clique, Sub graph, Clever Ant colony.

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Authors: Aki Happonen, Adrian Burian, Erwin Hemming

Abstract:

Fixed-point simulation results are used for the performance measure of inverting matrices using a reconfigurable processing element. Matrices are inverted using the Cholesky decomposition algorithm. The reconfigurable processing element is capable of all required mathematical operations. The fixed-point word length analysis is based on simulations of different condition numbers and different matrix sizes.

Keywords: Cholesky Decomposition, Fixed-point, Matrixinversion, Reconfigurable processing.

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Authors: Rizwan Nasir, Hilmi Mukhtar, Zakaria Man, Dzeti Farhah Mohshim

Abstract:

Carbon dioxide has been well associated with greenhouse effect, and due to its corrosive nature it is an undesirable compound. A variety of physical-chemical processes are available for the removal of carbon dioxide. Previous attempts in this field have established alkanolamine group has the capability to remove carbon dioxide. So, this study combined the polymeric membrane and alkanolamine solutions to fabricate the amine polymeric membrane (APM) to remove carbon dioxide (CO₂). This study entails the effect of three types of amines, monoethanolamine (MEA), diethanolamine (DEA), and methyldiethanolamine (MDEA). The effect of each alkanolamine group on the morphology and performance of polyether sulfone (PES) polymeric membranes was studied. Flat sheet membranes were fabricated by solvent evaporation method by adding polymer and different alkanolamine solutions in the N-Methyl-2-pyrrolidone (NMP) solvent. The final membranes were characterized by using Field Emission Electron Microscope (FESEM), Fourier Transform Infrared (FTIR), and Thermo-Gravimetric Analysis (TGA). The membrane separation performance was studied. The PES-DEA and PES-MDEA membrane has good ability to remove carbon dioxide. 

Keywords: Amine Polymeric membrane, Alkanolamine solution, CO2 Removal, Characterization.

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Authors: Weijian Rong

Abstract:

Soft topological spaces are considered as mathematical tools for dealing with uncertainties, and a fuzzy topological space is a special case of the soft topological space. The purpose of this paper is to study soft topological spaces. We introduce some new concepts in soft topological spaces such as soft first-countable spaces, soft second-countable spaces and soft separable spaces, and some basic properties of these concepts are explored.

Keywords: soft sets, soft first-countable spaces, soft second countable spaces, soft separable spaces, soft Lindelöf.

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Authors: Riham A. Ragheb

Abstract:

Water is a fundamental attraction in all cultures and among all classes of people,tourists and citizens. It is a favorite location for major tourism initiatives, celebrations and ceremonies. The vitality of any city depends on citizen action to take part in creating the neighborhoods they desire. Waterfront can provide extensive new areas of high quality public open space in parts of the city that are popular venues for social activities and also have the highest land values. Each city must have a character that can be used as a key attraction for the development. The morphology of a waterfront can be identified by both its physical characteristics and the socio-cultural activities that take place in the area. Alexandria has been selected as an area of study because it has a unique character due to its possession of a variety of waterfronts.

This paper aims to set some criteria of successful waterfront development and then through these criteria analyzing the development of the Qaitbay waterfront in the eastern harbor in Alexandria, Egypt. Hence, a comprehensive improvement of the waterfront areas is certainly needed to ensure a successful waterfront development radiated the sense of uniformity and coherence.

Alexandria can benefit from these criteria to develop its urban waterfront in order to preserve and revitalize its unique waterfront character and achieve mixed uses and tourism development.

Keywords: Place making, Qaitbay, responsive environment, sustainable urban design, waterfront development.

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Authors: M. Tazky, R. Hela, P. Novosad, L. Osuska

Abstract:

This paper deals with the possibility of safe incorporation fluidised bed combustion fly ash (waste material) into cement matrix together with next commonly used secondary raw material, which is high-temperature fly ash. Both of these materials have a very high pozzolanic ability, and the right combination could bring important improvements in both the physico-mechanical properties and the better durability of a cement composite. This paper tries to determine the correct methodology for designing green concrete by using modern methods measuring rheology of fresh concrete and following hydration processes. The use of fluidised bed combustion fly ash in cement composite production as an admixture is not currently common, but there are some real possibilities for its potential. The most striking negative aspect is its chemical composition which supports the development of new product formation, influencing the durability of the composite. Another disadvantage is the morphology of grains, which have a negative effect on consistency. This raises the question of how this waste can be used in concrete production to emphasize its positive properties and eliminate negatives. The focal point of the experiment carried out on cement pastes was particularly on the progress of hydration processes, aiming for the possible acceleration of pozzolanic reactions of both types of fly ash.

Keywords: High-temperature fly ash, fluidised bed combustion fly ash, pozzolanic, CaO (calcium oxide), rheology.

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Authors: Chamindi Dilkushi Senaratne

Abstract:

Sri Lanka has lived with the English language for more than 200 years. Although officially considered a link language, the phenomenal usage of English by the Sinhala-English bilingual has given rise to a mixed code with identifiable structural characteristics. The extensive use of the mixed language by the average Sri Lankan bilingual has resulted in it being used as a medium of communication by creative writers of bilingual advertisements in Sri Lanka. This study analyses the way in which English is used in bilingual advertisements in both print and electronic media in Sri Lanka. The theoretical framework for the study is based on Kachru’s analysis of the use of English by the bilingual, Muysken’s typology on code mixing theories in colonial settings and Myers-Scotton’s theory on the Matrix Language Framework Model. The study will look at a selection of Sinhala-English advertisements published in newspapers from 2015 to 2016. Only advertisements using both Sinhala and English are used for the analysis. To substantiate data collected from the newspapers, the study will select bilingual advertisements from television advertisements. The objective of the study is to analyze the mixed patterns used for creative purposes by advertisers. The results of the study will reveal the creativity used by the Sinhala –English bilingual and the morphological processes used by the creators of Sinhala-English bilingual advertisements to attract the masses.

Keywords: Bilingual, code mixing, mixed code, morphology, processes.

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Authors: Giovanni Incerti

Abstract:

The dynamic behaviour of a four-bar linkage driven by a velocity controlled DC motor is discussed in the paper. In particular the author presents the results obtained by means of a specifically developed software, which implements the mathematical models of all components of the system (linkage, transmission, electric motor, control devices). The use of this software enables a more efficient design approach, since it allows the designer to check, in a simple and immediate way, the dynamic behaviour of the mechanism, arising from different values of the system parameters.

Keywords: Four-bar linkage, Speed control, Dynamic analysis.

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Authors: Shuguo Yang, Xiaoyan Yang

Abstract:

It is practically significant to research the traffic flow of intersection because the capacity of intersection affects the efficiency of highway network directly. This paper analyzes the traffic conditions of an intersection in certain urban by the methods of queuing theory and statistical experiment, sets up a corresponding mathematical model and compares it with the actual values. The result shows that queuing theory is applied in the study of intersection traffic flow and it can provide references for the other similar designs.

Keywords: Intersection, Queuing theory, Statistical experiment, System metrics.

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Authors: Takashi Mitsuishi, Kiyoshi Sawada, Yasunari Shidama

Abstract:

The mathematical framework for studying of a fuzzy approximate reasoning is presented in this paper. Two important defuzzification methods (Area defuzzification and Height defuzzification) besides the center of gravity method which is the best well known defuzzification method are described. The continuity of the defuzzification methods and its application to a fuzzy feedback control are discussed.

Keywords: Fuzzy approximate reasoning, defuzzification, area method, height method.

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Authors: Nakhoon Baek

Abstract:

Stipples are desired for pattern fillings and transparency effects. In contrast, some graphics standards, including OpenGL ES 1.1 and 2.0, omitted this feature. We represent details of providing line stipples and polygon stipples, through combining texture mapping and alpha blending functions. We start from the OpenGL-specified stipple-related API functions. The details of mathematical transformations are explained to get the correct texture coordinates. Then, the overall algorithm is represented, and its implementation results are followed. We accomplished both of line and polygon stipples, and verified its result with conformance test routines.

Keywords: Stipple operation, OpenGL ES, Implementation.

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Authors: Ikbal Zammouri, Béchir Ayeb

Abstract:

In this paper, we propose a new method to describe fractal shapes using parametric l-systems. First we introduce scaling factors in the production rules of the parametric l-systems grammars. Then we decorticate these grammars with scaling factors using turtle algebra to show the mathematical relation between l-systems and iterated function systems (IFS). We demonstrate that with specific values of the scaling factors, we find the exact relationship established by Prusinkiewicz and Hammel between l-systems and IFS.

Keywords: Fractal shapes, IFS, parametric l-systems, turtlealgebra.

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Authors: Asma M. Milad, Mohammad B. Kassim, Wan R. Daud

Abstract:

Highly ordered TiO2 nanotube (TNT) arrays were fabricated onto a pre-treated titanium foil by anodic oxidation with a voltage of 20V in phosphoric acid/sodium fluoride electrolyte. A pretreatment of titanium foil involved washing with acetone, isopropanol, ethanol and deionized water. Carbon doped TiO2 nanotubes (C-TNT) was fabricated 'in-situ' with the same method in the presence of polyvinyl alcohol and urea as carbon sources. The affects of polyvinyl alcohol concentration and oxidation time on the composition, morphology and structure of the C-TN were studied by FE-SEM, EDX and XRD techniques. FESEM images of the nanotubes showed uniform arrays of C-TNTs. The density and microstructures of the nanotubes were greatly affected by the content of PVA. The introduction of the polyvinyl alcohol into the electrolyte increases the amount of C content inside TiO2 nanotube arrays uniformly. The influence of carbon content on the photo-current of C-TNT was investigated and the I-V profiles of the nanotubes were established. The preliminary results indicated that the 'in-situ' doping technique produced a superior quality nanotubes compared to post doping techniques.

Keywords: Anodization, photoelectrochemical cell, 'in-situ', post doping, thin film, and titania nanotube arrays.

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