Search results for: Vicker's hardness number.

Authors: Yan Su, Jane H. Davidson, F. A. Kulacki

Abstract:

The RANS method with Saffman-s turbulence model was employed to solve the time-dependent turbulent Navier-Stokes and energy equations for oscillating pipe flows. The method of partial sums of the Fourier series is used to analyze the harmonic velocity and temperature results. The complete structures of the oscillating pipe flows and the averaged Nusselt numbers on the tube wall are provided by numerical simulation over wide ranges of ReA and ReR. Present numerical code is validated by comparing the laminar flow results to analytic solutions and turbulence flow results to published experimental data at lower and higher Reynolds numbers respectively. The effects of ReA and ReR on the velocity, temperature and Nusselt number distributions have been di scussed. The enhancement of the heat transfer due to oscillating flows has also been presented. By the way of analyzing the overall Nusselt number over wide ranges of the Reynolds number Re and Keulegan- Carpenter number KC, the optimal ratio of the tube diameter over the oscillation amplitude is obtained based on the existence of a nearly constant optimal KC number. The potential application of the present results in sea water cooling has also been discussed.

Keywords: Keulegan-Carpenter number, Nusselt number, Oscillating pipe flows, Reynolds number

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Authors: Daniela I. Borissova, Ivan C. Mustakerov

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The paper addresses a problem of optimal staffing in open shop environment. The problem is to determine the optimal number of operators serving a given number of machines to fulfill the number of independent operations while minimizing staff idle. Using a Gantt chart presentation of the problem it is modeled as twodimensional cutting stock problem. A mixed-integer programming model is used to get minimal job processing time (makespan) for fixed number of machines' operators. An algorithm for optimal openshop staffing is developed based on iterative solving of the formulated optimization task. The execution of the developed algorithm provides optimal number of machines' operators in the sense of minimum staff idle and optimal makespan for that number of operators. The proposed algorithm is tested numerically for a real life staffing problem. The testing results show the practical applicability for similar open shop staffing problems.

Keywords: Integer programming, open shop problem, optimal staffing.

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Authors: A. Khaleel, S. Gao

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Both steady and unsteady turbulent mixed convection heat transfer in a 3D lid-driven enclosure, which has constant heat flux on the middle of bottom wall and with isothermal moving sidewalls, is reported in this paper for working fluid with Prandtl number Pr = 0.71. The other walls are adiabatic and stationary. The dimensionless parameters used in this research are Reynolds number, Re = 5000, 10000 and 15000, and Richardson number, Ri = 1 and 10. The simulations have been done by using different turbulent methods such as RANS, URANS, and LES. The effects of using different k-ε models such as standard, RNG and Realizable k-ε model are investigated. Interesting behaviours of the thermal and flow fields with changing the Re or Ri numbers are observed. Isotherm and turbulent kinetic energy distributions and variation of local Nusselt number at the hot bottom wall are studied as well. The local Nusselt number is found increasing with increasing either Re or Ri number. In addition, the turbulent kinetic energy is discernibly affected by increasing Re number. Moreover, the LES results have shown good ability of this method in predicting more detailed flow structures in the cavity.

Keywords: Mixed convection, Lid-driven cavity, Turbulent flow, RANS model, URANS model, Large eddy simulation.

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Authors: M. Yousaf, S. Usman

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The present study focused on the investigation of the effects of roughness elements on heat transfer during natural convection in a rectangular cavity using numerical technique. Roughness elements were introduced on the bottom hot wall with a normalized amplitude (A*/H) of 0.1. Thermal and hydrodynamic behaviors were studied using computational method based on Lattice Boltzmann method (LBM). Numerical studies were performed for a laminar flow in the range of Rayleigh number (Ra) from 103 to 106 for a rectangular cavity of aspect ratio (L/H) 2.0 with a fluid of Prandtl number (Pr) 1.0. The presence of the sinusoidal roughness elements caused a minimum to maximum decrease in the heat transfer as 7% to 17% respectively compared to smooth enclosure. The results are presented for mean Nusselt number (Nu), isotherms and streamlines.

Keywords: Natural convection, Rayleigh number, surface roughness, Nusselt number, Lattice Boltzmann Method.

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Authors: Hossein Khademolhosseini, Mehdi Hosseinzadeh

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The residue number system (RNS), due to its properties, is used in applications in which high performance computation is needed. The carry free nature, which makes the arithmetic, carry bounded as well as the paralleling facility is the reason of its capability of high speed rendering. Since carry is not propagated between the moduli in this system, the performance is only restricted by the speed of the operations in each modulus. In this paper a novel method of number representation by use of redundancy is suggested in which {rn- 2,rn-1,rn} is the reference moduli set where r=2k+1 and k =1, 2,3,.. This method achieves fast computations and conversions and makes the circuits of them much simpler.

Keywords: Binary to RNS converter, Carry save adder, Computer arithmetic, Residue number system.

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Authors: M. Zareiee, A. Dideban

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This paper addresses the problem of forbidden states in non safe Petri Nets. In the system, for preventing it from entering the forbidden states, some linear constraints can be assigned to them. Then these constraints can be enforced on the system using control places. But when the number of constraints in the system is large, a large number of control places must be added to the model of system. This concept complicates the model of system. There are some methods for reducing the number of constraints in safe Petri Nets. But there is no a systematic method for non safe Petri Nets. In this paper we propose a method for reducing the number of constraints in non safe Petri Nets which is based on solving an integer linear programming problem.

Keywords: discrete event system, Supervisory control, Petri Net, Constraint

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Authors: Abouzar Moshfegh, Mehrzad Shams, Goodarz Ahmadi, Reza Ebrahimi

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A 3D simulation study for an incompressible slip flow around a spherical aerosol particle was performed. The full Navier-Stokes equations were solved and the velocity jump at the gas-particle interface was treated numerically by imposition of the slip boundary condition. Analytical solution to the Stokesian slip flow past a spherical particle was used as a benchmark for code verification, and excellent agreement was achieved. The Simulation results showed that in addition to the Knudsen number, the Reynolds number affects the slip correction factor. Thus, the Cunningham-based slip corrections must be augmented by the inclusion of the effect of Reynolds number for application to Lagrangian tracking of fine particles. A new expression for the slip correction factor as a function of both Knudsen number and Reynolds number was developed.

Keywords: CFD, Cunningham correction, Slip correction factor, Spherical aerosol.

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Authors: Awadhesh Kumar Singh

Abstract:

Jayanti-s algorithm is one of the best known abortable mutual exclusion algorithms. This work is an attempt to overcome an already known limitation of the algorithm while preserving its all important properties and elegance. The limitation is that the token number used to assign process identification number to new incoming processes is unbounded. We have used a suitably adapted alternative data structure, in order to completely eliminate the use of token number, in the algorithm.

Keywords: Abortable, deterministic, local spin, mutual exclusion.

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Authors: Mehdi Hosseinzadeh, Somayyeh Jafarali Jassbi, Keivan Navi

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Residue Number System (RNS) is a modular representation and is proved to be an instrumental tool in many digital signal processing (DSP) applications which require high-speed computations. RNS is an integer and non weighted number system; it can support parallel, carry-free, high-speed and low power arithmetic. A very interesting correspondence exists between the concepts of Multiple Valued Logic (MVL) and Residue Number Arithmetic. If the number of levels used to represent MVL signals is chosen to be consistent with the moduli which create the finite rings in the RNS, MVL becomes a very natural representation for the RNS. There are two concerns related to the application of this Number System: reaching the most possible speed and the largest dynamic range. There is a conflict when one wants to resolve both these problem. That is augmenting the dynamic range results in reducing the speed in the same time. For achieving the most performance a method is considere named “One-Hot Residue Number System" in this implementation the propagation is only equal to one transistor delay. The problem with this method is the huge increase in the number of transistors they are increased in order m² . In real application this is practically impossible. In this paper combining the Multiple Valued Logic and One-Hot Residue Number System we represent a new method to resolve both of these two problems. In this paper we represent a novel design of an OHRNS-based adder circuit. This circuit is useable for Multiple Valued Logic moduli, in comparison to other RNS design; this circuit has considerably improved the number of transistors and power consumption.

Keywords: Computer Arithmetic, Residue Number System, Multiple Valued Logic, One-Hot, VLSI.

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Authors: A. Ghafouri, A. Falavand Jozaei, M. Salari

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In this paper, effects of using Alumina-water nanofluid on the rate of heat transfer have been investigated numerically. Physical model is a square enclosure with insulated top and bottom horizontal walls, while the vertical walls are kept at different constant temperatures. Two appropriate models are used to evaluate the viscosity and thermal conductivity of nanofluid. The governing stream-vorticity equations are solved using a second order central finite difference scheme, coupled to the conservation of mass and energy. The study has been carried out for the Richardson number 0.1 to 10 and the solid volume fraction 0 to 0.04. Results are presented by isotherms lines, average Nusselt number and normalized Nusselt number in different range of φ and Ri for forced, combined and natural convection dominated regime. It is found that higher heat transfer rate is predicted when the effects of nanoparticle is taken into account.

Keywords: Nanofluid, Heat Transfer Enhancement, Square Enclosure, Nusselt number.

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Authors: S. Damodaran, T. V. S.Sekhar

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The motion of a sphere moving along the axis of a rotating viscous fluid is studied at high Reynolds numbers and moderate values of Taylor number. The Higher Order Compact Scheme is used to solve the governing Navier-Stokes equations. The equations are written in the form of Stream function, Vorticity function and angular velocity which are highly non-linear, coupled and elliptic partial differential equations. The flow is governed by two parameters Reynolds number (Re) and Taylor number (T). For very low values of Re and T, the results agree with the available experimental and theoretical results in the literature. The results are obtained at higher values of Re and moderate values of T and compared with the experimental results. The results are fourth order accurate.

Keywords: Navier_Stokes equations, Taylor number, Reynolds number, Higher order compact scheme, Rotating Fluid.

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Authors: Novi Khila Firani, Elisa Nesdyaningtyas

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Kwashiorkor is one of nutritional problem in Indonesia, which lead to decrease immune system. This condition causes susceptibility to infectious disease, especially tuberculosis. Development of new tuberculosis vaccine will be an important strategy to eliminate tuberculosis in kwashiorkor. Previous research showed that 38-kDa Mycobacterium tuberculosis protein is one of the potent immunogen. However, the role of oral immunization with 38- kDa Mycobacterium tuberculosis protein to the number of lymphocytes in the rat model of kwashiorkor is still unknown. We used kwashiorkor rat model groups with 4% and 2% low protein diet. Oral immunization with 38-kDa Mycobacterium tuberculosis protein given with 2 booster every week. The lymphocytes number were measured by flowcytometry. There was no significant difference between the number of lymphocytes in the normal rat group and the kwashiorkor rat groups. It may reveal the role of 38-kDa Mycobacterium tuberculosis protein as a potent immunogen that can increase the lymphocytes number from kwashiorkor rat model same as normal rat.

Keywords: kwashiorkor rat, lymphocytes, 38-kDa Mycobacterium tuberculosis protein

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Authors: T. V. S. Sekhar, B. Hema Sundar Raju

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Laminar natural-convective heat transfer from a horizontal cylinder is studied by solving the Navier-Stokes and energy equations using higher order compact scheme in cylindrical polar coordinates. Results are obtained for Rayleigh numbers of 1, 10, 100 and 1000 for a Prandtl number of 0.7. The local Nusselt number and mean Nusselt number are calculated and compared with available experimental and theoretical results. Streamlines, vorticity - lines and isotherms are plotted.

Keywords: Higher order compact scheme, Navier-Stokes equations, Energy equation, Natural convection, Boussinesq's approximation and Mean Nusselt number.

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Authors: Naoya Ozaki, Takuya Watanabe, Ryosuke Matsumoto, Noriko Fukasawa

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In the metropolitan areas in Japan, in many stations, shopping areas are set up, and escalators and elevators are installed to make the stations be barrier-free. Further, many areas around the stations are being redeveloped. Railway business operators want to know how much effect these circumstances have on attractiveness of the station or number of passengers using the station. So, we performed a questionnaire survey of the station users in the metropolitan areas for finding factors to affect the attractiveness of stations. Then, based on the analysis of the survey, we developed a method to quantitatively evaluate attractiveness of the stations. We also developed an estimation method for number of passengers based on combination of attractiveness of the station quantitatively evaluated and the residential and labor population around the station. Then, we derived precise linear regression models estimating the attractiveness of the station and number of passengers of the station.

Keywords: Attractiveness of the station, estimation method, number of passengers of the station, redevelopment around the station, renovation of the station.

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Authors: Marija R. Jokanović, Vladimir M. Tomović, Mihajlo T. Jović, Branislav V. Šojić, Snežana B. Škaljac, Tatjana A. Tasić, Predrag M. Ikonić

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Proximate composition (moisture, protein, total fat, and total ash) and textural characteristics (hardness, adhesiveness, springiness, cohesiveness, chewiness and firmness and work of shear) of cooked sausages formulated from mechanically deboned chicken meat (MDCM) with addition of chicken offal (heart, gizzard or liver) were investigated. Chicken offal replaced equal weight (15 kg) of MDCM in standard sausage formulation. Regarding proximate composition sausage with heart addition was significantly (P<0.05) lower in moisture content (70.45%) than sausage with liver addition (71.35%), and significantly (P<0.05) the highest in total ash content (2.83%). Sausage with gizzard addition was significantly higher in protein content (9.77%) than sausage with liver addition (9.42%). Total fat content didn’t significantly (P>0.05) differ among all three sausages. The effect of offal addition was more notable in Warner-Bratzler shear test results than in texture profile analysis test. Firmness and work of shear were significantly different (P<0.05) among all three sausages. Sausage with liver addition was significantly (P<0.05) lower in hardness (1672 g) and chewiness (1020 g) and numerically the lowest in springiness (0.90) and adhesiveness (–70 g*s) comparing with other two sausages. Sausage with heart addition was significantly (P<0.05) higher in cohesiveness (0.74) comparing with other two sausages.

Keywords: Cooked sausage, mechanically deboned chicken meat, offal, proximate composition, texture

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Authors: Sanjib Kr Pal, S. Bhattacharyya

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Mixed convection of Cu-water nanofluid in an enclosure with thick wavy bottom wall has been investigated numerically. A co-ordinate transformation method is used to transform the computational domain into an orthogonal co-ordinate system. The governing equations in the computational domain are solved through a pressure correction based iterative algorithm. The fluid flow and heat transfer characteristics are analyzed for a wide range of Richardson number (0.1 ≤ Ri ≤ 5), nanoparticle volume concentration (0.0 ≤ ϕ ≤ 0.2), amplitude (0.0 ≤ α ≤ 0.1) of the wavy thick- bottom wall and the wave number (ω) at a fixed Reynolds number. Obtained results showed that heat transfer rate increases remarkably by adding the nanoparticles. Heat transfer rate is dependent on the wavy wall amplitude and wave number and decreases with increasing Richardson number for fixed amplitude and wave number. The Bejan number and the entropy generation are determined to analyze the thermodynamic optimization of the mixed convection.

Keywords: Entropy generation, mixed convection, conjugate heat transfer, numerical, nanofluid, wall waviness.

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Authors: Nien-Zheng Yew, Kung-Ming Tiong, Su-Ting Yong

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Number Link is a Japanese logic puzzle where pairs of same numbers are connected using lines. Number Link can be regarded as a dynamic multiple travelers, multiple entries and exits maze, where the walls and passages are dynamically changing as the travelers move. In this paper, we apply the Tremaux’s algorithm to solve Number Link puzzles of size 8x8, 10x10 and 15x20. The algorithm works well and produces a solution for puzzles of size 8x8 and 10x10. However, solving a puzzle of size 15x20 requires high computer processing power and is time consuming.

Keywords: Number Link, maze, puzzle, Tremaux’s algorithm

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Authors: Liu Shu, Dong Shangjia

Abstract:

Our goal is to effectively increase the number of boats in the river during a six month period. The main factors of determining the number of boats are duration and “select the priority trip". In the microcosmic simulation model, the best result is 4 to 24 nights with DSCF, and the number of boats is 812 with an increasing ratio of 9.0% related to the second best result. However, the number of boats is related to 31.6% less than the best one in 6 to 18 nights with FCFS. In the discrete duration model, we get from 6 to 18 nights, the numbers of boats have increased to 848 with an increase ratio of 29.7% than the best result in model I for the same time range. Moreover, from 4 to 24 nights, the numbers of boats have increase to 1194 with an increase ratio of 47.0% than the best result in model I for the same time range.

Keywords: Discrete duration model, “select the priority trip”, microcosmic simulation model.

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Authors: Marcela Karmazínová, Jindrich Melcher, Lubomír Vítek, Petr Cikrle

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The paper deals with the diagnostics of steel roof structure of the winter sports halls built in 1970 year. The necessity of the diagnostics has been given by the requirement to the evaluation design of this structure, which has been caused by the new situation in the field of the loadings given by the validity of the European Standards in the Czech Republic from 2010 year. Due to these changes in the normative rules, in practice existing structures are gradually subjected to the evaluation design and depending on its results to the strengthening or reconstruction, respectively. Steel roof is composed of plane truss main girders, purlins and bracings and the roof structure is supported by two arch main girders with the span of L = 84 m. The in situ diagnostics of the roof structure was oriented to the following parts: (i) determination and evaluation of the actual material properties of used steel and (ii) verification of the actual dimensions of the structural members. For the solution the nondestructive methods have been used for in situ measurement. For the indicative determination of steel strengths the modified method based on the determination of Rockwell’s hardness has been used. For the verification of the member’s dimensions (thickness of hollow sections) the ultrasound method has been used. This paper presents the results obtained using these testing methods and their evaluation, from the viewpoint of the usage for the subsequent static assessment and design evaluation of the existing structure. For the comparison, the examples of the similar evaluations realized for steel structures of the stadiums in Olomouc and Jihlava cities are briefly illustrated, too.

Keywords: Diagnostics, existing steel structure, sport hall, steel strength, indirect non-destructive methods, Rockwel’s hardness, destructive methods, actual dimensions, ultrasound method.

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Authors: Sukhbaatar Dorj, Erdenebaatar Altangerel

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As alternative to existing e-government measuring models, here proposed a new customer centric, service oriented, simple approach for measuring countries e-Governments. If successfully implemented, built infrastructure will provide a single egovernment index number for countries. Main schema is as follows. Country CIO or equal position government official, at the beginning of each year will provide to United Nations dedicated web site 4 numbers on behalf of own country: 1) Ratio of available online public services, to total number of public services, 2) Ratio of interagency inter ministry online public services to total number of available online public services, 3) Ratio of total number of citizen and business entities served online annually to total number of citizen and business entities served annually online and physically on those services, 4) Simple index for geographical spread of online served citizen and business entities. 4 numbers then combined into one index number by mathematical Average function. In addition to 4 numbers 5th number can be introduced as service quality indicator of online public services. If in ordering of countries index number is equal, 5th criteria will be used. Notice: This approach is for country’s current e-government achievement assessment, not for e-government readiness assessment.

Keywords: Countries e-government index, e-government, infrastructure for measuring e-government, measuring e-government.

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Authors: John M. Ikome, Martha E. Ikome, Therese Van Wyk

Abstract:

Productivity optimization of a company can significantly increase the company’s output and productivity which can be in the form of corrective actions of ineffective activities, process simplification, and reduction of variations, responsiveness, and reduction of set-up-time which are all under the classification of waste within the manufacturing environment. Deriving a means to eliminate a number of these issues has a key importance for manufacturing organization. This paper focused on a number of industrial engineering techniques which include a cause and effect diagram, to identify and optimize the method or systems being used. Based on our results, it shows that there are a number of variations within the production processes that can significantly disrupt the expected output.

Keywords: Optimization, fishbone diagram, productivity.

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Authors: Paula M. R. Correia, Marta Gonzaga, Luis M. Batista, Luísa Beirão-Costa, Raquel F. P. Guiné

Abstract:

The purpose of the present work was to develop an innovative food product with good textural and sensorial characteristics. The product, a new type of bread, was prepared with wheat (90%) and lupin (10%) flours, without the addition of any conservatives. Several experiences were also done to find the most appropriate proportion of lupin flour. The optimized product was characterized considering the rheological, physical-chemical and sensorial properties. The water absorption of wheat flour with 10% of lupin was higher than that of the normal wheat flours, and Wheat Ceres flour presented the lower value, with lower dough development time and high stability time. The breads presented low moisture but a considerable water activity. The density of bread decreased with the introduction of lupin flour. The breads were quite white, and during storage the colour parameters decreased. The lupin flour clearly increased the number of alveolus, but the total area increased significantly just for the Wheat Cerealis bread. The addition of lupin flour increased the hardness and chewiness of breads, but the elasticity did not vary significantly. Lupin bread was sensorially similar to wheat bread produced with WCerealis flour, and the main differences are the crust rugosity, colour and alveolus characteristics.

Keywords: Lupin flour, physical-chemical properties, sensorial analysis, wheat flour.

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Authors: Annur Suhadi, Haris B. Harahap, Zaim Arrosyidi, Epan, Darmapala

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Oilfields under waterflood often face the problem of plugging injectors either by internal filtration or external filter cake built up inside pore throats. The content of suspended solids shall be reduced to required level of filtration since corrective action of plugging is costly expensive. The performance of nutshell filters, where filtration takes place, is good using pecan and walnut shells. Candlenut shells were used instead of pecan and walnut shells since they were abundant in Indonesia, Malaysia, and East Africa. Physical and chemical properties of walnut, pecan, and candlenut shells were tested and the results were compared. Testing, using full-scale nutshell filters, was conducted to determine the oil content, turbidity, and suspended solid removal, which was based on designed flux rate. The performance of candlenut shells, which were deeply bedded in nutshell filters for filtration process, was monitored. Cleaned water outgoing nutshell filters had total suspended solids of 17 ppm, while oil content could be reduced to 15.1 ppm. Turbidity, using candlenut shells, was below the specification for injection water, which was less than 10 Nephelometric Turbidity Unit (NTU). Turbidity of water, outgoing nutshell filter, was ranged from 1.7-5.0 NTU at various dates of operation. Walnut, pecan, and candlenut shells had moisture content of 8.98 wt%, 10.95 wt%, and 9.95 wt%, respectively. The porosity of walnut, pecan, and candlenut shells was significantly affected by moisture content. Candlenut shells had property of toluene solubility of 7.68 wt%, which was much higher than walnut shells, reflecting more crude oil adsorption. The hardness of candlenut shells was 2.5-3 Mohs, which was close to walnut shells’ hardness. It was advantage to guarantee the cleaning filter cake by fluidization process during backwashing.

Keywords: Candlenut shells, walnut shells, pecan shells, nutshell filter, filtration.

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Authors: Laura Gjyli, Pirro Prifti, Lindita Mukli, Silvana Gjyli, Irida Ikonomi, Jerina Kolitari

Abstract:

Microbial air contamination of the outdoor air in Marine Durres-s Harbour (Durres, Albania) was estimated by sedimentation technique in August-October 2008. The sampling areas were: Ferry Terminal (FT), Fishery Harbor (FH), East Zone (EZ), Fuel Quay (FQ) and Apollonian Beach (AB). The aim of this study was to measure the number of aerobic plate count (mesophilic aerobic bacteria) and fungi (yeasts and molds) in the outdoor air in these areas. The number of colonies that were formed determines the number of cells at the moment in the outdoor air; respectively the number of mesophilic aerobic bacteria and yeasts and molds. The measure of bacteria and fungi used is CFU (Colony Forming Units) per Petri dish. It is said that marine harbours are very polluted areas. The aim of study was the definition of mesophilic aerobic bacteria and yeasts and molds number, and the comparison of microorganisms number in air sampling areas.

Keywords: Air microbiology, colony forming units, Marine Durres's Harbour, mesophilic aerobic bacteria, outdoor air, yeasts and molds.

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Authors: Kazuyoshi Mori

Abstract:

In this paper, we consider the parametrization of the discrete-time systems without the unit-delay element within the framework of the factorization approach. In the parametrization, we investigate the number of required parameters. We consider single-input single-output systems in this paper. By the investigation, we find, on the discrete-time systems without the unit-delay element, three cases that are (1) there exist plants which require only one parameter and (2) two parameters, and (3) the number of parameters is at most three.

Keywords: Linear systems, parametrization, Coprime Factorization, number of parameters.

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Authors: M.Jalali Azizpour, S.Norouzi, H.mohammadi Majd, M.M.Rabieh, D.Sajedipour, A. Jaderi

Abstract:

The mechanical and tribological properties in WC-Co coatings are strongly affected by hardness and elasticity specifications. The results revealed the effect of spraying distance on microhardness and elasticity modulus of coatings. The metallurgical studies have been made on coated samples using optical microscopy, scanning electron microscopy (SEM).

Keywords: Elasticity modulus, HVOF, Micro-indentation, Thermal spray, WC-Co

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Authors: R. M. Kashim

Abstract:

The study investigates the conceptual and procedural knowledge of rational number in primary school teachers, specifically, the primary school teachers level of conceptual knowledge about rational number and the primary school teachers level of procedural knowledge about rational numbers. The study was carried out in Bauchi metropolis in Bauchi state of Nigeria. A Conceptual and Procedural Knowledge Test was used as the instrument for data collection, 54 mathematics teachers in Bauchi primary schools were involved in the study. The collections were analyzed using mean and standard deviation. The findings revealed that the primary school mathematics teachers in Bauchi metropolis posses a low level of conceptual knowledge of rational number and also possess a high level of Procedural knowledge of rational number. It is therefore recommended that to be effective, teachers teaching mathematics most posses a deep understanding of both conceptual and procedural knowledge. That way the most knowledgeable teachers in mathematics deliver highly effective rational number instructions. Teachers should not ignore the mathematical concept aspect of rational number teaching. This is because only the procedural aspect of Rational number is highlighted during instructions; this often leads to rote - learning of procedures without understanding the meanings. It is necessary for teachers to learn rational numbers teaching method that focus on both conceptual knowledge and procedural knowledge teaching.

Keywords: Conceptual knowledge, primary school teachers, procedural knowledge, rational numbers.

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Authors: Wongsakorn Charoenpanitseri

Abstract:

The total chromatic number χ"(G) of a graph G is the minimum number of colors needed to color the elements (vertices and edges) of G such that no incident or adjacent pair of elements receive the same color Let G be a graph with maximum degree Δ(G). Considering a total coloring of G and focusing on a vertex with maximum degree. A vertex with maximum degree needs a color and all Δ(G) edges incident to this vertex need more Δ(G) + 1 distinct colors. To color all vertices and all edges of G, it requires at least Δ(G) + 1 colors. That is, χ"(G) is at least Δ(G) + 1. However, no one can find a graph G with the total chromatic number which is greater than Δ(G) + 2. The Total Coloring Conjecture states that for every graph G, χ"(G) is at most Δ(G) + 2. In this paper, we prove that the Total Coloring Conjectur for a Δ-claw-free 3-degenerated graph. That is, we prove that the total chromatic number of every Δ-claw-free 3-degenerated graph is at most Δ(G) + 2.

Keywords: Total colorings, the total chromatic number, 3-degenerated.

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Authors: C. Porkodi, R. Arumuganathan

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In this paper a Public Key Cryptosystem is proposed using the number theoretic transforms (NTT) over a ring of integer modulo a composite number. The key agreement is similar to ElGamal public key algorithm. The security of the system is based on solution of multivariate linear congruence equations and discrete logarithm problem. In the proposed cryptosystem only fixed numbers of multiplications are carried out (constant complexity) and hence the encryption and decryption can be done easily. At the same time, it is very difficult to attack the cryptosystem, since the cipher text is a sequence of integers which are interrelated. The system provides authentication also. Using Mathematica version 5.0 the proposed algorithm is justified with a numerical example.

Keywords: Cryptography, decryption, discrete logarithm problem encryption, Integer Factorization problem, Key agreement, Number Theoretic Transform.

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Authors: Adnan Z. Mkhelif

Abstract:

The production of number forms in English tends to be problematic for Iraqi learners of English as a foreign language (EFL), even at the undergraduate level. To help better understand and consequently address this problem, it is important to identify its sources. This study aims at: (1) statistically analysing Iraqi EFL undergraduates' performance in the production of number forms in English; (2) classifying learners' errors in terms of their possible major causes; and (3) outlining some pedagogical recommendations relevant to the teaching of number forms in English. It is hypothesized in this study that (1) Iraqi EFL undergraduates still face problems in the production of number forms in English and (2) errors pertaining to the context of learning are more numerous than those attributable to the other possible causes. After reviewing the literature available on the topic, a written test comprising 50 items has been constructed and administered to a randomly chosen sample of 50 second-year college students from the Department of English, College of Education, Wasit University. The findings of the study showed that Iraqi EFL undergraduates still face problems in the production of number forms in English and that the possible major sources of learners’ errors can be arranged hierarchically in terms of the percentages of errors to which they can be ascribed as follows: (1) context of learning (50%), (2) intralingual transfer (37%), and (3) interlingual transfer (13%). It is hoped that the implications of the study findings will be beneficial to researchers, syllabus designers, as well as teachers of English as a foreign/second language.

Keywords: L2 morphology, L2 number forms, L2 vocabulary learning, productive knowledge.

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