Search results for: Salem numbers

Authors: Kohei Inoue, Kenji Hara, Kiichi Urahama

Abstract:

We describe a relationship between integral images and differential images. First, we derive a simple difference filter from conventional integral image. In the derivation, we show that an integral image and the corresponding differential image are related to each other by simultaneous linear equations, where the numbers of unknowns and equations are the same, and therefore, we can execute the integration and differentiation by solving the simultaneous equations. We applied the relationship to an image fusion problem, and experimentally verified the effectiveness of the proposed method.

Keywords: Integral images, differential images, differential filters, image fusion.

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Authors: F. M. Abu-Salem, M. H. Mahmoud, M. H. El-Kalyoubi, A. Y. Gibriel, A. A. Abou-Arab Arab

Abstract:

Dried soy protein hydrolysate powder was added to the burger in order to enhance the oxidative stability as well as decreases the microbial spoilage. The soybean bioactive compounds (soy protein hydrolysate) as antioxidant and antimicrobial were added at level of 1, 2 and 3 %.Chemical analysis and physical properties were affected by protein hydrolysate addition. The TBA values were significantly affected (P < 0.05) by the storage period and the level of soy protein hydrolysate. All the tested soybean protein hydrolysate additives showed strong antioxidant properties. Samples of soybean protein hydrolysate showed the lowest (P < 0.05) TBA values at each time of storage. The counts of all determined microbiological indicators were significantly (P < 0.05) affected by the addition of the soybean protein hydrolysate. Decreasing trends of different extent were also observed in samples of the treatments for total viable counts, Coliform, Staphylococcus aureus, yeast and molds. Storage period was being significantly (P < 0.05) affected on microbial counts in all samples Staphylococcus aureus were the most sensitive microbe followed by Coliform group of the sample containing protein hydrolysate, while molds and yeast count showed a decreasing trend but not significant (P < 0.05) until the end of the storage period compared with control sample. Sensory attributes were also performed, added protein hydrolysate exhibits beany flavor which was clear about samples of 3% protein hydrolysate.

Keywords: Antioxidant, antimicrobial, isoflavones, bioactive peptide, antioxidant peptides, soybean protein hydrolysate.

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Authors: W. Abu Rayyan, A. Singh, A. M. Al-Jaafreh, W. Abu Dayyih, M. Bustami, S. Salem, N. Seder, K. Schröppel

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Hyphal growth and the transcriptional regulation to the host environment are key issues during the pathogenesis of C. albicans. Tec1p is the C. albicans homolog of a TEA transcription factor family, which share a conserved DNA-binding TEA domain in their N-terminal. In order to define a structure-function relationship of the C. albicans Tec1p protein, we constructed several mutations on the N terminal, C terminal or in the TEA binding domain itself by homologous recombination technology. The modifications in the open reading frame of TEC1 were tested for reconstitution of the morphogenetic development of the tec1/tec1 mutant strain CaAS12. Mutation in the TEA consensus sequence did not confer transition to hyphae whereas the reconstitution of the full-length Tec1p has reconstituted hyphal development. A deletion in one of glutamine-rich regions either in the Tec1p N-terminal or the C-terminal in regions of 53-212 or 637–744 aa, respectively, did not restore morphological development in mutant CaAS12 strain. Whereas, the reconstitution with Tec1p mutants other than the glutamate-rich region has restored the morphogenetic switch. Additionally, the deletion of the glutamine-rich region has attenuated the invasive growth and the heat shock resistance of C. albicans. In conclusion, we show that a glutamine-rich region of Tec1p is essential for the hyphal development and mediating adaptation to the host environment of C. albicans.

Keywords: Candida albicans, transcription factor, TEA domain, hyphal formation, morphogenetic development, TEC1, Tet-induced.

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Authors: M. Ghorbany

Abstract:

A square matrix over the complex field with non- negative integral trace is called a quasi-permutation matrix. For a finite group G the minimal degree of a faithful representation of G by quasi-permutation matrices over the rationals and the complex numbers are denoted by q(G) and c(G) respectively. Finally r (G) denotes the minimal degree of a faithful rational valued complex character of C. The purpose of this paper is to calculate q(G), c(G) and r(G) for the group S L(2, q) when extended by a certain group of order two.

Keywords: General linear group, Quasi-permutation

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Authors: Yan-zhao Yang

Abstract:

In this paper, some limit properties for mixing random variables sequences were studied and some results on weak law of large number for mixing random variables sequences were presented. Some complete convergence theorems were also obtained. The results extended and improved the corresponding theorems in i.i.d random variables sequences.

Keywords: Complete convergence, mixing random variables, weak law of large numbers.

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Authors: S. Bajalan, A. Shadaram, N. Hedayat, A. Shams Taleghani

Abstract:

The interaction between wakes of bluff body and airfoil have profound influences on system performance in many industrial applications, e.g., turbo-machinery and cooling fan. The present work investigates the effect of configuration include; airfoil-s angle of attack, transverse and inline spacing of the models, on frequency behavior of the cylinder-s near-wake. The experiments carried on under subcritical flow regime, using the hot-wire anemometry (HWA). The relationship between the Strouhal numbers and arrangements provide an insight into the global physical processes of wake interaction and vortex shedding.

Keywords: Airfoil, Cylinder, Strouhal, Wake interaction

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Authors: Hidehiko Okada

Abstract:

The author proposes an extension of particle swarm optimization (PSO) for solving interval-valued optimization problems and applies the extended PSO to evolutionary training of neural networks (NNs) with interval weights. In the proposed PSO, values in the genotypes are not real numbers but intervals. Experimental results show that interval-valued NNs trained by the proposed method could well approximate hidden target functions despite the fact that no training data was explicitly provided.

Keywords: Evolutionary algorithms, swarm intelligence, particle swarm optimization, neural network, interval arithmetic.

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Authors: Hayam M. Ibrahim, Ferial M. Abu-Salem

Abstract:

Medicinal plants are now gaining attractiveness in treatment of bacterial infections and food preservation. The objective of this study was to assess antibacterial activity of some medicinal plants on pathogenic bacteria. Screening of antibacterial activity of aqueous and methanol extracts of some plants: Jojoba, Ginger, Sage, Thyme and Clove against Bacillus cereus, Salmonella typhimurium, Staphylococcus aureus, Clostridium perfringens and Escherichia coli were investigated. Antibacterial activity was performed by agar diffusion and disc diffusion method. Jatropha, Jojoba, Clove and Ginger extracts showed notable bacterial activity in the first screening step then selected to be tested against Bacillus cereus (Gram+), Staphylococcus aureus (Gram+) and Salmonella typhimurium (Gram−) and their effect was compared using antibiotics as control. Screening results showed potential antibacterial activity of the tested plant extracts against the screened bacterial strains. It was found that methanol extracts exhibited higher antibacterial activity than aqueous extracts. Methanol extract of Jatropha showed the highest inhibition zone against Staphylococcus aureus (Gram+) with 24.00 mm diameter, compared to the other plant extracts followed by clove. Meanwhile, the inhibition zones of methanol extracts of Jojoba and Ginger were the same (12mm).The Gram-positive bacteria were found to be more sensitive to aqueous and methanol extracts than Gram-negative bacteria.

Keywords: Antibacterial activity, Food-borne pathogenic bacteria, Medicinal plants, Plant extracts.

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Authors: Arash Mir Abdolah Lavasani, Hamidreza Bayat

Abstract:

Heat transfer from two cam shape cylinder in side-byside arrangement had been studied numerically. The transverse gap between the centers of cylinders (T) is allowed to vary to change the pitch ratio (T/Deq). The equivalent diameter of the cylinder (Deq) is 27.6 mm and pitch ratio varies in range of 1≤T/Deq≤3. The Reynolds numbers based on equivalent circular cylinder are within 50≤ Reeq≤150. Results show that Nusselt number of cylinders increases about 1 to 36 percent when pitch ratio increases from 1 to 3.

Keywords: Cam shaped, side-by-side cylinders, numerical, heat Transfer.

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Authors: Azza A. Abou-Arab, Ferial M. Abu-Salem

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The influence of microwave drying methods on the nutritional and anti-nutritional composition and physical characteristics of banana peels was investigated. Banana peels were assessed for physical properties such as yield, pH value, bulk density, water holding capacity (WHC) and oil holding capacity (OHC). The results showed that, the yield of banana peels and pH value was significantly (P < 0.05) decreased by microwave drying (11.20% and pH 5.08, respectively) compared with control. Bulk density was increased by microwave drying and recorded 62.03 g/100 ml. The banana peels flour demonstrated that the highest WHC was 8.65 g water/g dry sample and OHC was 6.73 g oil/g dry sample compared to control. The results observed a significant decrease (P < 0.05) in moisture, fiber and total carbohydrates content of banana peels; whereas, the rates of ash, protein and fat content were increased after drying by microwave compared with control. The lignin content of banana peels was significantly increased (P < 0.05) by microwave drying and the recorded value was 8.31% dw. The results also revealed that the ascorbic acid content was significantly decreased by microwave drying and recorded 18.32 mg/100 g dw vis. 23.51 mg/100 g dw for control. With regarding the anti-nutrients, phytates, alkaloids, oxalates and hydrogen cyanides levels in banana peels, it was in the threshold value mentioned as safety restrict. These results demonstrated that the levels of phytates, alkaloids, oxalates and hydrogen cyanides were decreased by microwave drying methods which recorded 4.07%, 5.45%, 0.85% and 32.15%, respectively.

Keywords: Banana peels, microwave drying, physical characteristics, nutritional composition, anti-nutritional composition.

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Authors: Hsuan-Ku Liu

Abstract:

This paper investigates the solutions of two-point fuzzy boundary value problems as the form x = f(t, x(t)), x(0) = A and x(l) = B, where A and B are fuzzy numbers. There are four different solutions for the problems when the lateral type of H-derivative is employed to solve the problems. As f(t, x) is a monotone function of x, these four solutions are reduced to two different solutions. As f(t, x(t)) = λx(t) or f(t, x(t)) = -λx(t), solutions and several comparison results are presented to indicate advantages of each solution.

Keywords: Fuzzy derivative, lateral type of H-derivative, fuzzy differential equations, fuzzy boundary value problems, boundary value problems.

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Authors: B. S. Bokuleva, R. A. Avakova, A. A. Sultangubieva, U. Schamiloglu

Abstract:

It is discussed about modern usage of adopted words and their vocabularies, Turkism usage fields, phonetic, grammatical and lexis-semantic assimilation of the typological-morphological structures of entering to different Hindi languages in comparative typological aspects in this scientific article. The lexis vocabulary is rich, the prevalence area is wide and it has researched the entering process of vocabulary into the great languages of Turkic elements from the speakers- numbers. The research work has worked on the base of Hindi vocabulary.

Keywords: Adopted words, language communications, Turkism, Turkic languages.

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Authors: R.YadollahiFarsani, B. Ghasemi

Abstract:

A magnetohydrodynamic mixed convective flow in a cavity was studied in this paper. The lower surface of cavity was heated from below whereas other walls of the cavity were thermally isolated. The governing two-dimensional flow equations have been solved by using finite volume code. The effects of magnetic field were studied on flow and temperature field and heat transfer performance at a wide range of parameters, Such as Hartmann (0≤Ha≤100) and Reynolds (1≤Re≤100) numbers. The results showed that as Hartman number increases the Nusselt number, representing heat transfer from the cavity decreases.

Keywords: Cavity, Magnetic Field, Mixed Convection, Magnetohydrodynamic

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Authors: S. Sivakumar, Ravikiran Sangras, Vasudevan Raghavan

Abstract:

In this work, stationary hot-wire measurements are carried out to investigate the characteristics of a round free jet in its potential core region (0 ≤ x/d ≤ 10). Measurements are carried out on an incompressible round jet for a range of Reynolds numbers from 4000 to 8000, calculated based on the jet exit mean velocity and the nozzle diameter. The effect of flow velocity on the development characteristics of the jet in the core region is analyzed. Timeaveraged statistics, spectra of velocity and its higher order moments are presented and explained.

Keywords: Contoured nozzle, hot-wire anemometer, Reynolds number, velocity fluctuations, velocity spectra.

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Authors: M. Bakhtaoui, L. Merahi

Abstract:

The reliability of the filtered HVBK model is now investigated via some large eddy simulations (LES) of freely decaying isotropic superfluid turbulence. For homogeneous turbulence at very high Reynolds numbers, comparison of the terms in the spectral kinetic energy budget equation indicates, in the energy-containing range, that the production and energy transfer effects become significant except for dissipation. In the inertial range, where the two fluids are perfectly locked, the mutual friction maybe neglected with respect to other terms. Also, the LES results for the other terms of the energy balance are presented.

Keywords: Superfluid turbulence, HVBK, Energy budget, Large Eddy Simulation.

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Authors: K. Masera, A. K. Hossain

Abstract:

Hardly any neat biodiesel satisfies the European EN14214 standard for compression ignition engine application. To satisfy the EN14214 standard, various additives are doped into biodiesel; however, biodiesel additives might cause other problems such as increase in the particular emission and increased specific fuel consumption. In addition, the additives could be expensive. Considering the increasing level of greenhouse gas GHG emissions and fossil fuel depletion, it is forecasted that the use of biodiesel will be higher in the near future. Hence, the negative aspects of the biodiesel additives will likely to gain much more importance and need to be replaced with better solutions. This study aims to satisfy the European standard EN14214 by blending the biodiesels derived from sustainable feedstocks. Waste Cooking Oil (WCO) and Animal Fat Oil (AFO) are two sustainable feedstocks in the EU (including the UK) for producing biodiesels. In the first stage of the study, these oils were transesterified separately and neat biodiesels (W100 & A100) were produced. Secondly, the biodiesels were blended together in various ratios: 80% WCO biodiesel and 20% AFO biodiesel (W80A20), 60% WCO biodiesel and 40% AFO biodiesel (W60A40), 50% WCO biodiesel and 50% AFO biodiesel (W50A50), 30% WCO biodiesel and 70% AFO biodiesel (W30A70), 10% WCO biodiesel and 90% AFO biodiesel (W10A90). The prepared samples were analysed using Thermo Scientific Trace 1300 Gas Chromatograph and ISQ LT Mass Spectrometer (GC-MS). The GS-MS analysis gave Fatty Acid Methyl Ester (FAME) breakdowns of the fuel samples. It was found that total saturation degree of the samples was linearly increasing (from 15% for W100 to 54% for A100) as the percentage of the AFO biodiesel was increased. Furthermore, it was found that WCO biodiesel was mainly (82%) composed of polyunsaturated FAMEs. Cetane numbers, iodine numbers, calorific values, lower heating values and the densities (at 15 ^oC) of the samples were estimated by using the mass percentages data of the FAMEs. Besides, kinematic viscosities (at 40 °C and 20 °C), densities (at 15 °C), heating values and flash point temperatures of the biomixture samples were measured in the lab. It was found that estimated and measured characterisation results were comparable. The current study concluded that biomixture fuel samples W60A40 and W50A50 were perfectly satisfying the European EN 14214 norms without any need of additives. Investigation on engine performance, exhaust emission and combustion characteristics will be conducted to assess the full feasibility of the proposed biomixture fuels.

Keywords: Biodiesel, blending, characterisation, CI Engine.

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Authors: Eva Eggeling, Dieter W. Fellner, Torsten Ullrich

Abstract:

The objective of global optimization is to find the globally best solution of a model. Nonlinear models are ubiquitous in many applications and their solution often requires a global search approach; i.e. for a function f from a set A ⊂ Rn to the real numbers, an element x0 ∈ A is sought-after, such that ∀ x ∈ A : f(x0) ≤ f(x). Depending on the field of application, the question whether a found solution x0 is not only a local minimum but a global one is very important. This article presents a probabilistic approach to determine the probability of a solution being a global minimum. The approach is independent of the used global search method and only requires a limited, convex parameter domain A as well as a Lipschitz continuous function f whose Lipschitz constant is not needed to be known.

Keywords: global optimization, probability theory, probability of globality

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Authors: S. Y. Choi, Y. H. Na, J. H. Kim

Abstract:

In this work, thermoelastic damping effect on the hemi- spherical shells is investigated. The material is selected silicon, and heat conduction equation for thermal flow is solved to obtain the temperature profile in which bending approximation with inextensional assumption of the model. Using the temperature profile, eigen-value analysis is performed to get the natural frequencies of hemispherical shells. Effects of mode numbers, radii and radial thicknesses of the model on the natural frequencies are analyzed in detail. Furthermore, the quality factor (Q-factor) is defined, and discussed for the ring and hemispherical shell.

Keywords: Thermoelastic damping, hemispherical shell, quality factor

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Authors: Weerachi Sarakorn, I-Ming Tang

Abstract:

A mathematical model for the transmission of SARS is developed. In addition to dividing the population into susceptible (high and low risk), exposed, infected, quarantined, diagnosed and recovered classes, we have included a class called untraced. The model simulates the Gompertz curves which are the best representation of the cumulative numbers of probable SARS cases in Hong Kong and Singapore. The values of the parameters in the model which produces the best fit of the observed data for each city are obtained by using a differential evolution algorithm. It is seen that the values for the parameters needed to simulate the observed daily behaviors of the two epidemics are different.

Keywords: SARS, mathematical modelling, differential evolution algorithm.

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Authors: M. M. Kassem, A. S. Rashed

Abstract:

The time dependent progress of a chemical reaction over a flat horizontal plate is here considered. The problem is solved through the group similarity transformation method which reduces the number of independent by one and leads to a set of nonlinear ordinary differential equation. The problem shows a singularity at the chemical reaction order n=1 and is analytically solved through the perturbation method. The behavior of the process is then numerically investigated for n≠1 and different Schmidt numbers. Graphical results for the velocity and concentration of chemicals based on the analytical and numerical solutions are presented and discussed.

Keywords: Time dependent, chemical convection, grouptransformation method, perturbation method.

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Authors: Ezzatallah Baloui Jamkhaneh, Bahram Sadeghpour-Gildeh, Gholamhossein Yari

Abstract:

This purpose of this paper is to present the acceptance single sampling plan when the fraction of nonconforming items is a fuzzy number and being modeled based on the fuzzy Poisson distribution. We have shown that the operating characteristic (oc) curves of the plan is like a band having a high and low bounds whose width depends on the ambiguity proportion parameter in the lot when that sample size and acceptance numbers is fixed. Finally we completed discuss opinion by a numerical example. And then we compared the oc bands of using of binomial with the oc bands of using of Poisson distribution.

Keywords: Statistical quality control, acceptance single sampling, fuzzy number.

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Authors: Emin Özyılmaz

Abstract:

In this work, position vector of a time-like dual curve according to standard frame of D31 is investigated. First, it is proven that position vector of a time-like dual curve satisfies a dual vector differential equation of fourth order. The general solution of this dual vector differential equation has not yet been found. Due to this, in terms of special solutions, position vectors of some special time-like dual curves with respect to standard frame of D31 are presented.

Keywords: Classical Differential Geometry, Dual Numbers, DualFrenet Equations, Time-like Dual Curve, Position Vector, DualLorentzian Space.

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Authors: M. Hadi Mashinchi, M. Reza Mashinchi, Siti Mariyam H. J. Shamsuddin

Abstract:

In this paper a genetic algorithms approach for solving the linear and quadratic fuzzy equations Ãx̃=B̃ and Ãx̃² + B̃x̃=C̃ , where Ã, B̃, C̃ and x̃ are fuzzy numbers is proposed by genetic algorithms. Our genetic based method initially starts with a set of random fuzzy solutions. Then in each generation of genetic algorithms, the solution candidates converge more to better fuzzy solution x̃_b . In this proposed method the final reached x̃_b is not only restricted to fuzzy triangular and it can be fuzzy number.

Keywords: Fuzzy coefficient, fuzzy equation, genetic algorithms.

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Authors: P.-W. Tsai, J.-W. Chen, C.-W. Chen, C.-Y. Chen

Abstract:

In recent years, many researchers are involved in the field of fuzzy theory. However, there are still a lot of issues to be resolved. Especially on topics related to controller design such as the field of robot, artificial intelligence, and nonlinear systems etc. Besides fuzzy theory, algorithms in swarm intelligence are also a popular field for the researchers. In this paper, a concept of utilizing one of the swarm intelligence method, which is called Bacterial-GA Foraging, to find the stabilized common P matrix for the fuzzy controller system is proposed. An example is given in in the paper, as well.

Keywords: Half-circle fuzzy numbers, predictions, swarm intelligence, Lyapunov method.

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Authors: Z. Neffah, H. Kahalerras

Abstract:

A numerical study is made in a parallel-plate porous channel subjected to an oscillating flow and an exothermic chemical reaction on its walls. The flow field in the porous region is modeled by the Darcy–Brinkman–Forchheimer model and the finite volume method is used to solve the governing equations. The effects of the modified Frank-Kamenetskii (FKm) and Damköhler (Dm) numbers, the amplitude of oscillation (A), and the Strouhal number (St) are examined. The main results show an increase of heat and mass transfer rates with A and St, and their decrease with FKm and Dm.

Keywords: Chemical reaction, heat transfer, mass transfer, oscillating flow, porous channel.

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Authors: Omid Jadidi, Fatemeh Firouzi, Enzo Bagliery

Abstract:

Supplier selection, in real situation, is affected by several qualitative and quantitative factors and is one of the most important activities of purchasing department. Since at the time of evaluating suppliers against the criteria or factors, decision makers (DMS) do not have precise, exact and complete information, supplier selection becomes more difficult. In this case, Grey theory helps us to deal with this problem of uncertainty. Here, we apply Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method to evaluate and select the best supplier by using interval fuzzy numbers. Through this article, we compare TOPSIS with some other approaches and afterward demonstrate that the concept of TOPSIS is very important for ranking and selecting right supplier.

Keywords: TOPSIS, fuzzy number, MADM, Supplier selection

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Authors: Avinash Chandra, R. P. Chhabra

Abstract:

Natural convection heat transfer from a heated horizontal semi-circular cylinder (flat surface upward) has been investigated for the following ranges of conditions; Grashof number, and Prandtl number. The governing partial differential equations (continuity, Navier-Stokes and energy equations) have been solved numerically using a finite volume formulation. In addition, the role of the type of the thermal boundary condition imposed at cylinder surface, namely, constant wall temperature (CWT) and constant heat flux (CHF) are explored. Natural convection heat transfer from a heated horizontal semi-circular cylinder (flat surface upward) has been investigated for the following ranges of conditions; Grashof number, and Prandtl number, . The governing partial differential equations (continuity, Navier-Stokes and energy equations) have been solved numerically using a finite volume formulation. In addition, the role of the type of the thermal boundary condition imposed at cylinder surface, namely, constant wall temperature (CWT) and constant heat flux (CHF) are explored. The resulting flow and temperature fields are visualized in terms of the streamline and isotherm patterns in the proximity of the cylinder. The flow remains attached to the cylinder surface over the range of conditions spanned here except that for and ; at these conditions, a separated flow region is observed when the condition of the constant wall temperature is prescribed on the surface of the cylinder. The heat transfer characteristics are analyzed in terms of the local and average Nusselt numbers. The maximum value of the local Nusselt number always occurs at the corner points whereas it is found to be minimum at the rear stagnation point on the flat surface. Overall, the average Nusselt number increases with Grashof number and/ or Prandtl number in accordance with the scaling considerations. The numerical results are used to develop simple correlations as functions of Grashof and Prandtl number thereby enabling the interpolation of the present numerical results for the intermediate values of the Prandtl or Grashof numbers for both thermal boundary conditions.

Keywords: Constant heat flux, Constant surface temperature, Grashof number, natural convection, Prandtl number, Semi-circular cylinder

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Authors: Mahnaz Hosseinzadeh, Aliyeh Kazemi

Abstract:

In this paper, a method is proposed for solving Fuzzy Multi-Objective Linear Programming problems (FMOLPP) with fuzzy right hand side and fuzzy decision variables. To illustrate the proposed method, it is applied to the problem of selecting suppliers for an automotive parts producer company in Iran in order to find the number of optimal orders allocated to each supplier considering the conflicting objectives. Finally, the obtained results are discussed.

Keywords: Fuzzy multi-objective linear programming problems, triangular fuzzy numbers, fuzzy ranking, supplier selection problem.

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Authors: B. Fersadou, H. Kahalerras

Abstract:

This work deals with the problem of MHD mixed convection in a completely porous and differentially heated vertical channel. The model of Darcy-Brinkman-Forchheimer with the Boussinesq approximation is adopted and the governing equations are solved by the finite volume method. The effects of magnetic field and buoyancy force intensities are given by the Hartmann and Richardson numbers respectively, as well as the Joule heating represented by Eckert number on the velocity and temperature fields, are examined. The main results show an augmentation of heat transfer rate with the decrease of Darcy number and the increase of Ri and Ha when Joule heating is neglected.

Keywords: Heat sources, magnetic field, mixed convection, porous channel.

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Authors: Khidir R. Sharaf, Didar A. Ali

Abstract:

The nullity η(G) of a graph is the occurrence of zero as an eigenvalue in its spectra. A zero-sum weighting of a graph G is real valued function, say f from vertices of G to the set of real numbers, provided that for each vertex of G the summation of the weights f(w) over all neighborhood w of v is zero for each v in G.A high zero-sum weighting of G is one that uses maximum number of non-zero independent variables. If G is graph with an end vertex, and if H is an induced subgraph of G obtained by deleting this vertex together with the vertex adjacent to it, then, η(G)= η(H). In this paper, a high zero-sum weighting technique and the endvertex procedure are applied to evaluate the nullity of t-tupple and generalized t-tupple graphs are derived  and determined for some special types of graphs,

 Also, we introduce and prove some important results about the t-tupple coalescence, Cartesian and Kronecker products of nut graphs.

Keywords: Graph theory, Graph spectra, Nullity of graphs.

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