The purpose of this paper is to investigate the numerical solutions of the Burgers' and modified Burgers' equation using sextic B‐spline collocation method.
Abstract
Purpose
The purpose of this paper is to investigate the numerical solutions of the Burgers' and modified Burgers' equation using sextic B‐spline collocation method.
Design/methodology/approach
Crank‐Nicolson central differencing scheme has been used for the time integration and sextic B‐spline functions have been used for the space integration to the modified and time splitted modified Burgers' equation.
Findings
It has been found that the proposed method is unconditionally stable and obtained results are consistent with some earlier published studies.
Originality/value
Sextic B‐spline collocation method for the Burgers' and modified Burgers' equation is given.
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Keywords
Khaled Mostafa, Mohamed Ramadan and Azza El-Sanabary
This study aims to address a comprehensive and integrated investigations pertaining to the preparation of AgNPs with well-defined nano-sized scale using the aforementioned poly…
Abstract
Purpose
This study aims to address a comprehensive and integrated investigations pertaining to the preparation of AgNPs with well-defined nano-sized scale using the aforementioned poly (meth acrylic acid [MAA])–chitosan graft copolymer, which is cheap, nontoxic, biodegradable and biocompatible agent as a substitute for the traditionally used toxic reducing agents.
Design/methodology/approach
AgNPs are prepared under a range of conditions, containing silver nitrate and poly (MAA)–chitosan graft copolymer concentrations, time, temperature and pH of the preparation medium. To classify AgNPs obtained under the various conditions, ultraviolet–visible spectroscopy spectra and transmission electron microscopy images are used for characterization of AgNPs instrumentally in addition to the visual color change throughout the work. The work was further extended to study the application of the so prepared AgNPs on cotton fabric to see their suitability as antibacterial agent as well as their durability after certain washing cycles.
Findings
According to the current investigation, the optimal conditions for AgNPs formation of nearly 3–15 nm in size are 5 g/l, poly (MAA)–chitosan graft copolymer and 300 ppm AgNO3 in addition to carrying out the reaction at 60°C for 30 min at pH 12. Besides, the application of the so prepared AgNPs on cotton fabric displayed a substantial reduction in antibacterial efficiency against gram-positive and gram-negative bacteria estimated even after 10 washing cycles in comparison with untreated one.
Originality/value
To the best of the authors’ information, no comprehensive study of the synthesis of AgNPs using poly (MAA)–chitosan graft copolymer with a graft yield of 48% has been identified in the literature.
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Khaled Mostafa, Mohamed Ramadan and Azza El-Sanabary
The purpose of this study is to investigate the authors' previously prepared and fully characterized poly (methacrylamide)-chitosan nanoparticles (CNPs) graft copolymer having…
Abstract
Purpose
The purpose of this study is to investigate the authors' previously prepared and fully characterized poly (methacrylamide)-chitosan nanoparticles (CNPs) graft copolymer having 50.2% graft yield with respect to flocculation efficiency for ferric laurate aqueous dispersions. This was done to compare the ability of the latter cheap, biodegradable and ecofriendly hybrid natural-synthetic polymeric substrate as a flocculant in comparison with higher cost, nonbiodegradable and harmful polyacrylamide as a well-known synthetic flocculant counterpart.
Design/methodology/approach
The graft copolymerization process was carried out at 450°Cfor 120 min using (1.0 g) CNPs, methacrylamide (1.5 g), 100 mmol/l potassium chromate and 80 mmol/l mandelic acid. Fourier transform infrared spectroscopy, thermogravimetric analysis, elemental analysis and specific viscosity were used to characterize and analyze the resultant copolymer. The flocculation efficiency was conferred in terms of transmittance % and weight removal %. The main factors influencing the flocculation process, such as flocculent dose, flocculation medium pH, stirring speed, flocculation temperature and grafting extent, were comprehensively discussed.
Findings
The flocculation efficiency of the prepared copolymers revealed the following findings: increased by increasing the flocculant dose, pH, temperature and stirring speed to a maximum values denoted at 30 ppm, 6.0, 30°C and 50 r/min, respectively, then decreased thereafter; increased by increasing the extent of grafting within the range studied; showed a comparable flocculation efficiency in comparison with polyacrylamide as a synthetic polymeric flocculent; and, finally, a preliminary bridging mechanism representing the attraction between the anionic suspended particles ferric laurate and cationic poly (MAam)-CNPs graft copolymer has been projected.
Originality/value
The advancement addressed here is undertaken with using the authors’ poly (MAam)-CNPs graft copolymers having different extent of grafting (a point which is not cited in the literature especially for the authors’ prepared copolymer) as a hybrid natural-synthetic polymeric substrate as a flocculant for ferric laurate aqueous dispersions in comparison with the high cost and nondegradable polyacrylamide synthetic flocculant.
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A. Higazy, M.H. El‐Rafie, M.A. Ramadan and A. Hebeish
Poly (acrylic) starch composites were prepared by polymerizing acrylic acid, acrylamide alone or in admixtures with maize starch using KMnO4/citric acid as redox initiation. The…
Abstract
Poly (acrylic) starch composites were prepared by polymerizing acrylic acid, acrylamide alone or in admixtures with maize starch using KMnO4/citric acid as redox initiation. The cooked composite pastes were used as partial substituent of kerosene oil emulsion in the pigment printing pastes for cotton fabric. Printing was carried out under a variety of conditions including neutralization of the free carboxylic groups of the polyacrylic acid component in the composite or AA/Aam mixtures, composite concentration, and the type of pigment dyes. The effect of storage on the efficiency of the printing paste was also examined. The printed samples were assessed for colour strength (K/S) overall fastness properties. Results obtained indicate that:
This article proposes a relaxed gradient iterative (RGI) algorithm to solve coupled Sylvester-conjugate transpose matrix equations (CSCTME) with two unknowns.
Abstract
Purpose
This article proposes a relaxed gradient iterative (RGI) algorithm to solve coupled Sylvester-conjugate transpose matrix equations (CSCTME) with two unknowns.
Design/methodology/approach
This article proposes a RGI algorithm to solve CSCTME with two unknowns.
Findings
The introduced (RGI) algorithm is more efficient than the gradient iterative (GI) algorithm presented in Bayoumi (2014), where the author's method exhibits quick convergence behavior.
Research limitations/implications
The introduced (RGI) algorithm is more efficient than the GI algorithm presented in Bayoumi (2014), where the author's method exhibits quick convergence behavior.
Practical implications
In systems and control, Lyapunov matrix equations, Sylvester matrix equations and other matrix equations are commonly encountered.
Social implications
In systems and control, Lyapunov matrix equations, Sylvester matrix equations and other matrix equations are commonly encountered.
Originality/value
This article proposes a relaxed gradient iterative (RGI) algorithm to solve coupled Sylvester conjugate transpose matrix equations (CSCTME) with two unknowns. For any initial matrices, a sufficient condition is derived to determine whether the proposed algorithm converges to the exact solution. To demonstrate the effectiveness of the suggested method and to compare it with the gradient-based iterative algorithm proposed in [6] numerical examples are provided.
Details
Keywords
Melodena Stephens Balakrishnan
Marketing, Strategy, International Business.
Abstract
Subject area
Marketing, Strategy, International Business.
Study level/applicability
Post-Graduates' classes.
Case overview
This case focuses on the particularities of the Kentucky Fried Chicken (KFC) restaurant run by the Americana Group in Mecca, in the Kingdom of Saudi Arabia. It allows students in the service industry, and especially those interested in the quick service industry to understand some of the challenges of operating in a market with high volume and other specific local market conditions. Perhaps, it will also allow those organizations wishing to enter into emerging markets to realize that globalization does not mean standardization of all practices but rather values.
Expected learning outcomes
On completion of utilizing the case study as an exercise, students should be able to develop: Case-specific skills: critically examine the importance of the international business and marketing strategy in the Middle East and demonstrate this by analyzing real regional/ world examples using complex theoretical frameworks; identify examples of best practice and explain the dynamics toward international business and marketing strategy with reference to a range of theoretical models; and apply these in a meaningful way to the Middle East North Africa region. Discipline-specific skills: synthesize and critically evaluate a corpus of academic literature and government reports on international business and marketing strategy; and link international business and marketing strategy concepts and theories to real regional/world examples. Personal and key skills: reflect on the process of learning and undertake independen/self-directed learning (including time management) to achieve consistent, proficient and sustained attainment. Work as either a participant or a leader of a group and contribute effectively to the achievement of objectives in the field of international business and marketing strategy.
Supplementary materials
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A. Hebeish, M. H. El-Rafie, M. A. Ramadan and M. E. El-Naggar
Hydroxypropyl starch (HPS) is synthesized by using maize starch and different concentrations of both propylene oxide )PO) and sodium hydroxide (NaOH) with the intent to obtain HPS…
Abstract
Hydroxypropyl starch (HPS) is synthesized by using maize starch and different concentrations of both propylene oxide )PO) and sodium hydroxide (NaOH) with the intent to obtain HPS products which can better serve as a reducing and stabilizing agent during the preparation of silver nanoparticles. Such a preparation is carried out under a variety of conditions which include: pH, temperature, duration of the reaction medium, molar substitution (MS) of HPS, and concentration of both HPS and silver nitrate (AgNO3). The yield of silver nanoparticle colloids is monitored via color and ultraviolet (UV) visible spectral analyses whereas their evaluation is performed by making use of a transmission electron microscopy (TEM) to determine size and size distribution. The results obtained conclude that the optimum conditions for preparation of silver nanoparticle colloids with excellent size and size distribution which range from 6-8 nm could be produced by using 0.9 gm of HPS (MS = .84), 0.425 gm of AgNO3, a pH of 12, and temperature of 70°C for 15 minutes. Furthermore, the silver nanoparticle colloid solution prepared under these conditions is stable and remains without aggregation for more than six months. Thus preparation of a well stabilized silver nanoparticle solution with a concentration of 1608 ppm and a diameter of 9-18 nm can be achieved. A silver nanoparticle solution with these unique characteristics may be suitable for industrial applications.
Details
Keywords
R.M. Mohsen, A.M. Ramadan, K.A. Shaffei and A.S. Badran
A newly developed polyvinyl acetate (PVA) emulsion latex for adhesive has been prepared by the semicontinuous process using a newly developed octyl aldehyde sodium…
Abstract
A newly developed polyvinyl acetate (PVA) emulsion latex for adhesive has been prepared by the semicontinuous process using a newly developed octyl aldehyde sodium bisulphite‐potassium persulphate redox pair initiation system. In this work the amount of polyvinyl alcohol (PVA) as a protective colloid has been changed and it was found that only a little amount of (PVA) together with the newly developed adduct could cause a stable latex with excellent mechanical properties for bonding wood which favours this redox system in large industrial applictions. Also monodisperse latex particles with low polydispersity index can be prepared by using 1% PVA coupled with the newly developed redox system. Finally the developed latex has been incorporated and the corresponding shear strength were measured.
This paper aims to investigate the features of three vectorized iterative numerical schemes used to simulate the behavior of modified Burgers equation (MBE).
Abstract
Purpose
This paper aims to investigate the features of three vectorized iterative numerical schemes used to simulate the behavior of modified Burgers equation (MBE).
Design/methodology/approach
Two of the schemes comprise differential quadrature and finite difference methods, while the third scheme consists of only differential quadrature for the derivative approximations. Proposed schemes are simulated for well-posed problems of MBE having known the analytic solution. The computational complexity of the schemes is examined through monitoring the time taken to complete the simulation. The results are compared with the analytic solution with the help of discrete error norms. Also, the accuracy of the proposed schemes is compared with that of the existing schemes in the literature. Vectorized MATLAB programs of the schemes are used for all investigations.
Findings
It is observed that all the three schemes succeeded in producing a good replication of the exact solution. The results are closer to the analytical solution than the results in the literature. Among the three schemes, the scheme labeled as FDTDQS is found highly accurate and computationally cheaper using fewer grid points. From the vectorized MATLAB programs provided, it is evident that the implementation of the schemes is simple.
Originality/value
This study gives an idea about three numerical schemes for a highly nonlinear problem. This mathematical framework can be adopted to any one-dimensional partial differential equation as well, and the provided program will be helpful to generate more fast and accurate vectorized code in MATLAB.
Details
Keywords
A. Hebeish, M.A. Ramadan, M.E. El-Naggar and M.H. El-Rafie
Nano-sized silver particles at a concentration of 1620 ppm were prepared using hydroxypropyl starch (HPS) as a reductant of silver nitrate and a stabilizer for silver…
Abstract
Nano-sized silver particles at a concentration of 1620 ppm were prepared using hydroxypropyl starch (HPS) as a reductant of silver nitrate and a stabilizer for silver nanoparticles. A solution containing 1620 ppm silver nanoparticles was diluted to 50 ppm and 100 ppm. The diluted solution was applied to cotton fabrics in the presence and absence of a binder to impart antibacterial properties to the fabrics. The solution containing 50 ppm silver nanoparticles with 1% binder (Printofix® Binder MTB EG liquid) induces excellent and durable bactericidal activity in cotton fabrics. The finished fabrics were examined for morphological features and surface characteristics by making use of the SEM. The SEM pictures reveal that silver nanoparticles are deposited on the surface of fibrils (fabric fibres).