Search results for: analytical solutions

Authors: A. Ashjaran, R. Ghazi-saeidi, E. Yazdanshenas, A. Rashidi

Abstract:

In this research, the main aim is to investigate the antimicrobial effectiveness of ammonyx solutions finishing on Sweatshirt Sport with immersion method. 60 Male healthy subjects (football player) participated in this study. They were dressed in a Sweatshirt for 14 days and some microbes found on them were investigated. The antimicrobial effect of different ammonyx solutions(1/100, 1/500, 1/1000, 1/2000 v/v solutions of Ammonyx) on the identified microbes was studied by the zone inhabitation method in vitro. In the next step the Sweatshirt Sports were treated with the same different solutions of ammonyx and the antimicrobial effectiveness was assessed by colony count method in different times and the results were compared whit untreated ones. Some mechanical properties of treated cotton/polyester yarn that used in Sweatshirt Sport were measured after 30 days and were compared with untreated one. Finally after finishing, scanning electron microscopy (SEM) was used to compare the surfaces of the finished and unfinished specimens. The results showed the presence of five pathogenic microbes on Sweatshirt Sports such as Escherichia coli, Staphylococcus aureus, Aspergillus, Mucor and Candida. The inhalation time for treated on Sweatshirt Sports improved. The amount of colony growth on treated clothes reduced considerably and moreover the mechanical tests results showed no significant deterioration effect of studies properties in comparison to the untreated yarn. The visual examination of the SEM indicated that the antimicrobial treatments were applied usefully to fabrics.

Keywords: Pathogenic microbes, Sweatshirt Sports, Ammonyx, antimicrobial treatment

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Authors: Pan Wang, Yongkun Li

Abstract:

In this paper, a periodic predator-prey system with harvesting terms and Holling II type functional response is considered. Sufficient criteria for the existence of at least sixteen periodic solutions are established by using the well known continuation theorem due to Mawhin. An example is given to illustrate the main result.

Keywords: Periodic solution, predator-prey system, harvesting terms, continuation theorem.

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Authors: Mohammad Sadeghi, Behrouz Heidari, Korush Montazeri

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In this paper, we have focused on study of swelling kinetics and salt-sensitivity behavior of a superabsorbing hydrogel based on carboxymethylcellulose (CMC) and acrylic acid and 2- Buthyl methacrylate. The swelling kinetics of the hydrogels with various particle sizes was preliminary investigated as well. The swelling of the hydrogel showed a second order kinetics of swelling in water. In addition, swelling measurements of the synthesized hydrogels in various chloride salt solutions was measured. Results indicated that a swelling-loss with an increase in the ionic strength of the salt solutions.

Keywords: Carboxymethylcellulose, swelling kinetics, 2-hydroxypropylmetacrylate, acrylic acid.

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Authors: Zhouhong Li

Abstract:

In this paper, by applying Mawhin-s continuation theorem of coincidence degree theory, we study the existence of almost periodic solutions for neural multi-delay logarithmic population model and obtain one sufficient condition for the existence of positive almost periodic solution for the above equation. An example is employed to illustrate our result.

Keywords: Almost periodic solution, Multi-delay, Logarithmic population model, Coincidence degree.

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Authors: T. Cornelius

Abstract:

Masonry cavity walls are loaded by wind pressure and vertical load from upper floors. These loads results in bending moments and compression forces in the ties connecting the outer and the inner wall in a cavity wall. Large cavity walls are furthermore loaded by differential movements from the temperature gradient between the outer and the inner wall, which results in critical increase of the bending moments in the ties. Since the ties are loaded by combined compression and moment forces, the loadbearing capacity is derived from instability equilibrium equations. Most of them are iterative, since exact instability solutions are complex to derive, not to mention the extra complexity introducing dimensional instability from the temperature gradients. Using an inverse variable substitution and comparing an exact theory with an analytical instability solution a method to design tie-connectors in cavity walls was developed. The method takes into account constraint conditions limiting the free length of the wall tie, and the instability in case of pure compression which gives an optimal load bearing capacity. The model is illustrated with examples from praxis.

Keywords: Masonry, tie connectors, cavity wall, instability, differential movements, combined bending and compression.

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Authors: Mohammad Jafariahangari, Marjan Habibi, Miresmaeil Mirnabibaboli, Mirza Hassan Hosseini

Abstract:

Self-service technologies (SSTs) make an important contribution to the daily life of people nowadays. However, the introduction of SST does not lead to its usage. Thereby, this paper was an attempt on discovery of the most preferred SST in the customers’ point of view. To fulfill this aim, the Analytical Hierarchy Process (AHP) was applied based on Saaty’s questionnaire which was administered to the customers of e-banking services located in Golestan providence, northern Iran. This study used qualitative factors in association with the intention of consumers’ usage of SSTs to rank three SSTs: ATM, mobile banking and internet banking. The results showed that mobile banking get the highest weight in consumers’ point of view. This research can be useful both for managers and service providers and also for customers who intend to use e-banking.

Keywords: Analytical Hierarchy Process, Decision-making, Ebanking, Iran, Self-service technologies.

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Authors: Ali Khajeh Samani, Mario M. Attard

Abstract:

Lateral expansion is a factor defining the level of confinement in reinforced concrete columns. Therefore, predicting the lateral strain relationship with axial strain becomes an important issue. Measuring lateral strains in experiments is difficult and only few report experimental lateral strains. Among the existing analytical formulations, two recent models are compared with available test results in this paper with shortcomings highlighted. A new analytical model is proposed here for lateral strain axial strain relationship and is based on the supposition that the concrete behaves linear elastic in the early stages of loading and then nonlinear hardening up to the peak stress and then volumetric expansion. The proposal for the lateral strain axial strain relationship after the peak stress is mainly based on the hypothesis that the plastic lateral strain varies linearly with the plastic axial strain and it is shown that this is related to the lateral confinement level.

Keywords: Confined Concrete, Lateral Strain, Triaxial test, Postpeak behavior

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Authors: Ghasem Abbasnejad, Soheil Zarkandi, Misagh Imani

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In this article the homotopy continuation method (HCM) to solve the forward kinematic problem of the 3-PRS parallel manipulator is used. Since there are many difficulties in solving the system of nonlinear equations in kinematics of manipulators, the numerical solutions like Newton-Raphson are inevitably used. When dealing with any numerical solution, there are two troublesome problems. One is that good initial guesses are not easy to detect and another is related to whether the used method will converge to useful solutions. Results of this paper reveal that the homotopy continuation method can alleviate the drawbacks of traditional numerical techniques.

Keywords: Forward kinematics, Homotopy continuationmethod, Parallel manipulators, Rotation matrix

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Authors: Timothy Akinwande, Eddie C. M. Hui

Abstract:

Housing the urban poor has remained a challenge for many years across the world, especially in developing economies, despite the apparent research attention and policy interventions. It is apt to investigate the prevalent affordable housing (AH) provision challenges using unconventional approaches. It is pragmatic to thoroughly examine housing experts to provide supply-side solutions to AH challenges and investigate informal settlers to deduce solutions from AH demand viewpoints. This study, being the supply-side investigation of an ongoing research, interrogated housing experts to determine significant expert solutions. Focus group discussions and in-depth interviews were conducted with housing experts in Nigeria. Through descriptive, content, and systematic thematic analyses of data, major findings are that deliberate finance models designed for the urban poor are the most significant housing finance solution in developing economies. Other findings are that adequately implemented rent control policies, deliberate Public-Private Partnership (PPP) approaches like inclusionary housing and land-value capture, and urban renewal programs to enlighten and tutor the urban poor on how to earn more, spend wisely, and invest in their own better housing will effectively solve AH finance challenges. Study findings are informative for the best approaches to achieve effective, AH finance for the urban poor in Nigeria, which is indispensable for the achievement of sustainable development goals. This research’s originality lies in the exploration of experts’ opinions in relation to AH finance to produce an equation model of critical solutions to AH finance challenges. Study data are useful resources for future pro-poor housing studies. This study makes housing policy-oriented recommendations toward effective, AH for the urban poor in developing countries.

Keywords: Affordable housing, effective affordable housing, housing policy, housing research, sustainable development, urban poor.

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Authors: Mohamed Ali

Abstract:

The boundary layer flow and heat transfer on a stretched surface moving with prescribed skin friction is studied for permeable surface. The surface temperature is assumed to vary inversely with the vertical direction x for n = -1. The skin friction at the surface scales as (x-1/2) at m = 0. The constants m and n are the indices of the power law velocity and temperature exponent respectively. Similarity solutions are obtained for the boundary layer equations subject to power law temperature and velocity variation. The effect of various governing parameters, such as the buoyancy parameter λ and the suction/injection parameter fw for air (Pr = 0.72) are studied. The choice of n and m ensures that the used similarity solutions are x independent. The results show that, assisting flow (λ > 0) enhancing the heat transfer coefficient along the surface for any constant value of fw. Furthermore, injection increases the heat transfer coefficient but suction reduces it at constant λ.

Keywords: Stretching surface, Boundary layers, Prescribed skin friction, Suction or injection, similarity solutions, buoyancy effects.

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Authors: Yew Mun Hung, Ching Sze Lim, Tiew Wei Ting, Ningqun Guo

Abstract:

The effect of streamwise conduction on the thermal characteristics of forced convection for nanofluidic flow in rectangular microchannel heat sinks under isothermal wall has been investigated. By applying the fin approach, models with and without streamwise conduction term in the energy equation were developed for hydrodynamically and thermally fully-developed flow. These two models were solved to obtain closed form analytical solutions for the nanofluid and solid wall temperature distributions and the analysis emphasized details of the variations induced by the streamwise conduction on the nanofluid heat transport characteristics. The effects of the Peclet number, nanoparticle volume fraction, thermal conductivity ratio on the thermal characteristics of forced convection in microchannel heat sinks are analyzed. Due to the anomalous increase in the effective thermal conductivity of nanofluid compared to its base fluid, the effect of streamwise conduction is expected to be more significant. This study reveals the significance of the effect of streamwise conduction under certain conditions of which the streamwise conduction should not be neglected in the forced convective heat transfer analysis of microchannel heat sinks.

Keywords: fin approach, microchannel heat sink, nanofluid, streamwise conduction

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Authors: Maria V. Morozova, Yulia V. Emelyanova, Anastasia A. Levina, Elena S. Buyanova, Zoya A. Mikhaylovskaya, Sofia A. Petrova

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The solid solutions of lanthanum niobates substituted by yttrium, bismuth and tungsten were synthesized. The structure of the solid solutions is either LaNbO₄-based monoclinic or BiNbO₄-based triclinic. The series where niobium is substituted by tungsten on B site reveals phase-modulated structure. The values of cell parameters decrease with increasing the dopant concentration for all samples except the tungsten series although the latter show higher total conductivity.

Keywords: Impedance spectroscopy, LaNbO4, lanthanum ortho-niobates.

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Authors: Berk Kılıç, Derin Dalgıç, Ela Mia Sevilla Levi, Ömer Aydın

Abstract:

In this experiment our goal was to remove heavy metals from water. Generally, removing toxic heavy elements: Cu+2, Cr+6 and Fe+3, ions from their aqueous solutions has been determined with different kinds of plants’ peels. However, this study focuses on banana, peach, orange, and potato peels. The first step of the experiment was to wash the peels with distilled water and then dry the peels in an oven for 80 h at 80 °C. The peels were washed with NaOH and dried again at 80 °C for 2 days. Once the peels were washed and dried, 0.4 grams were weighed and added to a 200 mL sample of 0.1% heavy metal solution by mass. The mixing process was done via a magnetic stirrer. A sample of each was taken at 15-minute intervals and the level of absorbance change of the solutions was detected using a UV-Vis Spectrophotometer. Among the used waste products, orange showed the best results, followed by banana peel as the most efficient for our purposes. Moreover, the amount of fruit peel, pH values of the initial heavy metal solution, and initial concentration of heavy metal solutions were investigated to determine the effectiveness of fruit peels for absorbency.

Keywords: Absorbance, heavy metal, removal of heavy metals, fruit peels.

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Authors: Oral Lacin, Turan Calban, Fatih Sevim, Taner Celik

Abstract:

In this study, Pb²⁺ uptake by the hydroxyapatite nanopowders (n-Hap) from aqueous solutions was investigated by using batch adsorption techniques. The adsorption equilibrium studies were carried out as a function of contact time, adsorbent dosage, pH, temperature, and initial Pb²⁺ concentration. The results showed that the equilibrium time of adsorption was achieved within 60 min, and the effective pH was selected to be 5 (natural pH). The maximum adsorption capacity of Pb²⁺ on n-Hap was found as 565 mg.g^-1. It is believed that the results obtained for adsorption may provide a background for the detailed mechanism investigations and the pilot and industrial scale applications.

Keywords: Nanopowders, hydroxyapatite, heavy metals, adsorption.

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Authors: Saeed Vahidifar, Mohammad Nakhaee Sharif, Mohammad Ghaffari

Abstract:

Few people would dispute the fact that one of the most common applications of energy is creating comfort in buildings, so it is probably true to say that management of energy consumption is required due to the environmental issues and increasing the efficiency of mechanical systems. From the geographical point of view, Iran is located in a warm and semi-arid region; therefore, air-cooled chillers are usually used for cooling residential buildings, commercial buildings, medical buildings, etc. In this study, a heat exchanger was designed for providing laundry hot water by utilizing condenser heat lost base on analytical results of a 540-bed hospital in the city of Mashhad in Iran. In this paper, by using the analytical method, energy consumption reduces about 13%, and coefficient of performance increases a bit. Results show that this method can help in the management of energy consumption a lot.

Keywords: Energy management, air-cooled chiller, heat exchanger, hospital laundry system.

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Authors: Ömer Aktaş, Olga A. Suvorova, Oleg Tretyakov

Abstract:

The boundary value problem on non-canonical and arbitrary shaped contour is solved with a numerically effective method called Analytical Regularization Method (ARM) to calculate propagation parameters. As a result of regularization, the equation of first kind is reduced to the infinite system of the linear algebraic equations of the second kind in the space of L₂. This equation can be solved numerically for desired accuracy by using truncation method. The parameters as cut-off wavenumber and cut-off frequency are used in waveguide evolutionary equations of electromagnetic theory in time-domain to illustrate the real-valued TM fields with lossy and lossless media.

Keywords: Arbitrary cross section waveguide, analytical regularization method, evolutionary equations of electromagnetic theory of time-domain, TM field.

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Authors: Changjin Xu, Qianhong Zhang

Abstract:

In this paper, a delayed competitive system with the effect of toxic substances is investigated. With the aid of differential equations with piecewise constant arguments, a discrete analogue of continuous non-autonomous delayed competitive system with the effect of toxic substances is proposed. By using Gaines and Mawhin,s continuation theorem of coincidence degree theory, a easily verifiable sufficient condition for the existence of positive solutions of difference equations is obtained.

Keywords: Competitive system, periodic solution, discrete time delay, topological degree.

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Authors: Lv Yuhua

Abstract:

In this paper, by establishing a new comparison result, we investigate the existence of positive solutions for initial value problems of nonlinear systems of second order integro-differential equations in Banach space.We improve and generalize some results  (see[5,6]), and the results is new even in finite dimensional spaces.

Keywords: Systems of integro-differential equations, monotone iterative method, comparison result, cone.

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Authors: Li Xiguang

Abstract:

In this paper, by constructing a special operator and using fixed point index theorem of cone, we get the sufficient conditions for symmetric positive solution of a class of nonlinear singular boundary value problems with p-Laplace operator, which improved and generalized the result of related paper.

Keywords: Banach space, cone, fixed point index, singular differential equation, p-Laplace operator, symmetric solutions.

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Authors: G.H. Farrahi, S.A. Faghidian, D.J. Smith

Abstract:

A thin layer on the component surface can be found with high tensile residual stresses, due to turning operations, which can dangerously affect the fatigue performance of the component. In this paper an analytical approach is presented to reconstruct the residual stress field from a limited incomplete set of measurements. Airy stress function is used as the primary unknown to directly solve the equilibrium equations and satisfying the boundary conditions. In this new method there exists the flexibility to impose the physical conditions that govern the behavior of residual stress to achieve a meaningful complete stress field. The analysis is also coupled to a least squares approximation and a regularization method to provide stability of the inverse problem. The power of this new method is then demonstrated by analyzing some experimental measurements and achieving a good agreement between the model prediction and the results obtained from residual stress measurement.

Keywords: Residual stress, Limited measurements, Inverse problems, Turning process.

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Authors: Mansour Nikkhah-Bahrami, Masih Loghmani, Mostafa Pooyanfar

Abstract:

In this paper, an analytical approach for free vibration analysis of four edges simply supported rectangular Kirchhoff plates is presented. The method is based on wave approach. From wave standpoint vibration propagate, reflect and transmit in a structure. Firstly, the propagation and reflection matrices for plate with simply supported boundary condition are derived. Then, these matrices are combined to provide a concise and systematic approach to free vibration analysis of a simply supported rectangular Kirchhoff plate. Subsequently, the eigenvalue problem for free vibration of plates is formulated and the equation of plate natural frequencies is constructed. Finally, the effectiveness of the approach is shown by comparison of the results with existing classical solution.

Keywords: Kirchhoff plate, propagation matrix, reflection matrix, vibration analysis.

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Authors: S. M. Monavari, P. Hoasami, S. Tajziehchi, N. Khorramichokami.

Abstract:

The practice of burying the solid waste under the ground is one of the waste disposal methods and dumping is known as an ultimate method in the fastest-growing cities like Rasht city in Iran. Some municipalities select the solid waste landfills without feasibility studies, programming, design and management plans. Therefore, several social and environmental impacts are created by these sites. In this study, the suitability of solid waste landfill in Rasht city, capital of Gilan Province is reviewed using Regional Screening Method (RSM), Geographic Information System (GIS) and Analytical Hierarchy Process (AHP). The results indicated that according to the suitability maps, the value of study site is midsuitable to suitable based on RSM and mid-suitable based on AHP.

Keywords: Analytical Hierarchy Process (AHP), Geographic Information System (GIS), Rasht City, Regional Screening Method (RSM), Solid Waste Landfill

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Authors: A. Badoud, M. Khemliche, S. Latreche

Abstract:

The main objective developed in this paper is to find a graphic technique for modeling, simulation and diagnosis of the industrial systems. This importance is much apparent when it is about a complex system such as the nuclear reactor with pressurized water of several form with various several non-linearity and time scales. In this case the analytical approach is heavy and does not give a fast idea on the evolution of the system. The tool Bond Graph enabled us to transform the analytical model into graphic model and the software of simulation SYMBOLS 2000 specific to the Bond Graphs made it possible to validate and have the results given by the technical specifications. We introduce the analysis of the problem involved in the faults localization and identification in the complex industrial processes. We propose a method of fault detection applied to the diagnosis and to determine the gravity of a detected fault. We show the possibilities of application of the new diagnosis approaches to the complex system control. The industrial systems became increasingly complex with the faults diagnosis procedures in the physical systems prove to become very complex as soon as the systems considered are not elementary any more. Indeed, in front of this complexity, we chose to make recourse to Fault Detection and Isolation method (FDI) by the analysis of the problem of its control and to conceive a reliable system of diagnosis making it possible to apprehend the complex dynamic systems spatially distributed applied to the standard pressurized water nuclear reactor.

Keywords: Bond Graph, Modeling, Simulation, Monitoring, Analytical Redundancy Relations, Pressurized Water Reactor, Directed Graph.

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Authors: Farhad Kolahan, M. Hossein Abolbashari, Samaeddin Mohitzadeh

Abstract:

Several methods are available for weight and shape optimization of structures, among which Evolutionary Structural Optimization (ESO) is one of the most widely used methods. In ESO, however, the optimization criterion is completely case-dependent. Moreover, only the improving solutions are accepted during the search. In this paper a Simulated Annealing (SA) algorithm is used for structural optimization problem. This algorithm differs from other random search methods by accepting non-improving solutions. The implementation of SA algorithm is done through reducing the number of finite element analyses (function evaluations). Computational results show that SA can efficiently and effectively solve such optimization problems within short search time.

Keywords: Simulated annealing, Structural optimization, Compliance, C.V. product.

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Authors: Noor M. Abdulfattah, Ahmed M. Khalafallah, Nabil A. Kartam

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Despite the evident benefits of building information modeling (BIM) to the construction industry, it faces significant implementation challenges in the State of Kuwait. This study investigates the awareness of construction stakeholders of BIM implementation challenges, and identifies various solutions to overcome these challenges. Specifically, the main objectives of this study are to: (1) characterize the barriers that deter utilization of BIM, (2) examine the awareness of engineers, architects, and construction stakeholders of these barriers, and (3) identify practical solutions to facilitate BIM utilization. A questionnaire survey was designed to collect data on the aforementioned objectives from local companies and senior BIM experts. It was found that engineers are highly aware of BIM implementation barriers. In addition, it was concluded from the questionnaire that the biggest barrier is the lack of BIM training. Based on expert feedback, the study concluded with a number of recommendations on how to overcome the barriers of BIM utilization. This should prove useful to the construction industry stakeholders and can lead to significant changes to design and construction practices.

Keywords: Building information modeling, construction, challenges, information technology.

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Authors: Burak Köken, Hatice D. Arslan, Bilgehan Y. Çakmak

Abstract:

Analyzing the relation networks between the hospital buildings which have complex structure and distinctive spatial relationships is quite difficult. The hospital buildings which require specialty in spatial relationship solutions during design and selfinnovation through the developing technology should survive and keep giving service even after the disasters such as earthquakes. In this study, a hospital building where the load-bearing system was strengthened because of the insufficient earthquake performance and the construction of an additional building was required to meet the increasing need for space was discussed and a comparative spatial evaluation of the hospital building was made with regard to its status before the change and after the change. For this reason, spatial organizations of the building before change and after the change were analyzed by means of Space Syntax method and the effects of the change on space organization parameters were searched by applying an analytical procedure. Using Depthmap UCL software, Connectivity, Visual Mean Depth, Beta and Visual Integration analyses were conducted. Based on the data obtained after the analyses, it was seen that the relationships between spaces of the building increased after the change and the building has become more explicit and understandable for the occupants. Furthermore, it was determined according to findings of the analysis that the increase in depth causes difficulty in perceiving the spaces and the changes considering this problem generally ease spatial use.

Keywords: Architecture, hospital building, space syntax, strengthening.

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Authors: Chin Chin Wong, Chor Min Tan, Pang Leang Hiew

Abstract:

Business scenario is an important technique that may be used at various stages of the enterprise architecture to derive its characteristics based on the high-level requirements of the business. In terms of wireless deployments, they are used to help identify and understand business needs involving wireless services, and thereby to derive the business requirements that the architecture development has to address by taking into account of various wireless challenges. This study assesses the deployment of Wireless Local Area Network (WLAN) and Broadband Wireless Access (BWA) solutions for several business scenarios in Asia Pacific region. This paper focuses on the overview of the business and technology environments, whereby examples of existing (or suggested) wireless solutions (to be) adopted in Asia Pacific region will be discussed. Interactions of several players, enabling technologies, and key processes in the wireless environments are studied. The analysis and discussions associated to this study are divided into two divisions: healthcare and education, where the merits of wireless solutions in improving living quality are highlighted.

Keywords: Broadband Wireless Access, business scenarios, network deployment, Wireless Local Area Network.

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Authors: Ghassan A. Abed, Samir I. Badrawi

Abstract:

The advancement in wireless technology with the wide use of mobile devices have drawn the attention of the research and technological communities towards wireless environments, such as Wireless Local Area Networks (WLANs), Wireless Wide Area Networks (WWANs), and mobile systems and ad-hoc networks. Unfortunately, wired and wireless networks are expressively different in terms of link reliability, bandwidth, and time of propagation delay and by adapting new solutions for these enhanced telecommunications, superior quality, efficiency, and opportunities will be provided where wireless communications were otherwise unfeasible. Some researchers define 4G as a significant improvement of 3G, where current cellular network’s issues will be solved and data transfer will play a more significant role. For others, 4G unifies cellular and wireless local area networks, and introduces new routing techniques, efficient solutions for sharing dedicated frequency bands, and an increased mobility and bandwidth capacity. This paper discusses the possible solutions and enhancements probabilities that proposed to improve the performance of Transmission Control Protocol (TCP) over different wireless networks and also the paper investigated each approach in term of advantages and disadvantages.

Keywords: TCP, Wireless Networks, Cellular Systems, WLAN.

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Authors: Kejun Zhuang, Hailong Zhu

Abstract:

In this paper, the three species food chain model on time scales is established. The Monod–Haldane functional response and time delay are considered. With the help of coincidence degree theory, existence of periodic solutions is investigated, which unifies the continuous and discrete analogies.

Keywords: Food chain system, periodic solution, time scales, coincidence degree.

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Authors: Li Xiguang

Abstract:

In this paper, by constructing a special operator and using fixed point index theorem of cone, we get the sufficient conditions for symmetric positive solution of a class of nonlinear singular boundary value problems with p-Laplace operator, which improved and generalized the result of related paper.

Keywords: Banach space, cone, fixed point index, singular differential equation, p-Laplace operator, symmetric solutions.

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