Search results for: differential settlement

Authors: Fikile Xaki, Zendy Magayiyana

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The increasing population and urbanization, with the demand for land and development, has had adverse impacts on wetland areas which has resulted in changing the hydrology and water chemistry of wetlands, affecting the water supply and water quality in urban areas like the Highland View, a residential area in Mbizana, South Africa. The settlement development in Highland View has led to wetland degradation due to land uses like agriculture and conversion of wetland for settlement development. Interviews with the local community were conducted to show how settlement development on wetland affects them. The results indicated that the environmental rights of people as according to Section 24 of the South African Constitution are compromised, and sustainable development was not put into consideration during development. With the results from the survey - through questionnaires for the Mbizana Local Municipality and the community, it was clear that the community needs education and capacity building on wetland management and conservation. Geographic Information Systems (GIS) was used to map physical properties of the Highland View wetland and houses built on the wetland. With all the information gathered from the research, it was clear that local municipality, together with hydrologists, needs to develop an environmental management framework to protect the wetlands.

Keywords: sustainable development, wetlands, human settlement, water

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Authors: Musyimi Mbathi

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Information regarding social, political, demographic, economic and other attributes of human settlement is important for decision makers at all levels of planning, as they have to grapple with dynamic environments often associated with settlements. At the local level, it is particularly important for both communities and urban managers to have accurate and reliable information regarding all planning attributes. Settlement mapping, in particular, informal settlements mapping in Kenya, has over the past few years been carried out using modern tools like Geographic information systems (GIS) and remote sensing for spatial data analysis and planning. GIS tools offer a platform for integration of spatial and non-spatial data as well as visualisation of the settlements. The capabilities offered by these tools have enabled communities to participate especially in the planning and management of new infrastructure as well as settlement upgrading. Land tenure based projects within informal settlements have also relied on GIS and related tools with considerable success. Additionally, the adoption of participatory approaches and use of geo-information tools helped to provide a basis for all inclusive planning thus promoting accountability, transparency, legitimacy, and other dimensions of governance within human settlement planning. The paper examines the context and application of geo-information tools for planning within low-income settlements of Kenya. A case study of Kiambiu settlement will be used to demonstrate how the tools have been applied for planning and decision-making purposes.

Keywords: informal settlements, GIS, governance, modern tools

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Authors: Lev Idels, Arcady Ponosov

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Stochastic fractional differential equations have recently attracted considerable attention, as they have been used to model real-world processes, which are subject to natural memory effects and measurement uncertainties. Compared to conventional hereditary differential equations, one of the advantages of fractional differential equations is related to more realistic geometric properties of their trajectories that do not intersect in the phase space. In this report, a Peano-like existence theorem for nonlinear stochastic fractional differential equations is proven under very general hypotheses. Several specific classes of equations are checked to satisfy these hypotheses, including delay equations driven by the fractional Brownian motion, stochastic fractional neutral equations and many others.

Keywords: delay equations, operator methods, stochastic noise, weak solutions

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Authors: Hamid Oumer Seid

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Piled raft foundation (PRF) is a union of pile and raft working together through the interaction of soil-pile, pile-raft, soil-raft and pile-pile to provide adequate bearing capacity and controlled settlement. A uniform pile positioning is used in PRF; however, there is a wide room for optimization through parametric study under vertical load to result in a safer and economical foundation. Addis Ababa is found in seismic zone 3 with a peak ground acceleration (PGA) above the threshold of damage, which makes investigating the performance of PRF under seismic load considering the dynamic kinematic soil structure interaction (SSI) vital. The study area is located in Addis Ababa around Mexico (commercial bank) and Kirkos (Nib, Zemen and United Bank) in which input parameters (pile length, pile diameter, pile spacing, raft area, raft thickness and load) are taken. A finite difference-based numerical software, FLAC3D V6, was used for the analysis. The Kobe (1995) and Northridge (1994) earthquakes were selected, and deconvolution analysis was done. A close load sharing between pile and raft was achieved at a spacing of 7D with different pile lengths and diameters. The maximum settlement reduction achieved is 9% for a pile of 2m diameter by increasing length from 10m to 20m, which shows pile length is not effective in reducing settlement. The installation of piles results in an increase in the negative bending moment of the raft compared with an unpiled raft. Hence, the optimized design depends on pile spacing and the raft edge length, while pile length and diameter are not significant parameters. An optimized piled raft configuration (𝐴𝐺/𝐴𝑅 = 0.25 at the center and piles provided around the edge) has reduced pile number by 40% and differential settlement by 95%. The dynamic analysis shows acceleration plot at the top of the piled raft has PGA of 0.25𝑚2/𝑠𝑒𝑐 and 0.63𝑚2/𝑠𝑒𝑐 for Northridge (1994) and Kobe (1995) earthquakes, respectively, due to attenuation of seismic waves. Pile head displacement (maximum is 2mm, and it is under the allowable limit) is affected by the PGA rather than the duration of an earthquake. End bearing and friction PRF performed similarly under two different earthquakes except for their vertical settlement considering SSI. Hence, PRF has shown adequate resistance to seismic loads.

Keywords: FLAC3D V6, earthquake, optimized piled raft foundation, pile head department

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Authors: Wameed Alghazali, Shawn Kenny, Paul J. Van Geel

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Settlement of municipal solid waste (MSW) in landfills can be represented by mechanical settlement, which is instantaneous and time-dependent creep components, and biodegradation-induced settlement. Mechanical settlement is governed by the physical characteristics of MSW and the applied overburden pressure. Several research studies used oedometers and different size compression cells to evaluate the primary and mechanical creep compression indices/ratios. However, MSW is known for its heterogeneity, which means data obtained from laboratory testing are not necessary to be a good representation of the mechanical response observed in the field. Furthermore, most of the laboratory tests found in the literature were conducted on shredded samples of MSW to obtain specimens that are suitable for the testing setup. It is believed that shredding MSW samples changes the physical and mechanical properties of the waste. In this study, settlement field data was collected during the filling stage of Ste. Sophie landfill was used to estimate the primary and mechanical creep compression ratios. The field results from Ste. Sophie landfill indicated that both the primary and mechanical creep compression ratios of MSW are not constants but decrease with the increase in the applied vertical stress.

Keywords: mechanical creep compression ratio, municipal solid waste, primary compression ratio, stress level

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Authors: Mahtab Delfan Azari, Ali Noorzad, Ahmadreza Mahboubi Ardakani

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Municipal solid waste landfills have relatively high temperature which is caused by anaerobic and aerobic degradation. The temperature that is produced is almost 40-70°C. Since this temperature will remain for many years, considering it for studying landfill behavior and its soil is so important. By considering the temperature of landfill, the obtained results will become more logical and more realistic. Vertical displacement and differential settlement are two important values which are studied here. Differential displacements could expand cracks in liner and cover. If cracks appear in the liner, the leachate and gases will propagate to media and hence should be noticed carefully. The present research is focused on the thermo-hydro-mechanical modeling of landfill with finite element method. First, the heat transfer of the landfill is modeled and the temperature is estimated. Then, the results of thermo-hydro-mechanical results are presented to investigate landfill behavior more accurately.

Keywords: finite element method, heat transfer, landfill behavior, thermo-hydro-mechanical modeling

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Authors: Safitri Nur Wulandari, M. Ivan Adi Perdana, Prathisto L. Panuntun Unggul, R. Dary Wira Mahadika

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In road construction on the soft soil, we need a soil improvement method to improve the soil bearing capacity of the land base so that the soil can withstand the traffic loads. Most of the land in Indonesia has a soft soil, where soft soil is a type of clay that has the consistency of very soft to medium stiff, undrained shear strength, Cu <0:25 kg/cm2, or the estimated value of NSPT <5 blows/ft. This study focuses on the analysis of the effect on preloading load (embarkment) to the amount of settlement ratio on the under of embarkment that will impact on the building cracks around of embarkment. The method used in this research is a superposition method for embarkment distribution on 27 locations with undisturbed soil samples at some borehole point in Java and Kalimantan, Indonesia. Then correlating the results of settlement plate monitoring on the field with Asaoka method. The results of settlement plate monitoring taken from an embarkment of Ahmad Yani airport in Semarang on 32 points. Where the value of Cc (index compressible) soil data based on some laboratory test results, while the value of Cc is not tested obtained from empirical formula Ardhana and Mochtar, 1999. From this research, the results of the field monitoring showed almost the same results with an empirical formulation with the standard deviation of 4% where the formulation of the empirical results of this analysis obtained by linear formula. Value empirical linear formula is to determine the effect of compression heap area as high as 4,25 m is 3,1209x + y = 0.0026 for the slope of the embankment 1: 8 for the same analysis with an initial height of embankment on the field. Provided that at the edge of the embankment settlement worth is not equal to 0 but at a quarter of embankment has a settlement ratio average 0.951 and at the edge of embankment has a settlement ratio 0,049. The influence areas around of embankment are approximately 1 meter for slope 1:8 and 7 meters for slope 1:2. So, it can cause the building cracks, to build in sustainable development.

Keywords: building cracks, influence area, settlement plate, soft soil, empirical formula, embankment

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Authors: Mawarni Mohamed, Sharifah Shahira A. Hamid

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Leisure time is an important component to offset the sedentary lifestyle of the people. Women tend to benefit from leisure activities not only to reduce stress but also to provide opportunities for well-being and self-satisfaction. This study was conducted to investigate body composition and leisure time use among women in Selangor from the influences of community settlement. A total of 419 women aged 18-65 years were selected to participate in this study. Descriptive statistics, t-test and ANOVA were used to analyze the level of physical activity and the relationship between leisure-time use and body composition were made to analyze the physical lifestyles. The results showed that women with normal body composition seem to be involved in more passive activities than women with less weight gain and obesity. Thus, the study recommended that the government and other health and recreational agencies should develop more places and activities suitable for leisure preference for women in their community settlement so they become more interested to engage in more active recreational and physical activities.

Keywords: body composition, community settlement, leisure time, physical lifestyles

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Authors: Sateesh Kumar Pisini, Swetha Priya Darshini Thammadi, Sanjay Kumar Shukla

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Granular piles are a popular ground improvement technique in soft cohesive soils as well as for loose non-cohesive soils. The present experimental study has been carried out on granular piles in loose (Relative density = 30%) and medium dense (Relative density = 60%) sands with geogrid reinforcement within the sand bed over the granular piles. A group of five piles were installed in the sand at different spacing, s = 2d, 3d and 4d, d being the diameter of the pile. The length (L = 0.4 m) and diameter (d = 50 mm) of the piles were kept constant for all the series of experiments. The load-settlement behavior of reinforced sand bed and granular piles system was studied by applying the load on a square footing. The results show that the effect of reinforcement increases the load bearing capacity of the piles. It is also found that an increase in spacing between piles decreases the settlement for both loose and medium dense soil.

Keywords: granular pile, load-carrying capacity, settlement, geogrid reinforcement, sand

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Authors: Bashir Ahmad Amiri, Nsenda Lukumwena

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The developing economies are experiencing an unprecedented rate of urbanization, mainly the urbanization of poverty which is leading to sprawling of slums and informal settlement. Kabul, being the capital and primate city of Afghanistan is grossly encountered to the informal settlement where the majority of the people consider to be informal. Despite all efforts to upgrade and minimize the growth of these settlements, they are growing rapidly. Various interventions have been taken by the government and some international organizations from physical upgrading to urban renewal, but none of them have succeeded to solve the issue of informal settlement. The magnitude of the urbanization and the complexity of informal settlement in Kabul city, and the institutional and capital constraint of the government calls for integration and optimization of currently practiced strategies. This paper provides an overview of informal settlement formation and the conventional upgrading strategies in Kabul city to identify the dominant/successful practices and rationalize the conventional upgrading modes. For this purpose, Hothkhel has been selected as the case study, since it represents the same situation of major informal settlements of the city. Considering the existing potential and features of the Hothkhel and proposed land use by master plan this paper intends to find a suitable upgrading mode for the study area and finally to scale up the model for the city level upgrading. The result highlights that the informal settlements of Kabul city have high (re)development capacity for accepting the additional room without converting the available agricultural area to built-up. The result also indicates that the integrated multi-sector upgrading has the scale-up potential to increase the reach of beneficiaries and to ensure an inclusive and efficient urbanization.

Keywords: informal settlement, upgrading strategies, Kabul city, urban expansion, integrated multi-sector, scale-up

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Authors: A. I. Ma’ali, R. B. Adeniyi, A. Y. Badeggi, U. Mohammed

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An error estimation of the integrated formulation of the Lanczos tau method for some class of ordinary differential equations was reported. This paper is concern with the generalization of tau approximants and their corresponding error estimates for some class of ordinary differential equations (ODEs) characterized by m + s =3 (i.e for m =1, s=2; m=2, s=1; and m=3, s=0) where m and s are the order of differential equations and number of overdetermination, respectively. The general result obtained were validated with some numerical examples.

Keywords: approximant, error estimate, tau method, overdetermination

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Authors: Saeed Otarod

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In a different simple and straight forward analysis a closed-form integral solution is found for nonhomogeneous second order linear ordinary differential equations, in terms of a particular solution of their corresponding homogeneous part. To find the particular solution of the homogeneous part, the equation is transformed into a simple Riccati equation from which the general solution of non-homogeneouecond order differential equation, in the form of a closed integral equation is inferred. The method works well in manyimportant cases, such as Schrödinger equation for hydrogen-like atoms. A non-homogenous second order linear differential equation has been solved as an extra example

Keywords: explicit, linear, differential, closed form

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Authors: Lina Wu, Ye Li

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An equivalent relation between a harmonic form and a closed co-closed form is established on a complete non-compact manifold. This equivalence has been generalized for a differential k-form ω from Lq spaces to non-Lq spaces when q=2 in the context of p-balanced growth where p=2. Especially for a simple differential k-form on a complete non-compact manifold, the equivalent relation has been verified with the extended scope of q for from finite q-energy in Lq spaces to infinite q-energy in non-Lq spaces when with 2-balanced growth. Generalized Hadamard Theorem, Cauchy-Schwarz Inequality, and Calculus skills including Integration by Parts as well as Convergent Series have been applied as estimation techniques to evaluate growth rates for a differential form. In particular, energy growth rates as indicated by an appropriate power range in a selected test function lead to a balance between a harmonic differential form and a closed co-closed differential form. Research ideas and computational methods in this paper could provide an innovative way in the study of broadening Lq spaces to non-Lq spaces with a wide variety of infinite energy growth for a differential form.

Keywords: closed forms, co-closed forms, harmonic forms, L^q spaces, p-balanced growth, simple differential k-forms

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Authors: Mustafa Bayram Gücen, Coşkun Yakar

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In this study, we have investigated the strict stability of fuzzy differential systems and we compare the classical notion of strict stability criteria of ordinary differential equations and the notion of strict stability of fuzzy differential systems. In addition that, we present definitions of stability and strict stability of fuzzy differential equations and also we have some theorems and comparison results. Strict Stability is a different stability definition and this stability type can give us an information about the rate of decay of the solutions. Lyapunov’s second method is a standard technique used in the study of the qualitative behavior of fuzzy differential systems along with a comparison result that allows the prediction of behavior of a fuzzy differential system when the behavior of the null solution of a fuzzy comparison system is known. This method is a usefull for investigating strict stability of fuzzy systems. First of all, we present definitions and necessary background material. Secondly, we discuss and compare the differences between the classical notion of stability and the recent notion of strict stability. And then, we have a comparison result in which the stability properties of the null solution of the comparison system imply the corresponding stability properties of the fuzzy differential system. Consequently, we give the strict stability results and a comparison theorem. We have used Lyapunov second method and we have proved a comparison result with scalar differential equations.

Keywords: fuzzy systems, fuzzy differential equations, fuzzy stability, strict stability

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Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly

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Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.

Keywords: Parkinson's disease, step method, delay differential equation, two delays

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Authors: Farid Nouioua, Abdelouaheb Ardjouni

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In this article, we study the existence of positive periodic solutions of certain delay differential equations. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ Krasnoselskii's fixed point theorem to obtain sufficient conditions for the existence of a positive periodic solution of the differential equation. The obtained results improve and extend the results in the literature. Finally, an example is given to illustrate our results.

Keywords: delay differential equations, positive periodic solutions, integral equations, Krasnoselskii fixed point theorem

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Authors: Mehtap Lafcı

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In recent years, oscillation, periodicity and convergence of solutions of linear differential equations with piecewise constant arguments have been significantly considered but there are only a few papers for impulsive differential equations with piecewise constant arguments. In this paper, a first order nonlinear impulsive differential equation with piecewise constant arguments is studied and the existence of solutions and periodic solutions of this equation are investigated by using Carvalho’s method. Finally, an example is given to illustrate these results.

Keywords: Carvalho's method, impulsive differential equation, periodic solution, piecewise constant arguments

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Authors: Zenebu Adere Tola

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Informal settlements behave dynamically over space and time and the number of people living in such housing areas is growing worldwide. In the cities of developing countries especially in sub-Saharan Africa, poverty, unemployment rate, poor living condition, lack transparency and accountability, lack of good governance are the major factors to contribute for the people to hold land informally and built houses for residential or other purposes. In most of Ethiopian cities informal settlement is highly seen in peripheral areas this is because people can easily to hold land for housing from local farmers, brokers, speculators without permission from concerning bodies. In Adama informal settlement has created risky living conditions and led to environmental problems in natural areas the main reason for this was the lack of sufficient knowledge about informal settlement development. On the other side there is a strong need to transform informal into formal settlements and to gain more control about the actual spatial development of informal settlements. In another hand to tackle the issue it is at least very important to understand the scale of the problem. To understand the scale of the problem it is important to use up-to-date technology. For this specific problem, it is good to use high-resolution imagery to detect informal settlement in Adama city. The main objective of this study is to assess the spatiotemporal dynamics and environmental impacts of informal settlement using OBIA. Specifically, the objective of this study is to; identify informal settlement in the study area, determine the change in the extent and pattern of informal settlement and to assess the environmental and social impacts of informal settlement in the study area. The methods to be used to detect the informal settlement is object-oriented image analysis. Consequently, reliable procedures for detecting the spatial behavior of informal settlements are required in order to react at an early stage to changing housing situations. Thus, obtaining spatial information about informal settlement areas which is up to date is vital for any actions of enhancement in terms of urban or regional planning. Using data for this study aerial photography for growth and change of informal settlements in Adama city. Software ECognition software for classy to built-up and non-built areas. Thus, obtaining spatial information about informal settlement areas which is up to date is vital for any actions of enhancement in terms of urban or regional planning.

Keywords: informal settlement, change detection, environmental impact, object based analysis

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Authors: A. Shafaghat, H. Khabbaz, S. Moravej, Ah. Shafaghat

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The bearing capacity of closely spaced shallow footings alters with their spacing and the shape of footing. In this study, the bearing capacity and settlement of two adjacent footings constructed on a sand layer are investigated. The effect of different footing shapes including square, circular, ring and strip on sandy soil is captured in the calculations. The investigations are carried out numerically using PLAXIS-3D software and analytically employing conventional settlement equations. For this purpose, foundations are modelled in the program with practical dimensions and various spacing ratios ranging from 1 to 5. The spacing ratio is defined as the centre-to-centre distance to the width of foundations (S/B). Overall, 24 models are analyzed; and the results are compared and discussed in detail. It can be concluded that the presence of adjacent foundation leads to the reduction in bearing capacity for round shape footings while it can increase the bearing capacity of rectangular footings in some specific distances.

Keywords: bearing capacity, finite element analysis, loose sand, settlement equations, shallow foundation

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Authors: John Abubakar

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Access to decent housing is a global challenge. An estimated one billion people currently live in slum settlements globally. About 80 percent of these slum dwellers are in Asia and Africa. Nigeria accounts for a significant percentage of African slum dwellers because of its size. Addressing the challenge of slum settlement in Nigeria can have far reaching positive implications in Africa. A major slum settlement in Nigeria is Mararaba slum in Karu local government of Nasarawa state. The importance of this slum settlement hinges on its proximity to Abuja, Nigeria’s capital city. This study is an attempt at identifying the impact of self-help housing and government mass housing scheme in addressing the problem of housing access in Mararaba area of Karu local government, Nasarawa state. The research method used is the content analysis of existing literature. After the review of existing literature, the paper argues that self-help house is more impactful in addressing housing access in Mararaba area of Karu local government. Therefore, self-help housing should be recognized and incorporated into the housing policy of Nasarawa state. Both self-help housing and government mass housing programs are reviewed comparatively, and their strengths and weaknesses analyses.

Keywords: slum settlement, informal settlement, progressive improvement, holistic planning

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Authors: A. M. Sagir

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Discrete linear multistep block method of uniform order for the solution of first order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution.

Keywords: block method, first order ordinary differential equations, hybrid, self-starting

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Authors: Shenpu Liu

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Space syntax, a paradigm of the urban research, which manifests people’s intuitive and abstract perception of a material space with a solid mathematical way, explores how space represents its social characteristics. Taking Xiazhuang village and Shijia Village in Huzhou as an example and focusing on inward structure and street space, this article recognizes the connotative significance of the settlement with the aid of space syntax theory and quantitative analysis method from the perspective of spatial configuration to present relevant suggestions for its future planning and provides references for traditional rural settlement protection.

Keywords: Shijia village, space configuration, space syntax, traditional rural settlement, Xiazhuang village

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Authors: Fakhreddin Abedi, Wah June Leong

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Exponential stability of stochastic differential equations with non trivial solutions is provided in terms of Lyapunov functions. The main result of this paper establishes that, under certain hypotheses for the dynamics f(.) and g(.), practical exponential stability in probability at the small neighborhood of the origin is equivalent to the existence of an appropriate Lyapunov function. Indeed, we establish exponential stability of stochastic differential equation when almost all the state trajectories are bounded and approach a sufficiently small neighborhood of the origin. We derive sufficient conditions for exponential stability of stochastic differential equations. Finally, we give a numerical example illustrating our results.

Keywords: exponential stability in probability, stochastic differential equations, Lyapunov technique, Ito's formula

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Authors: Armin Ardekani, Mohammad Akbari

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We present a method of generating series solutions to large classes of nonlinear differential equations. The method is well suited to be adapted in mathematical software and unlike the available commercial solvers, we are capable of generating solutions to boundary value ODEs and PDEs. Many of the generated solutions converge to closed form solutions. Our method can also be applied to systems of ODEs or PDEs, providing all the solutions efficiently. As examples, we present results to many difficult differential equations in engineering fields.

Keywords: computational mathematics, differential equations, engineering, series

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Authors: Yusuf Sani Abubakar

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This paper investigates mechanisms of settlement of disputes at the Islamic Financial Institutions (IFIs). Dispute settlement at the Islamic Financial Institutions (IFIs) can be both through litigation as well as Alternative Dispute Resolution (ADR). The paper aims to investigate how disputes are settled at the Islamic Financial Institutions (IFIs), as it is natural to have disagreements between different parties involved in the business of Islamic Financial Institutions (IFIs). The paper adopts a qualitative methodology where the sources are taken from journals, books, websites etc. In analyzing the data obtained from the sources, content analysis will be used. In addition to writings on this topic by various writers, this paper will add to the literature and will recommend certain effective ways of solving disputes arising between parties participating in the business of Islamic Financial Institutions (IFIs).

Keywords: Islamic finance, dispute resolution, Islamic financial institutions, litigation

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Authors: Zhan Chen, Wenquan Bi

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This paper focuses on examining the strength of Midori against impossible differential attack. The Midori family of light weight block cipher orienting to energy-efficiency is proposed in ASIACRYPT2015. Using a 6-round property, the authors implement an 11-round impossible differential attack on Midori64 by extending two rounds on the top and three rounds on the bottom. There is enough key space to consider pre-whitening keys in this attack. An impossible differential path that minimises the key bits involved is used to reduce computational complexity. Several additional observations such as partial abort technique are used to further reduce data and time complexities. This attack has data complexity of 2 ⁶⁹·² chosen plaintexts, requires 2 ¹⁴·⁵⁸ blocks of memory and 2 ⁹⁴·⁷ 11- round Midori64 encryptions.

Keywords: cryptanalysis, impossible differential, light weight block cipher, Midori

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Authors: M. Jamil Amir, Rabia Iqbal, M. Yaseen

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In this paper, we solve some differential equations analytically by using differential transform method. For this purpose, we consider four models of Laplace equation with two Dirichlet and two Neumann boundary conditions and K(2,2) equation and obtain the corresponding exact solutions. The obtained results show the simplicity of the method and massive reduction in calculations when one compares it with other iterative methods, available in literature. It is worth mentioning that here only a few number of iterations are required to reach the closed form solutions as series expansions of some known functions.

Keywords: differential transform method, laplace equation, Dirichlet boundary conditions, Neumann boundary conditions

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Authors: Y. N. Reddy

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The class of differential-difference equations which have characteristics of both classes, i.e., delay/advance and singularly perturbed behaviour is known as singularly perturbed differential-difference equations. The expression ‘positive shift’ and ‘negative shift’ are also used for ‘advance’ and ‘delay’ respectively. In general, an ordinary differential equation in which the highest order derivative is multiplied by a small positive parameter and containing at least one delay/advance is known as singularly perturbed differential-difference equation. Singularly perturbed differential-difference equations arise in the modelling of various practical phenomena in bioscience, engineering, control theory, specifically in variational problems, in describing the human pupil-light reflex, in a variety of models for physiological processes or diseases and first exit time problems in the modelling of the determination of expected time for the generation of action potential in nerve cells by random synaptic inputs in dendrites. In this paper, we envisage the use of Liouville Green Transformation to find the solution of singularly perturbed differential difference equations. First, using Taylor series, the given singularly perturbed differential difference equation is approximated by an asymptotically equivalent singularly perturbation problem. Then the Liouville Green Transformation is applied to get the solution. Several model examples are solved, and the results are compared with other methods. It is observed that the present method gives better approximate solutions.

Keywords: difference equations, differential equations, singular perturbations, boundary layer

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Authors: Tahsin Toma Sabbagh, Ihsan Al-Abboodi, Ali Al-Jazaairry

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Allowable-bearing capacity is the competency of soil to safely carries the pressure from the superstructure without experiencing a shear failure with accompanying excessive settlements. Ensuring a safe bearing pressure with respect to failure does not tolerate settlement of the foundation will be within acceptable limits. Therefore, settlement analysis should always be performed since most structures are settlement sensitive. When visualising the movement of a soil wedge in the bearing capacity criterion, both vertically and horizontally, it becomes clear that by confining the soil surrounding the foundation, both the bearing capacity and settlement values improve. In this study, two sizes of spread foundation were considered; (2×4) m and (3×5) m. These represent two real problem case studies of an existing building. The foundations were analysed in terms of dimension as well as position with respect to a confining wall (i.e., sheet piles on both sides). Assuming B is the least foundation dimension, the study comprised the analyses of three distances; (0.1 B), (0.5 B), and (0.75 B) between the sheet piles and foundations alongside three depths of confinement (0.5 B), (1 B), and (1.5 B). Nonlinear three-dimensional finite element analysis (ANSYS) was adopted to perform an analytical investigation on the behaviour of the two foundations contained by the case study. Results showed that confinement of foundations reduced the overall stresses near the foundation by 65% and reduced the vertical displacement by 90%. Moreover, the most effective distance between the confinement wall and the foundation was found to be 0.5 B.

Keywords: bearing capacity, cohesionless soils, soil confinement, soil modelling, spread footings

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Authors: O. Acan, Y. Keskin

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In this study, we will carry out a comparative study between the reduced differential transform method, the adomian decomposition method, the variational iteration method and the homotopy analysis method. These methods are used in many fields of engineering. This is been achieved by handling a kind of 2-Dimensional and forth-order partial differential equations called the Kuramoto–Sivashinsky equations. Three numerical examples have also been carried out to validate and demonstrate efficiency of the four methods. Furthermost, it is shown that the reduced differential transform method has advantage over other methods. This method is very effective and simple and could be applied for nonlinear problems which used in engineering.

Keywords: reduced differential transform method, adomian decomposition method, variational iteration method, homotopy analysis method

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