Search results for: Foundation differential settlement

Authors: Nur Azzammudin Rahmat, Ismail Musirin, Ahmad Farid Abidin

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Economic load dispatch is performed by the utilities in order to determine the best generation level at the most feasible operating cost. In order to guarantee satisfying energy delivery to the consumer, a precise calculation of generation level is required. In order to achieve accurate and practical solution, several considerations such as prohibited operating zones, valve-point effect and ramp-rate limit need to be taken into account. However, these considerations cause the optimization to become complex and difficult to solve. This research focuses on the valve-point effect that causes ripple in the fuel-cost curve. This paper also proposes Differential Evolution Immunized Ant Colony Optimization (DEIANT) in solving economic load dispatch problem with valve-point effect. Comparative studies involving DEIANT, EP and ACO are conducted on IEEE 30-Bus RTS for performance assessments. Results indicate that DEIANT is superior to the other compared methods in terms of calculating lower operating cost and power loss.

Keywords: ant colony optimization (ACO), differential evolution (DE), differential evolution immunized ant colony optimization (DEIANT), economic load dispatch (ELD)

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Authors: Jorge Olivares, Fernando Maass, Pablo Martin

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Fractional derivatives have been considered recently as a way to solve different problems in Engineering. In this way, second kind modified Bessel functions are considered here. The order α fractional differential equations of second kind Bessel functions, Kᵥ(x), are studied with simple initial conditions. The Laplace transform and Caputo definition of fractional derivatives are considered. Solutions have been found for ν=1/3, 1/2, 2/3, -1/3, -1/2 and (-2/3). In these cases, the solutions are the sum of two hypergeometric functions. The α fractional derivatives have been for α=1/3, 1/2 and 2/3, and the above values of ν. No convergence has been found for the integer values of ν Furthermore when α has been considered as a rational found m/p, no general solution has been found. Clearly, this case is more difficult to treat than those of first kind Bessel Function.

Keywords: Caputo, modified Bessel functions, hypergeometric, linear fractional differential equations, transform Laplace

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Authors: Abhishek Jha, Manoj Kumar

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This paper proposes a new type of two wheels differential type odometry to estimate the next position and orientation of mobile robots. The proposed odometry is composed for two independent wheels with respective encoders. The two wheels rotate independently, and the change is determined by the difference in the velocity of the two wheels. Angular velocities of the two wheels are measured by rotary encoders. A mathematical model is proposed for the mobile robots to precisely move towards the goal. Using measured values of the two encoders, the current displacement vector of a mobile robot is calculated by kinematics of the mathematical model. Using the displacement vector, the next position and orientation of the mobile robot are estimated by proposed odometry. Result of simulator experiment by the developed odometry is shown.

Keywords: mobile robot, odometry, unicycle, differential type, encoders, infrared range sensors, kinematic model

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Authors: Nor-Edine Abriak, Mahfoud Benzerzour, Mouhamadou Amar, Abdeljalil Zri

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In this work, firstly we have studied the potential of raw sediments and sediments treated with lime or cement for use in a foundation layer and the base layer of a roadway. Secondly, we have examined mineral changes caused by the addition of lime or cement in order to explain the mechanical performance of stabilized sediments. After determining the amount of lime and cement required stabilizing the sediments, the compaction characteristics and Immediate Bearing Capacity (IBI) were studied using the Modified Proctor method. Then, the evolution of the three parameters, which are optimum water content, maximum dry density and IBI, were determined. Mechanical performances can be evaluated through resistance to compression, resistance under traction and the elasticity modulus. The resistances of the formulations treated with ROLAC®645 increase with the amount of ROLAC®645. Traction resistance and the elastic modulus were used to evaluate the potential of the formulations as road construction materials using the classification diagram. The results show that all the other formulations with ROLAC®645 can be used in subgrades and foundation layers for roads.

Keywords: sediment, lime, cement, roadway

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Authors: Kittipong Tripetch

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This paper proposes studies of input impedance of two types of the CMOS active inductor. It derives two input impedance formulas. The first formula is the input impedance of a grounded active inductor. The second formula is an input impedance of floating active inductor. After that, these formulas can be used to simulate magnitude and phase response of input impedance as a function of current consumption with MATLAB. Common mode rejection ratio (CMRR) of a fully differential bandpass amplifier is derived based on superposition principle. CMRR as a function of input frequency is plotted as a function of current consumption

Keywords: grounded active inductor, floating active inductor, fully differential bandpass amplifier

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Authors: Srinivasacharya Darbhasayanam, Jagadeeshwar Pashikanti

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This paper analyzes the Soret and Dufour effects on mixed convection flow, heat and mass transfer from an exponentially stretching surface in a viscous fluid with Hall Effect. The governing partial differential equations are transformed into ordinary differential equations using similarity transformations. The nonlinear coupled ordinary differential equations are reduced to a system of linear differential equations using the successive linearization method and then solved the resulting linear system using the Chebyshev pseudo spectral method. The numerical results for the velocity components, temperature and concentration are presented graphically. The obtained results are compared with the previously published results, and are found to be in excellent agreement. It is observed from the present analysis that the primary and secondary velocities and concentration are found to be increasing, and temperature is decreasing with the increase in the values of the Soret parameter. An increase in the Dufour parameter increases both the primary and secondary velocities and temperature and decreases the concentration.

Keywords: Exponentially stretching sheet, Hall current, Heat and Mass transfer, Soret and Dufour Effects

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Authors: Monika Rawat, Rahul Kumar

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Input output Buffer Information Specification (IBIS) models are used for describing the analog behavior of the Input Output (I/O) buffers of a digital device. They are widely used to perform signal integrity analysis. Advantages of using IBIS models include simple structure, IP protection and fast simulation time with reasonable accuracy. As design complexity of driver and receiver increases, capturing exact behavior from transistor level model into IBIS model becomes an essential task to achieve better accuracy. In this paper, an improvement in existing methodology of generating IBIS model for complex I/O interfaces such as Inter-Integrated Circuit (I2C) and Low Voltage Differential Signaling (LVDS) is proposed. Furthermore, the accuracy and computational performance of standard method and proposed approach with respect to SPICE are presented. The investigations will be useful to further improve the accuracy of IBIS models and to enhance their wider acceptance.

Keywords: IBIS, signal integrity, open-drain buffer, low voltage differential signaling, behavior modelling, transient simulation

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Authors: M. H. Aissa, Amar Bouzid Dj

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As known, many countries are now planning to build new wind farms with high capacity up to 5MW. Consequently, the size of the foundation increase. These kinds of structures are subject to fatigue damage from environmental loading mainly due to wind and waves as well as from cyclic loading imposed through the rotational frequency (1P) through mass and aerodynamic imbalances and from the blade passing frequency (3P) of the wind turbine which make them behavior dynamically very sensitive. That is why natural frequency must be determined with accuracy from the existing data of the soil and the foundation stiffness sources of uncertainties, to avoid the resonance of the system. This paper presents analytical expressions of stiffness foundation with large diameter in linear soil behavior in different soil stiffness profile. To check the accuracy of the proposed formulas, a mathematical model approach based on non-dimensional parameters is used to calculate the natural frequency taking into account the soil structure interaction (SSI) compared with the p-y method and measured frequency in the North Sea Wind farms.

Keywords: offshore wind turbines, semi analytical FE analysis, p-y curves, piles foundations

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Authors: J. P. Chollom, G. M. Kumleng, S. Longwap

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The search for higher order A-stable linear multi-step methods has been the interest of many numerical analysts and has been realized through either higher derivatives of the solution or by inserting additional off step points, supper future points and the likes. These methods are suitable for the solution of stiff differential equations which exhibit characteristics that place a severe restriction on the choice of step size. It becomes necessary that only methods with large regions of absolute stability remain suitable for such equations. In this paper, high order block implicit multi-step methods of the hybrid form up to order twelve have been constructed using the multi-step collocation approach by inserting one or more off step points in the multi-step method. The accuracy and stability properties of the new methods are investigated and are shown to yield A-stable methods, a property desirable of methods suitable for the solution of stiff ODE’s. The new High Order Block Implicit Multistep methods used as block integrators are tested on stiff differential systems and the results reveal that the new methods are efficient and compete favourably with the state of the art Matlab ode23 code.

Keywords: block linear multistep methods, high order, implicit, stiff differential equations

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Authors: Wu Yiqun, Weng Jiantao

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The human settlements of China are picked up from the land use vector map by interpreting the Thematic Map of 2014. This paper established the sustainable human settlements geographical division evaluation system and division model using GIS. The results show that: The density of human residential areas in China is different, and the density of sustainable human areas is higher, and the west is lower than that in the West. The regional differences of sustainable human settlements are obvious: the north is larger than that the south, the plain regions are larger than those of the hilly regions, and the developed regions are larger than the economically developed regions. The geographical distribution of the sustainable human settlements is measured by the degree of porosity. The degree of porosity correlates with the sustainable human settlement density. In the area where the sustainable human settlement density is high the porosity is low, the distribution is even and the gap between the settlements is low.

Keywords: GIS, geographical division, sustainable human settlements, China

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Authors: Muath Awadalla, Maen Awadallah

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Banking sector covers different activities including lending money to customers. However, it is commonly known that customers pay money they have borrowed including an added amount called interest. Compound interest rate is an approach used in determining the interest to be paid. The instant compounded amount to be paid by a debtor is obtained through a differential equation whose main parameters are the rate and the time. The rate used by banks in a country is often defined by the government of the said country. In Switzerland, for instance, a negative rate was once applied. In this work, a new approach of modeling the compound interest is proposed using Hadamard fractional derivative. As a result, it appears that depending on the fraction value used in derivative the amount to be paid by a debtor might either be higher or lesser than the amount determined using the classical approach.

Keywords: compound interest, fractional differential equation, hadamard fractional derivative, optimization

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Authors: Ramzi B. Albadarneh

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In this paper, we use the new definition of fractional derivative called conformable fractional derivative to derive some finite difference formulas and its error terms which are used to solve fractional differential equations and fractional partial differential equations, also to derive fractional Euler method and its error terms which can be applied to solve fractional differential equations. To provide the contribution of our work some applications on finite difference formulas and Euler Method are given.

Keywords: conformable fractional derivative, finite difference formula, fractional derivative, finite difference formula

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Authors: Faith-Michael E. Uzoka, Boluwaji A. Akinnuwesi, Taiwo Amoo, Flora Aladi, Stephen Fashoto, Moses Olaniyan, Joseph Osuji

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The overarching aim of this study is to develop a soft-computing system for the differential diagnosis of tropical diseases. These conditions are of concern to health bodies, physicians, and the community at large because of their mortality rates, and difficulties in early diagnosis due to the fact that they present with symptoms that overlap, and thus become ‘confusable’. We report on the first phase of our study, which focuses on the development of a fuzzy cognitive map model for early differential diagnosis of tropical diseases. We used malaria as a case disease to show the effectiveness of the FCM technology as an aid to the medical practitioner in the diagnosis of tropical diseases. Our model takes cognizance of manifested symptoms and other non-clinical factors that could contribute to symptoms manifestations. Our model showed 85% accuracy in diagnosis, as against the physicians’ initial hypothesis, which stood at 55% accuracy. It is expected that the next stage of our study will provide a multi-disease, multi-symptom model that also improves efficiency by utilizing a decision support filter that works on an algorithm, which mimics the physician’s diagnosis process.

Keywords: medical diagnosis, tropical diseases, fuzzy cognitive map, decision support filters, malaria differential diagnosis

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Authors: Evelyn Asante Yeboah, Kwabena O. Asubonteng, Justice Camillus Mensah, Christine Furst

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Smallholder-dominated mosaic landscapes in rural Africa are relevant for food production, biodiversity conservation, and climate regulation. Land-use transitions threaten the multifunctionality of such landscapes, especially the production capacity of arable lands resulting in food security challenges. Using land-cover maps derived from maximum likelihood classification of Landsat satellite images for the years 2002, 2015, and 2020, post-classification change detection, landscape metrics, and key informant interviews, the study assessed the implications of rubber plantation expansion and oil business development on the food production capacity of Ahanta West District, Ghana. The analysis reveals that settlement and rubber areas expanded by 5.82% and 10.33% of the landscape area, respectively, between 2002 and 2020. This increase translates into over twice their initial sizes (144% in settlement change and 101% in rubber change). Rubber plantation spread dominates the north and southwestern areas, whereas settlement is widespread in the eastern parts of the landscape. Rubber and settlement expanded at the expense of cropland, palm, and shrublands. Land-use transitions between cropland, palm, and shrubland were targeting each other, but the net loss in shrubland was higher (-17.27%). Isolation, subdivision, connectedness, and patch adjacency indices showed patch consolidation in the landscape configuration from 2002 to 2015 and patch fragmentation from 2015 to 2020. The study also found patches with consistent increasing connectivity in settlement areas indicating the influence of oil discovery developments and fragmentation tendencies in rubber, shrubland, cropland, and palm, indicating springing up of smaller rubber farms, the disappearance of shrubland, and splitting up of cropland and palm areas respectively. The results revealed a trend in land-use transitions in favor of smallholder rubber plantation expansion and oil discovery developments, which suggest serious implications on food production systems and poses a risk for food security and landscape multifunctional characteristics. To ensure sustainability in land uses, this paper recommends the enforcement of legislative instruments governing spatial planning and land use in Ghana as embedded in the 2016 land-use and spatial planning act.

Keywords: food production systems, food security, Ghana’s west coast, land-use transitions, multifunctional rural landscapes

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Authors: Adel M. Belal, Sameh Abu El-Soud, Mariam Farid

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This study presents the effect of reinforcement inclusions (fibers-geogrids) on fine sand bearing capacity under strip footings. Experimental model tests were carried out using a rectangular plates [(10cm x 38 cm), (7.5 cm x 38 cm), and (12.5 cm x 38 cm)] with a geogrids and randomly reinforced fibers. The width and depth of the geogrid were varied to determine their effects on the engineering properties of treated poorly graded fine sand. Laboratory model test results for the ultimate stresses and the settlement of a rigid strip foundation supported by single and multi-layered fiber-geogrid-reinforced sand are presented. The number of layers of geogrid was varied between 1 to 4. The effect of the first geogrid reinforcement depth, the spacing between the reinforcement and its length on the bearing capacity is investigated by experimental program. Results show that the use of flexible random fibers with a content of 0.125% by weight of the treated sand dunes, with 3 geogrid reinforcement layers, u/B= 0.25 and L/B=7.5, has a significant increase in the bearing capacity of the proposed system.

Keywords: earth reinforcement, geogrid, random fiber, reinforced soil

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Authors: Razmik Atabekyan, V. Atabekyan

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This article discusses a new alternative method for determination of seismic loads on buildings, based on resistance of structures to deformations of vibrations. The basic principles for determining seismic loads by spectral method were developed in 40… 50ies of the last century and further have been improved to pursuit true assessments of seismic effects. The base of the existing methods to determine seismic loads is response spectrum or dynamicity coefficient β (norms of RF), which are not definitively established. To this day there is no single, universal method for the determination of seismic loads and when trying to apply the norms of different countries, significant discrepancies between the results are obtained. On the other hand there is a contradiction of the results of macro seismic surveys of strong earthquakes with the principle of the calculation based on accelerations. It is well-known, on soft soils there is an increase of destructions (mainly due to large displacements), even though the accelerations decreases. Obviously, the seismic impacts are transmitted to the building through foundation, but paradoxically, the existing methods do not even include foundation data. Meanwhile acceleration of foundation of the building can differ several times from the acceleration of the ground. During earthquakes each building has its own peculiarities of behavior, depending on the interaction between the soil and the foundations, their dynamic characteristics and many other factors. In this paper we consider a new, alternative method of determining the seismic loads on buildings, without the use of response spectrum. The following main conclusions: 1) Seismic loads are revealed at the foundation level, which leads to redistribution and reduction of seismic loads on structures. 2) The proposed method is universal and allows determine the seismic loads without the use of response spectrum and any implicit coefficients. 3) The possibility of taking into account important factors such as the strength characteristics of the soils, the size of the foundation, the angle of incidence of the seismic ray and others. 4) Existing methods can adequately determine the seismic loads on buildings only for first form of vibrations, at an average soil conditions.

Keywords: seismic loads, response spectrum, dynamic characteristics of buildings, momentum

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Authors: Malika El Kyal, Ahmed Machmoum

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We prove the superlinear convergence of asynchronous multi-splitting methods applied to differential equations. This study is based on the technique of nested sets. It permits to specify kind of the convergence in the asynchronous mode.The main characteristic of an asynchronous mode is that the local algorithm not have to wait at predetermined messages to become available. We allow some processors to communicate more frequently than others, and we allow the communication delays to be substantial and unpredictable. Note that synchronous algorithms in the computer science sense are particular cases of our formulation of asynchronous one.

Keywords: parallel methods, asynchronous mode, multisplitting, ODE

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Authors: Ammara Mehmood, Aneela Zameer, Muhammad Asif Zahoor Raja, Muhammad Faisal Fateh

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In this work, the strength of bio-inspired computational intelligence based technique is exploited for parameter estimation for the periodic signals using Continuous Differential Evolution (CDE) by defining an error function in the mean square sense. Multidimensional and nonlinear nature of the problem emerging in sinusoidal signal models along with noise makes it a challenging optimization task, which is dealt with robustness and effectiveness of CDE to ensure convergence and avoid trapping in local minima. In the proposed scheme of Continuous Differential Evolution based Signal Parameter Estimation (CDESPE), unknown adjustable weights of the signal system identification model are optimized utilizing CDE algorithm. The performance of CDESPE model is validated through statistics based various performance indices on a sufficiently large number of runs in terms of estimation error, mean squared error and Thiel’s inequality coefficient. Efficacy of CDESPE is examined by comparison with the actual parameters of the system, Genetic Algorithm based outcomes and from various deterministic approaches at different signal-to-noise ratio (SNR) levels.

Keywords: parameter estimation, bio-inspired computing, continuous differential evolution (CDE), periodic signals

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Authors: Rizwan Rizwan

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This paper provides an overview of Federated Learning (FL) and its application in enhancing data security, privacy, and efficiency. FL utilizes three distinct architectures to ensure privacy is never compromised. It involves training individual edge devices and aggregating their models on a server without sharing raw data. This approach not only provides secure models without data sharing but also offers a highly efficient privacy--preserving solution with improved security and data access. Also we discusses various frameworks used in FL and its integration with machine learning, deep learning, and data mining. In order to address the challenges of multi--party collaborative modeling scenarios, a brief review FL scheme combined with an adaptive gradient descent strategy and differential privacy mechanism. The adaptive learning rate algorithm adjusts the gradient descent process to avoid issues such as model overfitting and fluctuations, thereby enhancing modeling efficiency and performance in multi-party computation scenarios. Additionally, to cater to ultra-large-scale distributed secure computing, the research introduces a differential privacy mechanism that defends against various background knowledge attacks.

Keywords: federated learning, differential privacy, gradient descent strategy, convergence, stability, threats

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Authors: Somar Boubou, Tatsuo Narikiyo, Michihiro Kawanishi

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In this work, we address the problem of 3D object recognition with depth sensors such as Kinect or Structure sensor. Compared with traditional approaches based on local descriptors, which depends on local information around the object key points, we propose a global features based descriptor. Proposed descriptor, which we name as Differential Histogram of Normal Vectors (DHONV), is designed particularly to capture the surface geometric characteristics of the 3D objects represented by depth images. We describe the 3D surface of an object in each frame using a 2D spatial histogram capturing the normalized distribution of differential angles of the surface normal vectors. The object recognition experiments on the benchmark RGB-D object dataset and a self-collected dataset show that our proposed descriptor outperforms two others descriptors based on spin-images and histogram of normal vectors with linear-SVM classifier.

Keywords: vision in control, robotics, histogram, differential histogram of normal vectors

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Authors: Helmi Temimi

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In this paper, we study the super-convergence properties of the discontinuous Galerkin (DG) method applied to one-dimensional mth-order ordinary differential equations without introducing auxiliary variables. We found that nth−derivative of the DG solution exhibits an optimal O (hp+1−n) convergence rates in the L2-norm when p-degree piecewise polynomials with p≥1 are used. We further found that the odd-derivatives and the even derivatives are super convergent, respectively, at the upwind and downwind endpoints.

Keywords: discontinuous, galerkin, superconvergence, higherorder, error, estimates

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Authors: Robert G. Nini

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Soil consolidation is one of the biggest problem facing engineers. The consolidation process has an important role in settlement analysis for the embankments and footings resting on clayey soils. The settlement amount is related to the compression and the swelling indexes of the soil. Because the predominant upper soil layer in Lebanon is consisting mainly of clay, this layer is a real challenge for structural and highway engineering. To determine the effect of load and drainage on the engineering consolidation characteristics of Lebanese soil, a full experimental and synthesis study was conducted on different soil samples collected from many locations. This study consists of two parts. During the first part which is an experimental one, the Proctor test and the consolidation test were performed on the collected soil samples. After it, the identifications soil tests as hydrometer, specific gravity and Atterberg limits are done. The consolidation test which is the main test in this research is done by loading the soil for some days then an unloading cycle was applied. It takes two weeks to complete a typical consolidation test. Because of these reasons, during the second part of our research which is based on the analysis of the experiments results, some correlations were found between the main consolidation parameters as compression and swelling indexes with the other soil parameters easy to calculate. The results show that the compression and swelling indexes of Lebanese clays may be roughly estimated using a model involving one or two variables in the form of the natural void ratio and the Atterberg limits. These correlations have increasing importance for site engineers, and the proposed model also seems to be applicable to a wide range of clays worldwide.

Keywords: atterberg limits, clay, compression and swelling indexes, settlement, soil consolidation

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Authors: Gleda Kutrolli, Maksi Kutrolli, Etjon Meco

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SARS-CoV-2 virus is currently one of the most infectious pathogens for humans. It started in China at the end of 2019 and now it is spread in all over the world. The origin and diffusion of the SARS-CoV-2 epidemic, is analysed based on the discussion of viral phylogeny theory. With the aim of understanding the spread of infection in the affected countries, it is crucial to modelize the spread of the virus and simulate its activity. In this paper, the prediction of coronavirus outbreak is done by using SIR model without vital dynamics, applying different numerical technique solving ordinary differential equations (ODEs). We find out that ABM and MRT methods perform better than other techniques and that the activity of the virus will decrease in April but it never cease (for some time the activity will remain low) and the next cycle will start in the middle July 2020 for Norway and Denmark, and October 2020 for Sweden, and September for Finland.

Keywords: forecasting, ordinary differential equations, SARS-COV-2 epidemic, SIR model

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Authors: N. S. S. Rao, Tapan Kumar Das, Latiful Pasha

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Tata Projects Limited (TPL) located in Hyderabad, India has taken up the challenging venture of executing the entire civil works for India’s largest Blast Furnace with a capacity of 4554 cum at Jindal Steel and Power Limited (JSPL), Angul, Odisha, India. The following write-up briefly elaborates the various steps and methodologies involved in the construction of the foundation for this India’s largest blast furnace.

Keywords: blast furnace, construction, qualitative, approach

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Authors: Irshana Muhamadhu Razmy

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Education is one of the main necessities for a modern society to access wealth as well as to achieve social well-being. Education contributes to enhancing as well as developing the social and economic status of an individual and building a vibrant community within a strong nation. The student dropout problem refers to students who enrolled in a school and are later unable to complete their grade education due to multiple factors). In Sri Lanka, the tea plantation sector is a prominent sector. The tea plantation sector is different from other plantation sectors such as palm oil, rubber, and coconut. Therefore, the present study particularly focuses on the influencing factors of student dropout in the tea plantation sector in Sri Lanka by conducting research in the Labookellie estate in Nuwera Eliya District. this research has opted to use both qualitative and quantitative methods. This study examines the factors associated with student dropout namely the family, school, and the social by the characteristic (gender, grade, and ethnicity) in the plantation area in the Labookellie estate.

Keywords: student dropout, school, plantation settlement, social environmental

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Authors: Lina Wu, Ye Li, Jia Liu

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We are interested in solving Liouville-type problems to explore constancy properties for maps or differential forms on Riemannian manifolds. Geometric structures on manifolds, the existence of constancy properties for maps or differential forms, and energy growth for maps or differential forms are intertwined. In this article, we concentrate on discovery of solutions to Liouville-type problems where manifolds are Euclidean spaces (i.e. flat Riemannian manifolds) and maps become real-valued functions. Liouville-type results of vanishing properties for functions are obtained. The original work in our research findings is to extend the q-energy for a function from finite in L^q space to infinite in non-L^q space by applying p-balanced technique where q = p = 2. Calculation skills such as Hölder's Inequality and Tests for Series have been used to evaluate limits and integrations for function energy. Calculation ideas and computational techniques for solving Liouville-type problems shown in this article, which are utilized in Euclidean spaces, can be universalized as a successful algorithm, which works for both maps and differential forms on Riemannian manifolds. This innovative algorithm has a far-reaching impact on research work of solving Liouville-type problems in the general settings involved with infinite energy. The p-balanced technique in this algorithm provides a clue to success on the road of q-energy extension from finite to infinite.

Keywords: differential forms, holder inequality, Liouville-type problems, p-balanced growth, p-harmonic maps, q-energy growth, tests for series

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Authors: Gilbert Makanda

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The problem of the teaching of mathematics is studied using differential equations. A mathematical model for knowledge acquisition in mathematics is developed. In this study we adopt the mathematical model that is normally used for disease modelling in the teaching of mathematics. It is assumed that teaching is 'infecting' students with knowledge thereby spreading this knowledge to the students. It is also assumed that students who gain this knowledge spread it to other students making disease model appropriate to adopt for this problem. The results of this study show that increasing recruitment rates, learning contact with teachers and learning materials improves the number of knowledgeable students. High dropout rates and forgetting taught concepts also negatively affect the number of knowledgeable students. The developed model is then solved using Matlab ODE45 and \verb"lsqnonlin" to estimate parameters for the actual data.

Keywords: differential equations, knowledge acquisition, least squares, dynamical systems

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Authors: F. Waffo Tchuimmo, G. S. Kwandio Dongoua, C. U. Yves Mbono Samba, O. Dafounansou, L. Nana

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The strength criterion is an important condition of great interest to guarantee the stability of the structural elements. The present work is based on the study of the free vibration of Euler’s Bernoulli column of equal strength in compression while considering its own weight and the axial load in compression and tension subjected to symmetrical boundary conditions. We use the differential quadrature method to investigate the first fifth naturals frequencies parameters of the column according to the different forms of geometrical sections. The results of this work give help in making a judicious choice of type of cross-section and a better boundary condition to guarantee good stability of this type of column in civil constructions.

Keywords: free vibration, equal strength, self-weight, tip force, differential quadrature method

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Authors: S. S. Abas, Y. M. Yatim

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In this paper the unsteady, slender, symmetric dry patch in an infinitely wide and thin liquid film of Newtonian fluid draining under gravity down an inclined plane in the presence of strong surface-tension effect is considered. A similarity transformation, named a travelling-wave similarity solution is used to reduce the governing partial differential equation into the ordinary differential equation which is then solved numerically using a shooting method. The introduction of surface-tension effect on the flow leads to a fourth-order ordinary differential equation. The solution obtained predicts that the dry patch has a quartic shape and the free surface has a capillary ridge near the contact line which decays in an oscillatory manner far from it.

Keywords: dry patch, Newtonian fluid, similarity solution, surface-tension effect, travelling-wave, unsteady thin-film flow

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Authors: Surendra Kumar Patel

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Disability is not just a health problem; it is a complex phenomenon, reflecting the interaction between features of a person’s age and physiology. Population ageing is a major demographic issue for India in the 21st century. Older population of India constituted 8% of total population, while 5.19% has affected by disability of older age group. Objective of the present research paper is to examine the state wise differential in disability among 60+ population and to access the health care of disabled population especially the 60+ disabled persons. The data sources of the present paper are census 2001 and 2011. For analyzing the state wise differentials by disability types and comparative advantage of data, rate, ratio, and percentage have been used. The Standardized Index of Diversity of Disability (SIDD) studies differential and diversity in disability. The results show that there are 5.19% persons have disability among 60+ population and sex differential not very significant, as it is 5.3 % of male and 5.05% in female in India but place of residence shows significant variation from 2001 to 2011 census. There is huge diversity in disability prevalence among 60+ in India, highest in Sikkim followed by Rajasthan, approximately, they comprise 11%, and the lowest found in Tamil Nadu as 2.53%. This huge gap in prevalence percentage shows the health care needs of highly prevailing states.

Keywords: disability, Standardized Index of Diversity of Disability (SIDD), differential and diversity in disability, 60+ population

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